Financial Transaction Networks to Describe and Model Economic Systems

by Carolina Mattsson

B.S. in Physics, Lehigh University B.A. in International Relations, Lehigh University

A dissertation submitted to

The Faculty of the College of Science of Northeastern University in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy

March 23, 2020

Dissertation directed by David Lazer University Distinguished Professor of Political Science and Computer and Information Sciences

1 Dedication

To all those who have ever wondered where their money goes.

2 Acknowledgements

For help navigating these ideas and putting them into words I thank everyone who’s crossed paths with me in the past six years, especially those of you who made a habit of it. I would most like to acknowledge my collaborators and co-authors. It has been a joy to work with Brennan Klein on Chapter 5, and to discuss elements of earlier chapters with Geoff Canright. Chapters 3 and 4 owe much to an extensive and fruitful collaboration with Guy Stuart. Nor could this work have been done without the support and contributions of our co-authors Soren Heitmann and Shafique Jamal. For additional insight into mobile money operations, I thank Qiuyan Xu, Sinja Buri, John Irungu Ngahu, and Morne Van Der Westhuizen. In addition to my co-authors, thank you to my adivser (David Lazer), my committee (Silvia Prina, Christoph Riedl, Alessandro Vespignani, and Irena Vodenska), as well as Bilge Erten, Claudia Sahm, Leo Torres, Hyejin Youn, Vincent Zountenbier and others for key comments along the way. I’d also like to give a shout out to the JP Caffe Nero and Pimentel Market (especially Victoria, Alvin, and Juan) for space to think and inspiration. My dissertation, perhaps more than most, could not have come together without institutional courage and professional kindness. I would like to express sincere gratitude towards Northeastern University, Microfinance Opportunities, and the National Science Foundation for the freedom to pursue such wide-ranging research. Thank you for supporting Network Science and network scientists. The Graduate Research Fellowship Program (Grant No. 1451070), the INTERN Program, and NU Assistantships have my humble appreciation. In gaining access to data I also thank the Partnership for Financial Inclusion, the International Finance Corporation, Cignifi Inc., and Telenor Research; these companies have my respect for taking on publicity risk in order to pursue impactful science in the public interest. On a more personal level, I would like to thank a number of people at these companies for supporting me and my research efforts for many years before anything could come of it: Guy Stuart, Geoff Canright, Kenth Engø-Monsen, Soren Heitmann, Qiuyan Xu, and Sara

3 Wadia-Fascetti. While on the topic, thank you to David Lazer for supporting my ambitions since before I even applied and opening doors for me that I would never have known existed. Most of all, I appreciate your genuine curiosity towards my ideas and your trust in my capabilities as a researcher. My committee has my enduring appreciation, along with Claudia Sahm, for taking on the extra effort to review work somewhat outside your wheel-house. To Alessandro Vespignani and Christoph Riedl, in particular, thank you for challenging me on all the right points. To Irena Vodenska and Silvia Prina, thank you for being just as curious as I am about where this can go. To Claudia Sahm, thank you for appearing out of nowhere with insightful comments on writing style and a warm welcome into Economics. Thank you also to Tina Eliassi-Rad for your infectious energy and drive. Your all’s vote of confidence will stay with me—thank you for telling me I deserve a PhD. Throughout this time my greatest source of support has come from the Network Science Institute and basically everyone in it. I thank David Lazer, Alessandro Vespignani, Mark Giannini, and surely others for conjuring into existence a Network Science PhD program in the first place. Thank you also for placing some of your faith in me for that first cohort. I am grateful for the years of solidarity from my fellow “musketeers” and the others students forging this path, especially Devin Gaffney, Dina Mistry, Lisa Friedland, Kaiyuan Sun, and Mike Foley. We’ve come a long way. The highlight of this adventure has been adding new friends with every passing year and I would like to say thank you for that to Soodi Milanlouei, Matt Simonson, Leo Torres, Jessica Davis, Syed Arefinul Haque, Brennan Klein, Ryan Gallagher, Chia-Hung Yang, Briony Swire Thompson, Stefan McCabe, Rezvan Sherkati, Janette Bricero, Mark Giannini, Sarah Shugars, Janina Bröker, Jason Radford, Ieke de Vries, Alice Patania, Jean-Gabriele Young, Stefan Wojcik, Navid Dianati, Phil Chodrow, Adam Abonde,˚ Paolo Barucca, James Stanfill, Xindi Wang, Hanyu Chwe, Harrison Hartle, Lucas Almeida, Charles Levine, IstvánKovács,Pim Van der Hoorn, Stefano Balietti

4 Simone Grabner, Rutuja Uttarwar, Juniper Lovato, Nicole Samay, Ana Pastore y Piontti, Ronald Robertson, Munik Shrestha, Yanchen Liu, Zach Fulker, Ben Miller, Tim Sakharov, Joy Xu, Alice Schwarze, Marco Pangallo, Federico Battiston, Maksim Kitsak, etc. etc. etc. Finally, I would like to express love and gratitude to my family and friends- from-elsewhere. Thank you for your steadfast encouragement; I can be single-minded and lord knows each of you has heard the spiel countless times. Thank you to the folks at RIAC (especially Anab Egal) for a sense of purpose when I needed one, and to the folks at Dirty Water Saloon (especially Bucky Chappell, Sharon Ulery, and Bob Sweeney) for dance-y distraction at key moments. Thank you to Marianna Faria Quadros, Paola Furlanetto, Caroline Daniels, and Zoe Cooksey for making my time in Boston so pleasant. Thank you also to Will & Fatin Lind and (of course) to Mr. Darcy. Thank you to Kebra Ward. Thank you to Fruzsina Veress, IstvánKovács,and Réka Mizsei for hikes and other fun. Thank you to Simon Mattsson for the countless chairlift rides where no question is too big or too crazy. So much gratitude goes to old friends for sticking this out with me, especially Amanda Burroughs, Sachee Nahata, Cas Arroyo, Zz Riford, Kirsten Kaplan, Laura Worden, and Amanda Olsson. My most heartfelt thank you is reserved for Vincent Zoutenbier—thank you for bringing companionship, joy, and a whole other circle of lovely people into my life. To my grandparents, thank you for the drive to better the world through my work with deliberate kindness. And lastly, to my parents, thank you for passing on to me a love of science along with everything else you have given me. I cannot thank you enough. Please know that I do not speak for any of those listed, misspelled, or mistakenly omitted. Any fault you may find herein is entirely my own.

5 Abstract of Dissertation

Financial transactions are the fundamental unit of economic activity, and we would like to be able to study how many millions of transactions come together to create economies as a whole. This dissertation develops the network science, computational tools, and economic theory that we need in order to get started. First, I delve into the basic bookkeeping practices that define financial transactions as such. This lets us describe financial transaction processes mathematically, and suggests a computational approach that would let us analyze transaction records from payment systems in light of this representation. Next, I use this approach to study the movement of e-money through a mobile money system in East Africa as a network of monetary flow. Sequential transaction motifs can isolate particular economic actions by users, and these different activities create networks with prominent hubs, random structure, geographic assortativity, and even suspicious-looking cliques. While the details are specific to this mobile money system, we would expect to see related structures within our economy as a whole from large corporations, peer-to-peer transfers, localized business, and opportunities for strategic coordination. If and when we get a chance to study transaction data from other payment systems, we can improve and extend our knowledge of money-flow networks to include the particular slice of economic activity that those systems support. Then, I quantify the circulation of money through this same mobile money system. My results show that the directionality of transactions would have us question whether our intuitions about social networks necessarily apply to economic networks. The importance of cycles in transaction networks helps illuminate the especially thorny challenges that payment system providers face in growing their operations. Given that these providers make up the payment infrastructure our economy relies on, this raises further questions about precisely how our monetary system operates. Finally, I consider how we might approach modeling economic systems as financial transaction processes. There is a simple set of assumptions, each backed by economic theory, that fit together neatly into an

6 alternative minimal model of a growing entrepreneurial economy. While very simple, this toy model nevertheless retains and lets us explore path-dependency, endogenous dynamics, and emerging inequality in economic systems. As a whole, the key insight from this dissertation is that ﬁnancial transaction processes are something we can describe mathematically, study empirically, and seek to understand via modeling. We can indeed build up an understanding of how millions of transactions come together to create economies as a whole. The ingredients are all here, and our challenge going forward lies in aligning the eﬀorts of interested researchers across considerable disciplinary divides.

7 Table of Contents

Dedication...... 2

Acknowledgements...... 3

Abstract of Dissertation...... 6

Table of Contents...... 8

List of Figures...... 9

List of Tables...... 14

Chapter 1 Introduction...... 16

Chapter 2 Financial Transaction Processes...... 30

Chapter 3 Networks of Monetary Flow...... 42

Chapter 4 Circulation of Money...... 64

Chapter 5 Toy Economies...... 88

Chapter 6 Conclusion...... 108

References...... 111

8 List of Figures

Figure 2.1: Visual schematic of the “follow-the-money” transformation An ordered series of deposits, transfers, payments, and withdrawals (left) create a transaction network (center). Arrows show the movement of money, sized to convey amount. Pieces of these transactions are then allocated into balance-respecting trajectories (right) that represent the movement of money from depositing agents, through users, and on to companies and withdrawing agents. 37

Figure 2.2: Visual schematic of two allocation heuristics An illustration of the allocation outcomes for a simple series of transactions involving one account. This highlighted account is represented by a stack for last-in-first-out allocation, and a pool for well-mixed allocation. The account receives two $100 transactions, and later sends $50 to two different accounts. The last-in-first-out heuristic uses the most recent incoming transaction to fund the outgoing transactions, creating two $50 trajectories. The mixing heuristic pulls evenly from both incoming transactions, creating four $25 trajectories. Empty arrows are as-yet un-allocated funds...... 39

Figure 3.1: Core structure of entry-exit networks A visualization of the 4000-node core of the (A) digital payment and (B) digital transfer networks. The network of aggregated in-out trajectories shows a distinct structure among 1500 nodes of the innermost core likely engaging in (C) commission gaming and the 4000 nodes in the next tier facilitating (D) money storage or other non-digital activity. The top 10% most signiﬁcant links are displayed; isolates are hidden. Nodes are colored by geographic location at the highest sub-national administrative areas in the country, when known from cellular records. Agents who joined the network too recently for this (about half) are dark grey. Corporations are black points, and appear only at the center of the hubs in (A)...... 54

9 Figure 3.2: Scaled distribution of trajectory durations The distribution over the duration of time between cash-in transactions (that begin trajectories) and payment or withdrawal transactions (that end trajectories). Shown in color are the four distinguishable economic actions identiﬁed above. The distribution is weighted such that each cash-in contributes one observation, and the areas are scaled to reﬂect the proportion of cash-in transactions captured by each activity. The x-axes are log scaled...... 60

Figure 4.1: Time series mobile money maturity measures TUE and DUE Daily timeseries of the TUE and DUE, calculated for that day’s deposits into the system under a 21-day cutoﬀ. In red are the absolute value of the measures; burgundy are values normalized by deposit transaction. These series show weekly, monthly, and possibly yearly cyclicality. The value of TUE jumps in September 2016 in response to a known intervention. The normalized version of both measures show a gradual decline in maturity, across the system, over time...... 76

Figure 4.2: Users aﬀecting change in TUE, by amount deposited Three histograms comparing the month before and after the IFC intervention (August vs. October). Users are grouped by total turnover in that month. Plotted are the number of users in each group, the total deposits made by that group, and the share of those deposits that were subsequently re-transacted. Note that a small number of users with especially high total turnover deposit a disproportionately large share...... 78

Figure 4.3: Re-transaction and savings across cohorts The fraction of (deposit-normalized) incoming funds that are digitally re-transacted by users (within 21 days) or kept in their accounts for longer than 21 days, aggregated by adoption cohort. Colors correspond to these cohorts. The contribution of recent adopters to the total (deposit-normalized) circulation is rising over the same period, which brings down the TUE and has little eﬀect on the DUE... 80

10 Figure 4.4: Hyperbolic decay of deposit-normalized “savings” balances Share of deposit-normalized funds that remain untouched in user accounts (under last-in-first-out) for each day beyond 21 days. The solid curves reflect the system-wide draw-down funds that had been used to build up a savings balance, colored by the date those funds entered the account they are in. The red dashed and dotted curves show three representative hyperbolic fits to the empirical decay curves...... 85

Figure 5.1: Best-choice entrepreneurial network of 50 nodes The structure and normalized PageRank distribution of an entrepreneurial network with 50 nodes, where entry was strongly selective of the best network location (k = 9). The initial nodes are purple (bottom right) while the newest are blue and orange (top left). Nodes are colored by InfoMap [142] communities and sized by PageRank [131] (with 5% random jumps)...... 100 Figure 5.2: Random-choice entrepreneurial network of 50 nodes The structure and normalized PageRank distribution of an entrepreneurial network with 50 nodes, where entry was selected at random (k = 0). The two most prominent purple nodes were both members of the initial six-node ring. Nodes are colored by InfoMap [142] communities and sized by PageRank [131] (with 5% random jumps)... 101 Figure 5.3: Good-choice entrepreneurial network of 50 nodes The structure and normalized PageRank distribution of an entrepreneurial network with 50 nodes, where entry was imperfectly selected based on advantageous network location (k = 4). The actions of the nodes create emergent, but not distinct, network sub-structures. Nodes are colored by InfoMap [142] communities and sized by PageRank [131] (with 5% random jumps)...... 102 Figure 5.4: Sub-network structure of simulated economies The extent of network compression possible at diﬀerent selection-intensities. Shown in grey are one hundred independent simulations at each power of k, and shown in purple is the average over them. Darker lines correspond to higher selection-intensity. The compression is calculated using the “description length” of the network from the hierarchical InfoMap algorithm [142], and is reported as a fraction of the uncompressed “description length”...... 104

11 Figure 5.5: Node dynamics of simulated economies The PageRank for each node in our entrepreneurial growth model, as the networks grow. Each plot is a superposition of ten independent simulations. Darker lines correspond to nodes who entered early on in the simulation. The two panels show the node dynamics for networks resulting from weak and strong selection-intensity, respectively.. 105

Figure 6.1: Deposit vs. trajectory size The histogram of trajectory sizes is compared to that of deposit transactions into the mobile money system. Both distributions cover several orders of magnitude and show a pronounced preference for round numbers. The x-axis is log scaled...... 138 Figure 6.2: Empirical decay of savings balance and hyperbolic fits Empirical decay of amount- and deposit-normalized savings balance, defined as funds remaining within an account beyond 3, 21, and 35 days under last-in-first-out. In red are representative fits of a hyperbolic decay function to the data. The start date refers to the day this money entered this account. Note that the amount- weighted curves were fit to a smoothed version of the decay, not that which is shown...... 143

Figure 6.3: Estimated DURsvg over time at various cutoff times The estimate of the DURsvg for funds that become savings balance on a given date, for a range of cutoff times. Note that the amount- weighted hyperbolic curves were fit to a smoothed version of the amount-weighted empirical decay...... 144 Figure 6.4: Time series of TUE and DUE at 14, 21, 28, and 35 day cutoffs In red are the absolute value of the measures; in burgundy are the deposit-normalized...... 145 Figure 6.5: Sub-network structure under varied noise The extent of network compression possible at different selection-intensities, for a set of sampling fractions (left) and PageRank “alpha” parameters (right). Shown in grey are twenty independent simulations at each power of k, and shown in purple is the average over them. Darker lines correspond to higher selection-intensity. The compression is calculated using the “description length” of the network from the hierarchical Infomap algorithm [142], and is reported as a fraction of the uncompressed “description length”...... 147

12 Figure 6.6: Node dynamics under varied noise The PageRank for each node as the networks grows under strong selection-intensity (k = 8), for a set of sampling fractions (left) and PageRank “alpha” parameters. Each plot is a superposition of ten independent simulations. Darker lines correspond to nodes who entered early on in the simulation...... 148 Figure 6.7: Sub-network structure under varied initial conditions The extent of network compression possible at diﬀerent selection- intensities, for a set of initial conditions. Shown in grey are twenty independent simulations at each power of k, and shown in purple is the average over them. Darker lines correspond to higher selection-intensity. The compression is calculated using the “description length” of the network from the hierarchical Infomap algorithm [142], and is reported as a fraction of the uncompressed “description length”...... 149 Figure 6.8: Node dynamics under varied noise The PageRank for each node as the networks grows under strong selection-intensity (k = 8), for a set of initial conditions. Each plot is a superposition of ten independent simulations. Darker lines correspond to nodes who entered early on in the simulation...... 150 Figure 6.9: Two in- and out- links on entry Description of a growing network model with four incoming links. First, a network snapshot and PageRank distribution at 40 nodes under high selection-intensity (k = 45). Then, the extent of network compression possible at different selection-intensities. Finally, the node dynamics under this model under high (but still imperfect) selection-intensity (k = 40). 152

13 LIST OF TABLES

Table 3.1: Mobile money transaction types The six most common transaction types in the mobile money data. The number of records of one type is reported as a percentage of all transaction records, and the average amount of these transactions is denoted in US Dollars at purchasing power parity (PPP) with the local currency. Popularity is the percentage of users who made at least one transaction of this type. The average or median number of transactions refers to those made by these users, excluding those with zero transactions of this type. Less popular services are not shown, so the percentages do not add up to 100%...... 46

Table 3.2: Detailed summary of trajectory motifs A summary of the trajectories observed when following all cash-ins through the mobile money system using the greedy (last-in-ﬁrst-out) heuristic. Shown are eight of the possible motifs, where the arrows correspond to the movement of e-money. The number of trajectories observed to follow a motif is reported as a percentage of all unique trajectories beginning with a cash-in. The number of deposits is reported as the percentage of all cash-ins that went on to follow that motif; the median duration is the time in which half of those cash-ins had moved through that motif, and the average duration is the average across those cash-ins. Not shown are more niche actions or incomplete trajectories, i.e. money that remains in the system at the end of the ﬁnite data collection window. For this reason, the percentages do not add up to 100%...... 49

14 Table 3.3: Description of highlighted sets of agents A comparison of highlighted sets of agents, described by their coreness rank within the specified entry-exit network. The average number of unique users, cash-ins, and average cash-in amount is calculated over the values for the agents in that set. In-out is the average percentage of cash-ins to those agents that went on to follow the “in-out” motif. Near Tier is the average percentage of cash-ins to an agent that fall at or within $1 above the commission tier (USD at PPP). Gain is the average percentage of the revenue earned by the provider on the cash-ins and cash-outs at that agent that is captured by the agent as commission. The percentage of agents in this set that are “established” is inferred by how many of them also appeared in a companion dataset from just over a year earlier...... 56 Table 3.4: Quantitative network measures A comparison of the aggregated entry-exit networks. The number of cash-in deposits captured by this network is reported as a percentage of all cash-in transactions. The percentage of this total captured by the core of this network is reported as such. Modularity quantifies the geographic assortativity of the network using assignments of agents to sub-national administrative areas in the country, which is known for around half of all agents. This metric is unitless and ranges from -1 to 1. The Gini coefficient across agents quantifies the inequality of where trajectories begin and end. This metric is unitless and and ranges from 0 to 1. The description length is an information theoretic measure that decreases as the Infomap algorithm exploits sub-network structure to compress the network. The recipients of digital payments, i.e. corporations, do not have a well-defined location nor do they facilitate cash-ins; we do not calculate modularity or run Infomap on the “payments” network...... 57

15 Chapter 1

Introduction

16 There are two establishments in my neighborhood that I frequent more so than any others: Caffe Nero down in Central JP and Pimentel Market across the street from my apartment. At Caffe Nero I can buy myself a hot tea and a chocolate croissant for $6.53. At Pimentel this would get me a gallon of milk and a pack of Maria cookies. Either way, my $6.53 would join with millions upon millions of other transactions happening today that make the economy into what it will be tomorrow. Today’s patronage strengthens local businesses, today’s purchases reinforce successful supply chains, and today’s investment decisions adjust worldwide flows of funds. Since I can’t spend my same $6.53 both at Caffe Nero and at Pimentel, it might be worth considering which of the two would be making tomorrow’s local economy into one that better provides for the residents of Jamaica Plain. That’s tricky. Caffe Nero is a large, multi-national corporation, but their Centre St. location employs many for good wages and they pride themselves on a sustainable supply chain. Pimentel is a locally owned business that sources substantial inventory from local producers but mostly from GOYA and Anheuser-Busch. They recently expanded, which is excellent, and likely means they are spending a good portion of their profits on loan re-payments. I can’t pretend to know anything about the investment practices of their bank, except that it supported the development of my local area in this particular case. Whether tomorrow’s economy will be one that continues to support the residents of Jamaica Plain, of the city of Boston, of the state, of the country, or of the world is anything but straightforward. Economic dynamics move rapidly beyond the control of any one person, and this becomes a highly complex question. The effect of my $6.53 almost certainly washes out, but not so for other events. The purchase of one large company by another will redirect the former’s profits in ways that could be consequential for their partners in particular areas [98]. Major trends in purchasing habits will favor some business-models over others [61, 172]. Outbreaks of a novel virus can stress supply chains, with knock-on effects around the world [49].

