Working Paper S e r i e s

W P 1 1 -4 FEB R U A R Y 2 0 1 1

A Generalized Fact and Model of Long-Run Economic Growth: Kaldor Fact as a Special Case

Daniel Danxia Xie

Abstract This paper provides new evidence on the long-run relationship between economic growth and labor’s share in national income, based on a comprehensive panel data set for 123 countries from 1950 to 2004. Xie’s primary finding is that labor’s share follows a cubic relationship with real GDP per capita over the long process of development. At the beginning of the modern economic growth process, the share of labor in national income first decreases until an initial threshold is reached. After that, labor’s share keeps increasing until the country’s GDP per capita reaches a second threshold before falling again. Xie argues that these dynamics apply not only to the less developed countries in the postwar years, but also to the advanced countries like the United States and the United Kingdom during their early economic take-offs, starting in the late 18th and 19th century, respectively. Finally, he proposes a two-sector constant elasticity of substitution (CES)-type growth model and simulates the model to replicate and explain the possible mechanism behind such a nonlinear pattern of movements in labor’s share.

JEL Codes: O41, P21, E32. Keywords: Constant elasticity of substitution, Kaldor fact, Kuznets curve, Labor’s share, Structural change.

Daniel Xie is a nonresident visiting research fellow at the Peterson Institute for International Economics. He is a PhD student in economics at the University of Chicago. His email is [email protected].

Note: The author is grateful to Fernando Alvarez, Jeffrey Frankel, Dale Jorgenson, Dani Rodrik, Harald Uhlig, and Richard Zeckhauser for invaluable teachings and advice. The author would also thank David Autor, Joseph Gagnon, Morris Goldstein, Olivier Jeanne, Samuel Kortum, Michael Mussa, Robert Shimer, Robert Solow, Nancy Stokey, Arvind Subramanian, and Michael Woodford for superb comments and suggestions.

Copyright © 2011 by the Peterson Institute for International Economics. All rights reserved. No part of this working paper may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by information storage or retrieval system, without permission from the Institute.

1750 Massachusetts Avenue, NW Washington, DC 20036-1903 Tel: (202) 328-9000 Fax: (202) 659-3225 www.piie.com 1 Introduction

One of the most important empirics upon which the modern growth theory is built (Solow 1957) is that the labor and capital shares in national income are roughly constant over time. As one of his six stylized facts, Kaldor (1957) summarized it as, “It was known for some time that the share of wages and the share of profits in the national income has shown a remarkable constancy in ‘developed’ capitalist economies of the United States and the United Kingdom since the second half of the 19th century.” This echoes Keynes’ surprise (1939), “I mean the stability of the proportion of the national dividend accruing to labor, irrespective apparently of the level of output as a whole and of the phase of the trade cycle. This is one of the most surprising, yet best-established, facts in the whole range of economic statistics, both for Great Britain and for the United States… It is the stability of the ratio for each country which is chiefly remarkable, and this appears to be a long-run, and not merely a short-period, phenomenon.” On the other hand, Kuznets (1959) challenges the view of constancy of factor shares cross country or over time. Most recently, there has been a small literature trying to reconcile the Kaldor fact with structural transfor- mation, for example, Kongsamut, Rebelo, and Xie (2001); Ngai and Pissarides (2007); and Acemoglu and Guerrieri (2008). In this paper, I will provide new empirical evidence on the long-run relationship between economic growth and labor’s share in national income. I construct a comprehensive panel data set of labor’s share for 123 countries from 1950 to 2004 (most countries in this data set have data available from 1970 to 2004). My primary finding is that labor’s share tracks a cubic relationship with real GDP per capita over the long process of development. At the beginning of the economic take-off, the share of labor in national income will first decrease until a threshold of US$3,000 is reached (denominated in 2000 constant US dollars). With empirical support from the latest research in economic history, I would also argue that this pattern applies not only to the less developed countries since 1950, but also to the advanced countries like the United States and the United Kingdom in their earliest stages of development. After this first threshold is passed, labor’s share will keep increasing until the country’s real GDP per capita reaches the next threshold, around US$15,000. After that, labor’s share will follow a downward trend again. To explore the mechanism behind such nonlinear and non-monotonous movements in the labor’s share, I build a growth model based on a two-sector constant elasticity of substitution (CES) production function and consumer preference specification, following Engel’s law. In short, my findings can be seen as a generalization of the Kaldor fact and Solow-type growth model, to characterize the panoramic process of modern economic growth. The emphasis on structural transformation can be traced back to Simon Kuznets, who summarizes the main quantitative characteristics of modern economic growth in his Nobel Prize lecture (Kuznets 1973), “…the rate of structural transformation of the economy is high. Major aspects of structural change include the shift away from agriculture to nonagricultural pursuits and, recently, away from industry

