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Cesifo Working Paper No. 9141 A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Pakhnin, Mikhail Working Paper Collective Choice with Heterogeneous Time Preferences CESifo Working Paper, No. 9141 Provided in Cooperation with: Ifo Institute – Leibniz Institute for Economic Research at the University of Munich Suggested Citation: Pakhnin, Mikhail (2021) : Collective Choice with Heterogeneous Time Preferences, CESifo Working Paper, No. 9141, Center for Economic Studies and Ifo Institute (CESifo), Munich This Version is available at: http://hdl.handle.net/10419/236683 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte. may exercise further usage rights as specified in the indicated licence. www.econstor.eu 9141 2021 June 2021 Collective Choice with Hetero- geneous Time Preferences Mikhail Pakhnin Impressum: CESifo Working Papers ISSN 2364-1428 (electronic version) Publisher and distributor: Munich Society for the Promotion of Economic Research - CESifo GmbH The international platform of Ludwigs-Maximilians University’s Center for Economic Studies and the ifo Institute Poschingerstr. 5, 81679 Munich, Germany Telephone +49 (0)89 2180-2740, Telefax +49 (0)89 2180-17845, email [email protected] Editor: Clemens Fuest https://www.cesifo.org/en/wp An electronic version of the paper may be downloaded · from the SSRN website: www.SSRN.com · from the RePEc website: www.RePEc.org · from the CESifo website: https://www.cesifo.org/en/wp CESifo Working Paper No. 9141 Collective Choice with Heterogeneous Time Preferences Abstract This paper reviews recent research on the aggregation of heterogeneous time preferences. Main results are illustrated in simple Ramsey models with two or three agents who differ in their discount factors. We employ an intertemporal view on these models and argue that preferences of a decision maker should be represented by a sequence of utility functions. This allows us to clarify the issue of dynamic inconsistency and relate it to simple properties of discounting. We distinguish between private and common consumption cases. In the private consumption case, we discuss the properties of sequences of Paretian social welfare functions and explain why the notion of Pareto optimality under heterogeneous time preferences becomes problematic. In the common consumption case, we focus on the problem of collective choice under heterogeneous time preferences, discuss the difficulties with dynamic voting procedures and review some ways to overcome them. We conclude by highlighting the implications of our discussion for the problem of choosing an appropriate social discount rate. JEL-Codes: D150, D710, H430, O400. Keywords: collective decisions, social welfare function, heterogeneous agents, time consistency, voting, social discount rate. Mikhail Pakhnin Department of Economics European University at St. Petersburg 6/1A Gagarinskaya st. Russia – St. Petersbug 191187 [email protected] This paper has greatly benefited from the comments and suggestions of Kirill Borissov, Daniel Eckert, Clemens Puppe and Ronald Wendner. I am also grateful to PAO Severstal for the support. 1 Introduction Time preference the intrinsic propensity of an individual to postpone immedi- ate gratification in exchange for larger but delayed rewards lies at the core of economic analysis. Both theoretical and empirical contributions suggest that time preference (patience) is a fundamental factor influencing economic development. In many macroeconomic models, the rate of time preference often determines the most relevant variables, e.g., the long-run income distribution and growth. A vast amount of literature on time preferences is devoted to the analysis of representative agent models (see, e.g., the review by Hamada and Takeda, 2009). However, the representative agent assumption is subject to serious criticism, as people in the real world differ in many characteristics affecting their economic decisions. Kirman (1992, p. 117) argues that this reduction of the behavior of a group of heterogeneous agents ::: is not simply an analytical convenience as often explained, but is both unjustified and leads to conclusions which are usually misleading and often wrong. While it is clear that there are many sources of heterogeneity (e.g., wealth or education), variation in time preferences is arguably the most important of them, as it underlies human behavior. It is generally acknowledged that people are not equally patient, and there is no convergence toward an agreed-on or unique rate of time preference. Hence an attempt to employ the representative agent assumption in growth models faces serious difficulty, as it is unclear, which rate of time preference should be used. Despite a large empirical literature on discounting (see Frederick et al., 2002; Cohen et al., 2020, for extensive reviews), researchers have only recently empha- sized the apparent heterogeneity in time preferences both at individual and country levels. A number of recent large-scale international surveys show that people in the real world value the future differently, and average patience plays a decisive role in the process of economic development. Falk et al. (2018) analyze the results of the 2012 Global Preference Survey covering 80000 individuals from 76 countries. They find that average patience across countries varies by 1.7 of a standard deviation, and the within-country variation is much larger than the cross-country variation: the former amounts to 86.5% in the total individual-level variation in patience, while the latter explains only the remaining 13.5%. Moreover, in the world population as a whole, time preferences vary significantly with individual characteristics such as gender or 2 age. Wang et al. (2016) report the results of a survey comprising about 7000 students from 53 countries. They also find that the measured level of patience is heterogeneous both at individual and country levels, which cannot be explained by differences in interest or inflation rates. Their estimations imply that the median annual discount rate among the considered countries is 100%, ranging from 14% in Australia to 1567% in Bosnia and Herzegovina. International surveys also pave the way for econometric analysis of the links between time preferences and economic growth at the aggregate level. Dohmen et al. (2018) in a sample of 76 countries find that average degree of patience in a country is causally related to economic development. Patience alone explains about 40% of the variation in per capita income, and it strongly correlates with the accumulation of physical capital, quantity and quality of schooling, and pro- ductivity growth. H¨ubnerand Vannoorenberghe (2015) obtain similar results in a panel of 89 countries. They show that average degree of patience has a strong positive impact on income per worker, total factor productivity and capital stock. In their sample, patience also explains about 40% of the cross-country variation in income. They report that increasing patience by one standard deviation raises per-capita income by between 43% and 78%. Thus empirical evidence unambigu- ously suggests that heterogeneity in time preferences should be explicitly taken into account in economic modeling. The canonical theoretical framework for studying heterogeneity in time pref- erences was proposed in a seminal paper by Ramsey (1928). After developing a model of optimal capital accumulation which is now widely known as the optimal growth model (the Ramsey model), he also considered a model with many agents who differ in their time preferences. He conjectured that in a stationary equi- librium the whole capital stock belongs to the most patient agent in the society whose consumption is the largest. All other, less patient agents, consume only at a subsistence level necessary to support their lives. This property of an equilibrium in many-agent models is referred to in the literature as the Ramsey conjecture.1 Ramsey (1928) neither spelled out the details of his many-agent model nor 1The connection between intertemporal choice and economic growth has long occupied the minds of economists. Adam Smith (1776) saw the propensity to save and invest capital instead of spending it immediately as a virtue which leads to the accumulation of all types of capital and increases the wealth of nations. The problem of what determines this propensity was explored by John Rae (1834), who argued that there are differences in the strength of the desire to accumulate among different individuals. People whose desire to accumulate is low become poor, while people
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