17 Answering this question with a locally-relevant level of detail would require an understanding of the economy beyond anything that we have today. We would need to be able to model national economic dynamics, and global economic forces, precisely enough that we could provide local economic forecasts. This would sound entirely impossible, except that it is not without precedent! Modern storm forecasts inform local evacuation decisions, and modern epidemic forecasts inform local response efforts. Our meteorological and epidemiological models operate today with a level of precision that was unimaginable a only few decades ago. One could perhaps imagine forecasting which particular towns might be expected to lose out following a large acquisition, allowing local officials to prepare for a local rise in unemployment before it reaches them. Locally predictive economic models are worth working towards, even if they aren’t around the corner. Such models would be transformative—allowing for realistic simulation of future scenarios and in-silico testing of economic policy. And they may be closer than they seem. Already, there is substantial research effort being put into developing “stress tests” for key financial infrastructure [22,34,81,149,171] and models of cascading failure for key supply chains [33,82,83]. We can use meteorological and epidemiological models as aspirational guides in where to direct our efforts. Locally predictive economic models would need to combine a sound mathematical representation of economic systems with accurate local data about its current state. It is especially important that the system’s representation relate to the data used in monitoring it. So long as the underlying theoretical logic of the model is a sound approximation of reality, then both mathematical representations and data sources can be refined over time. If we can develop such a logic for modelling, then we have somewhere to start. This dissertation develops an underlying logic for economic modeling based on the notion that financial transactions are the fundamental unit of economic activity: In this chapter, I introduce the notion that economies are what emerge out of

18 millions upon millions of individual transactions, and review related literature. My conclusion is that we stand on the cusp of a new generation of economic models— the ingredients are all here. The field of network science is increasingly successful at modeling emergent phenomena, financial service providers are amassing digital records of an increasing fraction of real economic activity, and macroeconomic theory is increasingly deliberate about representing the constraints of financial accounting as well as economic relationships. In Chapter 2, I delve into the basic bookkeeping practices that define financial transactions as such. The chapter describes financial transaction processes mathematically, and puts forward a computational approach that would let us analyze transaction records from payment systems in light of this representation. In Chapter 3, I use this approach to reveal large-scale patterns in the movement of money facilitated by a mobile money payment system over a period of 10 months. Different user activities follow particular sequences of transactions that create networks of monetary flow with prominent hubs, random structure, geographic assortativity, and suspicious cliques. While the details are specific to this system, we can expect to find similar network structure within economic systems that include large corporations, peer-to-peer transfers, localized business, and opportunities for strategic coordination. In Chapter 4, I develop a methodology to monitor the the extent to which a digital payment system supports sustained circulation of money, i.e. its “maturity”. Doing so with transaction-level granularity lets us ask what changes in user behavior among which users lead to changes in maturity. We quantify the maturity of a mobile money system in East Africa over a period of eight months and find that this system undergoes a decline in maturity, contrary to expectations. Although the user base of the system is growing rapidly, later adopters are less inclined to re-use funds. Users are also lessening in their propensity to store balances within the system for long periods of time. That these phenomenon dominate the trend in maturity points to a conspicuous absence of peer-to-peer network effects that would generate network

19 externalities. Mobile money providers can be deliberate about fostering peer-to-peer effects, which are unlikely to appear spontaneously, by aiming to create cycles in the transaction networks they support. In Chapter 5, I interpret several strands of economic thought as simplifying assumptions around a financial transaction process, distilling out what may be essential dynamics of a growing entrepreneurial economy. This becomes a toy model where identical economic entities each look to enter at an advantageous position; even in its simplicity this model retains rich dynamics that reflect path-dependency, endogenous dynamics, and emergent inequality. This approach to agent-based economic modeling can build empirically testable hypotheses out of under-explored economic ideas. By taking the perspective of financial transaction processes, a great many existing approaches to agent-based modeling of economic systems gain access to new theoretical and empirical groundings. Finally, I conclude with some thoughts on several broad research areas where much work remains to be done in developing a new generation of economic models. Given time and effort and the patience to cross disciplines, data-driven agent-based modeling of financial transaction processes could one day provide a full-fledged alternative for aggregating up from the micro-economy to the macro-economy.

Economic and Financial Network Data

The expansion of digital infrastructure in recent years has opened up a world of observational data to new areas of science. Digital behavioral traces have greatly expanded the methodological possibilities in many ﬁelds, giving researchers ﬂy-on- the-wall detail about people’s movement, communication, media use, and purchasing habits at scale. Network science, which can help bring existing network theories to bear on large datasets of micro-level data, has been instrumental to deepening our understanding of social systems, and developing data-driven forecasting of socio-

20 technical systems. [105,170] Within economics, the meticulous collection and curation of business records in Japan is a testament to the possibilities that data hold for the field as a whole. Japanese researchers have brought techniques from statistical physics to study empirical distributions of income, firm sizes, firm productivity, business cycles, and price dynamics on a national scale [9]. Even more interesting is the data available on production networks which represent economic producers, or firms, and the supplier relationship between these entities. Network representations of production networks have been heralded as a way to bridge microeconomics, with its focus on the behavior of individual firms, and macroeconomics, with its focus on broader economic outcomes [37]. Misako Takayasu and ca-authors have a series of papers exploring Japanese production networks and their possible evolution under different models of business consolidation [112,144,162]. Intriguingly, it appears to be possible to model the movement of money through this firm-firm network well enough to recover much of the variation in company sales [99]. Others have studied the propagation of supply chain shocks over the Japanese production network [10]. Most impressively, this rich vein of research has produced the closest thing to a locally predictive national-scale economic model currently in existence (to my knowledge). Using the empirical production network of Japanese firms, Hiroyasu and Yasuyuki (2017) predict the economic disruption that would result from a future tsunami. They model individual firms as agents who adjust transactions with their actual suppliers in logical ways in response to disruptions passed over the empirical production network. Their prediction for the total economic loss due to a future earthquake is calibrated based on the known economic loss following the 2011 Tohoku earthquake and tsunami [82,83]. Although we can all hope their predictions are never put to the test, their work is a testament to what network modeling can aim for when integrated with large-scale data about interactions in the real economy. Empirical network research in other areas of economics and finance, wherever

21 large-scale data is available, is ascendant. Serrano et al. (2007) provided an early empirical categorization of the world trade web, a weighted and directed network between countries where the financial links reach into the billions and trillions of dollars [151]. Giulia Iori and co-authors mapped the Italian overnight money market, where Italian banks lend liquidity reserves to one another temporarily, in 2008 [85]. Many others have conducted empirical studies of global trade and credit networks since. Most relevant to financial processing, researchers have studied the detailed functioning of the very core of our modern financial processing architecture – inter- bank settlement clearing systems. These are large value payment systems that process financial transactions among banks and other large players. Kyriakopoulos et. al. (2009) represent the Austrian Real Time Interbank Settlement System (ARTIS), as a series of networks aggregated at a daily level to study broad patterns of transaction networks. They find that the degree and weighted degree are surprisingly uncorrelated [102]. Soramäkiet. al. (2006) find that the time-aggregated topology of these systems can change considerably in response to large disruptions, using data from the Fedwire Funds Service that covered the period immediately following the attacks of September 11, 2001 [154]. More recently, the central banks who oversee inter-bank settlement clearing systems have been particularly interested in time-disaggregated analyses and models that incorporate liquidity concerns of the entities within them. Marco Galbiati, Kikko Soramäki,and others have developed detailed models of temporal activity on these systems as transactions are demanded of banks [23,66,68].

With the advent of data science, there has been growing interest also in individual-level data from public-facing payment systems. Farrel & Greig (2015) study a sample of the JPMorgan Chase & Co. customer base, ﬁnding widespread volatility in incomes and expenditures [60]. Zanin et. al. (2016) study a dataset of credit card transactions between individual customers and businesses processed by the largest bank in Spain over the course of one year. They represent their data as

22 a bipartite network, presenting degree distributions and descriptions of cyclicality for the transactions in hopes of creating a synthetic generative model with similar characteristics and fewer privacy concerns. Substantively, they find strong cyclicality in our day-to-day financial transactions [180]. Macroeconomists have recognized that transaction records from public-facing payment systems have the potential to improve economic measurement. Most ambitiously, Aladangady et. al. (2019) use transaction data from a card transaction processor to construct macroeconomic consumption statistics [6]. Mobile money systems are some of the most well-studied of public-facing payment systems at the level of individuals. Blumenstock, Eagle, and Fafchamps (2014) pioneered research in this area, directly studying the response of calling and top up transfer, a precursor to mobile money, after an earthquake in Rwanda in 2008 [28]. While the total value of transfers was only around $84, they offer striking evidence that informal risk-sharing can be directly observed. Economides and Jeziorski (2017) analyze more complex patterns of sequential transactions on mobile money systems, particularly sequential deposits and withdrawals. They exploit a surprise rate increase to determine the price elasticity of different transaction types, which they define primarily based on distance. They find that long-distance transfers are less elastic than short distance ones, and that the value of moving money 1km in distance electronically is around 1.25% [52]. Due in part to the salience of network boundaries (i.e. deposits and withdraws) within public-facing payment systems, they remain largely unexplored from a network perspective.

Economic and Financial Network Theory

Network-based theory has been a part of economics since long before relevant large-scale data became available. Powell (1990) reviews his contemporaries, seeking to deﬁne an economic structure that falls between the market (entirely open) and the

23 firm (entirely closed) that conveys more than a simple continuum between them. This network form of economic organization describes the range of intricate relationships that firms can maintain with one another, where reciprocal exchange and ongoing communication facilitates trust and information sharing. Powell describes network organization as nimble and better able to adapt to changing circumstances than either markets or firms [173]. Uzzi (1997) explicitly maps the economic networks of firms in the garment industry, finding that firms maintain both market and network relations with other firms. While one-off transactions (across market relationships) are more common and firms maintain few stronger relationships, a disproportionate share of business goes to established ties [168]. White (2004) takes the concept a step further, arguing that networks of exchange relations are what create markets in the first place. Rather than responding to demand within existing markets, networked firms often seek to establish new niches for their products [177]. As impressive, on-point, and well-cited as is the foundational work in network organization, the direction of the field appears to have tacked back toward Granovetter [75] and the paradigm currently refers more to social and knowledge networks among (or even within) firms [167, 169]. It is worth noting that there are strong empirical correlations also at the individual level between social network location and personal economic status [109]. In this vein, but on a macroeconomic scale, there is work in development economics that treats economies as a whole as networks of industries related by shared production knowledge [79]. Theoretical network approaches persist in studying economic activity, but phenomenally rarely are the relationships in question defined by actual economic transactions. The early work Brian Uzzi and that of Harrison White are the exceptions that prove the rule. Researchers have also created entirely hypothetical models of economies as exchange relations among economic entities. Dragulescu & Yakovenko (2000) introduce a model of a transaction process within a closed economic system, where money is conserved, that allows drawing direct parallels to statistical mechanics [48].

24 Bouchaud & Mezard (2000) model wealth accumulation as the outcome of exchange and random variation, reproducing broadly-found Pareto distributions of wealth under a mean field approximation [31]. Others have extended this model over a series of synthetic network topologies, finding that network structure affects the resulting wealth distribution. Specifically, complex networks produce heavy-tailed wealth distributions that are a combination of log-normal and power-law distributions [70]. Researchers have also sought to relate transaction processes to the exchange equations from monetary economics. Yougui Wang & Ning Ding have a series of papers considering the distribution of “holding times” that money would exhibit under various models for money-transfer processes. Under a closed system, where such distributions are necessarily stationary, the average “holding time” is closely related to the macroeconomic notion of the velocity of money [174–176].

When it comes to integrating network theory with empirical study in economics, the most well-developed literature comes from development economics and builds upon an established area of research on ways in which the poor handle high susceptibility to risk. Without access to formal loans and insurance mechanisms to cope with unexpected expenses, people turn to each other. Consumption patterns in poor, rural villages are remarkably smooth suggesting that risk-sharing measures are prevalent, although imperfect at the level of whole villages [166]. Field studies mapping the credit networks underlying village risk sharing systems have found that households primarily receive help from existing social connections, such as friends and relatives, in the form of informal loans or transfers [58]. Beyond the village-level, ﬁnancial relationships to migrant workers and family members in other areas also contribute to risk-sharing. Remittances from overseas migrants have been shown to respond dramatically to income shocks aﬀecting entire regions, replacing upwards of 60% of lost income in households with international migrants [179]. Further research has generalized these results, showing that remittances moderate risks to income also for idiosyncratic shocks to individual households [101]. There is also research showing

25 that mobile money services can improve the responsiveness of risk-sharing financial relationships. Jack & Suri (2014) show that adoption of mobile money allowed Kenyan households to entirely smooth consumption when affected by adverse events, compared to a 7% drop. Again, Blumenstock, Eagle, and Fafchamps (2014) directly observe the flow of a primitive and unofficial version of mobile money (mobile airtime) to affected persons in response to a 2008 earthquake in rural Rwanda. Empirical work in this area has been consistently integrated with theory to the point where it has even been modeled by researchers like Matt Jackson and Marcel Fafchamps [57,90,91]. Network theory within development economics also blurs distinctions between firms, households, and financial players. There is a rich literature on informality and the persistent lack of a distinction between firms and households in practice (see [17,44]). There is also less of a distinction between regular businesses and financial entities in economies where bank credit is generally not available. Within many informal economies, businesses rely on their strong producer-supplier ties for essential credit [56]. Individuals rely on their social connections [58,90,179]. Similarly, Fergus Lyon and others have catalogued the mix financial, economic, and social relationships that underpin agricultural production in a region of Ghana [110]. Meanwhile in other sub-disciplines, upheavals in the financial sector in 2008 led to the largest recession since the Great Depression and a wholesale rethinking of financial and macroeconomic modeling by many prominent figures. Specifically, it accelerated the study of systemic risk in financial systems [149]. Descriptions and models of cascading failure on empirical credit networks and asset ownership networks have played a substantial role in defining the concept. Financial crises can propagate between economic entities over links representing financial obligations between them as well as ownership ties, and strategies that lower risk for individuals in these systems (like diversification) actually serve to increase the fragility of the system as a whole [22, 54, 81]. Financial cascades can of course propagate over to other economic networks, such as international trade [33]. Recently, inter-bank credit

26 networks and asset ownership networks have been jointly studied with the clear conclusion that greater complexity in these markets means that less information on the risk from any one asset is available to market participants, contributing again to heightened systemic risk [21]. Post-2008 banking regulators have taken aspects of systemic risk seriously and begun to require systemic stress tests of key ﬁnancial players. Macroprudential policymakers would do well to include dependencies among assets explicitly into such tests [34,81,171].

Competing Paradigms

Not all of the post-2008 advances in macroeconomic modeling have been data-driven, however. On the more theoretical side, influential figures from economic history are re-emerging as freshly relevant. Hyman Minsky’s view of accounting rules as the strongest motivator for financial entities deftly explains how individual banks and corporations can end up with no choice but to amplify economic downturns in pursuit of liquidity [121]. The behavior of securities and money market traders, as modeled by Treynor, are receiving renewed scrutiny in a world where much of the financial system relies on liquid markets for credit (which ceased to operate during the crisis) rather than relationships with traditional lenders. Integrating these perspectives into a modern paradigm, the “Money View” developed by Perry Mehrling provides an understanding of markets from the perspective of those creating them. These market-makers charge for their services and do what they must to protect themselves from the financial forces hitting them with every transaction [122]. Interestingly, the “Money View” even ventures into the actual hierarchical structure of payment systems [123]. From this perspective, the payment systems run by central banks are above those run by deposit-taking banks are above those run by other financial service providers because these providers clear their transactions via banks who clear their transactions via large-value or inter-bank settlement clearing systems.

27 This theoretical work is directly applicable to empirical work on financial transaction networks in that it describes the logic underlying how payment systems interact. Related paradigms of macroeconomic modeling also received a post-2008 boost. While not explicitly concerned with networks, the stock-flow-consistent modeling framework of “Post-Keynesian” economists dovetails nicely with financial network concepts. Specifically, they argue that one sector’s financial outflows are always another sector’s financial inflows and that macroeconomic models aught to maintain accounting consistency at all times [26]. This modeling paradigm has very recently been extended to model individual-level transactions: Caiani et. al. (2016) simulate an economy made up of many thousands of individual households, firms, and banks transacting with one another via specifically defined market interactions. This is undoubtedly state-of-the-art macroeconomic modeling, and endorsed by Joseph Stiglitz, a Nobel Prize winning economist. As compared to mainstream macroeconomic models, the authors contend that their paper “propose[s] a macroeconomic framework based on the combination of the Agent Based and Stock Flow Consistent approaches” that is “thoroughly validated” in that it “match[es] many empirical regularities, ranking among the best performers in the related literature, and that these properties are robust across different parameteriza- tions.” However, in the light of the rest of the literature reviewed for this dissertation, the work completely misses several of the most exciting recent advancements of rele- vance to economic modeling. First, no empirical data is used to inform the proposed model at the level of the agents themselves. The parameters for action of individual agents are entirely prescribed by the modeler and the validation consists of how well the model outputs match time-series of macroeconomic indicators (although time is not continuous within the model). Second, while the markets are not defined to be perfect, or even perfectly clearing, but they are random and memoryless. This sidesteps the substantial body of research showing that economic relationships are enduring and form intricate, complex networks. Lastly, while this model is technically

28 accounting consistent it accomplishes that by performing each step of the model sequentially. This means that transactions on the labor market happen on the same simulated time-scale as transactions on the inter-bank clearing system. [35] Even with these limitations, Caiani et. al. (2016) is highly notable in that they present a macro-scale economic model that is implemented at the scale of individual transactions. As are similar, related, models [14, 46,138]. Recently, such models have achieved forecasting success on par with highly optimized mainstream macroeconomic models [135]. The lowest-level implementation choices of these agent-based models is also highly revealing—economic transactions are programmed into these models as ﬁnancial transactions processed by payment systems.

Conclusion

The promising synergy between accounting consistent models of realistic financial systems, individual-level transaction data, and network economic theory is all the more striking when absent. This literature review has detailed several exciting research directions that have embraced one or two of these components, and this dissertation will build off of their efforts. The hope is that a modeling paradigm that embraces all three will provide an underlying theoretical logic that is a simpler and more sound approximation of reality. At the very least, models based on this combined paradigm would make wildly different assumptions than do today’s state-of-the-art economic models. And there’s something to be said for that, as well.

29 Chapter 2

Financial Transaction Processes

30 Financial transactions are the fundamental unit of economic activity, and we would like to be able to study how many millions of transactions come together to create economies as a whole. A good place to begin is with the administrative records generated by the systems that process ﬁnancial transactions. Modern payment systems range in scale from local credit circuits to digital payment platforms to national real-time gross settlement systems; these are all knitted together into an elaborate monetary infrastructure [71]. Public-facing payment systems are mostly private and their ﬁnancial transaction records are severely under-studied.

Payment infrastructure is increasingly digital, and data science is increasingly popular, so transaction records are increasingly accessible for research [6,28,52,60,86, 180]. Large-scale data from ubiquitous digital systems has revolutionized how we can study many social systems, and our economic/ﬁnancial/monetary system ought not to be an exception [105].

Leveraging financial transaction records to do science is a matter of relating how the bookkeeping done by payment systems touches on ideas within many related, but largely separate, areas of study. Unlike, say, social network data with social network theory, we do not yet have a clear perspective with which to approach financial transaction records from payment systems. A transactions is the most basic of economic actions, but payment systems record only the trace they are leaving in the financial system. A transaction is as “micro” as one can get, but money is more of a “macro” topic. Transaction networks are considered within macroeconomics [6], economic sociology [168], data science [60], and physics [48]. Payment systems as infrastructure are considered within development economics [118], monetary economics [154], economic history [122], economic anthropology [74], and regulatory law [140]. While this makes it all especially exciting, it means we need a perspective that can help us translate insights across fields if we are to take full advantage of this newly accessible data.

31 I suggest we consider financial transaction records from payment systems as observations from a financial transaction process. Such processes are a specific kind of walk processes on a temporal network, wherein transaction records reveal the flow of money through the accounts in a payment system. Whatever way we choose to analyze financial transaction networks, and for whatever purpose, the insights will be transferable across domains so long as it make sense from this perspective. I lay out a specific toolbox from network science that can be used to make sense of financial transaction data from this perspective.

Financial transaction networks

Networks simultaneously represent micro- and macro-level aspects of a system, together, and we would like to be able to apply the full force of Network Science towards studying financial transaction records from payment systems. Now, a single financial transaction record can (of course) be considered to be a link in a network. However, existing tools are not altogether adequate. Few off-the-shelf tools would be usable without considerable modifications to the underlying data, and so it is unclear what “network” we would actually be looking at once we throw whatever we might have at it. A large-scale data set of financial transactions would be a big, weighted, directed, temporal network. Each transaction is a record of an account that is the source of funds, and account that is the recipient of funds, an amount, and a timestamp. The link is necessarily both weighted and directed, and it appears only as an instantaneous interaction in continuous time. There are few frameworks for representing such data as networks, and they all fall short. Time-aggregated network analysis does not capture the experience of individual users, for whom financial transactions are instantaneous links in continuous time. Modern frameworks that use sequences of static networks [141,163], or multilayer

32 networks [12], likewise do not help us make sense of hundreds of millions of transactions happening one at a time. As an added complication, financial transactions are weighted and directed in ways that one cannot ignore. This means that even basic concepts for analyzing temporal networks, like time-respecting paths and inter-event times, do not immediately generalize. [80] This chapter puts forward a self-consistent framework for making sense of financial transaction records from payment systems. It establishes what, exactly, are our nodes and links. The intention is to provide a precise, concrete, and rigorous perspective from which such data can be considered a network. Once this is established, network analysis can be used to study any number of discipline-specific questions.

Financial transactions move money

This dissertation notes and leverages a key feature of payment system records: financial transactions move money. Implicit in these data are particular constraints that apply to the movement of money, specifically. Put simply, no one is allowed to spend the same dollar twice: if you were to use all your money to purchase a bike, then you would have none left with which to purchase a latte. Contrast this to a rumor or the flu, which you can absolutely share first with your bike mechanic and later with the barista. Since you cannot purchase the latte, that purchase would never appear in the data. Moreover, payment systems themselves are what enforce these accounting constraints. In our simple example, it would be your own bank that steps in to decline your debit card at the coffee shop. Transactions that break accounting rules are not allowed, and payment systems see to it that they do not occur. In practice, accounting can be done in a decentralized manner (cash), a centralized manner (checking), or even algorithmically (blockchain). Either way, payment system providers must enforce accounting or risk having to honor duplicated funds using money of their own.

33 Transactions are recorded by the same entity that enforces basic accounting, making this a global constraint. Money is thus conserved under the transaction processes that we observe via transaction records. Note that physics-style models of transaction processes make sure to conserve money [176]. Indeed, conservative dynamics are even reflected in the terms we use to describe the dynamics of money, like flow and circulation. Conservative dynamics help us pin down, conceptually, what is and is not our “network”. Crucially, transaction processes as defined here can act only on funds already in existence. Related processes that do change the amount of money in circulation within a payment system would necessarily be external to our network representation. They are conceptually distinct. We consider the issuance and cancellation, credit and repayment, or mining and destruction of money to define the boundary within which our conservative transaction process plays out.