2 to services; a change in the scale of productive units, and a related shift from personal enterprise to impersonal organization of economic firms, with a corresponding change in the occupational status of labor.” Kuznets identifies two grand transformations. The first is industrialization, during which economic resources are transferred from the agricultural or feudal sector to the industrial sector. However, the timing of industrialization varies tremendously among countries. The Industrial Revolution in Great Britain, the first industrialization in human history, started from the end of the 18th century, while some emerging economies like China are experiencing a similar process two centuries later. The second transformation is from industry to services. Beyond Kuznets, I will provide new evidence and ascribe the second decline of labor’s share in my empirical findings to a possible ongoing third economic transformation, the rise of the finance and real estate sector in the later phase of economic development. Kuznets (1955) was among the first researchers to deal with the inequality problem in early economic development, as summarized by the classical “Kuznets Curve.” As the size of agriculture shrinks, the size of industry grows, and inequality increases due to the large gap between the two sectors. In a classical framework, Lewis (1954) assumes the real wage is fixed in terms of agricultural goods and that there will be disguised unemployment before it can be consumed by the industrial sector. With Lewis’ oversimplified model, it is very easy to explain why labor’s share will go down at the beginning of industrialization: because of the surplus labor and stagnation of the wage. In contrast, Jorgenson (1961, 1967) and Ranis and Fei (1961) successfully applied a neoclassical approach to modeling the transitional process. In the recent literature, Blanchard (1997, 1998), Caballero and Hammour (1998), Rodrik (1999), Acemoglu (2003), Blanchard and Giavazzi (2003), and Bentolila and Saint-Paul (2003) have explored various factors behind the movements of labor’s share, mainly focusing on the OECD countries in the postwar period. Young (2006) uses postwar US data to challenge the relatively constancy of aggregate factor shares, following the methodology of Solow (1958). Ruiz (2005) provides empirical evidence on the nonconstancy in factor shares for Spain using its time series data from 1955 to 2005. In contrast, my research emphasizes the movements of labor’s share in long-run economic development and transformation, with the least developed countries included. On the other hand, Gollin (2002) and Bernanke and Gurkaynak (2001) design delicate methodologies to adjust labor’s share for the developing countries. With their adjustment for the noncorporate sector in developing countries, labor’s share is pulled closer to the level of the developed world. However, they limit their exploration to cross-country comparisons and do not take into consideration the possibility of nonlinear dynamics in different stages of development. The seminal paper by Arrow et al. (1961) proposed the CES production function with empirical support. Leontief (1964) also criticized the Cobb-Douglas function, “…whenever a working economist

3 was called on to describe in numbers or to interpret in analytical terms the relationship between the inputs of capital and labor and the final product of a plant, an industry, or a national economy as a whole, he was more likely than not to reach out for the Cobb-Douglas production function… But now this remarkable career is apparently coming to an end. The old formula is being rapidly replaced by a new, improved recipe: the constant elasticity of substitution production function…” Most recently, Duffy and Papageorgiou (2000) revived a literature in economic growth and adopted the CES-form production function. Acemoglu (2003) assumes an elasticity of substitution that is lower than one. Estimates by Antras (2004) for the United States suggest an elasticity lower than one, even probably below 0.5. Solow (2008) presents a review of this new small literature. My theoretical model is built upon a new two-sector CES specification. Another literature related to my research is the Unified Growth Theory initiated by Galor and Weil (2000) and Hansen and Prescott (2002). This literature intends to integrate the Malthusian stagnation with modern economic growth in a unified framework. This paper is organized as follows. Section 2 presents my main empirical findings characterizing the evolution of labor’s share during long-run development. Section 3 offers sectoral analysis of the movements in labor’s share and examines the empirical evidences behind the three economic transformations. Section 4 tries to test my empirical findings with the economic history of the United Kingdomthe three and economicthe United transformations.States. Section 5 develops Section a two-sector4 tries to testunified my growthempirical model, findings aiming with at the economic history of the United Kingdom and the United States. Section 5 develops a two-sector explainingunified the growth nonlinear model, and nonmonotonousaiming at explaining dynamics the of nonlinear labor’s share. and Section nonmonotonous 6 performs adynamics simple of simulationlabor’s based share. on Section the proposed 6 performs growth amodel. simple Section simulation 7 concludes based the on paper. the proposed growth model. Section 7 concludes the paper. 2 Evolution of Labor’s Share and New Panel Analysis 2 EVOLUTION OF LABOR’S SHARE AND NEW PANEL ANALYSIS In this section, I will present new empirical results on the movements of labor’s share in national income. In sectionIn this 2.1 section, I first Idiscuss will present various newdefinitions empirical of labor’s results share on andthe explainmovements why I ofchoose labor’s my shareown in national income. In section 2.1 I first discuss various definitions of labor’s share and explain why I definition.choose mySection own 2.2 definition. shows the Sectionmain panel 2.2 regression shows theresults. main In panelsection regression 2.3 I provide results. additional In section robust 2.3 I checks,provide using additional a variety of robustcontrol checks,variables. using a variety of control variables.

2.1 2.1Various Various Definitions Definitions of Labor of Labor’s’s Share Share

TheThe simplest simplest definition definition of labor of’s sharelabor’s in nationalshare in income national is the income ratio of is compensation the ratio of compensation to the employees to the to GDPemployees minus indirect to GDP taxes minus as (1), indirect taxes as (1),

Corporate employee compensation Labor Share  (1) (1) GDP  indirect taxes

These data are generally available in the United Nations System of National Accounts. However, according to this simple formula, some countries seem to have too low of shares of labor income. Gollin (2002) attributes the abnormally lower value of labor’s share in many developing countries to the failure of incorporating the income of the self-employed and noncorporate employees into the “employee compensation.” Gollin thus names specification (1) as a naive method and improves the measure of labor’s share by adopting several adjustments. One of Gollin’s well-accepted corrections is4 shown by (2),

Corporate employee compensation Labor Share  (2) GDP  indirect taxes  OSPUE

After this adjustment, some countries’ labor shares are boosted up significantly. Bernanke and Gurkaynak (2001) generally confirm Gollin’s methodology, and they especially prefer the estimation formula of (2). The other method is to adjust the GDP data by assuming the corporate and noncorporate workers receive the same average earnings, as calculated by (3),

Corporateemployeecompensation ShareLabor  Corporateemployees (3) forcelaborTotal unemployed (GDP  indirecttaxes)