Transaction processes on networks

On networks, conservative dynamics are represented as walk processes and these are studied in precise mathematical detail. Masuda et. al. (2017) provide a taxonomy of random walks where a transaction process would be categorized as a weighted, continuous-time, node-centric, passive walk on a temporal network [114]. The deﬁning feature of passive walk processes is that links in the temporal network are what move the walkers; the transactions are the process. This meas that the time scale at which walkers are moving is the time scale at which the network itself changes, and this seriously complicates analysis. Many of the central results for random-walk processes on networks no longer hold when these two time scales are one and the same [133]. Masuda et. al. (2017) also distinguish between passive processes where activity centers on nodes, to those where activity centers on edges. They provide examples

34 for edge-centric passive walk processes, such as diffusion over temporal networks. Transaction processes are an example of the node-centric variety; it is almost always either one counter-party or the other that initiates a transaction. Often it is the sender who initiates (ex. a payment), but there are transaction types where the recipient initiates (ex. a direct debit). That transaction processes are node-centric is important because the choices we make in how to represent accounts can have a substantial impact. Different heuristics governing the movement of walkers through nodes can produce dramatically different walk statistics on temporal networks [145]. Unless we are very deliberate about we choose to represent accounts, there will be an inherent ambiguity to transaction processes vis-à-visthe movement of money.

Trajectories through temporal networks

We can avoid ambiguity from node-centric walk processes when we have data directly from the process, itself. Click-streams, travel itineraries, and shipping logs are examples where data consists of known trajectories that individually observed “walkers” have followed through their network. Researchers have introduced methods for ﬁnding central nodes [134] and detecting communities [143] on the networks revealed by such trajectory data. If we consider each trajectory as a statistical observation, it would be possible to create a network representation of the system that would be able to approximate the observed trajectories using random walks [103,148]. In theory, one could use this approach directly on trajectories of individually marked bills through an economy. Hobbyist eﬀorts such as “Where’s George?” provide some idea of the diversity of trajectories that physical bills take through an economy as a whole. [32] In practice, however, individually marked bills are not exhaustively tracked and exhaustively tracked (i.e. centrally cleared) money is not individually marked.

35 Trajectories as ﬂows of money

To generalize beyond trajectories of individual bills, we must consider trajectories of money more generally. These would correspond to observable sequences of transactions followed by the same funds. The trajectories of money that could be observed given a set of transactions would be constrained not only by sequential time but also by the balance in each account at every step. We might call them —balance-respecting trajectories. In the language of network science, then, transaction processes are a weighted, continuous-time, node-centric, passive walk on a temporal network and balance- respecting trajectories are observed instances of such a walk process. Thankfully, this translates to observed instances of money having moved through a particular series of accounts when used to settle transactions made by those accounts at particular times. In the language of monetary economics, trajectories of money are observed monetary flows at the finest resolution one could possibly define them.

Follow the money

This section defines a data transformation that turns financial transaction records into a dataset of balance-respecting trajectories. The idea is to recover sequential patterns in transaction data. Each trajectory represents a specific amount of money observed to move through a specific sequence of accounts following a particular sequence of transactions. We rely on the rules of basic accounting to build out trajectories, respecting the balance in every account at every point in time. This guarantees that the resulting trajectories are consistent with a conservative process; money could indeed flow along the resulting set of balance-respecting trajectories.

36 Transactions to trajectories

The “follow the money” transformation traces money from the point at which it enters a digital payment system to the point at which it leaves. Figure 2.1 illustrates this transformation for a simple series of transactions among agents (who facilitate deposits and withdrawals), users, and companies. The arrows represent the movement of digital money, and the resulting set of balance-respecting trajectories follow interpretable sequential motifs. The orange trajectory follows a “payment” motif, where a user receives digital money via a deposit and subsequently uses it for a payment to a company. A similar sequence where the funds are used for a smaller purchase is shown in purple. The light blue trajectory follows a “storage” motif, where a user is keeping their money digital within the system without making a digital transaction.

Figure 2.1: Visual schematic of the “follow-the-money” transformation An ordered series of deposits, transfers, payments, and withdrawals (left) create a transaction network (center). Arrows show the movement of money, sized to convey amount. Pieces of these transactions are then allocated into balance-respecting trajectories (right) that represent the movement of money from depositing agents, through users, and on to companies and withdrawing agents.

37 Algorithmic implementation

We implement “follow-the-money” using a dynamic programming algorithm that allocates money to outgoing transactions using existing funds from prior incoming transactions. The underlying algorithm records intermediate objects, branches, that represent portions of transactions. Root branches are portions of transactions that begin trajectories. As new transactions appear, existing branches provide the funds to service them, building up a tree-like structure of references. Leaf branches are portions of transactions that end trajectories. Once the algorithm reaches a leaf branch, it has uncovered a complete trajectory and recursively traverses back toward the root branch. The sequence of transactions, nodes, and durations encountered on the way back to the root branch become the basic features of that balance-respecting trajectory. Follow-the-money is implemented concurrently for all accounts in the system as transactions appear in sequence or in continuous time.

Allocation heuristics

However we choose to allocate funds, balance-respecting trajectories will preserve key time and accounting constraints on the system as a whole and keep trajectories interpretable as the flow of money. But precisely which existing funds to allocate to which outgoing transactions is not uniquely defined; money is fungible. We must choose an allocation heuristic that defines how accounts in the system keep track of the money passing through them, determining what existing funds get assigned to an outgoing transaction. Two such heuristics with particularly strong theoretical foundations: a mixing heuristic and a last-in-first-out heuristic. Which heuristic is most appropriate will depend primarily on the intended use of the transformed data. For example, the last-in-first-out heuristic is helpful in exploring intentional user choices. On the other hand, general analyses that invoke the concept

38 of a random walk would be better served by the mixing heuristic. Data problems will tend to make the mixing heuristic less appealing.

Figure 2.2: Visual schematic of two allocation heuristics An illustration of the allocation outcomes for a simple series of transactions involving one account. This highlighted account is represented by a stack for last-in-first-out allocation, and a pool for well-mixed allocation. The account receives two $100 transactions, and later sends $50 to two different accounts. The last-in-first-out heuristic uses the most recent incoming transaction to fund the outgoing transactions, creating two $50 trajectories. The mixing heuristic pulls evenly from both incoming transactions, creating four $25 trajectories. Empty arrows are as-yet un-allocated funds.

Last-in-first-out heuristic The last-in-first-out tracking heuristic represents each account as a stack of money, and the funds added most recently are the first to be spent. More specifically, money from incoming transactions is added to the receiving account’s stack, on top of any existing funds in the account. To fill outgoing transactions, money is removed from the top of the account’s stack. This heuristic is in many ways the simplest possible, and is quite intuitive. An account that receives a $100 deposit and promptly pays rent will generate a straightforward $100 trajectory from whatever processed their deposit, through their account, and on to their landlord. It also has the attractive property that the results for a series of transactions is not affected by past transactions, including the size of the accounts in question. The individual paying their rent creates the same $100 trajectory irrespective of whether they have $10 in their account or $10,000. In some ways, this parallels how people

39 may think about money and thus introduces a stylized representation of savings into the system. Colloquially, dusty old money collects at the bottom of an account until the user needs to dip into it.

Mixing heuristic The mixing heuristic represents each account as a well-mixed pool. Under this formulation, money from incoming transactions joins existing funds in the account with no added distinction. To ﬁll outgoing transactions, money is drawn evenly from the account’s pool. Each earlier incoming transaction contributes to outgoing ones in proportion to its share of the account balance. This heuristic has the attractive property that it recovers all possible paths that a unit of money could have taken through the system, with a weight corresponding to the path’s relative likelihood under the balance-respecting constraint. This approaches the notion of a random walk in network science. It also dovetails nicely with the economic conception of money as perfectly fungible—any unit of currency is considered entirely equivalent to any other. Caution is warranted, however, because this heuristic is not independent of the past. Only completely emptying an account makes certain paths through it impossible; accounts with small balances constrain the universe of possible paths to a greater extent. With a ﬁnite time window into a given system we must know or infer the initial balance of every account for the mixing heuristic to work as advertised.

Network boundary

Deﬁning the network boundary is how we limit the follow-the-money transformation to tracing only money moving as a result of the transaction process we are studying. Speciﬁcally, we must determine what transactions are root, leaf, and regular branches. The payment system domain already provides the terminology we need to describe network boundaries: “deposits” and “withdrawals” add or remove money from the system while ”transfers” circulate money within it. These distinctions are often salient for providers and thus feature prominently in transaction records.

40 The details will depend on the intended analysis and on the idiosyncrasies of the bookkeeping practices of the particular provider. Often, it will be most relevant to define the network boundary such that trajectories trace funds through the user-facing side of a payment system. That way the observed movement of money is due to the user-driven transaction process. But one might also wish to study the provider-facing side of payment systems that, which accommodate users’ deposits and withdraws. The code presented alongside this paper presents options for defining the boundary of the system based on known transaction types, known account types, inferred account types, and several combinations. Not defining a boundary treats the system as fully contained.

Conclusion

We have considered the bookkeeping function of financial transactions, and the payment systems within which they take place. We noted that the constraints imposed on transactions by basic accounting are substantial and imposed system-wide. This means that financial transaction networks are weighted, directed, temporal networks with conservative dynamics. Luckily for us, conservative dynamics are well-studied on temporal networks and this actually lets us describe financial transaction processes mathematically. According to this representation, observable (i.e. balance-respecting) trajectories of money through a network given a transaction process would be observed monetary flows at the finest resolution one could possibly define them. One we have trajectories, there is a whole toolbox of network science to pull from. I use the logic behind this mathematical representation to put forward a computational approach that would transform a payment system’s transaction records into balance-respecting trajectories. In the chapters that follow, I will put this to use.

41 Chapter 3

Networks of Monetary Flow

42 The movement of money within an economy is primarily studied in aggregated form, using data on monetary flows between industries. The movement of money at smaller scales has long been impractical to consider empirically, and thus also under-explored conceptually. Modern payment infrastructure, however, is relatively centralized and increasingly digital. As people and companies conduct business, they are leaving a treasure trove of data about the real economy—at the finest possible resolution—on the servers of financial institutions worldwide. A small but growing group of researchers has begun to use such datasets to explore the economic and financial behavior of individuals [6, 28, 52, 60]. Others have analyzed the financial transactions taking place within payment systems as networks, seeking to capture the overall structure of such systems [23,86,100,102,154,180]. However, we currently lack a way to relate individual behavior to the structure of the system as is conveyed by the movement of money. We would like to be able to study how millions of individual transactions come together to create large-scale patterns in the movement of money. In this work, we address a concrete version of this question: how do we build a network representation of monetary flow though a payment system from its financial transaction records? Such a representation would encode the structure of monetary flow at the scale of the system, with a level of resolution equal to that at which money changes hands. We consider a large dataset of mobile money transaction records from a provider in East Africa, which covers ten months of activity for millions of users. Mobile money is a new global industry that has expanded rapidly across Africa, South Asia, and Southeast Asia since the late 2000s [78]. Mobile money providers support a digital version of the local currency (e-money). They host e-money accounts, process transfers, and service payments for users over their cellular infrastructure, where digital transactions are instantaneous. Digital services are facilitated by a large cadre of on-the-ground mobile money agents. These agents represent the provider and are physically located in the area they service. Mobile money agents offer conversion

43 between cash and e-money, as would a teller, but they run their own operations often in conjunction with a retail shop. Mobile money agents are paid on commission. [42] Typical sequential patterns, which we call motifs, are suitable for isolating the most common actions taken by mobile money users. Well-known use cases for mobile money, such as digital payments, digital transfers, and money storage, generally involve several sequential transactions of different types. For instance, paying a bill using the mobile money system might entail first depositing cash and then making a digital payment. To study these sequences empirically, we trace e-money as it moves through the mobile money system. We trace e-money from when it enters the mobile money system to when it exits, and group observed trajectories by the motif they follow. We create aggregated entry-exit networks where the nodes are the mobile money agents or corporations at the start and end of the observed trajectories. The links can be weighted to represent the movement of money, or the absolute flow of money, through the mobile money system as a whole. We focus on the trajectories that begin with cash deposits to agents, and the aggregated networks that gives each deposit equal weight. We discover that each user activity moves money through a different network structure at the system scale: digital payments result in a hub-and-spoke network, digital transfers form a largely amorphous network, while money storage and other activity that involves no digital transactions creates a network with geographic assortativity. Within this last network, we also uncover systematic gaming of the commissions system by a small subset of mobile money agents. This fraudulent behavior appears to be coordinated within scores of small, isolated groups of agents. In each case, trajectories let us observe individuals’ actions and aggregate their effect on the movement of money up to the scale of the entire system. We also find that user activity moves e-money through the corresponding motifs in anywhere from minutes to months, thus returning that e-money to provider-facing

44 accounts at substantially different rates. There are differences in these distributions between activities: commission gaming and bill payments happen considerably faster, on average, than do person-to-person transfers. But more importantly, the underlying distribution in return time for each of the activities range across several orders of magnitude. Empirical heterogeneity in return times greatly complicates estimation and interpretation of the velocity of money, a related theoretical concept from macroeconomics, at smaller scales. The methodology presented here brings the tools of network science, current and future, into reach for studying how money moves within payment systems. Conceptually, the network structure of money flow within an economy is a different angle from which to consider the interaction of scales in economics. Network analysis could provide another way to measure the economic power of “hubs” (ex. large firms) or the economic independence of “communities” (ex. regions). Moreover, payment systems themselves are what connect the monetary system to the underlying economy and studying the movement of money they support can provide an empirical grounding for ambitious lines of inquiry in monetary economics.

Mobile Money Data

We analyze a dataset of administrative transaction records collected in real time by a mobile money provider in East Africa.1 The data collection period ran from Jun 1, 2016 to Apr 1, 2017 and the dataset contains over 300 million transaction records generated by over 5 million anonymous users. This activity was facilitated by over 40,000 anonymous mobile money agents. Each record includes the sender, recipient, time stamp, amount, fee, type, and resulting balances of each transaction.

1The files were extracted by the provider, prepared and anonymized by Cignifi Inc., and provided to the author in their role as a consultant with Microfinance Opportunities by the International Finance Corporation under the Partnership for Financial Inclusion. Use of this data for the present study was ruled Exempt, Category #4 by Northeastern University IRB# 18-07-16.

45 Table 3.1 summarizes the most common transaction types in this data. Users can deposit money by giving cash to a mobile money agent, who then places e-money onto their account (cash-in). A withdrawal reverses this process (cash-out). Users can transfer e-money to other users using the person-to-person (p2p) service. Bill payment transactions (bill-pay) are payments to utilities or other large corporations. Mobile airtime (top-up) and mobile data (data) purchases are payments to the provider. Generally, mobile airtime and mobile data purchases are micro-transactions in that they are orders of magnitude smaller than other transaction types. Our analysis focuses on the most common activities.

Type Description Records Amount Popularity Transactions Average Average Median

Cash-in Deposit via agent 24.1% $42.96 95.9% 17.0 7

Cash-out Withdrawal via agent 19.3% $47.91 94.3% 13.9 7

P2P Person-to-person transfer 5.9% $52.80 78.5% 5.1 4

Top-up Mobile airtime purchase 41.8% $ 0.82 79.9% 35.4 13

Data Mobile data purchase 4.0% $ 0.86 17.9% 15.1 4

Bill-pay Bill payment 3.4% $20.58 24.0% 9.5 3 Table 3.1: Mobile money transaction types The six most common transaction types in the mobile money data. The number of records of one type is reported as a percentage of all transaction records, and the average amount of these transactions is denoted in US Dollars at purchasing power parity (PPP) with the local currency. Popularity is the percentage of users who made at least one transaction of this type. The average or median number of transactions refers to those made by these users, excluding those with zero transactions of this type. Less popular services are not shown, so the percentages do not add up to 100%.

Most transactions are ones where e-money either enters or exits the system; the network boundary is very prominent. Deposits and withdrawals of e-money are the most popular, in that such transactions are made by the largest fraction of users. Indeed, mobile money recipients often choose to withdraw their e-money into cash straight away rather than to keep it in their accounts or send it onward. [156] Mobile airtime purchases are the most common type of transaction in the data, and they

46 are indeed small. Person-to-person transfers, which keep e-money in circulation, are also popular but users make fewer of them so they are less common in the data. It is worth noting that surveys of users show that person-to-person transfers are the most popular service [84] indicating that users do not consider deposits and withdrawals to be separate actions, necessarily. Given the salience of the network boundary, we reconsider oft-described use cases for mobile money as sequential patterns of transaction types—motifs. Our analysis focuses on the motifs that begin as cash-in transactions; Table 3.2 shows a detailed breakdown of the transformed data by eight of the most common motifs. Paying a bill using the mobile money system would generally entail a cash-in transaction followed by a bill-pay transaction. Similarly, e-money from a cash-in can be used to purchase mobile airtime or mobile data. These are all well-known use cases of mobile money systems [78]. Another prototypical sequential pattern is the digital transfer motif, which involves three transactions: a cash-in, then a p2p, and then a cash-out [118]. Note that p2p transactions that are not subsequently withdrawn keep money in circulation within the mobile money system. E-money from a cash deposit can also be withdrawn again into cash without undergoing any digital transactions at all. This creates an in-out motif that is fairly common in mobile money systems, and there are several accepted explanations. Economides & Jeziorski (2017) describe this use case as money storage, a way to avoid carrying cash while travelling and to avoid storing cash at home over the short or medium term [52]. Money stored over a longer period of time becomes savings, so this sequential pattern would also occur if users were maintaining e-money in their mobile money accounts as a form of savings. This is less common [87]. Informal, over-the-counter, person-to-person transfers can also create the in-out motif. Often called a direct deposit, this action avoids the p2p transaction step; the sender cashes in to the recipient’s account, rather than their own, with the cooperation of (or at the behest of) the depositing agent [152].

47 Sequential transactions following the in-out motif might also arise from oppor- tunism on the part of mobile money agents. Encouraging and exploiting over-the- counter transfers is one of several ways by which agents could game mobile money systems so as to raise their earnings. More directly, agents can manipulate oﬃcial commissions by acting strategically. Gaming is possible because agents earn a commission for facilitating both cash-ins and cash-outs, while providers earn revenue from this activity only from transaction fees charged on the cash-outs. Furthermore, agent commissions have a tiered structure. Agents can take advantage by splitting larger cash-in transactions into several smaller ones nearer the tier, eﬀectively collecting multiple commissions for a single deposit. Since deposits incur no provider-imposed fee, this can be taken to an extreme and agents have been known to control user accounts for the sole purpose of earning themselves commissions. Under the commission structure of this particular provider, such brazen gaming would entail making many small deposits (maximizing the commission) and fewer large withdrawals (minimizing the provider-imposed fee). Since commission gaming comes at the expense of the mobile money provider, this whole range of actions are generally considered fraudulent.

Methods

Balance-respecting trajectories

We use the “follow-the-money” transformation to trace e-money through this mobile money system. In this particular implementation, we allocate funds using a last-in-ﬁrst-out heuristic. In the context of mobile money data, such allocation ensures that a user who deposits $100 through a mobile money agent, and then promptly pays a $100 utility bill, will generate a straightforward $100 e-money trajectory from the agent that processed their deposit, through their account, and on to the utility. We deﬁne the network boundary using the transaction types supplied in the data. Cash-in

48 Motif Exit Schematic Trajectories Deposits Duration Median Average In-out Cash-out 30.7% 71.5% 10.1 hrs 82.5 hrs Transfer Cash-out 8.2% 11.3% 27.8 hrs 126.8 hrs Circulation Cash-out 1.9% 1.4% 90.3 hrs 231.7 hrs Payment Billpay 4.0% 6.6% 0.26 hrs 27.1 hrs Circulating payment Billpay 0.7% 0.3% 47.1 hrs 152.0 hrs Micro-payment Topup/Data 41.0% 5.1% 34.7 hrs 135.5 hrs Circulating micro-payment Topup/Data 13.1% 0.8% 79.8 hrs 219.2 hrs Table 3.2: Detailed summary of trajectory motifs A summary of the trajectories observed when following all cash-ins through the mobile money system using the greedy (last-in-ﬁrst-out) heuristic. Shown are eight of the possible motifs, where the arrows correspond to the movement of e-money. The number of trajectories observed to follow a motif is reported as a percentage of all unique trajectories beginning with a cash-in. The number of deposits is reported as the percentage of all cash-ins that went on to follow that motif; the median duration is the time in which half of those cash-ins had moved through that motif, and the average duration is the average across those cash-ins. Not shown are more niche actions or incomplete trajectories, i.e. money that remains in the system at the end of the ﬁnite data collection window. For this reason, the percentages do not add up to 100%. transactions, bulk payments from corporations to users, and deposits from ordinary bank accounts form one side of the network boundary: beginning trajectories. Cash- out transactions, ATM withdrawals, bill payments, micro payments, and withdrawals to ordinary bank accounts form the other side: ending trajectories. Person-to-person transfers and transactions involving merchants occur within the network boundary. Provider-facing transaction types are ignored unless they end existing trajectories. Note that the senders (recipients) of cash-in (cash-out) transactions are mobile money agents. The recipients of mobile airtime, mobile data, and bill payment transactions are large corporations, whose subsequent transactions are handled ad-hoc by the provider. We do account for transaction fees charged by the mobile money provider and reference account balance information provided in the transaction data. We use

49 a size cutoﬀ at one unit of the local currency. We do not use a time cutoﬀ.

Entry-exit networks

From the data set of trajectories, we create entry-exit networks that describe the overall movement of e-money through the system. The nodes in these networks are the mobile money agents or corporations (payment recipients) at the start or end of each observed trajectory, and we combine together the balance-respecting trajectories with the same start- and end-points. A link means that users moved money from that start-point to that end-point.

Sub-networks We produce the aggregated entry-exit network using the eight motifs in Table 3.2. The ﬁrst encompasses all “payment” and “micro-payment” trajectories along with their circulating counterparts. The second includes all trajectories following a “transfer” or “circulation” motif. The last combines all trajectories following the “in-out” motif.