Bernanke and Gurkaynak (2001) also proposed the imputed operating surplus of private unincorporated enterprises (OSPUE) method, by (4) and (5), the three economic transformations. Section 4 tries to test my empirical findings with the theeconomic three economic history of transformations. the United Kingdom Section and 4 thetries United to test States. my empirical Section findings5 develops with a two-sectorthe economicunified growth history model, of the aiming United at Kingdom explaining and the the nonlinear United States. and nonmonotonous Section 5 develops dynamics a two-sector of unifiedlabor’s growthshare. Section model, 6aiming performs at explaining a simple simulation the nonlinear based and on nonmonotonous the proposed growth dynamics model. of labor’sSection share. 7 concludes Section the 6 performspaper. a simple simulation based on the proposed growth model. Section 7 concludes the paper. 2 EVOLUTION OF LABOR’S SHARE AND NEW PANEL ANALYSIS 2 EVOLUTION OF LABOR’S SHARE AND NEW PANEL ANALYSIS In this section, I will present new empirical results on the movements of labor’s share in national Inincome. this section, In section I will 2.1 present I first discussnew empirical various results definitions on the of movements labor’s share of andlabor’s explain share why in national I income.choose my In sectionown definition. 2.1 I first Section discuss 2.2 various shows definitions the main panelof labor’s regression share andresults. explain In section why I 2.3 I chooseprovide my additional own definition. robust checks, Section using 2.2 shows a variety the ofmain control panel variables. regression results. In section 2.3 I provide additional robust checks, using a variety of control variables. 2.1 Various Definitions of Labor’s Share 2.1 Various Definitions of Labor’s Share The simplest definition of labor’s share in national income is the ratio of compensation to the Theemployees simplest to definitionGDP minus of indirectlabor’s sharetaxes inas national(1), income is the ratio of compensation to the employees to GDP minus indirect taxes as (1), Corporate employee compensation  Labor Share Corporate employee compensation (1) Labor Share  GDP  indirect taxes (1) GDP  indirect taxes These Thesedata are data generally are generally available in available the United in Nations the United System Nations of National System Accounts of .National However, Accounts . according However, to Thesethis according simple data formula,are to generally this some simple countries available formula, seem in some theto have United countries too lowNations ofseem shares System to of have labor of too National income. low of Gollin Accounts shares of. (2002)However,labor attributes income. according the Gollin abnormally to (2002) this lower simple attributes value formula, of thelabor’s abnormally some share countriesin many lower developing seem value to of havecountries labor’s too tosharelow the of failurein shares many of labordeveloping income. countries Gollin (2002)to the failure attributes of incorporating the abnormally the lower income value of theof labor’sself-employed share in and many of incorporating the income of the self-employed and noncorporate employees into the “employee developingnoncorporate countries employees to the into failure the “employee of incorporating compensation.” the income Gollin of the thus self-employed names specification and (1) compensation.”noncorporateas a naive methodGollin employees thus and names improves into specification the the“employee measure (1) as compensation.” ofa naive labor’s method share and Gollin by improves adopting thus the names several measure specification adjustments. of labor’s (1) shareasOne by a adoptingnaiveof Gollin’s method several well-accepted and adjustments. improves Onecorrections the of measure Gollin’s is shownwell-acceptedof labor’s by (2),share corrections by adopting is shown several by (2), adjustments. One of Gollin’s well-accepted corrections is shown by (2), Corporate employee compensation  (2) Labor Share Corporate employee compensation (2) Labor Share  GDP  indirect taxes  OSPUE (2) GDP  indirect taxes  OSPUE After this After adjustment, this adjustment, some countries’ some laborcountries’ shares laborare boosted shares up are significantly. boosted up Bernanke significantly. and Gurkaynak Bernanke (2001) After and thisgenerally Gurkaynak adjustment, confirm (2001) someGollin’s generally countries’ methodology, confirm labor and Gollin’sshares they especiallyare methodology, boosted prefer up the significantly. and estimation they especially Bernankeprefer the andestimation Gurkaynak formula (2001) of (2). generally confirm Gollin’s methodology, and they especially formula of (2). prefer the The estimation other method formula is to of adjust (2). the GDP data by assuming the corporate and noncorporate workersThe other The receive othermethod the method is sameto adjust isaverage to the adjust GDP earnings, thedata GDP by asassuming datacalculated by the assuming corporateby (3), the and corporate noncorporate and noncorporateworkers receiveworkers the same receive average the earnings, same average as calculated earnings, by (3), as calculated by (3), Corporateemployeecompensation ShareLabor  (3) CorporateCorporateemployeesemployeecompensation forcelaborTotal unemployed (GDP  indirecttaxes) (3) ShareLabor  Corporateemployees (3) forcelaborTotal unemployed (GDP  indirecttaxes) Bernanke and Gurkaynak (2001) also proposed the imputed operating surplus of private BernankeunincorporatedBernanke andand Gurkaynak enterprises (2001) (2001) (OSPUE) also also proposed method,proposed the by imputedthe (4) imputed and operating (5), operating surplus surplus of private of private unincorporatedunincorporated enterprises enterprises (OSPUE) (OSPUE) method, method, by (4) and by (5), (4) and (5),

Corporate employee compensation Labor Share  Corporate employee compensation (4) Labor Share    GDPGDP indirectindirect taxes taxes Im Im putedputed OSPUE OSPUE

forcelaborTotal forcelaborTotal  unemployed unemployedCorporateCorporate employees employees Im puted OSPUEOSPUE (5) forcelaborTotal forcelaborTotal unemployedunemployed (Operating(Operating Surplus Surplus Corporate Corporate employee employee compensati compensation) on)

Admittedly, the Gollin method of adjustment can help to mitigate some of the anomalies, for Admittedly, Admittedly, the the Gollin Gollin method method of of adjustment adjustment can can help help to mitigateto mitigate some some of the of anomalies,the anomalies, example:for example: Without Withoutadjustment,Without adjustment, adjustment, Niger’s labor Niger’s Niger’s share laboris laborcalculated share share isas calculated isabout calculated 16 percent as about as withabout 16 the percent 16 naive percent with withthe the method,naive but method,method, rises up but butto aroundrises rises up up 60 to topercent around around with 60 60 percent the percent adjustment. with with the theHowever, adjustment. adjustment. as Bernanke However, However, and as Gurkaynak Bernanke as Bernanke and and (2001)Gurkaynak put, there (2001) (2001)are only put, put, a few there there countries are are only only that a fewhavea few countriesOSPUE countries (or that mixedthat have have income) OSPUE OSPUE data (or available.mixed(or mixed income) Gollin income) data data available. GollinGollin (2002) (2002) covers covers only only about about 30 30 countries. countries. Bernanke Bernanke and and Gurkaynak Gurkaynak (2001) (2001) expand expand (2002) covers only about 30 countries. Bernanke and Gurkaynak (2001) expand the coverage to about the coverage toto about about 50 50 countries. countries. I finallyI finally gathered gathered data data for forabout about 60 countries60 countries that thathave have data data 50 countries.available I that thatfinally satisfiessatisfies gathered the the demandsdata demands for about of of (2). 60(2). Mycountries My dataset dataset that covers havecovers dataabout aboutavailable 2,700 2,700 thatobservations observationssatisfies theof of employees’ compensation, of which only 800 observations have corresponding mixed income demandsemployees’ of (2). My compensation, dataset covers aboutof which 2,700 only observations 800 observations of employees’ have compensation, corresponding of which mixed only income data. Moreover, taking taking a aclose close look look at at the the data, data, I find I find countries countries with with mixed mixed income income data dataavailable available 800 areobservations either developed have corresponding countries ormixed poor income countries data. only Moreover, having taking a few aobservations. close look at the data, I find are either developed countries or poor countries only having a few observations. Moreover, according to my analysis, disparate calculating methodologies do not change Moreover, according to my analysis, disparate calculating methodologies do not change much the relative time series trend in the movements of the labor share for a specific country. In muchtable 1, the I show relative the timecorrelation series betweentrend in the naivemovements measure of (1) the and labor sophisticated share for ameasure specific (2). country. The In tabledependent 1, I show variable the iscorrelation the “classical” between definition the naive of labor’s measure share (1) by and Gollin sophisticated (2002). The measure correlation (2). The dependentis high. In particular variable iswhen the “classical”I control the definition country fixed of labor’s effect inshare column by Gollin (3), I get (2002). a coefficient The correlation isvery high. close In toparticular 1. when I control the country fixed effect in column (3), I get a coefficient very close In addition, to 1. there are some limitations5 for these adjustment methods. The explicit or implicit Inintention addition, of therethe adjustments are some limitationsproposed by for Gollin these (2002) adjustment and followed methods. by TheBernanke explicit and or implicitGurkaynak intention (2001) ofis tothe narrow adjustments the analysis proposed within by the Gollin formal (2002) sector, and or followedthe modern by corporated Bernanke and Gurkaynaksector. It might (2001) be good is to enoughnarrow for the modern analysis economic within the analysis, formal but sector, it will or mask the modern many facts corporated that sector.are essential It might for studyingbe good enoughlong-run for development, modern economic as emphasized analysis, by butKuznets, it will “the mask shift many from facts that arepersonal essential enterprise for studying to impersonal long-run organization development, of economic as emphasized firms” asby well Kuznets, as the “thedual shifteconomy from personalemphasized enterprise by Jorgenson to impersonal (1961). organization of economic firms” as well as the dual economy emphasized Gollin by (2002) Jorgenson only conducts (1961). cross-country analysis, so do Bernanke and Gurkaynak (2001). Gollin (2002)(2002) findsonly someconducts relatively cross-country poor countries analysis, like soIndia do hadBernanke a labor’s and share Gurkaynak as high (2001).as 0.84 inGollin 1980, (2002) and Vietnam finds some got the relatively same number poor incountries 1989. These like Indianumbers had are a labor’s even much share larger as high asthan 0.84 that in of 1980, the United and Vietnam States and got Japan. the same A hypothesis number into 1989.reconcile These these numbers seemingly are abnormaleven much larger thanfacts thatis that of athe country’s United laborStates income and Japan. share Amight hypothesis firstly decrease to reconcile at the these beginning seemingly of economic abnormal factsdevelopment is that a and country’s then rise labor again income at a later share stage. might Cross-country firstly decrease analysis at thein previous beginning research of economic cannot capture these interesting and crucial dynamics, especially during economic development and then rise again at a later stage. Cross-country analysis in previous research transformation. cannot capture these interesting and crucial dynamics, especially during economic

transformation.2.2 Primary Panel Analysis

2.2In this Primary research, Panel I adopt Analysis the panel method with fixed effects, so the naive measure of labor’s share can be good enough when the country-specific characteristics are controlled. Although Indifferent this research, countries I adoptcould havethe panel disparate method shares with of fixeda self-employed effects, so (notthe naiveincorporated) measure sector, of labor’s share can be good enough when the country-specific characteristics are controlled. Although different countries could have disparate shares of a self-employed (not incorporated) sector, countries with mixed income data available are either developed countries or poor countries only having a few observations. Moreover, according to my analysis, disparate calculating methodologies do not change much the relative time series trend in the movements of the labor share for a specific country. In table 1, I show the correlation between the naive measure (1) and sophisticated measure (2). The dependent variable is the “classical” definition of labor’s share by Gollin (2002). The correlation is high. In particular when I control the country fixed effect in column (3), I get a coefficient very close to 1. In addition, there are some limitations for these adjustment methods. The explicit or implicit intention of the adjustments proposed by Gollin (2002) and followed by Bernanke and Gurkaynak (2001) is to narrow the analysis within the formal sector, or the modern corporated sector. It might be good enough for modern economic analysis, but it will mask many facts that are essential for studying long-run development, as emphasized by Kuznets, “the shift from personal enterprise to impersonal organization of economic firms” as well as the dual economy emphasized by Jorgenson (1961). Gollin (2002) only conducts cross-country analysis, so do Bernanke and Gurkaynak (2001). Gollin (2002) finds some relatively poor countries like India had a labor’s share as high as 0.84 in 1980, and Vietnam got the same number in 1989. These numbers are even much larger than that of the United States and Japan. A hypothesis to reconcile these seemingly abnormal facts is that a country’s labor income share might firstly decrease at the beginning of economic development and then rise again at a later stage. Cross-country analysis in previous research cannot capture these interesting and crucial dynamics, especially during economic transformation.