Weighting For the link weight, we use the sum over the size of trajectories as a fraction of the initial cash-in transaction. This emphasizes the user activity involved in moving money, rather than reflecting mostly the largest transactions. The weighted out-degree of an agent corresponds to the number of cash-ins they facilitated. These networks thus represent the movement of money through the mobile money system as a whole, emphasizing the activity of users rather than the absolute flow of money, which would be strongly affected by the largest transactions. The statistical techniques used to filter links [41] and compress the network [29] both take link weights to be statistical “observations”; cash-in deposits each contribute a total link weight of one and thus correspond to a single observation. It is worth noting that an analysis of other questions, such as cash re-balancing needs or profitability, would do better to use absolute amounts as link weights. Entry-exit networks aggregated using the absolute

50 size of trajectories would represent the total ﬂow of e-money. This would eﬀectively re-scale link weights by the size of cash-in transactions, giving proportionately more weight to larger deposits.

Geographic assignment The assignment of agents to sub-national administrative areas of the country is based on inferences from mobile calling records. Transaction and calling records were linked via a shared unique identifier, a hashed phone number. The cellular calling records come from a period of six months that ended thirteen months before this data was collected, and includes the cellular tower through which outgoing calls were routed. Crucially, the provider shared a file that included the geographic location of most of the towers in this older data. Roughly half of the agents in the dataset appear in the earlier cellular records, and we assume they did not move in the meantime. This is not unreasonable, as agent often operate their business in conjunction with a retail shop or other fixed locations. We assume that the agents who do not appear in the earlier data joined the provider as agents within the year prior. Accounts were linked to the cellular tower through which a plurality of its outgoing cellular calls were routed over the full six months. We placed the GPS locations of these cell towers within administrative areas using QGIS and the shape files for the highest sub-national administrative areas of the country available from GADM, the Database of Global Administrative Areas [65].

Network visualization We use the weighted version of k-core, s-core [53], to isolate the core 4000 nodes for the “payment” and “transfer” network and the core 5500 nodes for the “in-out” network. We identify the the top 10% of links within these cores according to “noise corrected backboning” [41]. Within the in-out core, the 1500 nodes with the highest s-core values have qualitatively diﬀerent network structure and are shown separately. We use the open source graph visualization

51 software Gephi [20]. 2

Quantitative comparison

We use the full entry-exit networks to calculate quantitative network measures, considering the sub-graph of the 1500 suspicious agents separately. We run stand- alone hierarchical Infomap [29] with unrecorded teleportation at a 15% probability, where the destination of jumps are chosen in proportion to the account’s out-strength. The information-theoretic measure used in this algorithm – description length – allows us to quantify the extent of sub-network structure. This measure gives the average number of bits needed to describe one step in an inﬁnite random walk on the network, and the algorithm exploits sub-network structure to minimize that value. We compare the value of the measure under compression to that of the uncompressed network, for the best of four runs. Random networks cannot be compressed, remaining near 0% compression, while a network with increasingly rich multilevel subgroup organization would approach 100% compression. We also calculate the generalized modularity [62] using the geographic locations of agents at the highest sub-national administrative areas in the country. This measure compares the amount of money moving between nodes within the same module to that which would be expected at random, and can range from -1 to 1. A value of 0 corresponds to random expectation; a value of 1 corresponds to a network where money moves only between agents within the same geographic area. We report the value as calculated across the subset of agents for whom geographic location is known.

2For the “payment” network and “commission gaming” subgraph we used the OpenOrd layout with default parameters. This highlights and separates the tightly clustered groups of nodes in these networks. For the “transfer” and “money storage” networks we used the Force Atlas 2 layout with “scaling” set to 25, and otherwise default parameters. The nodes are sized by out-strength within each sub-plot on a negative quadratic spline. The nodes are colored consistently across the sub-plots, by the highest administrative area of the country to which the account was assigned. Not shown are isolates and links below the 10% threshold.

52 Results

We focus on the observed trajectories of e-money through the mobile money system that begin with cash-in transactions, and group them by the motifs they follow. Our ﬁrst group combines all trajectories that end in a bill payment or micro-payment, and these motifs together capture 12.7% of cash-in transactions. The next group encompasses the prototypical digital transfer motif, as well as similar motifs with more than one person-to-person transaction. These motifs also capture 12.7% of cash-in transactions. Finally, we aggregate together all of the trajectories following the in-out motif, which reﬂects money storage or other activity that involves no digital transactions. 71.5% of cash-in transactions follow this motif. For each of these groups of motifs, we create entry-exit networks that describe the resulting movement of e-money through the system. The nodes in these networks are the mobile money agents or corporations at the start or end of each observed trajectory. The links between them are directed, and we give each deposit equal weight in calculating the aggregated link weight. The total weighted out-degree of an agent then corresponds to the number of cash-ins they facilitated.

Economic actions produce distinct structures of money ﬂow

We find that mobile money facilitates four distinguishable economic actions: digital payments, digital transfers, commission gaming, and money storage or other non-digital activity. These activities move money through the system to form four decidedly different network structures: hub-and-spoke, amorphous, tightly grouped, and geographically assortative. Figure 3.1 visualizes the weighted core of our three aggregated networks, showing the top 10% most significant links within the core [41, 53]. The network structure of (A) digital payments and (B) digital transfers appear strikingly different. When making digital payments, users move e-money from agents

53 Figure 3.1: Core structure of entry-exit networks A visualization of the 4000- node core of the (A) digital payment and (B) digital transfer networks. The network of aggregated in-out trajectories shows a distinct structure among 1500 nodes of the innermost core likely engaging in (C) commission gaming and the 4000 nodes in the next tier facilitating (D) money storage or other non-digital activity. The top 10% most signiﬁcant links are displayed; isolates are hidden. Nodes are colored by geographic location at the highest sub-national administrative areas in the country, when known from cellular records. Agents who joined the network too recently for this (about half) are dark grey. Corporations are black points, and appear only at the center of the hubs in (A). 54 all over the country into the accounts of a handful of large corporations, who become the obvious hubs. In contrast, users making digital transfers move e-money through the system from everywhere to everywhere else in a manner that appears very close to random. Weighted k-core analysis reveals two distinct structural patterns within the in-out network. The innermost core of 1500 agents capture 13.1% of all cash-in transactions as in-out motifs just among themselves (C). These agents form small and densely connected subgroups that are less connected to one another. This diﬀers substantially from the structure among the next tier of 4000 agents that is indicative of the structure of the bulk of the in-out network and shows a general geographic assortativity (D).

Evidence for systematic commission gaming

We deem the innermost core of the in-out entry-exit network to reﬂect systematic commission gaming, predominantly, and proceed to consider it separately. These 1500 mobile money agents are a rather distinct set: only 7.6% of them are also at the core of the payment or transfer networks, whereas this number is 51.7% for the next 4000 by core number. The errant set includes less than 4% of all agents, and they distinguish themselves with behavior that is consistent with engaging in systematic commission gaming. The average mobile money agent earns as commission 95.0% of the fee revenue that they generate for the provider in facilitating cash-ins and cash-outs. The provider’s break-even point is clearly somewhere below 100%. On average, these 1500 agents earn as commission fully 231.9% of the revenue they generate for the provider. We see evidence these agents are splitting deposits to reach such high commissions. While they serve about as many unique customers as does the average agent, these agents facilitate many times more cash-in deposits that are many times smaller. Moreover, a cash-in with one of these agents is four times as likely to fall within $1 of a tier in the commission structure as one with an average agent. This is clear evidence of gaming. Finally, these agents facilitate almost

55 no digital transactions; 95.0% of their cash-ins follow the in-out motif. This means they may also be encouraging and exploiting over-the-counter transfers to raise their earnings further. The average values for agents within all highlighted sets are reported in Table 3.3. The innermost core of agents are aberrant according to several relevant indicators in ways that are consistent with manipulating the commissions they earn. The average group size in the commission manipulation sub-graph is 4.9; the average such agent is in a group of size 9.9.

Network Coreness Users Cash-ins Amount In-out Near Tier Gain Established All 836 1802 $50.59 66.63% 18.01% 95.04% 48.34% payments 1-4000 2491 5380 $43.16 64.50% 17.22% 89.88% 75.71% transfers 1-4000 1517 2932 $50.12 66.48% 14.95% 80.32% 66.25% in-out 1-1500 872 8867 $ 9.76 94.95% 76.34% 231.94% 33.93% in-out 1501-4000 1834 3659 $45.40 68.78% 16.49% 82.59% 69.65% Table 3.3: Description of highlighted sets of agents A comparison of highlighted sets of agents, described by their coreness rank within the speciﬁed entry-exit network. The average number of unique users, cash-ins, and average cash-in amount is calculated over the values for the agents in that set. In-out is the average percentage of cash-ins to those agents that went on to follow the “in-out” motif. Near Tier is the average percentage of cash-ins to an agent that fall at or within $1 above the commission tier (USD at PPP). Gain is the average percentage of the revenue earned by the provider on the cash-ins and cash-outs at that agent that is captured by the agent as commission. The percentage of agents in this set that are “established” is inferred by how many of them also appeared in a companion dataset from just over a year earlier.

Money storage and other non-digital activity

Without the errant contingent of agents, the in-out entry-exit network reﬂects regular mobile money activity that involves no digital transactions. The established explanation for such activity is money storage, but in our case it likely includes also mobile savings and over-the-counter transfers to some extent. We do not endeavor to distinguish between these actions, and especially not the intent behind them, as doing

56 so would require stronger assumptions or additional data. In other mobile money systems, such as those with designated over-the-counter or savings services, it may be possible to distinguish these actions.

Network structure of economic actions

Beyond visualization, we can quantify structural differences in the patterns of money flow created user activity. In Table 3.4 we report several measures for the full entry-exit networks corresponding to the four distinguishable mobile money actions. We also report the Gini coefficient across agents of the number of deposits entering the system, and those same trajectories exiting the system.

Network Deposits Modularity Agent Gini Description Length Full Core Full Known Entry Exit Initial Compressed Reduction Payments 12.7% 19.5% – – 0.56 1.00 – – – Transfers 12.7% 2.6% 0.05 0.13 0.57 0.55 14.7 bits 14.7 bits 0.06% Gaming 13.1% 100% 0.12 0.45 0.98 0.98 10.1 bits 3.8 bits 62.30% Money storage 58.4% 4.9% 0.13 0.27 0.54 0.55 14.8 bits 13.9 bits 5.58% Table 3.4: Quantitative network measures A comparison of the aggregated entry- exit networks. The number of cash-in deposits captured by this network is reported as a percentage of all cash-in transactions. The percentage of this total captured by the core of this network is reported as such. Modularity quantifies the geographic assortativity of the network using assignments of agents to sub-national administrative areas in the country, which is known for around half of all agents. This metric is unitless and ranges from -1 to 1. The Gini coefficient across agents quantifies the inequality of where trajectories begin and end. This metric is unitless and and ranges from 0 to 1. The description length is an information theoretic measure that decreases as the Infomap algorithm exploits sub-network structure to compress the network. The recipients of digital payments, i.e. corporations, do not have a well-defined location nor do they facilitate cash-ins; we do not calculate modularity or run Infomap on the “payments” network.

Pronounced subgroups in the structure of commission gaming We have established that these mobile money agents are acting strategically, in that their

57 behavior reflects the fee and commission scheme. These also move money amongst each other primarily within small subgroups, a curious network structure that may reflect deliberate coordination. This activity captures 13.1% of cash-in transactions. Infomap achieves a full 63.2% reduction in description length of the network, indicating that this network contains rich multilevel subgroup structure. Cash is often deposited and withdrawn from agents within the same groups of around ten agents. Although this is one particular case, this finding suggests that our analysis approach can surface particular kinds of strategic coordination, whether or not they are desirable, within payment systems. Future work on fraud detection in mobile money systems that flag individual in-out sequences with specific evidence of agent wrongdoing would allow researchers to further isolate and characterize commission gaming.

Geographic assortativity in the structure of money storage and other non- digital activity Regular in-out activity captures a remarkable 58.4% of cash-in transactions, with an internal community structure driven by geography. This is an unexpectedly large share of all activity; the system is intended for digital transfers and they are the most popular service according to surveys [84]. However, behavioral trace data carries different observational implications than do stratified surveys. In particular, the median mobile money transaction is not made by the median user, but rather by an especially active user who makes many transactions [118,178]. Money storage and other non-digital activity is prominent in the data because it reflects an important use-case among high-activity users. This activity is structured by geography. Infomap achieves a 5.6% reduction in the description length as it finds community structure to the non-digital network. A generalized modularity of 0.27 by geographic location indicates that this structure is aligned with geography.

Randomness in the structure of digital transfers Digital transfer activity captures 12.7% of cash-in transactions and forms an amorphous network with near-

58 random structure. In contrast to the other use-cases, Infomap recovers next to no structure within the network of digital transfer activity. The algorithm achieves a negligible 0.06% reduction in description length. Digital transfers show some geographic assortativity, with a modularity of 0.13, but little centralization. The 4000 agents at the core process 2.6% of the cash-in transactions moving over it, which is not much more than naive expectation. That the structure of digital transfers is stubbornly amorphous is quite surprising, especially since mobile money has been unevenly adopted following existing contours of socioeconomic inequality [78]. Much as those supporting the development of mobile money would like to pinpoint areas where digital circulation is succeeding especially well, this is not possible in this particular case.

Prominent hubs in the structure of digital payments Digital payment activity captures 12.7% of cash-in transactions, and these funds end up paid to just over 300 corporate accounts. The large corporations who receive payments are “hubs” that hold prominent positions with respect to the movement of money within this mobile money system. The provider itself is one of these, as they are the recipient of e-money used to purchase mobile airtime and mobile data.

Temporal structure of economic activities

We find that digital payments, digital transfers, commission gaming, and money storage or other non-digital activity also show different temporal structure. The trajectories corresponding to these activities move through the mobile money system over a period of time, and the profile of these durations differs substantially. Figure 3.2 shows the distribution of trajectory durations, scaled and weighted to reflect the proportion of cash-in transactions captured by each activity. The temporal structure of commission gaming and of digital transfers have the least overlap. Most commission gaming occurs within the same day while the

59 Figure 3.2: Scaled distribution of trajectory durations The distribution over the duration of time between cash-in transactions (that begin trajectories) and payment or withdrawal transactions (that end trajectories). Shown in color are the four distinguishable economic actions identified above. The distribution is weighted such that each cash-in contributes one observation, and the areas are scaled to reflect the proportion of cash-in transactions captured by each activity. The x-axes are log scaled. majority of digital transfers take more than one day to move through the system. Digital payments show a bi-modal distribution, reflecting differences in two of the constituent actions: bill payments and micro payments. Cash-in deposits intended for bill payments routinely exit the system within a few minutes to an hour. Mobile airtime and mobile data purchases, on the other hand, are often made using the small sums that have remained in a mobile money account for days or even weeks. Money storage and other non-digital activity shows a very broad distribution, underscoring the difficulty in distinguishing actions that leave similar behavioral traces in the data. Notably, we see wide variation in the duration distribution within each activity. We know to expect differences across use-cases in the amount of time e-money remains in the mobile money system. Mbiti and Weil (2013) estimate the turnover rate, or

60 “transactions velocity”, of mobile money in the M-Pesa system. They note that their estimate reflects an average over a hybrid system where money is both transacted rapidly and stored for longer periods of time. [118] They highlight a counter-intuitive observational effect: most of the e-money we see is used by those with rapid turn-over, but at any given moment most of the e-money in the system is held by those with slow turn-over. Our results show that we must contend with such effects also within any particular economic activity on mobile money systems. Indeed, the underlying duration distribution is logarithmic. When values range across several orders of magnitude, the average becomes uncharacteristic of the distribution. The velocity of money is a theoretical concept defined by macroeconomic accounting relationships between money supply and price level, and is often treated as a single average value across an economy. It is related to the “transactions velocity”, and there are methods that estimate the economy-wide velocity of money when average turnover rates differ across payment systems or sectors. [107, 155, 178] It may be possible to extend these methods to incorporate heterogeneity also within payment systems. Producing empirical measures comparable to the velocity of money at a sub-network scale, or even for individual accounts, is a promising direction for future research.

Discussion

In this paper, we ﬁnd clear diﬀerences in the network and temporal structure of the movement of money across several distinct uses of a mobile money system. Several common use cases for mobile money—making a payment, transferring money, and storing funds—are interpretable as sequential combinations of mobile money transactions. Tracing funds through the system let us tease them apart. We group balance-respecting trajectories by the motifs they follow, relating observed individual- scale activity to system-scale network structure and back again. The resulting networks

61 contain prominent hubs, random structure, geographic assortativity, and evidence of strategic behavior. Money moves through these patterns at highly heterogeneous rates. Our results give a hint as to what structures one would expect to find within the movement of money through an economy as a whole. The large corporations who receive payments are “hubs” in the mobile money network. We can expect systemically important companies to hold such prominent positions with respect to the movement of money within any economy. At the same time, geographic constraints on the opportunities for firms to do business are very real. Similarly, some amount of peer-to-peer activity that bypasses more centralized economic structures is to be expected almost anywhere. Strategic coordination is a field of its own within economics, and applying game theory to network formation can predict the existence of particular structural features [90]. Although the structural features we find are general, the particular activities we see reflect the affordances of mobile money, the incentive structure of this particular provider, and the economy of the country in which it operates. It is worth considering what appears to be largely missing from this mobile money system. An established bank in a more digitized economy might capture a wider range of economic activities such as receiving wages, buying products, paying suppliers, and servicing loans. A large-value payment system used by banks and major firms might capture investment decisions and financial trading. Those used by government agencies could capture taxation, allocation, and redistribution. The structure of money flow that results from any of these activities, and their relative share within a particular economy, are open empirical questions. It will not always be possible to isolate different user actions as cleanly as done here. We are fortunate that the most common sequential transaction combinations in the data correspond directly to only one, or a few, well-documented use cases of mobile money. Furthermore, these are described in a robust substantive literature,

62 technical publications, and available survey data. [52,78, 84,87,118,152,156, 178] On the other hand, other payment systems may have more detailed account labels or transaction descriptions. In some cases it may be possible to conduct surveys that directly ask about the intent behind common motifs. Even without any substantive information, constructing money-flow networks would be useful for describing and interpreting the movement of money through any payment system. Network analysis can identify important nodes, pronounced subgroups, and community structure. These tasks are all intensely studied in network science, and could provide new ways to measure the economic power of large firms and the economic independence of regions from the flow of money. Ongoing advances in the field, particularly in trajectory-based approaches to temporal network analysis [103, 148], stand poised to expand the possibilities even further. Our methodology is also brings “big data” into reach for novel questions in monetary economics, inviting empirical research and theoretical development. We observe units of money as they move between accounts within a particular payment system, revealing the time dimension of money at the same level of granularity at which transactions occur. Turnover rates in this mobile money system differ widely even across instances of the same use-case. This underlying heterogeneity complicates estimation of the related theoretical concept, the velocity of money. This is defined via an accounting identity in standard monetary economics and is often assumed to have a single value across an economy. With expanded empirical tools, it may be possible to extend existing ways of incorporating differences in average velocity between payment systems [155] and sectors [107] down to sub-networks, communities, or even individuals.

63 Chapter 4

Circulation of Money

64 Modern payment infrastructure is diverse, fragmented, and in the midst of change. New, public-facing, digital payment systems have proliferated in recent years as private providers deploy a number of innovative models. Some examples include mobile money (ex. M-Pesa in Kenya), peer-to-peer payment applications (ex. Venmo in the USA, or Swish in Sweden), regional credit circuits (ex. Sardex in Sardinia), and cryptocurrencies (ex. Bitcoin). Uptake of these and similar services has brought renewed attention to money as infrastructure [140], and exposed how limited is our scientific understanding of public-facing payment systems.1 Mobile money, in particular, is a global industry with the potential to improve the financial lives of billions [4, 160, 161]. Mobile money services have expanded rapidly across Africa, South Asia, and Southeast Asia since the late 2000s and further development continues to be supported by international initiatives [78,132]. However, the development of mobile money has lagged in many areas and demand has yet to emerge for much beyond simple transfer services. Even for the most successful systems, uptake of more complex financial services has been limited and e-money is far from displacing the central role of cash [84, 156, 159]. In some areas, limited development is dampening the long-term prospects of mobile money services and hampering financial inclusion efforts. Providers and proponents of mobile money services are interested in monitoring and improving the maturity of the systems for which they are responsible. Thankfully, the operation of these systems is something that we can study, directly. Mobile money systems generate digital transaction records that makes possible spectacularly detailed research: we know that residents of Rwanda sent $84 worth of airtime transfers (a precursor to mobile money) to persons affected by an earthquake in 2008, and that

1We understand much better the operation of large-value payment systems (LVPS), which are critical infrastructure for the monetary system [102,154]. Researchers have been especially interested in using transaction records from LVPS to improve the modeling of scenarios where they might fail or get close to failure [23]. Macroeconomists also have some understanding of how (average) transaction behavior within such systems combine into monetary aggregates [107, 155].

65 using e-money rather than cash to move funds by 1 km in Tanzania during December of 2012 was valued at around 1.25% of the average transaction [28,52]. But this specificity of knowledge on these questions contrasts sharply with our predominantly conceptual understanding of how mobile money systems operate. Mobile money as public-facing digital monetary infrastructure has been studied primarily in aggregate [116,118,178] and in theory [89]. In this chapter, we conceptualize more mature mobile money systems as those where e-money acts more like money: funds circulate within the system serving as both a means of exchange and as a store of value. This approach is comparable across systems of different sizes and currencies—the idea is to quantify maturity for any mobile money system so that we can study the broader forces affecting all such systems. The question becomes: how do we measure the extent of circulation of e-money within a mobile money system from its empirical transaction records? This work defines a pair of measures that quantify two dimensions of within- system circulation from a provider’s own transaction records. We measure how many times funds are re-transacted within the system before exiting the system (Transactions Until Exit or TUE) and how long funds remain within the system (Duration Until Exit or DUE). Summarized as an average, the TUE can be seen as a direct measurement of the length of the “e-money loop”, as put forward by Isaac Mbiti and David N. Weil [117,118]. Because our measures are built from transaction level data, they remain interpretable at any temporal granularity can help us better understand changes over time. We track the maturity of a mobile money system in East Africa over eight months2. This particular mobile money service has millions of users and was undergoing strong growth over the observation period—robust adoption by new users, an

2The files were extracted by the provider, prepared and anonymized by Cignifi Inc., and provided to the author in their role as a consultant with Microfinance Opportunities by the International Finance Corporation under the Partnership for Financial Inclusion. Use of this data for the present study was ruled Exempt, Category #4 by Northeastern University IRB# 18-07-16.