2.2 Primary Panel Analysis

In this research, I adopt the panel method with fixed effects, so the naive measure of labor’s share can be good enough when the country-specific characteristics are controlled. Although different countries could have disparate shares of a self-employed (not incorporated) sector, which can be captured by the constant item in a fixed effect panel model, the comovement of labor’s share in the (formal) incorporated sector and the whole economy seems to be fairly high, as proved in table 1. The main purpose of this research is to explore the long-run movements of labor’s share over time, so the panel method with fixed effects is an appropriate choice. My new empirical exploration is based on several major databases, including the United Nations System of National Accounts, the EU KLEMS Growth and Productivity Accounts, various national sources, as well as the latest research findings for various countries. If a country’s labor share data is covered by different sources, I prefer to choose the data source with the longest time series. Even if different countries may use disparate definitions of labor’s share, panel methodology can help to correct

6 this because I care mainly about the evolution over time within a country. For national GDP data, I use the Penn World Table (PWT6.2) real GDP per capita (rgdpch, chain series), i.e., international dollars in 2000 constant prices. Labor’s share in national income follows equation (1). The primary panel regression results are shown in table 2. Columns (1) and (2) use the yearly data with country fixed effects controlled. Column (1) also controls the time fixed effect of each year, whereas column (2) treats time as a linear variable. Columns (3) and (4) illustrate the panel regression results with all variables in five-year averages, as in the standard growth regression practices. In addition, I also try specifications of quadratic and higher power relationships with 1n(rgdpch) in columns (5) and (6), in which the coefficients are not statistically significant. The basic findings in table 2 illustrate a strong cubic relationship between labor’s share and the level of economic development. It is reasonable to think the commodity exporters might have a different economic structure—very disparate sector compositions and thus “disturb” the relationship between the labor’s share and GDP level. Therefore, I have additionally checked this relationship by removing the commodity exporters, and show the new regression results in table A1. The cubic relationship is kept very well after removing the most important 22 commodity exporters (in terms of the commodity exports value to GDP ratio).

2.3 Robustness Checks with Standard Controls

In this section, I add standard control variables used in the long-run economic growth literature. All exercises in this subsection are panel regressions with both country and time fixed effects. The new results are presented in table 3. All variables are in five-year averages. Firstly, in all the exercises the cubic relationship between the labor’s share and the per capita GDP level is very robustly kept. In column (1) I add the updated school year variable by Barro and Lee (2000). Column (2) illustrates that the average human capital level follows a reversed U-shape relationship with labor’s share. Investment generally increases the labor’s share with other factors controlled, although this relationship is not always robust. However, population growth rate, institutional quality (from the Polity Project, as preferred by the present growth literature), and openness do not have very strong statistical relationships with the labor’s share over time. Column (5) shows that inflation has a strong, negative correlation with labor’s share, which is consistent with research elsewhere. In table A2 I show the corresponding regression results with the commodity exporters removed, and no obvious changes are found in the value and significance of the new set of coefficients. I can recover and characterize the explicit relationship between the labor’s share and real GDP per capita according to the coefficients derived from these regressions. Figure 1 exemplifies this long-term relationship diagrammatically. The horizontal axis lines out the per capita real GDP level. After an

7 economy just moves onto the track of modern economic growth, its labor’s share will firstly experience a continuous drop until the first minimum value is attained. I can solve this numerically. The first minimum of the labor’s share is reached at GDP level around US$3,000 in per capita terms (in 2000 constant US dollars). After passing this first turning point, the labor’s share begins to rise monotonously for quite a long time with the economic growth going on. Then the second turning point, a local maximum is reached. I can solve and see this local maximum of labor’s share is approximately arrived at a per capita GDP level of US$15,000 (in 2000 US dollars). The modern economic growth theory and the Kaldor fact have mainly focused on the smoother portion of the curve, and this is why a constant labor’s share is generally assumed and agreed on. To depict this with real data, in figure 2 I scatter the labor’s share versus real GDP per capita with pooled data for four periods, 1970–74, 1980–84, 1990–94, and 2000–2004. Moreover, figures 3–6 demonstrate all countries’ data in each period respectively along with the fitted curves. This can also help to explain the “puzzles” encountered in the research of Gollin (2002) and Bernanke and Gurkaynak (2001): Why do some poor countries have such high labor’s share? The nonlinear and nonmonotonous movements of the labor’s share as demonstrated by figure 1 could provide a feasible answer. It just so happens that many least developed countries are located on the portion of the curve before the first turning point and are undergoing a durative reduction in labor’s share right now. This will be confirmed with detailed discussions on what is happening in the present China and India in the next section (section 3.2). At the same time, many middle-income countries have marched to the portion of the curve between the first local minimum and the local maximum, and so they are currently seeing a gradual rise in their labor’s share. This will be discussed in detail in section 3.3. Finally, a small number of developed countries have arrived at the third part of the curve after exceeding the second turning point and will endure a drop in their labor’s share again. I describe this recent stage of development as “financialization” and will conduct deeper analysis in section 3.4.

3 Behind the Veil of the Long-Run Movements in Labor’s Share

I attribute the nonlinear and nonmonotonous pattern in the movements of labor’s share to the grand economic transformations. Some researchers like Kuznets stress the importance of production transfor- mation, while others like Engel underline the evolution of the consumers’ preferences. Probably these two forces have joined together to stimulate the unremitting evolution of the national economy as well as labor’s share. In this section, I conduct a sectoral decomposition analysis of the change in labor’s share over time to prepare for later statistical explorations. I then go on to discuss the three grand economic transformations that have happened or are happening right now.

8 K sector i at time t 1. Thus I have K v  .1 I use    vvv to represent the change K K ti 1,  ,1, titii 3.1 Asector Sectoral i at D timeecomposition t 1. Thus in Ithe have Evolution Ki1v of L.1abor I use’s S hare  vvv to represent the change sector i at time t 1. Thusi I have  v  .1 I use  ti 1,   vvv to represent the change,1, titii sectorsector i at at time time tt 1ti ..1, ThusThus II havehave i1v ti 1,  .1.1 I I ,1, titii use use     vvv ,1, titii to to representrepresent thethe changechange of value-added sharei1 of sector i romi 1 t ti  to1, t  .1 Labor’s share of sector,1, titii i at time t 1 is i1 t t DL L L I denoteof value-added the change of share aggregate of sector labor’sK sharei rom in thet towhole t  economy.1 Labor’s from share to +of 1 sectorby = i att+1 – timet. Labor’s t 1 is l  , and i  t  lll . i t  i  i  of value-added shareof of ti value-added1, sector  rom share ,1, of to sectortititi .1 Labor’s romK share to tof sector.1 Labor’s at share time oft sector1 is at time t  1 is sectorshareiofl at at value-added timetime, and t + t 1 can1. share Thusbe decomposed Iof have sectorlll .  intovi ti romsectors1, .1t following Ito use t .1 (6). Labor’s I assume sharevvv there,1, titii to ofare represent sector K economic i the at sectorstime change int 1 is ti  1,  ,1,  ititi i1     K l ti 1, , and  ,1, sectorl ti 1, ,lll ititi and. i at time t ,1, 1.  Thuslll ititi . I have  v ti 1, .1 I use  vvv ,1, titii to represent the change l ti 1, , and  ,1, lll ititi . i1      total, Kand vi,t+1 represents the value-added sectorshare of isector at time i at timet 1t +. Thus1. Thus I have I have  v ti 1, 1. I use  vvv ,1, titii to represent the change of value-added share of sector i rom t to t  .1 Labor’s share of sector i i at1 time t 1 is K  Llv K ofDK vvalue-addedv v sharettiti  11,1, (6) of sector i rom t to t  .1 Labor’s sharei oft sectort i at time t 1 is l ti 1, ,I use and K i = i,t+1 – ,1, i,t to representlll ititi . the change of value-added share of sector rom to + 1. Labor’s share of i1  Llv ttiti  11,1, (6) of value-added share of sector i rom t to t  .1 Labor’s share of sector i at time t 1 is  Llv ttiti  11,1, (6)l ti  1, , and   Llv ttiti  11,1, ,1, (6)  lll ititi .  sectori i1 at time t + 1 isLlv lttiti  11,1, , (6)and l – l = Dl . i1 i1 i,t+1 i,t+1 i,t l i , and  lll . i1 ti 1,  ,1, ititi K K K K K  K    Llv Becausettiti  11,1, (6)  1, tti  , LLvLv ttti , I can use (7) to decompose L by sectors. From  K K K K  Because  Llv Ki 1(6) (6)  Ki 1 K  LLvLv , I can use (7) to decompose L by sectors. From Becausei 1  Because  ttiti  11,1,  LLvLv 1, , I cantti  use ,(7) to decomposeLLvLv ttti , I can use  (7)L to by decompose sectors. From  L by sectors. From  1, tti , i1 ttti 1, tti i1 , ttti  i1 i 1 Becausei1 i1 1, tti  i1 ,  LLvLv ttti , I  canLlv ttiti  11,1, use (6) (7) to decompose L by sectors. From time t to t  ,1  sector i’s additional  deviation from the aggregate labor’s share at t is i 1 i 1 i1 time t to K t  ,1 sectorK i’s additional deviation from the aggregate labor’s share at t is time t to t  ,1 sectortime it’s to additional t  ,1 sector deviation i’s additional from the aggregate deviation labor’sfrom the share aggregate at t is labor’s share at t is representedt  by K   i 1,1, Llv Kttiti  ),( which is the product of theD sector’s value-added sharet at time BecausetimeBecause to t 1, ,1 sectortti ,’s additionalLLvLv ttti ,, II cancan deviation use use (7) (7) to from to decompose decompose the aggregate L by sectors.L labor’s by sectors. From share time From at t to t is + represented Becausei1 by  i1  1,1,  Llv ttiti ),( which LLvLv is ,the I can product useK (7) of tothe decompose sector’sK value-added L by sectors. share Fromat time represented by representedt 1  1,1, and Llv thettiti ),( by deviation which is 1, the of 1,1, tti itsproduct Llv sectoralttiti ),( , which of thelabor’s is sector’sttti the share product value-added at time of the t sector’s 1share from at value-added thetime aggregate share labor’s at time share 1 sectorrepresented i ’s additional by deviationi1  from1,1,  Llv ithettiti ),( 1 aggregate which is labor’s the product share at of t is the represented sector’s byvalue-added v .(l –L share), which at time  t 1 and the deviation of its sectoral labor’s Because share  at time1, tti t 1 from, thei,tLLvLv +1ttti aggregate, Ii,t can+1 uset labor’s (7) to decomposeshare L by sectors. From  time t to t  ,1 sector i’s additional deviation from thei aggregate1 labor’si1 share at t is t 1 and the deviationtimetoft  1time of andt andits tot sectoral. thethe deviationdeviation sectorlabor’s of of ishare ’sitsits additional sectoralsectoral at time labor’slabor’s deviationt 1 shareshare from from theatat time time theaggregate aggregate tt 1 labor’s from from labor’s thethe share aggregateaggregate share at labor’slabor’st is shareshare is theof product time t of. tthe sector’s,1  value-added share at time t + 1 and the deviation of its sectoral labor’s share of time t . representedof time by t .  1,1, Llv ttiti ),( whichtime is the t product to t  of,1 sectorthe sector’s i’s additional value-added deviation share atfrom time the aggregate labor’s share at t is at timerepresentedof K time t + 1 fromt . by the aggregate  labor’s1,1,  Llv ttiti ),( share which of time is thet. product of the sector’s value-added share at time t 1 and the deviation of its sectoral labor’s share at time t 1 from the aggregate labor’s share K  represented by  1,1,  Llv ttiti ),( which is the product of the sector’s value-added share at time K tK1 and the 1,1, deviationttiti )( LLlv of (7)its sectoral labor’s share at time t 1 from the aggregate labor’s share K of time ti.1  1,1, ttiti )(  LLlv (7)    1,1, ttiti )(  LLlv (7)  1,1, ttiti )(  LLlv (7) t 1 and the deviation of its sectoral labor’s share at time t 1 from the aggregate labor’s share  ofi 1time t .  1,1, ttiti )(  LLlv (7) (7) i1 i1  of time t . K i 1 I further decompose (7) by changes of sectoral value-added shares and labor’s share, K  1,1, I ttiti further)(  LLlv decompose (7) (7) by changes of sectoral value-added shares and labor’s share,  K I furtheri1 decompose I (7)further  by1,1, changes decomposettiti )(  LLlv of (7) sectoral (7) by value-addedchanges of sectoral shares andvalue-added labor’s share, shares and labor’s share, followingI further I further decompose (8) and decompose (9). (7) Inby (9)changes (7) I use by of changes lsectoral,ti to represent value-addedof sectoral , sharesvalue-added Ll tti ,and which labor’s sharesmeans share, andthe following deviationlabor’s (8) share, of the     followingi 1 (8) and (9). In (9) I use l ,ti to represent 1,1, ttiti )( LLlv  Ll (7), which means the deviation of the following (8) and (9). In (9) I use l ,ti to represent ,ti Ll , which means, the deviationtti of the and following(9). In (9) I (8) use and (9).to represent In (9) I l i,tuse–Lit , 1, lwhich totti means represent the deviation ,  Ll tti ,of which the sectoral means labor’s the deviationshare from of the Ifollowingsectoral further decomposelabor’s (8) and share (9). (7) Infrom by (9) changesthe I use aggregate l of,ti sectoral to