66 expanding cadre of agents, and an increasing number of total transactions. Our measures are quite sensitive to the system’s dynamics. Both TUE and DUE pick up on cyclicality corresponding to recurring patterns in work and pay, which are disrupted by holidays. The time series of TUE also reveals a 38% increase in digital re-transactions during September of 2016 that corresponds to a known intervention by the International Finance Corporation (IFC). This success of this intervention is attributable in large part to achieving an especially large response by a small group of especially large-value users. The effect on maturity is more modest, but still substantial, when we consider each deposit transaction to contribute equally. Most importantly, our measures reveal an underlying downward trend in maturity across the mobile money system. This is both surprising and concerning. Conventional wisdom holds that mobile money services, like mobile telephony, would benefit from network externalities as their systems grow [15]. Our data show that a countervailing force—self-selection by users in adopting the service—is outweighing the peer-to-peer effects crucial to triggering positive externalities. The balances that users are building up over longer periods of time are also becoming more ephemeral, possibly an unintended consequence of improved accessibility. Our results help explain why the development of mobile money services has reached a limit in many areas—maturity may have a U-shaped relationship with system growth. If this East African mobile money service with millions of users is any guide, then few (if any) mobile money services have reached the inflection point where direct peer-to-peer effects materialize. Instead of benefiting from positive “network externalities” as their systems grow, providers must contend with countervailing pressures; declining maturity places ever-greater reliance on the agent infrastructure. If mobile money providers continue to see an increasing marginal cost per additional user, then a goal of universal access becomes less economical. This would be of particular concern to those looking to further financial inclusion. Thankfully, the notion of maturity as within-network circulation of e-money

67 provides an alternative intuition. Peer-to-peer eﬀects are expected to take hold when those receiving money already have the intention of sending it onward, digitally. It is cycles of transactions within a payment system that supports circulation [86]. Mobile money providers can be deliberate about developing positive externalities by aiming to “close the e-money loop”. Mobile money services might seek to attract not just more users but the right users. Finally, the methodology presented here has applications far beyond mobile money. Macroeconomists recognize that transaction records from public-facing payment systems have the potential to improve economic measurement. Most ambitiously, Aladangady et. al. (2019) use transaction data from a card transaction processor to construct macroeconomic consumption statistics [6]. Large-scale data from digital monetary infrastructure has local granularity, ﬁne temporal resolution, and can be updated in near real-time. Our work shows that direct empirical measurement of monetary indicators from such data is entirely possible. The work that remains is to reconcile what we can measure about how money actually moves with our understanding of money in aggregate and in theory.

Mobile Money

Mobile money providers host accounts for their users and provide transfer and payment services over the cellular infrastructure (ie. via Short Message Service (SMS), Unstructured Supplementary Service Data (USSD), or Application Programming Interface (API)) [78]. Providers service conversion with cash via a large cadre of mobile money agents, operating on the model of agent banking as described in [42]. Mobile money users can deposit into (withdraw from) their accounts by giving (receiving) cash from mobile money agents; agents are paid on commission. Most mobile money providers also oﬀer conversion to and from bank accounts through an interface with the banking system. Some providers also maintain a system of Automatic Teller

68 Machines (ATMs) that can effect conversion with cash. Mobile money providers have struggled to develop mature payment systems that are financially sustainable, even as their services have grown in popularity and impact. Of recurring concern are instances of fee avoidance, evasion, and fraud [115]. More common are over-the-counter (OTC) activities that, while rarely malicious, nonetheless circumvent intended channels and reduce provider revenues from transaction fees [152]. OTC person-to-person transfers, or “direct deposits”, entail a sender cashing in to the recipient’s account, rather than their own, with the cooperation of (or at the behest of) the depositing agent [8]. More generally, there is a widespread tendency for customers to withdraw their e-money soon after receiving it [4,156]. These usage patterns are costly for providers: transfers or payments are serviced over the cellular infrastructure, whereas servicing deposits and withdrawals entails compensating mobile money agents and re-balancing stocks of cash among them [164]. Against this backdrop, providers and proponents of mobile money services are looking to monitor and improve the maturity of mobile money systems. Digital cellular infrastructure is highly scalable, especially in comparison to physical agent infrastructure. Moreover, the digital infrastructure of mobile money carries the promise of supporting more complex digital financial services [159]. Savings, loans, insurance, business management, and access to financial markets offer additional business opportunities for providers and contribute to financial development in these economies.

Maturity as sustained circulation of money

The conventional notion of money is one of circulating tokens that act simultaneously as a unit of account, a means of exchange, and a store of value. Here, we consider a fully “mature” payment system to be one that supports sustained

69 circulation of money in this sense of the term—its tokens are used as a means of exchange and as a store of value to the extent that these tokens serve as their own unit of account.

Fully mature payment systems are generally limited to national currencies, notwithstanding periodic attempts to establish private ones [147]. For such systems, their money maintains its value in real terms irrespective of convertibility into other forms of money. As an historical example, there was some concern in the 1960s that the dollar note would lose its value when the Federal Reserve broke convertibility of dollars into gold. That concern was misplaced, as the dollar itself was already in sustained circulation worldwide. [97]

Most public-facing digital payment systems support a derivative form of money, guaranteeing convertibility on demand. Mobile money providers, speciﬁcally, support the circulation of a digital version of the country’s local currency (e-money). In most jurisdictions, they are required to back each unit of e-money, dollar-for-dollar, by holding funds in trust accounts at a domestic bank [78, 126]. This precludes concerns about solvency, which could threaten the convertibility guarantee and thus conﬁdence in the system. Even so, liquidity management issues among mobile money agents [164], or government actions [30], can leave conversion services temporarily inaccessible.

The maturity of derivative systems varies widely [19], and providers have a clear incentive to improve their system’s maturity. Mobile money systems beneﬁt directly from greater circulation of money within their systems since they produce revenue from transaction fees. More generally, providers incur much lower costs when users transfer money within their system than when users add or remove money from their system. Aﬀecting conversion, on the other hand, requires the provider to maintain an interface with outside systems. Maintaining locations where users can obtain physical currency (ex. agents and ATMs) is especially costly.

70 Direct Measurement

Here, we introduce a way to measure the circulation of money—directly—using a provider’s own digital transaction records. Our idea is to quantify the extent to which a payment systems’ tokens are used as money, in the sense that they serve as a means of exchange and as a store of value. A payment system that approaches the idealized notion of sustained circulation would become increasingly “mature” along both dimensions.

Transaction records

Our study uses administrative transaction records from a mobile money provider in East Africa. This dataset contains over 300 million transaction records generated by over 5 million anonymous users and facilitated by over 40,000 anonymous agents. As is typical of financial transaction data, each record includes the accounts that sent and received a transaction, its timestamp, and its monetary value. Each transaction also includes a descriptive transaction type where the kind of account held by the sender and recipient is clear. This mobile money system has a user-facing side where the movement of money is user-driven, and a provider-facing side that accommodates users’ activity. We want our measures of system maturity to reflect user-driven activity, and so we use the transaction type information to define who is a mobile money “user”. For instance, we infer that the sender of a cash-in deposit or recipient of a cash-out withdrawal is a mobile money agent. Similarly, we infer that the sender/recipient of a deposit/withdrawal from an ordinary bank account or ATM is a bank; that the recipient of a bill payment or sender of a bulk payment is a corporation; and that the recipient of a mobile airtime purchase is the provider. We consider accounts to be user-facing so long as they are party to at least one e-money transaction on

71 the expected side and never reveal themselves to be provider-facing.3 Transactions from regular users to a provider-facing account are deemed to be “exits” from the user-facing mobile money system; we include digital “exits” for the TUE measure. Transactions between non-user accounts are ignored.

Tracing the movement of money

If we are to measure the circulation of money using transaction records, we cannot consider individual transactions in isolation from other transactions. Sustained circulation implies that the same funds are re-transacted multiple times. In practice, re-transaction occurs whenever the same account both receives and makes transactions. These transactions are recorded separately, and our approach begins by tracing the movement of money over sequential transactions.

We use the “follow-the-money” transformation introduced in Chapter 2 to trace out trajectories of money. We define the boundary of our system in reference to the user-facing accounts; each trajectory describes the path a specific amount of money took from the point at which those funds entered the user-facing system to the point at which they exited. We allocate funds using the last-in-first-out heuristic and account for transaction fees charged by the mobile money provider. We use account balance information provided in the transaction data and a size cutoff at one unit of the local currency. In estimating our time-series we use a time cutoff of 21 days. The choice of cutoff does not affect our conclusions (see Appendix).

3Accounts with oﬃcially recognized merchant activity (of which there are very few) may or may not be seen as user-facing. Most such accounts also conduct provider-facing activities. Likewise, large corporations are considered to be provider-facing because the transactions they receive are subsequently handled on an ad-hoc basis by the provider.

72 Transactions Until Exit and Duration Until Exit

A particular trajectory (f) corresponds to funds that moved along a sequence of transactions (fi). The size of each trajectory (af ) can be considered either the amount of money or the fraction of the deposit transaction observed to follow that trajectory. The length (lf ) of a trajectory is the number of sequential transactions that those funds experienced within the system. The duration (∆tf ) of a trajectory is the total time that money stayed within the system. Quantifying the extent of circulation within the system is straightforward using trajectories. Transactions Until Exit (TUE, Equation 4.1) corresponds to the average length of the trajectories that funds follow through a payment system. Duration Until Exit (DUE, Equation 4.2) is the average duration for funds moving through the system. These measures are well-deﬁned for any set of deposits into the payment system, under either weighting scheme. We compute these measures for all the deposits into the system each day, creating two time series.

P P f lf · af f ∆tf · af TUE = lf = P (4.1) DUE = ∆tf = P (4.2) f af f af

These two measures capture two aspects of circulation within a payment system, and thus its maturity. That funds take several sequential steps within a system (i.e. TUE) shows that users are ﬁnding reason to use digital money to execute these transactions; these tokens are being used as a means of exchange. That particular funds remain within the system for a long period of time (i.e. DUE) shows that users are choosing to store their money in that form; these tokens are being used as a store of value. They are complementary, but not independent, and would both approach inﬁnity under sustained circulation of funds. Please see the next section and the Appendix for additionally detailed versions

73 of these equations. In our ﬁnal calculations we incorporate transaction fees, ﬁnite time considerations, and the contribution of digital exit transactions (for TUE).

Contribution by particular accounts

We would like to be able to ask whether and to what extent certain sets of accounts support the sustained circulation of money within a payment system. Since accounts move funds along trajectories, we can quantify the extent to which particular accounts drive trends and changes in TUE and DUE over time. Every transaction step (i) of each trajectory (f) moves money into the transaction recipient’s account

(rf,i). This account holds onto that particular amount of money (af,i) for a particular duration of time (∆tf,i). Mathematically, all the occasions when we see money entering a focal account can be considered within a double summation over all trajectories (f) and all steps (i) under the condition that this account is the transaction recipient at that step. Equation 4.3 defines the total amount of money entering a focal set of accounts, N. This becomes the denominator to the weighted averages that define the contribution these accounts make to TUE and DUE. Equations 4.5 and 4.4 define the average duration of time that money remains within these accounts, ∆tN , and the fraction of funds that they re-transact, lN . These values can be calculated for any set of user accounts.

X X aN = af,iδ(rf,i,N) (4.3) f i 1 X X lN = δ(rf,i+1,U) · af,iδ(rf,i,N) (4.4) aN f i 1 X X ∆tN = ∆tf,i · af,iδ(rf,i,N) (4.5) aN f i

74 where, for the set of all user accounts U and focal set N:

( 1 n ∈ N δ(n, N) = 0 otherwise

When the focal set, N, is the set of all user accounts, U, these measures reproduce TUE and DUE (as defined Equations 4.1 and 4.2) except in the normalizing P factor. Replacing aU by f af in Equations 4.4 and 4.5 defines an alternative formulation of TUE and DUE. The values of af,i, δ(rf,i+1,U), and ∆tf,i are always precisely defined so this alternative formulation can be used to calculate TUE and

DUE when the values of lf and ∆f are ambiguous. This is especially useful in cases where trajectories might not have the same size at every transaction step i, such as when payment system providers charge transaction fees.

Results

The maturity of this mobile money system is highly dynamic. Figure 4.1 shows the daily time-series of the TUE and DUE, calculated over all deposit transactions made that day. For each measure, the absolute value gives every unit of money equal weight and the normalized value gives every deposit transaction equal weight. The system exhibits strong cyclically: weekly patterns corresponding to work vs. week days, monthly patterns corresponding to the pay periods of salaried workers, and changes in these patterns during holidays. While the time period does not cover a full year, there is some indication of seasonality. There is a dramatic shift in TUE in September 2016 that corresponds to a known intervention, and is discussed in the following section. Undertaken by the International Finance Corporation (IFC), this eﬀort targeted the re-transaction of deposited funds and raised the system-wide TUE by around 38%. However, the extent to which e-money is circulating within this mobile money system remains quite low.

75 Transactions Until Exit Duration Until Exit

0.50 Normalization: Normalization: Dollars 180 Dollars Deposits 0.45 Deposits

150 0.40 Hours

0.35 120 Digital transaction steps Digital transaction

0.30 90

Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17

Estimated with cutoff time of 21 days Estimated with cutoff time of 21 days

On average, only between one third and one half of the e-money deposited into the system is digitally transacted even once. This corresponds to a substantially shorter e-money loop than documented for M-Pesa in 2009 [117]. On average, the funds entering this system remain in the system for around a week under last-in-ﬁrst-out. Most consequentially, we uncover a gradual decline in both TUE and DUE when their values are normalized to give every deposit transaction equal weight. Each of these measures is capturing a counter-intuitive trend. The decline in TUE can be attributed to change in the user base as the system grows and a conspicuous lack of peer-to-peer network eﬀects. The decline in DUE is driven by higher turnover of long-term balances, possibly a downside to greater accessibility.

Leveraging heterogeneity for eﬀective interventions

Beginning in September of 2016 the mobile money provider undertook an intervention into their system in partnership with the IFC. This intervention speciﬁcally

76 targeted OTC P2P behavior, where the sender of a P2P transaction deposits cash into the recipient’s account, rather than their own [8,152]. Of particular interest to the provider were the revenue implications of this behavior, which avoids the (digital) P2P transaction step and the associated transaction fee. OTC P2P requires the cooperation of the depositing agent, and this intervention focused on discouraging agents from allowing this behavior. The intervention prioritised large-value transactions.

The IFC intervention targeted OTC P2P behavior, which depresses the share of deposit transactions that are subsequently re-transacted. We ﬁnd users re-transacted a greater share of their deposits as a result of the intervention. Figure 4.2 compare the month before and after the IFC intervention (August vs. October) across users grouped by total turnover. The highest turnover users increased their re-transaction share by 18 percentage points while the intervention had a more modest eﬀect on the behavior of users, overall.

Moreover, this system is heterogeneous with respect to amount wherein a small percentage of all users deposited the majority of funds into the system. The absolute TUE of the system responded more dramatically to the IFC intervention because the greatest change in behavior came from users with a disproportionately large eﬀect on the measure. Notably, absolute dollar values are what matter when it comes to revenue as generated by transaction fees. The IFC intervention was successful at raising overall maturity, and the system’s ﬁnancial sustainability, in large part because it targeted high-value transactions.

More generally, heterogeneity means that our absolute TUE measure will be especially responsive to changes in the circulation patterns of large-value deposits. If we more are interested in typical usage patterns across the system, we would do better to consider the value of TUE when normalized by the size of deposit transactions. Doing so, we identify an underlying decline in system-wide maturity over time. This we discuss in the next section.

77 Percent of Percent of Share subsequently all users total deposited re−transacted

>5k

2k−5k

1k−2k

500−1k

200−500 USD at PPP

100−200

50−100 August

<50 October

0% 4% 10% 16% 20% 24%0% 4% 10% 16% 0% 20% 40% 60%

Decline in system-wide maturity

The underlying trend in deposit-normalized TUE and DUE is one of gradual decline. This is a puzzle, because the observation period coincides with a series of positive developments for the mobile money service. The system was undergoing robust user growth, saw increasing activity levels, and substantially expanded access during these eight months. To understand why maturity would decline with otherwise positive system developments, we note that changes over time can happen both when existing users change their behavior and when cohorts of adopters vary in their composition. As such, we quantify the contribution to TUE and DUE by three cohorts of

78 accounts as defined by their period of adoption. We distinguish “early”, “regular”, and “recent” adopters using our transaction data and an earlier set of transaction data from the same provider. Early adopters are those whose accounts also appear within the earlier transaction data set, which covered a period of six months ending just over a year prior. These adopters began using this mobile money service sometime before May, 2015. Regular adopters are those who did not transact within the earlier period, but who made transactions within the first three months of this data collection period. These adopters began using this mobile money service sometime between May, 2015 and September, 2016. Finally, we consider those accounts with no transactions in the first three months of the data collection period to be recent adopters. Each cohorts contains between 1.75 and 2.5 million accounts. We find that the decline in TUE is attributable primarily to changes in the composition of the user base, as recent adopters contribute systematically less to digital re-transaction. Figure 4.3 shows that each cohort digitally re-transacts a remarkably stable fraction of incoming funds (under deposit-normalization) from November, 2016 through February, 2017. What is changing is their relative contribution to the total circulation. In November, the early cohort is responsible for around half of the deposit-normalized circulation through the system, and the recent adopters contribute less than 10%. By February, the early cohort is down to 40% while the regular and recent adopters each contribute about 30%. As the contribution of recent adopters to the total TUE rises, the average value is declining. The decline in deposit-normalized DUE is not attributable to changes in the composition of the user base. Earlier adopters are, if anything, less likely to be building up a balance during this time. A substantial fraction of recent adopters appear to use the mobile money system to build up savings, initially. This behavior is not sustained, however, and recent adopters become more similar to existing users over time. Later, we show that declining DUE comes from greater volatility in longer-term balances.

79 Contribution to TUE by cohort Contribution to DUE by cohort 0.4 0.08

0.3 0.06

0.2 0.04 Fraction saved* Fraction Fraction re−transacted* Fraction Oct Nov Dec Jan Feb Mar Oct Nov Dec Jan Feb Mar *within cutoff time of 21 days *beyond cutoff time of 21 days

0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.1 0.1 Oct Nov Dec Jan Feb Mar Oct Nov Dec Jan Feb Mar Share of measure Share of measure

Cohort Early Regular Recent Cohort Early Regular Recent

Figure 4.3: Re-transaction and savings across cohorts The fraction of (deposit- normalized) incoming funds that are digitally re-transacted by users (within 21 days) or kept in their accounts for longer than 21 days, aggregated by adoption cohort. Colors correspond to these cohorts. The contribution of recent adopters to the total (deposit-normalized) circulation is rising over the same period, which brings down the TUE and has little eﬀect on the DUE.

Network externalities from the circulation of money

That new users, on their own, would bring a system’s maturity down is perhaps not so surprising. Liebowitz & Margolis (1994) note two reasons why network service providers could expect an increasing marginal cost per additional user. The first is physical, in the sense that it costs more to extend a network infrastructure into less populated areas. But the second reflects the dynamics of adoption, itself, in the sense that the avid users who join earlier will likely require less support than those who join later [108]. That prominent users are likely to adopt earlier has been shown also in the case of banks adopting automatic clearing house (ACH) digital payment systems [73,95]. What we are seeing is such a self-selection effect. But that a negative self-selection effect dominates the system-wide trend in

80 TUE is both surprising and concerning. Many of the companies building out mobile money networks are the very same companies that overcame the infrastructural challenges of setting up mobile phone networks [5]. Like cellular services, mobile money services are commonly considered to benefit from “network externalities” as their systems grow [15]. One would expect positive externalities from wider adoption, especially peer-to-peer effects, to out-weigh negative self-selection effects and to be reflected in rising system maturity. The absence of positive externalities for mobile money services would be of particular concern to proponents looking to further financial inclusion. If mobile money providers are left with an increasing marginal cost per additional user, it becomes suddenly much less economical to have universal access as a goal. Generally, network externalities are a phenomenon described and studied in terms of a system’s growth by adoption [51, 94, 108]. Efficiencies of scale (for the provider) combine with rising usefulness of the service (for the consumer) to create a point at which networks “take off” leading to strongly increasing returns for the provider. Peer-to-peer effects are key to generating this positive feedback loop. In the case of cellular services, users find more reason to make calls and send texts using a provider’s network when more of those they wish to communicate with are on it. In the case of mobile money, we would expect users to find more reasons to transact digitally as more of their counterparties begin accepting e-money. And also to rely more heavily on their mobile-phone-based wallet as a greater share of their transactions take place digitally. Other, less direct, feedback is also possible. More mobile money users can support a better agent infrastructure such that all users see a higher level of service. Happening system-wide, direct peer-to-peer effects would directly contribute to rising maturity. That the TUE of a growing mobile money system, already with millions of users, shows a consistently downward trend runs counter to this expectation. The conspicuous absence of evidence for positive peer-to-peer effects

81 would have us question whether assumptions about peer-to-peer effects carry over from mobile telephony to mobile money services. And so it is worth considering in what ways money is consequentially different from communication. Indeed, elements of network structure and user behavior—beyond adoption—are known play a role in determining the contours of network externalities [3]. Our results can be explained by noting that raising within-network circulation of money is categorically more difficult than raising within-network communication. This is because communication is often mutual while the circulation of money goes primarily one-way. In the case of mobile telephony, the likelihood that a given call will be made within-network rises monotonically with each additional user. On the other hand, the prevailing usage pattern within a mobile money network is for transferred funds to be quickly cashed out [4,156,159]. The marginal user entering the network might have little knock-on effect, whatsoever. One new user depositing and sending funds via mobile money would inspire little additional circulation if the alters that receive that e-money withdraw it almost immediately. And even if some of their e-money does get re-transacted, then the next account to receive it is also most likely to withdraw the funds. Our new user’s e-money keeps getting “stuck”. For within-network circulation to rise, more users would need to choose to keep more of their money digital until they make their next transaction digitally. Unlike in the case of communication, this is substantively separate from increasing adoption. Consider an example: domestic remittances are the most common use-case for mobile money [88], and remittance recipients would presumably like to use that e-money for any number of household purchases. They are unlikely to keep that money digital unless the local businesses they wish to purchase from will accept e-money. Among small and medium sized enterprises (SMEs) in East Africa, perceived usefulness is a key feature of mobile money adoption decisions [93]. From the perspective of an informal merchant who operates entirely in cash, they would need to weigh the cost of cash-out fees on any e-money paid them against the benefits of accepting e-money.