representlabor’s value-added share , at Ll timetti ,shares which t . andmeans labor’s the deviationshare, of the sectoral labor’s share from the aggregate labor’s share at time t . sectoral labor’s sharethe aggregatesectoral from Ithe labor’sfurther aggregate share sharedecompose at labor’sfromtime t .the (7) share aggregateby changesat time labor’s tof. sectoral share value-addedat time t . shares and labor’s share, sectoral K labor’s share from the aggregate  I furtherlabor’s decomposeshare at time (7) t by. changes of sectoral value-added shares and labor’s share, following (8) and (9). In (9) I use l ,ti to represent , Ll tti , which means the deviation of the K  ,ti   K followingK , (8) and (9). In, (9)ttiiiti )]([][ I use LLllvv l (8) to represent , Ll tti , which means the deviation of the K  sectoral labor’si1 , share from the, aggregatettiiiti )]([][  following LLllvv labor’s (8) share (8) and at time (9). Int . (9) I use l ,ti to represent , Ll tti , which means the deviation of the , , , ttiiiti )]([][  LLllvv (8) , ttiiiti )]([][  LLllvv  sectorali1 , labor’s share from, ttiiiti the)]([][ aggregate LLllvv (8) labor’s share at time t . i1 i1 i1 sectoral labor’s share from the aggregate labor’s share at time t . K K   KK    K , K [ , , ,tiiti ,ttiiiti ti )]([][ LLllvv (8) ,tiiii ]  Llvlvlvlv (9)     K  i1 Ki1[ ,  ,ti , ttiiiti )]([][  LLllvv  (8)]  Llvlvlvlv ,ti  , ,tiiti  ,tiiii  [ , ,tiiti  [ , ,tiiti ,tiiii ],ti Llvlvlvlv (9) ,tiiii ] Llvlvlvlv (9)   ii11[ , ,tiiti ,ti ,tiiii ,]  Llvlvlvlv (9) , ttiiiti )]([][ LLllvv (8) i1 i1  i1 K Therei 1 are four components in the decomposition equation (9): K   [ , There ,aretiiti four,ti components in,tiiii ]the decompositionLlvlvlvlv (9) equation (9): There are four componentsThere(1)There[ are inare fourthelv four: decomposition thecomponentscomponents pure,ti within-sector in in theequation the decompositionK decomposition change] (9): Llvlvlvlv effect (9)equation equation of the (9): labor’s (9): share, given a constant i1 There , are,  fouriti ,tiiti components in the decomposition,tiiii equation (9): (1)i1 , lv iti : the pure within-sector[ change, effect,tiiti ,ofti the labor’s share,,tiiii ] given Llvlvlvlv a (9) constant (1) ,  lv iti : the pure(1)(1) within-sector v , . D llv iti : :the the pure change pure within-sector within-sector effect of change the changelabor’s effect effect share,of the oflabor’sgiven the labor’sshare,a constant given share, a constant given avalue-added constant (1)value-addedi,t,  lv iiti : share the pure as in within-sector time t i1 change effect of the labor’s share, given a constant There are four components in the decomposition equation (9): value-added shareshare asvalue-added asin intime time t t share as in time t Therevalue-added(2) are,ti lv four,ti :share thecomponents deviation as in time inof t thesector decomposition i’s labor’s shareequation from (9): the average level at time t . This  (1) ,  lv iti : the pure within-sector change effect of the labor’s share, given a constant (2)(2) v , ti . llv i,t, ti : :the the deviation deviation of sector of sector Therei ’s labor’s i are’s labor’s sharefour fromcomponents share the fromaverage inthe levelthe average decompositionat time level t. This at timedescribes equation t . This (9): (2)  lv ,ti : the deviation(1)(2) i,t, of lv lv ,sectoriti ti :: the the puredeviationi’s labor’s within-sector of share sector from changei’s the labor’s averageeffect share of level the from labor’s at thetime average share, t . This given level aat constant time t . This ,ti describes,ti  ,sectorti : i’s idiosyncrasy in termsi of its labor income share. t (2) ,ti lv the deviation of sector ’s  labor’s: share from the average level at time . This value-addedsectordescribes i ’s shareidiosyncrasy sector as in timeini ’sterms idiosyncrasyt of its labor(1) inincome terms, share. lv ofiti its the labor pure income within-sector share. change effect of the labor’s share, given a constant (3)  lv : the joint effectt of the sectoral size change and within-sector labor share change describes sector i’svalue-addeddescribes idiosyncrasy sectorsectorii share in termsii ’s’sas idiosyncrasy idiosyncrasyin of time its labor ininincome termsterms share.ofof itsits laborlabor incomeincome share.share. (2) (3)lv ,ti :D v the. D deviationllv : the joint of sector effect i of’svalue-added labor’sthe sectoral share sharesize from change as the in averagetime and within-sectort level at time labor t . This share change (3)  lv : the, ti joint(3)(3) effecti  lv ofiii : the:the the jointsectoral joint effect effect size of the changeof sectoralthe sectoral and size within-sector change size change and within-sectorlabor and sharewithin-sector labor change share labor change share change ii   ii  (2)(3)(4) ,ti lv  lv ,lv ti ,ii ti : :: the the the deviation purejoint effect effect of of sectorof sectoral the sectorali’s sizelabor’s sizechange share change given from and athe constant within-sector average labor’s level labor atshare time share as tin .change This time t  D i.  i,t describes (4)sector vi li ’s : idiosyncrasythe pure effect in of termssectoral(2) of size its  changelaborlv ,ti : the incomegiven deviation a constantshare. of labor’s sector share i’s labor’sas in time share t from the average level at time t . This (4)  lv ,ti : the pure effect of sectoral,ti size change given a constant labor’s share as in time t (4)  lv ,ti : the pure(4) effecti  lv ofK,ti sectoral: the pure size effect change of sectoral given a sizeconstant change labor’s given share a constant as in time labor’s t share as in time t i describesi  sector,ti i’s idiosyncrasy in terms of its labor income share. (3) (4)I  Inotice lv noticeii : i the lv K joint: thelv effect, ti pure 0 ,, of effectandand the thenthen sectoralof thesectoral the decomposition decomposition size size change change can and can begiven within-sector rewritten be rewrittena constant as (10), labor as labor’s (10), share share change as in time t K  K ,ti  describes sector i’s idiosyncrasy in terms of its labor income share. (3)  ilv 1 : the joint effect of the sectoral size change and within-sector labor share change I notice K ii ,ti lv ,ti  0 , and then the decomposition can be rewritten as (10), I notice  lv ,ti  I0 notice, and then  thelv decomposition,ti  0 , and then can the bedecomposition rewritten as (10),can be rewritten as (10), ,ti i1 ,ti ,ti  (3)  lv ii : the joint effect of the sectoral size change and within-sector labor share change i1 (4) iI lv notice,ti : the i pure1 ,ti lv effect0 of, and sectoral then thesize decomposition change given acan constant be rewritten labor’s as share (10), as in time t  (4)  lv i 1,ti : the pure effect of sectoral size change given a constant labor’s share as in time t K i K  (4) i  lv ,ti : the pure effect of sectoral size change given a constant labor’s share as in time t I notice  ,ti lv ,ti  0 , and then the decomposition can be rewritten as (10), i1 I notice  ,ti lv ,ti  0 , and then the decompositionK  can be rewritten as (10), i1 I notice  ,ti lv ,ti  0 , and then the decomposition can be rewritten as (10), i1