82 These fees are not negligible and would impact their profit margins unless their suppliers already accept e-money. Their suppliers would face similar considerations. Mobile money providers thus face a substantial challenge in harnessing direct peer-to-peer effects for one-way payments. Mobile money users transact with e-money primarily when the marginal benefit of receiving a payment in e-money outweighs the cost of cashing that e-money out [88]. So except in cases where cash is an unattractive option, a user can be expected to accept payment in e-money first when they have confidence that this e-money will subsequently be accepted by counter-parties to payments they might want to make in the near future. We can expect direct peer- to-peer effects to take hold when areas of the system can support long chains of transactions stretching on towards the indefinite future. In short, the mobile money transaction network would need cycles (i.e. closed loops). There is some evidence that positive network externalities do emerge out of cyclic structure within payment systems. Iosifidis et. al. (2018) have found that closed loops are key to the robust performance in recent years of Sardex, a successful digital credit circuit started in Sardinia in 2009. This payment system supports especially many cycles and especially long chains of transactions as compared to random networks [86]. While this system is not directly comparable to mobile money, as it supports primarily business-to-business transactions and operates on a basis of credit, it is an illustrative case. The funds circulating within Sardex are not directly convertible into any other form money; the provider does not offer conversion into Euros. This means that the system could barely operate at all unless direct peer-to-peer effects were present, but it does and it is developing well. Mobile money providers can, and should, be deliberate about generating peer-to-peer effects within their systems by emphasizing cycles. The concept of the “e-money loop” and our TUE measure is especially useful, here. As the number of sequential mobile money transactions increases, there is a greater and greater chance that e-money will begin to circle back on itself. Unless it does, positive network externalities are unlikely to

83 take hold. Providers can aim to “close the e-money loop” by seeking to attract users who are well-placed to continue trajectories of money, and encouraging transactions that do.

Ephemerally in long-term balances

The decline in DUE over time is not a self-selection effect. Rather, users are changing their behavior over time. Figure 4.3 gives us some indication that newer users are those most likely to be building up a balance. As time goes on those users are likely to begin drawing down their balances, as well, and the trend is not sustained. To understand the decline in DUE over time, we must consider changes in longer-term trends surrounding users’ e-money balances. Recall that we are “following” funds though this system according to the last-in-first-out heuristic. Earlier amounts are left undisturbed, introducing a stylized representation of “savings” that echoes the subjective experience of building up a balance in ones account. With DUE, a big part of what we are measuring is how long until a user “dips into” money they have been saving since it entered their account. By introducing a time-cutoff, we can consider the dynamics of longer-term savings balances separately from shorter-term balances arising out of funds that are quickly withdrawn or spent. We consider together all the (deposit-normalized) funds that we saw entering a user-facing account on a given day, and has remained untouched for longer than three weeks. These funds were used to build up a balance that is still in existence, and we are interested in how durable are these longer-term “savings” balances. Figure 4.4 shows how quickly users collectively “dip into” these balances after they managed to keep them in existence for over three weeks. The decay of savings balances closely follows a hyperbolic curve (see Appendix I), and the rate of decline is becoming progressively steeper over the data collection period. Note that this is the case for all

84 cohorts.

Figure 4.4: Hyperbolic decay of deposit-normalized “savings” balances Share of deposit-normalized funds that remain untouched in user accounts (under last-in- first-out) for each day beyond 21 days. The solid curves reflect the system-wide draw-down funds that had been used to build up a savings balance, colored by the date those funds entered the account they are in. The red dashed and dotted curves show three representative hyperbolic fits to the empirical decay curves.

Declining DUE thus reﬂects that the balances users are building up have become more ephemeral—accounts who do manage to save beyond three weeks are drawing down those funds sooner and sooner thereafter. One explanation for this is the improved accessibility and visibility of mobile money. Perhaps the greatest challenge to accumulating a savings balance, especially for those with small margins, is keeping funds away from everyday needs. Many informal savings arrangements, such as rotating savings cooperatives, are designed to overcome these challenges and other strategies, such as borrowing in order to save, re-purpose available ﬁnancial

85 tools for this purpose [17]. Even something as simple as a locked box can facilitate savings by making it easier to leave that money alone [50]. As mobile money accounts become more easily accessible, more visible, and more consistently used they may be less able to fulfill this function. It is worth noting that the average lifetime of longer-term balances could readily diverge for systems where many more are building up balances than drawing them down. Strictly speaking, this would render DUE infinite. In such cases, providers might consider monitoring a less sensitive indicator of the distribution of durations within their systems (ex. the median or the fraction of funds that reach a cutoff value). This also points to a promising direction for future theoretical work in better understanding heterogeneity in the use of money as a store of value.

Discussion

We have identified two positive forces in the development of mobile money services—wider adoption and greater accessibility—that nonetheless reduce the maturity of the system as a whole. This runs counter to common assumptions about the role “network externalities” play in the development of mobile money systems; our intuitions need updating. Mobile payment networks are categorically different from mobile communication networks in that money usually goes only one-way. Direct peer-to-peer effects are unlikely to materialize on their own, because within- network circulation is considerably more difficult to support than within-network communication. Mobile money providers must look beyond adoption if they wish to harness network externalities with their systems. Providers can be deliberate about developing peer-to-peer effects by encouraging longer chains, even cycles, of transactions. Proponents of mobile money ought to emphasize “closing the e-money loop”. This intuition supports the emerging consensus among practitioners that a reluctance

86 towards adoption by informal merchants, and their suppliers, is a key hurdle currently facing many mobile money providers. Our computational methodology can hep monitoring progress towards more mature mobile money systems. We define two complementary measures of circulation directly from a providers’ own transaction records: Transactions Until Exit (TUE) and Duration Until Exit (DUE). Digital payment systems that better facilitate exchange will have higher TUE. Digital payment systems that better serve as a store of value will have higher DUE. Both measures will rise as systems achieve greater within-network circulation of e-money, and can be readily compared across countries with different currencies or companies of different sizes. More generally, this work highlights the impact of behavioral heterogeneity on public-facing digital payment systems. We have quantified differences in average behavior across groups of users as defined by size and by adoption cohort. Large variation over additional dimensions of behavior in this system—both across users and within individuals—have yet to be fully explored. As such, it is not clear if our results are aberrant or to be expected relative to other public-facing digital payment systems. Modeling and simulation of probabilistic transaction processes (see [176]) can give us a better grasp of the expected effect of highly skewed distributions of activity levels, transaction sizes, and inter-event times. In time, such work could improve our understanding of money in public hands.

87 Chapter 5

Toy Economies

88 Considering economic systems through the lens of financial transaction processes may be a way to accelerate advancements in the modeling of these systems. Focusing on transactions among individual entities in an economy gives us a concrete entry point into economic theory that has had less of an established connection to economic modeling, historically. There is a possibility for powerful new insights. This perspective also places a great many existing approaches to modeling economic systems on equal footing. We can meaningfully compare models that reflect different disciplinary paradigms by asking in what ways they seek to, and to what extent they succeed at, approximating real-world transaction processes. Finally, making this connection explicit opens a new avenue for improving all these models: empirical transaction data. This chapter looks to distill out the essential dynamics of a growing entrepreneurial economy into a toy model using simplifying assumptions pulled from diverse and well-established areas of economic thought. The theory surrounding payment systems, cash flow, and durable economic ties have rather neat analogues within network science, and this lets us define a radically simple model. Each incoming economic agent strives for a network position that promises high cash flow; that’s it. Intriguingly, this is enough to produce complex endogenous dynamics. The patterns in how this highly stylized system grows are reminiscent of the path-dependence, emergent inequality, and creative destruction known to appear within entrepreneurial economies. These dynamics are highly interesting, on their own, and there is much we might learn about economic systems by exploring any number of variations of the specific toy model presented here. Our model is perhaps best seen as a hypothesis- generating tool around the dynamics driving larger-scale economic trends. Moreover, our model is itself but one of stupendously many agent-based models (ABMs) that can be used to study economic systems in this way. Most compelling about our approach, looking forward, might be the extent to which its underlying logic establishes common

89 ground between several existing approaches that might otherwise be difficult to relate to one another. ABMs are seen as an increasingly promising tool and several research communities have developed their own specific approaches: matching models, exchange models, and network models among them. [35, 82,175] Each approach has uncovered key insights about economic systems, and some have achieved considerable realism. Matching models, exchange models, and network models build off of entirely separate sets of assumptions about who participates in an economy and how they interact, revealing major blind spots among one anther. And yet, they all seek to represent financial transaction processes in one way or another. Our toy model shows that relating economic theory to financial transaction processes might produce powerful intuitions about complex economic dynamics— we should check! Each of the simplifying assumptions we employ is amenable to direct empirical study using suitable records of real-world financial transactions. Crucially, so can the assumptions behind any individual-level mechanistic economic model. With the logic and data of financial transaction processes we might begin to join together the insights and efforts of several established research communities in modern economic modeling. All together, data-driven agent-based modeling of financial transaction processes could one day provide a full-fledged alternative for aggregating up from the micro-economy to the macro-economy.

Models of Financial Transaction Processes

Mechanistic economic models—wherein we seek to represent the actual actions taking place within an economy—can be more or less complicated and focus on different aspects of economic systems. But in any case, their aim is to reproduce with some fidelity something about real-world financial transaction processes. Any particular model will be predicated on a set of simplifying assumptions about these

90 processes, which may or may not be empirically true. The crucial point is that we can consider all such models, their assumptions and their results, through the lens of the universe of transactions occurring within actual economies. This lets us consider and compare the major assumptions made by a set of existing approaches to agent-based modeling of economic systems, and their limitations.

Matching Models of Financial Transaction Processes

Agent-based simulations at an economy-wide scale are an emerging state-of- the-art for macroeconomic modeling [35, 43, 135]. Such simulations model whole economic systems as transactions among millions of individuals, thousands of firms, and hundreds of banks [46,106]. Transaction processes are based on particular markets with an explicit matching process [113,138]. These models ensure that the outflows of one sector are always the inflows of another, maintaining “stock-flow consistency” across the simulated macro-economy [26]. Many matching models are implemented as actual financial transactions between accounts within a fixed financial system, which is exceptionally reasonable. Many agent-based simulations use double-entry bookkeeping to keep track of agents’ actions within the model [46]. More complicated models define more realistic payment systems, although it is unclear whether this introduces the possibility of payment disruption into the model [14,35,135]. But matching models also embed agents within a fixed economic system. Underlying the transaction process of almost any macroeconomic model is a basic distinction between firms, households, and banks [46,113]. This is certainly a valid approximation to make within the context of a nation-state with a well-established legal infrastructure that enforces these distinctions. But if we venture beyond this context, it becomes clear that this distinction may be less inherent to economic systems than modern macroeconomic models would have us believe. Within development economics, there is a rich literature on informality and

91 the persistent lack of a distinction between firms and households in practice (see [17,44]). There is also less of a distinction between regular businesses and financial entities in economies where bank credit is generally not available. Within many informal economies, businesses rely on their strong producer-supplier ties and other relationships for essential credit [56, 110]. Individuals rely on their social connections [58,90,179]. But even in developed countries, the legal distinctions between households, companies, and financial entities are not always made nor necessarily enforced. There are entire industries, notably the US market for rough and polished diamonds, that eschew established legal systems in favor of dispute resolution grounded in personal reputation and community sanction [25]. Companies readily pursue both industrial and financial sources of revenue, notably General Motors and its long-time auto- lending subsidiary General Motors Acceptance Corporation (later Ally Financial). Digital management innovations fueling the “gig economy” have made it a challenge for governments to enforce the difference between an employee and a contractor [45,63]. Within agent-based macroeconomic models, these distinctions must be made even for a minimal model because the transaction process is based on markets with an explicit matching process [113,138]. However, we know from toy synthetic economies with completely unrelated (if equally prescriptive) matching processes that many phenomena can perhaps be understood without such strong assumptions [55].

Exchange Models of Financial Transaction Processes

Physicists have developed models of transaction processes based on a population of identical agents and simple stochastic exchange among them. These exchange models abstract away from distinctions between households, firms, and any other agents who participate in an economy just by defining the transaction process they study without reference to these categories. When the modeled system is a closed payment system, the distribution of holdings must be stationary under the defined

92 process because money is conserved [38,48]. Researchers have also sought to relate exchange models of transaction processes to the monetary system. Yougui Wang & Ning Ding have a series of papers that incorporate the exchange equations from monetary economics. Under a closed system, the average “holding time” of money in an exchange model is closely related to the macroeconomic notion of the velocity of money [174–176]. It is also possible to model open payment systems, where the transactions to be executed are random and exogenous [67]. It is notable that very simple models of transaction processes—a stochastic system with identical economic agents—can produce a drift towards inequality. When extended to include a stochastic process of wealth creation, it is easy to reproduce heavy-tailed distributions of wealth within exchange models [31]. It is less clear how more complicated versions of these exchange transaction processes would relate to real-world economic processes like entrepreneurial growth.

Network Models of Financial Transaction Processes

A somewhat different approach is to begin detailed network data on economic relationships, such as real-world or inferred networks of customer-supplier ties between firms. On top of such network data, relatively simple agent-based models of transaction processes can be tremendously powerful. To model the propagation of supply chain shocks, for instance, these models conceptualize individual firms as agents who adjust transactions with their customers and suppliers in logical ways in response to disruptions passed over the empirical production network [82, 83]. Given their fidelity to detailed data, a wide range of reasonable behavioral assumptions are likely to produce valid approximations of overall system dynamics. These can produce (experimental) economic forecasts. Less directly, a fruitful vein of network models represent financial transaction

93 processes as random or biased walks on static or slowly evolving production networks [112,144,162]. Intriguingly, it appears to be possible to model the movement of money through such networks well enough to recover much of the variation in company sales [99]. One might also consider a larger class of network models of economic systems where influence is generalized, but also clearly driven by some underlying transaction process. For instance, the propagation of bankruptcies along customer- supplier ties [72] or even productivity improvements along aggregated input-output relationships between sectors [120]. Partly because of their theoretical association with input-output networks, and other aggregated trade networks, production networks of have been heralded as a way to bridge microeconomics, with its focus on the behavior of individual firms, and macroeconomics, with its focus on broader economic outcomes [37]. However, it is worth noting that aggregated input-output networks may or may not reflect the relevant empirical structures (see [96]) in the context of any particular financial transaction process. In stark contrast to matching and exchange models, however, network models of financial transaction processes have generally eschewed questions that involve non-corporate economic entities that do not appear in production network data. These models necessarily reflect only a piece of a larger economic system where money circulates all they way back around. Like matching models, they have stuck very close to the formalized economic systems visible in economic network data from developed nations.

Minimal Model of an Entrepreneurial Economy

This work seeks to define a model of a growing economy that draws more directly from our understanding of financial transaction processes, both theoretically and mathematically (see Chapter 1). Specifically, we aim for a minimally complicated model that would let us explore the most basic dynamics of the simplest economic

94 systems. Prioritizing parsimony means making sizeable assumptions about financial transaction processes that nevertheless preserve key aspects of economic dynamics; this can be justified on both theoretical and empirical grounds. To move towards this, we make four key assumptions. Each of them draws from a well-developed stream of economic thought, in its own right. Together they reduce the bewilderingly complicated reality of our financial and economic systems down to a maximally simplistic model—a toy entrepreneurial economy represented as a growing money-flow network. Precisely because it is so simple, this toy model can give us broad intuitions of what to expect when we observe real economic systems.

Universal Payment System Approximation

We begin by assuming that our economy operates entirely within a single, universal payment system. This is a simplification, as the infrastructure that we rely on to clear transactions is a complicated system of interacting payment systems [68, 71, 92, 150]. We know that monetary aggregates actually emerge out of multiple payment systems [155], and that there are cross-country differences in the quality of retail payment system integration [124]. Even so, it is a very well-justified simplification. The “money view” advanced by Perry Mehrling offers a theoretical perspective within which we can consider our actual monetary infrastructure as set up to approximate the ideal of a single, universal payment system [122]. Indeed, approximating a “general purpose payment system” is the actual policy objective of payment system regulators in many countries [158]. Crucially, we have a solid understanding of what this assumption would make us blind to. One is that improvements to payment system integration can improve economic outcomes by lowering transaction costs, as has been the case with mobile money in East Africa [88]. Another is that payment systems can fail, or get close to failure, during periods of widespread disruption such as the events of September 11,

95 2001. [23,154]. Modeling work by Galbiati & Soramäki(2012) shows that payment systems also become more fragile and less able to process transactions as participants allocate them less liquidity [67]. This we would need to consider separately. An especially interesting limitation is that the universal payment system assumption would never allow for a run to occur. Runs are especially damaging financial panics that can happen when a particular payment system comes to be perceived as less trustworthy than other payment systems; as many try to withdraw their money at once this perception becomes self-fulfilling. The Great Depression saw widespread runs on banks and such panics spread through correspondent networks, the very system that allowed for nationally integrated payment processing [64,139]. Notably, bank distress was more likely in periods of illiquidity. Money market mutual funds (MMMF) during the 2008 financial crisis offer a more recent of payment systems experiencing runs [146]. The perception that shares in these funds were equivalent to other forms of dollar-denominated money proved illusory when the MMMF providers were unable to maintain their (implicit) guarantee of convertibility into dollar-denominated bank deposits after the collapse of Lehman Brothers. Confidence in MMMF shares as money ended abruptly. Holders began selling off shares, which exacerbated pressure on MMMFs to stay solvent; many did not. After these events during the 2008 financial crisis, the regulations governing MMMFs were updated substantially [111]. While it is intriguing that the two largest financial downturns in American history both involved contagious runs on key payment systems, each such panic is likely to be unique in many ways and it may make sense to study them separately. The noted limitations are an excellent reason to make explicit the Universal Payment System Approximation in our economic models. By recognizing its limitations, we can be confident in using models based on this approximation for studying a wide range interesting questions. We can work to develop our understanding of payment system integration, (financial) transaction costs, illiquidity, and runs in

96 other ways.

Further Assumptions

First, we simplify the transaction process by assuming that it occurs primarily over already-established economic ties. Economic sociologists have long argued that there exists a “network” form of economic organization that falls between the market and the firm [173,177]. This intellectual tradition emphasizes the strong (yet flexible) relationships that firms maintain with a small number of other firms. While one-off transactions across market relationships are prevalent, survey studies have found that a disproportionate share of business goes to established ties [168]. To the extent that transactions over customer-supplier ties happen substantially faster than those relationships themselves change, we can employ the static approximation for temporal networks [133]. This means we can work with walk processes over networks of customer-supplier ties instead of fully resolved transaction networks. By allowing some probability of random jumps we designate a fraction of transactions to be one-offs with random other firms in the system, which adds some noise. Second, we note that the steady-state of a walk process on the network of customer-supplier ties is a notion of economic equilibrium. Leontief & Brody (1993) build out a mathematical relationship between the the steady-state of an input- output matrix describing the flow of money between sectors of the economy and the Fisher equation for the velocity of money. They argue that this steady-state offers an alternative notion of economic equilibrium requiring fewer assumptions. [107] While their derivation is based on aggregated input-output statistics, the theoretical connection extends to the steady-state of a walk process on a disaggregated network of customer-supplier ties; the equilibrizing assumption is that a company receiving more in revenue will pass this along to its suppliers and vice versa. Indeed, there is some empirical evidence that money-flow models can recover the sales of companies

97 from real-world customer-supplier networks, given key parameters from the real-world economy [99]. Under this approximation, we can use random-walk based network measures to rank and group economic entities by their position within the network structure. Finally, we define the motivation of the agents entering our system according to the Minskian economic tradition. We note that basic accounting rules apply to all accounts within a payment system, which highlights a deep similarity among agents within that system. Specifically, all economic entities must always bring in more money than they spend in order to continue participating in the economy. This is an exceptionally clear incentive, and the heterodox economic tradition has a term for it: Minsky’s “survival constraint”. [121] Within a money-flow network, this would seem to suggest that economic agents would aspire to an advantageous network position that sees a lot of turnover. Mathematically, this would correspond to high centrality on a money-flow network under a walk process. So, in our minimally complex model of an entrepreneurial economy: The economy is a money-flow network where each node an economic entity, and the links between them are customer-supplier ties. The network is growing as nodes go into business, which they do by selecting customers and suppliers. Crucially, economic entities look to join the network at an advantageous position where they would see high turnover at economic equilibrium.

Model Implementation

In our implementation of this toy model, we also aim for the greatest possible simplicity. Our network is directed, but unweighted. We initialize the model with a uni-directional ring of six nodes. At each time step a new node enters the network, choosing to place a single in-link and a single out-link to existing nodes. In making this choice of where to join the network, the node ﬁrst generates a random sample of

98 i−1 m possible network locations. Node i selects 0.8 · m · m/2 pairs of existing nodes with replacement. We then quantify the expected turnover at equilibrium for this node at each sampled network location by calculating the PageRank score [131] (we include a 5% random jump probability). The node then chooses a network position in proportion to its PageRank score at that position, weighted by a power of k. When k = 0, the node is choosing randomly. When k = 9, the node is almost always choosing the sampled position with the highest PageRank value (or choosing randomly between multiple positions with that same value). Once a node has joined the network, they take no further actions. Please see Appendix IV for additional parameter speciﬁcations.

Results

The result is a network that grows in many directions at once and folds back in on itself in a manner that is highly path-dependent and fundamentally endogenous. Although each node follows the same script, the structure of the network that a node sees as they are entering it is changing with every step. One could contend that different nodes end up using different “strategies” in response to the different opportunities presented them. Some get especially “lucky” in finding advantageous network position at which to enter the toy economy.

Endogenous growth

Within this network model, opportunities come and go. Figure 5.1 shows the network structure created by very savvy entrepreneurs who nearly always choose to join at the best of their sampled network locations (k = 9). The dynamics of this model is such that new nodes will tend to reinforce a growing network sub-structure until it suddenly becomes more advantageous to break oﬀ from it. There is then a moment of ﬂux until a new self-reinforcing sub-structure emerges. Prior network

99 sub-structures are left behind, which is picked up on by the Infomap algorithm [142]. In this particular simulation, the initial nodes are purple (bottom right) while the newest are blue and orange (top left). The time-ordering and stochasticity in the simulation (i.e. “luck”) combine to produce a system with unequal turnover, as measured by PageRank.

) 100 k n a R e g a P ( P

0.2 0.4 0.6 0.8 PageRank (normalized)

Figure 5.1: Best-choice entrepreneurial network of 50 nodes The structure and normalized PageRank distribution of an entrepreneurial network with 50 nodes, where entry was strongly selective of the best network location (k = 9). The initial nodes are purple (bottom right) while the newest are blue and orange (top left). Nodes are colored by InfoMap [142] communities and sized by PageRank [131] (with 5% random jumps).

With entirely random selection of network location, on the other hand, early nodes are at an advantage and random diﬀerences compound. Figure 5.2 shows the network structure created nodes who choose randomly from their sampled network locations (k = 0). The dynamics of this model is such that older nodes tend to accumulate more links, and thus a more central location with respect to money-ﬂow, simply by virtue of having more chances to snag incoming links. In this particular

100 simulation, the two most prominent purple nodes were both members of the initial six-node ring. There is little in the way of network sub-structure. Time-ordering and stochasticity again produce inequality in turnover across nodes, but with an opposite trend with respect to early entrants. ) k

n 100 a R e g a P ( P

0.2 0.4 0.6 0.8 PageRank (normalized)

Figure 5.2: Random-choice entrepreneurial network of 50 nodes The structure and normalized PageRank distribution of an entrepreneurial network with 50 nodes, where entry was selected at random (k = 0). The two most prominent purple nodes were both members of the initial six-node ring. Nodes are colored by InfoMap [142] communities and sized by PageRank [131] (with 5% random jumps).

Finally, we consider imperfect strategic selection of network location. Figure 5.3 shows the network structure created by nodes who choose from their sampled network locations according to the PageRank they would see to a power of k = 5. Also with this more moderate selection-intensity the incoming nodes create emergent network sub- structures, but these are less distinct. The time-ordering and stochasticity intermingle to produce inequality in turnover across nodes, with neither trend dominating.

101 ) 0

k 10 n a R e g a P ( P

0.2 0.4 0.6 0.8 PageRank (normalized)

Figure 5.3: Good-choice entrepreneurial network of 50 nodes The structure and normalized PageRank distribution of an entrepreneurial network with 50 nodes, where entry was imperfectly selected based on advantageous network location (k = 4). The actions of the nodes create emergent, but not distinct, network sub-structures. Nodes are colored by InfoMap [142] communities and sized by PageRank [131] (with 5% random jumps).

Path-dependence and emergent sub-network structure

We can quantify the extent of emergent network sub-structure within the networks our model generates using the compression metric used in the hierarchical Infomap algorithm [29]. This information-theoretic measure, the “description length”, gives the average number of bits needed to describe one step in an inﬁnite random walk on the network. The Infomap algorithm itself exploits a network’s sub-structure to minimize this value; we compare the value of the measure under compression to that of the uncompressed network. A network with increasingly rich sub-structure would allow for greater compression. Across a range of selection-intensities, our toy model produces networks with

102 emergent sub-network structure. Figure 5.4 shows the extent of network compression possible at different selection-intensities, over one hundred independent simulations at each power of k and their average. Notice that the variation between individual simulations is substantially larger than the average difference across selection-intensities, which is perhaps the most interesting. Our toy model creates networks with considerable dependence on early stochastic developments within the simulation itself; it is strongly path-dependent. Strong path-dependence is a persistent feature of complex systems [165], socio-technical systems [170], and economic systems [11]. More specifically, Nathan Nunn (2009) makes the argument that path-dependence is a key reason why past events can have important long-term effects on economic development [129]. Particularly disruptive historical occurrences, including the African slave trade [127,128] and the division of Germany following World War II [137], had demonstrable long-term effects due to path-dependence in the economy. Our toy model suggests that the very structure of economic connections can itself carry memory. To the extent that our assumptions hold, history matters for economic development even entirely endogenously. Although the evolution of each network is path-dependent, different parameters underlying the network growth process produces different system behavior on average. Specifically, a higher selection-intensity corresponds to more sub-network structure. For small networks, a wide range of selection-intensities produce networks with a structure intermediate to that of the best-choice and random-choice dynamics. As networks grow, selection-intensities above k = 3 and below k = 7 consistently produce an intermediate structure. With a selection intensity at and below k = 3, strategic actions do not overcome the stochasticity in the simulations and the sub-network structure does not stay more complex than that of random-choice. With a selection intensity at and above k = 7, best-choice dynamics dominate creating clear sub- network structure that is nonetheless highly susceptible to stochastic errors; we see erratic rates of compression once these begin to occur.

103 PR^9 1.05 PR^8 1.00 PR^7 PR^6 0.95 PR^5 PR^4 0.90 PR^3 0.85 PR^2 PR^1

Compression 0.80 PR^0

0.75

0.70

0.65 20 40 60 80 100 Number of nodes

Figure 5.4: Sub-network structure of simulated economies The extent of network compression possible at diﬀerent selection-intensities. Shown in grey are one hundred independent simulations at each power of k, and shown in purple is the average over them. Darker lines correspond to higher selection-intensity. The compression is calculated using the “description length” of the network from the hierarchical InfoMap algorithm [142], and is reported as a fraction of the uncompressed “description length”.

Node dynamics and inequality

Finally, we consider the modeled dynamics of individual nodes within these toy economies. Our entrepreneurial growth model produces substantial inequality across nodes for each of the selection intensities we study. Some nodes are substantially “luckier” in that they enter at a more advantageous position, both initially and as the network continues to grow. As selection-intensity increases, there are clear diﬀerences in who beneﬁts from the forces driving inequality between nodes. Figure 5.5 shows the dynamics of each

104 node’s PageRank within a network growing under weak and strong selection-intensity, respectively. With fewer nodes making strongly strategic choices as they enter the network, the early nodes win out. Early nodes with prominent locations in the network maintain their prominence as incoming nodes choose to join the system primarily in locations that reinforce their prominence. Entering with just two links and a weakly strategic outlook, later nodes are unlikely to enter and stay at highly favorable positions. In contrast, when most nodes are making strongly strategic choices as they enter the network, the early nodes lose out. As everyone behind them enters at the most favorable position possible, or close to it, the economy as a whole moves away from them and they are unable to react. It is worth considering to what extent this mirrors tensions within real economies and echoes the classic Schumpeterian perspective on creative destruction.

Pagerank dynamics, power=2 Pagerank dynamics, power=8

0.25 0.25

0.20 0.20

0.15 0.15

PageRank 0.10 0.10

0.05 0.05

0.00 0.00 10 20 30 40 50 10 20 30 40 50 Number of nodes Number of nodes

Figure 5.5: Node dynamics of simulated economies The PageRank for each node in our entrepreneurial growth model, as the networks grow. Each plot is a superposition of ten independent simulations. Darker lines correspond to nodes who entered early on in the simulation. The two panels show the node dynamics for networks resulting from weak and strong selection-intensity, respectively.

105 Discussion

We have put forward a toy model of a growing, entrepreneurial, economy based on the perspective of financial transaction processes as temporal networks. Our simplifying assumptions come from well-established veins of economic thought. The result is a toy economy that is remarkably minimal, even as it retains rich dynamics. This establishes what could be a powerful intuition about what to expect from any growing, entrepreneurial, economy where our assumptions are reasonable: path-dependence, endogenous dynamics, and emergent inequality. This work shows that these known but under-explored properties of economic systems might be entirely expected and simple to model. In minimizing the complexity of our model, we make bold approximations that are justified by theory but not empirically true. Entrepreneurs face many practical limitations when they seek to enter the economy, much economic activity happens on intermediate timescales, and our fragmented payment system does not live up the universal ideal. Just like everybody else, we also make assumptions that are justified only by convenience and definitely not empirically true. We know that existing entities adjust their customer-supplier ties to seek ongoing economic advantage, that established customer-supplier links can have wildly different sizes in terms of their total transaction value, and that the turnover rate of money is bursty within accounts and heterogeneous across accounts. Thankfully, the movement of money often has the benefit of being directly observable; we are leaving a treasure trove of data about the real economy on the servers of financial institutions worldwide [6, 60, 86, 115, 154]. Even in the absence of whole-network data, there is no reason we cannot collect survey data on the ego-network structure and transaction patterns of actual households, firms, and banks. For instance, one could generalize the financial diaries methodology developed to study the spending habits of the financial vulnerable [40,125,157]. Every assumption

106 on which our toy model relies can be empirically tested, refined, and improved upon by taking a data-driven approach. Thankfully, also, the modeling of network dynamics is rapidly improving. More sophisticated walk processes can already incorporate weighted edges [114] and non-markovian dynamics [104]. Re-examining exchange models as walks on a temporal network should allow network scientists to incorporate distributions in holding times [133, 175]. Intriguingly, walk processes can be made self-aware such that money-flow could avoid or reinforce itself [153]. Finally, the choices made by rational actors in joining or rewiring a network can be explicitly represented using discrete choice and random utility theory [130]. Every implementation decision in this minimal model can be made increasingly sophisticated to reflect actual economic systems in greater and greater detail. Notably, within the toy model we present the economic agents are all identical, they act in a “rational” way with respect to long-term economic equilibrium, and there is no separate mechanism for credit or investment. These same simplifications are roundly criticized for their artificially stabilizing effect on standard, macroeconomic, general equilibrium models [36]. And yet, under our alternative theoretical framework they leave us with substantively interesting dynamics. On its own, these dynamics are an intriguing direction for model-based study. More generally, our work show that agent-based economic modeling has access to both deep theoretical grounding and direct empirical grounding through the lens of financial transaction processes. Well-developed economic ideas around payment systems, cash flow, and durable economic ties are ready to provide tangible interpretation. Methodologies from earlier chapters and financial diaries surveys are ready to test both our long-held and our freshly-formulated assumptions. Given time and effort, data-driven agent-based modeling of financial transaction processes could one day provide a full-fledged alternative for aggregating up from the micro-economy to the macro-economy.

107 Chapter 6

Conclusion

108 I hope that I have convinced you that we have everything we need to begin working towards locally predictive economic modeling in a deliberate fashion. The ingredients are all here: network science offers flexible mathematical representations, financial transaction records from public-facing payment systems are increasingly available to researchers, and Economics is reviving useful alternative theoretical paradigms. Simulation-style modeling of transaction processes stands poised to bring these elements together. Our challenge lies in aligning the efforts of widely disparate fields. This dissertation’s key insight is that financial transaction processes are something we can describe mathematically, study empirically, and seek to understand via modeling. I have sought to present a coherent picture of where we are by pulling together veins of research from development economics, monetary economics, input- output economics, economic sociology, and economic history alongside data science, network science, and computational social science. Building on this broad foundation, I have begun developing the network science, computational tools, and economic theory that we need to move forward. Using my approach, we can study networked patterns in the flow of money through an economy. Within a mobile money payment system, we could isolate particular economic actions by users with sequential transaction motifs. These different activities create large-scale networks of monetary flow with prominent hubs, random structure, geographic assortativity, and even suspicious-looking cliques. These network structures are not likely to be limited to mobile money. Our economy as a whole includes large corporations, peer-to-peer transfers, localized business, and opportunities for strategic coordination. If and when we get a chance to study transaction data from other payment systems, we can improve and extend our knowledge of money-flow networks to include the particular slice of economic activity that those systems support. Such a line of research would eventually give us an idea of how money actually moves through economies as a whole.

109 Using my approach, we can quantify the circulation of money through individual public-facing payment systems. How we pay one another is clearly a networked process, yet the directionality of transactions means that our intuitions about processes on social networks might not necessarily apply. Transaction networks are perhaps less about clustering and more about cycles. This helps illuminate the especially thorny challenges that payment system providers face in supporting our day-to-day economic lives. Given that these providers together create the very infrastructure our economy relies on to keep the books, this raises further questions about precisely how our monetary system operates. A line of research exploring this question more literally is an exciting opportunity for monetary economics. Using my approach, we can diversify the theoretical grounding of agent-based modeling through the lens of financial transaction processes. Even a remarkably simple model of a growing system where economic agents strive for a network position that promises high cash flow retains rich dynamics. Path-dependence, endogenous dynamics, and emergent inequality as properties of economic systems might have powerfully intuitive explanations in the dynamics of growing money-flow networks. Being explicit about how we model financial transaction processes allows interpretation using economic ideas around payment systems, cash flow, and durable economic relationships. This perspective also places a great many existing approaches to agent-based modeling of economic systems on equal footing, and opens a new avenue for improving all such models: empirical transaction data. These are three broad research directions with spectacular promise and clear synergy. The network science, computational tools, and economic theory that we need to move forward are all connected by the logic of financial transaction processes. Through this lens, insights from a diverse array of research directions become interpretable across disciplines. If we are deliberate about it, we can accelerate advancements in any of these directions by incorporating the progress made in any of the others.

110 References

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127 Appendix

128 Appendix I

Mobile Money – a primer

Mobile money is a fascinating innovation, pioneered in developing countries, that leverages the mobile communication infrastructure to facilitate digital financial transactions and provide simple digital financial services. Mobile money is a new global industry that has seen rapid expansion across Africa, South Asia, and Southeast Asia. However, mobile money providers have struggled to develop sustainable payment systems. Of specific concern is that mobile money customers often choose to withdraw their e-money into cash straight away rather than to keep it in their accounts or send it onward [156]. This widespread tendency is costly for providers - servicing transfers between users happens over scalable digital infrastructure, whereas servicing cash-in and cash-out transactions requires compensating on-the-ground agents and physically re-balancing stocks of cash among them. Analysis tools that can make sense of mobile money transaction data and models that can explore the growth of payment systems are of direct interest to mobile money providers and the development agencies that support the industry. The priorities of development practitioners, such as mobile savings, credit, and insurance, have struggled to gain traction even as mobile money adoption has risen rapidly [76]. At the individual level it is clear that mobile money has been primarily adopted as a means to do more easily and cheaply things that customers were already doing, especially sending remittances. As customers have gained familiarity with mobile money ecosystems, and providers have extended product offerings, behaviors have begun to change. In 2015, eight years after mobile money launched in Kenya it is the world’s most mature market for mobile money. Even so, only 36% of users reported keeping money in their account for extended periods, and only 35% had ever made transactions beyond person-to-person transfers and airtime top-up. Elsewhere

129 the numbers are even smaller. Reconciling the on-the-ground decisions of everyday people with macro-scale development objectives is a rich area of study in development economics. The world’s poor are the agents of their own lives who often respond in unexpected ways to the plethora of initiatives, policies, and programs aimed at improving their livelihoods [17]. Randomized controlled trials is one important approach to quantifying the impact of interventions in the context of development economics [18]. Studies that take this approach to understand the impact of mobile money leverage cases where adoption was externally imposed. Aker at. al. (2016) find that the distribution of cash to drought-affected households in Niger was more effective when done using mobile money, raising nutrition compared to control groups. However, 98% of recipients immediately withdrew their disbursement into cash, raising the question of whether results were driven by efficiency gains (lower travel time to collect the disbursements) that could have been accomplished through other means and are highly dependent on the agent infrastructure versus through beneficial features of mobile money itself (such as providing greater control of the disbursement to the female recipients) [4]. Targeting a different demographic, Blumenstock et.al (2015) convinced a set of firms in Afghanistan to adopt mobile money as their method of paying wages to their workers, maintaining a random control group. They find that savings for the company were considerable, but find no measurable difference in the welfare of employees over 6-8 months despite an uptick in mobile money usage [27]. Overall, these studies are inconclusive about the benefits of mobile money per-se when it is not freely adopted. That mobile money has been readily adopted in many developing countries raises the possibility that is it not well suited to being studied as a development intervention. Understanding the broader scope of mobile money usage and it’s implications is perhaps more of an observational question. Observational studies of mobile money are plentiful with academic articles, independent reports, and

130 industry reports covering many aspects of mobile money at both microeconomic and macroeconomic scales. Person to person transfers are the most common use of mobile money. In December 2015 71.7% of the $8.9 billion transacted over mobile money systems were person-to-person (P2P) transfers [78]. While person to person transactions can encompass several economic activities, surveys have consistently shown that remittances are the most prominent. The widespread use of mobile money for remittances has macro-scale implications for the simple reason that remittances feature prominently in the economies of developing countries, particularly among the poor. Fafchamps and Lund (2003) conducted household surveys in rural areas of the northern Philippines in 1994 and 1995, reporting that net gifts and informal loans accounted for 17% of household income, on average [58]. Adams Jr. 1998 conducted household surveys in rural areas of the four poorest districts in Pakistan over five years beginning in 1986, reporting that domestic and international remittances accounted for on average 5% and 8% of income, respectively [1]. In their 2010 study of M-Pesa use, Jack & Suri (2014) report that a majority of Kenyan households interviewed had sent or received remittances in the past six months, with gross volumes amounting to around 9% of monthly consumption. These are substantial values. International remittances, for which data is more readily available, have been estimated and studied at the macroeconomic scale. Between 1999 and 2001 global remittance inflows to developing countries were smaller than foreign direct investment, but exceed capital market flows and official development assistance, providing substantial development finance [136]. These inflows have also been related directly to poverty reduction, using a dataset complied for 71 developing countries [2]. International remittances were the fastest growing product offering for mobile money providers in 2015 [78].The effects of mobile money on domestic and international remittances may have substantial macroeconomic implications.

131 A small, but growing, fraction of mobile money users also use mobile money for business transactions [93,119]. Note that whether a P2P transaction is business related would not be readily apparent. A 2014 FinAccess survey of businesses in Nairobi, the most mature market for mobile money in the world, found that roughly a third of small and medium sized enterprises had adopted mobile money [24]. Beck et. al (2015) go on to use this data to quantify the effect of mobile money on trade credit relationships between businesses, finding that the 24% of businesses in the survey that maintain trade credit relationships with suppliers were more likely to adopt mobile money. The authors attribute this effect to the lower incidence of theft over mobile money, and the higher cost of theft to businesses relying on trade credit. They calculate that mobile money can have increased output in this sector by a third of a percent - likely an underestimate as the enterprises surveyed are larger and more formal than others in Nairobi. While trade credit is an important source of funds for most firms in developing countries, smaller and informal enterprises are less likely to have access to formal sources of credit and are more likely to rely on it [56]. Given the importance of trade credit, especially in the informal sector, the effect of mobile money on these transactions has macroeconomic implications, as well. Indeed, there is some macroeconomic evidence that the informal sector is a beneficiary of mobile phone penetration at the expense of development in the formal sector [13].

Mobile money accounts are also used for saving by a substantial fraction of mobile money users. Keeping savings safe from themselves and from pressing (but not crucial) needs is a substantial challenge facing persons without bank accounts. Many informal savings arrangements, such as rotating savings cooperatives, are designed to overcome these challenges and other strategies, such as borrowing in order to save, repurpose available financial tools for this purpose (see Chapter 8 of [17]). Dupas and Robinson 2013 find that just providing a secure place to put savings that is designated as such (ie. a locked box) is helpful for a majority of people as it simplifies mental accounting [50]. Mobile money accounts appear to fulfill this role. Demombynes

132 and Thegeya 2012 report that in late 2010 around 15% of Kenyans used mobile money as a savings account, and that being registered for mobile money increased the likelihood of reporting any savings by 32% controlling for demographics. They go on to find that bank-integrated mobile savings accounts offering a modicum of interest are no more attractive to most customers than simply storing a balance on their regular account [47]. This may be changing, recent numbers show that 46% of mobile money accounts carried a positive balance in June of 2015 and that dedicated mobile savings accounts are on the rise [78]. Not all evidence is positive, Blumenstock et al. 2015 found that a majority of subjects who received their salary over mobile money did save using their accounts. But, overall levels of savings after 6-8 months were indistinguishable from the control group, indicating that saving with mobile money may discourage use of more informal means of saving [27]. Even in 2010, when only a small fraction of mobile money customers used the service in this way, the combined increase in savings prompted economists to consider the macroeconomic implications. In most jurisdictions, every unit of mobile money issued by the mobile money provider is backed by deposits of actual currency in bank accounts held by the provider. As the total amount of issued e-money rises, this will affect the money supply and inflation to the extent that banks increase lending [87]. Others note that the velocity of this parallel currency relative to the local currency would also affect macroeconomic calculations, while noting that the velocity of money is difficult to measure for any particular means of exchange [117]. Mobile money is also being leveraged for bulk payments and bulk collections, financially connecting individuals directly to their governments, their employers, and their utility companies. In December 2015, of the $8.9 billion transacted over mobile money systems, 11.4% was in bill payments and 8.4% was in bulk disbursements [78]. At the micro scale researchers have found that bulk payments via mobile money bring substantial savings to the paying organization (so long as the mobile money infrastructure is well-developed). In the case of wage payments in Afghanistan,

133 Blumenstock et. al. (2015) find no overall increase in welfare for recipients based solely on the means by which they are paid [27]. On the other hand, Aker at. al. (2016) find that the distribution of cash to drought-affected households in Niger via mobile money raised welfare significantly compared to other delivery mechanisms [4]. The decrease in transaction costs for bulk payments (and bulk collections) would appear to benefit those who bore large costs under the alternative transaction mechanism. More dramatically, this dynamic may have moved some transactions into the realm of the possible. For example, several countries allow people to pay their taxes via mobile money [39]. This broader reach may be encouraging governments to extend their enforcement of the tax code to previously ignored sections of the economy, such as informal businesses [7]. This adds another way in which mobile money can have an effect on the equilibrium between formal and informal sectors of the economy. A smaller group of mobile money users—generally richer and more urban—are using mobile money for everyday transactions like paying cab fare and shopping. In December 2015, 4.1% of the $8.9 billion transacted over mobile money systems was in merchant payments [78], although this likely underestimates the business-to-customer segment of mobile money as business owners can also accept P2P transactions directly from customers. These everyday uses of mobile money point to a possible future where mobile money really could be better than cash for people in developing economies, operating similarly to debit cards in developed countries. The transition away from cash towards electronic payments has been studied in the developed country context, with the conclusion that the shift has been generally beneficial from a cost-benefit perspective [69]. Finally, a small fraction of mobile money users are using the service to participate in branchless baking - where banks offer financial products like insurance, credit, and savings via mobile phone. Mobile money has made offering formal insurance, credit, and savings to wide swaths of the population of developing countries more viable; uptake is growing, but services remain relatively small [77].

134 Mobile money has spread rapidly into certain sectors where the technology dramatically reduced transaction costs, and more slowly into sectors where it may yet do so. The sectors most affected by mobile money are substantial pieces of many developing economies in their own right, and perhaps poised to become even more so. Mobile money accounts also provide a simple yet important financial service, and a growing fraction of users do store money on their accounts. Taken together, the phenomenon of mobile money is blurring the line between formal and informal in developing economies and challenging conventional ideas of financial development. Formal insurance products compete with well-established informal remittance arrangements, and mobile money has made those arrangements more efficient. Formal credit products compete with well-established trade credit arrangements, and mobile money has made those arrangements more efficient. Some of the most innovative formal savings products, according to a leading industry publication, are based on providing formal group savings accounts to existing informal savings groups [77].

Appendix II

Minor implementation considerations

Transaction Fees Payment system providers often charge transaction fees, which are paid by users for access to the service. If each transaction contains information on the fee or fees that users pay to use the service (ie. the revenue the provider is generating from running the service), then money must be diverted to pay them. The size of trajectories will then decay as they move through the system, with more and more of it allocated to fees. This means that the size of the trajectory is also indexed by the step along the trajectory. In its implementation, this decay is incorporated as a list of revenues that are paid at that step of the trajectory. Note that providers may have diﬀerent conventions for recording fee/revenue.

135 One option is to include a column that speciﬁes the fee, which is pulled from the sender’s account alongside the transaction amount (ie. the sender pays). Another option is for the speciﬁed fee to be removed from the transaction amount before it enters the recipient’s account (ie. the recipient pays). It is also possible for providers to charge both kinds of fees, or to note the fees they charge as entirely separate transactions.

Balance information If the transaction ﬁle contains information on the balance of accounts at the time of a transaction, this can be useful. Discrepancies between the algorithm’s internal accounting and the known balances can expose missing transactions. Although it is impossible to know where the money came from, it can be useful to note the discrepancy by inferring the existence of a deposit or withdrawal that brings the internally calculated balance back into line with what is given. Note that accounting imperatives of the transaction override even a given balance.

Size cutoﬀ It is sometimes useful to limit the granularity at which money is followed. The mixing heuristic, in particular, will create many tiny trajectories rather quickly when many accounts maintain non-zero balances. A closed system would also end up with increasingly many, increasingly tiny, trajectories over time. This will eventually overwhelming memory capacity, and so it is useful to place a lower bound on the size of trajectories. To do so, anytime allocating funds to a transaction would create a branch that is too small the existing branch instead becomes a leaf branch, ending the trajectory.

Time cutoff Within the framework of balance respecting trajectories, it is straightforward to introduce time-cutoffs. With time-cutoffs accounts are directed to forget the history of money that has remained in their account for longer than a that period of time. When such money is subsequently transacted, this account becomes the

136 starting point of a new trajectory. This would also be useful in cases where the fully resolved algorithm becomes computationally untenable.

Memory usage and runtime

The transformed data will almost certainly be larger than original. Follow- the-money does not keep the full data in memory, but does command considerable resources especially under the mixing heuristic. It cannot be easily parallelized. For the data set used in this work the greedy heuristic took 12 hours and used 20G memory while the mixing heuristic took 48 hours and used 60G of memory.

Appendix III

Trajectories are interesting objects in their own right, and show pronounced heterogeneity in size. Deposit transactions into this system, shown in red in Figure 6.1, are already distributed over several orders of magnitude – there are deposits of around 1 USD at PPP and of several thousand. The process of tracing money through a payment system also creates more, smaller trajectories. In this particular system, we see more deposits of $100 (PPP) or more than we do trajectories of that size, as downstream transactions split these deposits into many smaller trajectories. Particularly prominent in this data are the large number of small topup payments that split oﬀ many millions of small trajectories.

IIII

Incorporating digital “exits” into the TUE

Real-world payment systems support a range of transaction types that may not ﬁt neatly into the categories of deposits, transfers, and withdrawals. For instance,

137 Figure 6.1: Deposit vs. trajectory size The histogram of trajectory sizes is compared to that of deposit transactions into the mobile money system. Both distributions cover several orders of magnitude and show a pronounced preference for round numbers. The x-axis is log scaled. mobile money systems generally support bill payment and mobile airtime purchases. E-money also exits the system as transaction fees, i.e. revenue for the provider. These are all processed digitally and each is a real, desirable, e-money transaction from the perspective of the provider. Although the recipients of these transactions are not regular users of the system—as in the condition of Equation 4.4—we do want them to contribute positively to TUE.

To accomplish this, we consider the exit type for each ﬂow (fa). To include digital exits in the calculation of TUE, one could modify lf within Equation 4.1 so that digital exits contribute. However, this is mathematically equivalent to modifying the equation by the fraction of ﬂows that end in a digital exit. Like so:

P P f lf · af f δ(fa, adig) · af TUE = lf = P + P (6.1) f af f af where adig refers to the set of digital exit types.

138 Finite time formulation of DUE and TUE

In theory, it is possible to calculate exact values of TUE and DUE for any set of deposits from empirical transaction records. In practice, we would like to be able to provide timely estimates of TUE and DUE for ongoing monitoring of payment system maturity. Measures of system maturity, when calculated for all the deposits on a given day, necessarily quantifies user behavior after that day—how long those funds remain within the system and how much they are re-transacted going forward. We may not know the length and duration of the longest trajectories for months or years, and computing TUE or DUE without those values will be an underestimate. In this work, we impose a cutoff time beyond which we no longer track the funds moving through an account on an individual basis. Funds that are no longer tracked remain in the account and contribute to its present balance. But if and when these funds are “dipped into” for a new transaction, this will begin a new trajectory rather than extending prior ones. Such a cutoff can be introduced in the process of tracing out trajectories of money from the underlying transaction data. [115] Flows where the duration between sequential transactions (∆tf,i) is larger than the cutoff will be split into a flow that ends as savings and a flow that begins as savings. This modified set of trajectories includes ones that begin with just-deposited funds and those that begin from savings. We define the cutoff duration relative to the point in time at which funds enter an account, keeping the stylized representation consistent across all accounts in the system. An account’s “savings balance” is the amount of money within an account that has remained in that account for longer than the cutoff time. A suitable cutoff time drastically reduces the fraction of flows with an unclear beginning or end, allowing for timely measurement of TUE and DUE. They become, effectively, measures of the anticipated values should current conditions continue; this is more useful in practice. A suitable procedure for estimating DURsvg will avoid underestimation from finite-time effects. Equations 6.2-6.3 present the finite-time modification of TUE and DUE.

139 Each equation includes an additional term, TUEsvg and DUEsvg, that captures the estimated additional contribution to the measure from funds after they become savings. These terms are deﬁned by a simple algebraic equations where all other terms can be directly estimated. The average length and duration of trajectories that begin as savings is known from the empirical data; as is the fraction of those trajectories that return to savings. To ﬁnd DUEsvg, we must also estimate the average duration after which funds that become savings are re-transacted. For this we model the dynamics of the total savings balance, with all the accounts in the system considered together.

P P f lf · af f δ(fa, asvg) · af TUE = dep + dep · TUE (6.2) P a P a svg fdep f fdep f where P P lf · af δ(fa, asvg) · af TUE = fsvg + fsvg · TUE svg P a P a svg fsvg f fsvg f P P f ∆tf · af f δ(fa, asvg) · af DUE = dep + dep · DUE (6.3) P a P a svg fdep f fdep f where P P lf · af δ(fa, asvg) · af DUE = DUR + fsvg + fsvg · TUE svg svg P a P a svg fsvg f fsvg f and DURsvg is the estimated duration until re-transaction for savings balance.

Estimating DURsvg

How quickly users dip into their “savings” beyond a certain point is an empirical question, and it directly affects the average Duration Until Exit (DUE). We use the distribution of inter-transaction times found by “follow the money” without a cutoff to generate the decays that we wish to approximate. To produce our estimate, we fit

140 the empirical decay in the system-wide savings balance over time to a decay function with known mathematical properties (see Figure 6.2). The decay in the system-wide savings balance under last-in-ﬁrst-out is hyperbolic, a BAL = − b svg (1 + k · t) , where t corresponds to the number of days since the funds entered this account.

For a given cutoff time c, we normalize BALsvg to be 1 at that point in time and fit the tail of the decay. That is, we use a nonlinear least squares fit to estimate the parameters of a hyperbolic decay beginning at c until the end of the data-collection window.

Equation 6.4 shows the derivation of the DURsvg using this ﬁt and Equation 6.5 gives the simpliﬁed form.

Z x a DURsvg = − b dt (6.4) c 1 + k · t or a · ln(k · x + 1) a · ln(k · c + 1) DUR = − b · x − − b · c svg k k where a − b x = bk 1 a DUR = · a · ln − 1 + b · (k · c + 1) (6.5) svg k b · (k · c + 1)

We estimate the DURsvg for all funds that become savings balance on a given day, so long as that estimate is finite. The estimated values for DURsvg is substantially more stable when flows are normalized by the size of deposit transactions, as large-valued re-transactions cause discontinuities that are difficult to fit. For the absolute balance, the hyperbolic curves were fit to a smoothed version of the decay

(kernel-density smoothing at a bandwidth of 5 days). System-wide value of DURsvg is

141 assumed to ﬂuctuate gradually over time, and we use a cubic spline with substantial smoothing in our calculations of DUE. Note that the average inter-transaction time under random-mixing allocation would be equivalent to the concept of average “holding time” in physics-style models of transaction processes [176]. These models, however, examine closed systems and focus on stationary distributions of “holding time”. This work is, as far as I am aware, the ﬁrst to consider this topic empirically.

Robustness of TUE and DUE to cutoﬀ time

142 Decay in savings balance Decay in savings balance (deposit−normalized) Defined with a cutoff at 3 days Defined with a cutoff at 3 days

1.00 Start date: 1.00 Start date: 2017−04−01 2017−03−01 2017−04−01 2017−02−01 2017−03−01 2017−01−01 2017−02−01 0.75 2016−12−01 0.75 2017−01−01 2016−11−01 2016−12−01 2016−10−01 2016−11−01 2016−09−01 2016−10−01 2016−08−01 2016−09−01 2016−07−01 2016−08−01 0.50 2016−06−01 2016−07−01 0.50 2016−06−01

Hyperbolic fit*: Hyperbolic fit: 0.25 2016−07−01 0.25 2016−07−01 2016−10−01 2016−10−01 2017−01−01 0.00 2017−01−01 Remaining savings balance, as a fraction balance, Remaining savings 0 28 56 84 112 140 168 196 224 252 280 308 as a fraction balance, Remaining savings 0.00 Days since in−transaction 0 28 56 84 112 140 168 196 224 252 280 308 *Fit using kernel−smoothed decay values Days since in−transaction Decay in savings balance Decay in savings balance (deposit−normalized) Defined with a cutoff at 21 days Defined with a cutoff at 21 days

Figure 6.2: Empirical decay of savings balance and hyperbolic fits Empirical decay of amount- and deposit-normalized savings balance, defined as funds remaining within an account beyond 3, 21, and 35 days under last-in-first-out. In red are representative fits of a hyperbolic decay function to the data. The start date refers to the day this money entered this account. Note that the amount-weighted curves were fit to a smoothed version of the decay, not that which is shown.

143 Duration Until Re−transacted for savings Duration Until Re−transacted for savings Using amount−normalized balance at various cutoffs Using deposit−normalized balance at various cutoffs

3000 3000

Cutoff: Cutoff: 2000 40 2000 40

30 30

Hours 20 Hours 20

1000 10 1000 10

0 0 Jun 16 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16Dec 16 Jan 17 Feb 17Mar 17 Apr 17 Jun 16 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16Dec 16 Jan 17 Feb 17Mar 17 Apr 17

*Splines at 1−5 weeks with smoothing parameter of 0.6 *Splines at 1−5 weeks with smoothing parameter of 0.6

144 Transactions Until Exit Duration Until Exit

0.50 Normalization: Normalization: Dollars 180 Dollars Deposits 0.45 Deposits

150 0.40 Hours

0.35 120 Digital transaction steps Digital transaction

0.30 90

Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17

Estimated with cutoff time of 14 days Estimated with cutoff time of 14 days Transactions Until Exit Duration Until Exit

0.50 Normalization: Normalization: Dollars 180 Dollars Deposits 0.45 Deposits

150 0.40 Hours

0.35 120 Digital transaction steps Digital transaction

0.30 90

Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17

Estimated with cutoff time of 21 days Estimated with cutoff time of 21 days Transactions Until Exit Duration Until Exit

0.50 Normalization: Normalization: Dollars 180 Dollars Deposits 0.45 Deposits

150 0.40 Hours

0.35 120 Digital transaction steps Digital transaction

0.30 90

Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17

Estimated with cutoff time of 28 days Estimated with cutoff time of 28 days Transactions Until Exit Duration Until Exit

0.50 Normalization: Normalization: Dollars 180 Dollars Deposits 0.45 Deposits

150 0.40 Hours

0.35 120 Digital transaction steps Digital transaction

0.30 90

Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17 Jul 16 Aug 16 Sep 16 Oct 16 Nov 16 Dec 16 Jan 17 Feb 17 Mar 17

Estimated with cutoff time of 35 days Estimated with cutoff time of 35 days

Figure 6.4: Time series of TUE and DUE at 14, 21, 28, and 35 day cutoﬀs In red are the absolute value of the measures; in burgundy are the deposit-normalized.

145 IV

Robustness towards sampling sparsity and PageRank “alpha”

Sparser sampling and greater dampening in the calculation of PageRank each introduce additional randomness into the network growth process. Sparser sampling makes for noisier sub-network structure; greater dampening within the PageRank calculation smooths stochasticity at higher selection-intensities even as it lowers the eﬀect size. Sparser sampling has a limited aﬀect on node dynamics under high selection-intensity, while smoothing the PageRank calculation diminishes the ability of later nodes to overcome the initial advantage of older nodes.

146 Sampling share: 0.9 Sampling share: 0.8 1.10 PR^9 1.05 PR^9 1.05 PR^8 PR^8 PR^7 1.00 PR^7 1.00 PR^6 PR^6 0.95 0.95 PR^5 PR^5 PR^4 0.90 PR^4 0.90 PR^3 PR^3 PR^2 0.85 PR^2 0.85 PR^1 PR^1

Compression 0.80 PR^0 Compression 0.80 PR^0

0.75 0.75

0.70 0.70

20 40 60 80 100 20 40 60 80 100 Number of nodes Number of nodes

Sampling share: 0.8 PageRank 'alpha': 0.9

1.05 PR^9 1.05 PR^9 PR^8 PR^8 1.00 PR^7 1.00 PR^7 PR^6 PR^6 0.95 PR^5 0.95 PR^5 0.90 PR^4 PR^4 PR^3 0.90 PR^3 0.85 PR^2 PR^2 0.85 PR^1 PR^1

Compression 0.80 PR^0 Compression PR^0 0.80 0.75 0.75 0.70 0.70

20 40 60 80 100 20 40 60 80 100 Number of nodes Number of nodes

Sampling share: 0.7 PageRank 'alpha': 0.85

1.05 PR^9 PR^9 1.05 PR^8 PR^8 1.00 PR^7 PR^7 PR^6 1.00 PR^6 0.95 PR^5 PR^5 0.95 0.90 PR^4 PR^4 PR^3 PR^3 0.85 PR^2 0.90 PR^2 PR^1 PR^1 0.80 Compression PR^0 Compression 0.85 PR^0 0.75 0.80 0.70 0.75 0.65 20 40 60 80 100 20 40 60 80 100 Number of nodes Number of nodes

Figure 6.5: Sub-network structure under varied noise The extent of network compression possible at diﬀerent selection-intensities, for a set of sampling fractions (left) and PageRank “alpha” parameters (right). Shown in grey are twenty independent simulations at each power of k, and shown in purple is the average over them. Darker lines correspond to higher selection-intensity. The compression is calculated using the “description length” of the network from the hierarchical Infomap algorithm [142], and is reported as a fraction of the uncompressed “description length”.

147 Sampling share: 0.9 PageRank 'alpha': 0.95

0.25 0.25

0.20 0.20

0.15 0.15

PageRank 0.10 PageRank 0.10

0.05 0.05

0.00 0.00 10 20 30 40 50 10 20 30 40 50 Number of nodes Number of nodes

Sampling share: 0.8 PageRank 'alpha': 0.9

0.25 0.25

0.20 0.20

0.15 0.15

PageRank 0.10 PageRank 0.10

0.05 0.05

0.00 0.00 10 20 30 40 50 10 20 30 40 50 Number of nodes Number of nodes

Sampling share: 0.7 PageRank 'alpha': 0.85 0.30

0.25 0.25

0.20 0.20

0.15 0.15

PageRank 0.10 PageRank 0.10

0.05 0.05

0.00 0.00 10 20 30 40 50 10 20 30 40 50 Number of nodes Number of nodes

Figure 6.6: Node dynamics under varied noise The PageRank for each node as the networks grows under strong selection-intensity (k = 8), for a set of sampling fractions (left) and PageRank “alpha” parameters. Each plot is a superposition of ten independent simulations. Darker lines correspond to nodes who entered early on in the simulation.

148 Robustness towards initial conditions

Initial conditions matter substantially for the early dynamics of growth of individual networks, but less so for averages over time. The main eﬀect is one of timing—larger cycles to start makes symmetry-breaking easier, facilitating the early emergence of (discretely measurable) sub-network structure.

Size of initial cycle: 8 Sampling share: 0.8 1.05 PR^9 1.05 PR^9 1.00 PR^8 PR^8 PR^7 1.00 PR^7 0.95 PR^6 PR^6 0.95 PR^5 PR^5 0.90 PR^4 0.90 PR^4 PR^3 PR^3 0.85 PR^2 0.85 PR^2 PR^1 PR^1 0.80 Compression PR^0 Compression 0.80 PR^0

0.75 0.75

0.70 0.70

20 40 60 80 100 20 40 60 80 100 Number of nodes Number of nodes

Size of initial cycle: 4 Size of initial cycle: 2

1.05 PR^9 1.05 PR^9 PR^8 PR^8 1.00 PR^7 1.00 PR^7 PR^6 PR^6 0.95 0.95 PR^5 PR^5 PR^4 PR^4 0.90 0.90 PR^3 PR^3 0.85 PR^2 0.85 PR^2 PR^1 PR^1

Compression 0.80 PR^0 Compression 0.80 PR^0

0.75 0.75

0.70 0.70

0 20 40 60 80 100 0 20 40 60 80 100 Number of nodes Number of nodes

Figure 6.7: Sub-network structure under varied initial conditions The extent of network compression possible at diﬀerent selection-intensities, for a set of initial conditions. Shown in grey are twenty independent simulations at each power of k, and shown in purple is the average over them. Darker lines correspond to higher selection-intensity. The compression is calculated using the “description length” of the network from the hierarchical Infomap algorithm [142], and is reported as a fraction of the uncompressed “description length”.

149 Size of initial cycle: 8 Size of initial cycle: 6

0.25 0.25

0.20 0.20

0.15 0.15

PageRank 0.10 PageRank 0.10

0.05 0.05

0.00 0.00 10 20 30 40 50 10 20 30 40 50 Number of nodes Number of nodes

Size of initial cycle: 4 Size of initial cycle: 2 0.5 0.30

0.25 0.4

0.20 0.3

0.15 0.2 PageRank PageRank 0.10

0.1 0.05

0.00 0.0 10 20 30 40 50 0 10 20 30 40 50 Number of nodes Number of nodes

Figure 6.8: Node dynamics under varied noise The PageRank for each node as the networks grows under strong selection-intensity (k = 8), for a set of initial conditions. Each plot is a superposition of ten independent simulations. Darker lines correspond to nodes who entered early on in the simulation.

150 Robustness towards links on entry

It is more difficult to overcome the pull of randomness when we allow incoming nodes more than one in- and out- link. Even with just four links to place (and six ways to orient them) incoming nodes face a combinatorial explosion of options as the network grows. With many more “opportunities” to choose from one must be choosier to achieve an edge over others and spur a reaction from the system as whole. When nodes enter with two in- and out-links we see the emergence of complex sub-network structure first at substantially higher selection-intensities than in the one in- and out-link case. Note that the initial configuration for this version of the model is a two-link ring, i.e. a directed version of an non-randomized Watts–Strogatz network with m = 4. The two in- and out- link case highlights the extreme limitations of random sampling for studying the dynamics of this model. From the perspective of growing networks, agents in all but the simplest of toy economic systems (not to mention real ones) face an options space that is effectively unbounded. Exploring the contours of even this toy model might best be done from an evolutionary perspective, where the boundlessness of possibilities is a feature not a bug. As in evolutionary models of a repeated prisoners’ dilemma [16] or stylized stock market [59], some strategies might be well placed to take advantage of particular competing strategies while some might be especially robust to the strategies of others.

151 ) 0 k 10 n a R e g a P ( P

0.2 0.4 0.6 0.8 PageRank (normalized)

Two in- and out- links on entry 1.050 PR^45 0.16 1.025 PR^40 0.14 PR^35 1.000 PR^30 0.12 PR^25 0.975 PR^20 0.10 0.950 PR^15 PR^10 0.08 0.925 PR^5 PageRank 0.06 Compression PR^0 0.900 0.04 0.875 0.02 0.850 0.00 10 15 20 25 30 35 40 10 15 20 25 30 35 40 Number of nodes Number of nodes

Figure 6.9: Two in- and out- links on entry Description of a growing network model with four incoming links. First, a network snapshot and PageRank distribution at 40 nodes under high selection-intensity (k = 45). Then, the extent of network compression possible at diﬀerent selection-intensities. Finally, the node dynamics under this model under high (but still imperfect) selection-intensity (k = 40).

152