9 K  K [  ]  Llvlvlv (10)  , ,tiiiiiti  (10) [ i,1 ,tiiiiiti ] Llvlvlv (10) i1

  Therefore,Therefore, the thecomponents components (1) (1) ,  lv iti , (3)  lv ii , and (4) i  lv ,ti capture capture the the three three types of Therefore, the components (1) ,  lv iti , (3)   lv ii , and (4) i  lv ,ti capture the three types of types of sectoral contribution contribution to to the the aggregate aggregate change change in the in thenational national labor’s labor’s share sharefrom timefrom t timeto t + 1.t to t  .1 sectoral contribution to the aggregate change in the national labor’s share from time t to t  .1 3.2 The 3.2First The Grand First T ransfGrandormation: Transformation: Industrialization Industrialization 3.2 The First Grand Transformation: Industrialization AgricultureAgriculture in many developingin many developing countries has countries very high has labor’s very share. high labor’sIn premodern share. societyIn premodern agricul- society turalAgriculture productionagricultural isin mainly many production conducted developing is mainly by countriesthe conductedfarmers’ has hands byvery thelargely high farmers’ without labor’s hands the share. helplargely Inof premoderncapital-intensive without the society help of agriculturalcapital-intensive production equipment. is mainly After conducted industrialization by the farmers’ is finally hands completed, largely agriculture without the will help become of equipment.capital-intensivea capital-intensive After industrialization equipment. sector is with Afterfinally new industrialization completed, supplies ofagriculture mechanical is finally will equipmentbecome completed, a capital-intensive and agriculture fertilizers sectorfromwill becomethe witha new capital-intensiveindustrial supplies of sector, mechanical sector as evidenced withequipment new by supplies andthe experiencesfertilizers of mechanical from of the OECD industrial equipment countries. sector, and as evidencedfertilizers by from the the experiencesindustrial of OECD sector, Subramanian countries. as evidenced (2008) byraises the concernexperiences about of sluggish OECD wagecountries. growth in China. According to Bai Subramanianand Qian (2009), (2008) labor’s raises share concern in China’s about agriculture sluggish wageis around growth 0.85 inand China. has been According relatively to Subramanian (2008) raises concern about sluggish wage growth in China. According to Bai and Bai stableand Qian from (2009), 1978 to labor’s 2004. Thisshare value in China’s is much agriculture higher than is that around in industry 0.85 and and has services. been relatively In the Qianstable (2009),past from 15labor’s years,1978 share labor’sto in2004. China’s share This agriculture in value industry is ismuch hasaround kept higher 0.85 decreasing andthan has that beenwhereas in relativelyindustry that in stableand the services. servicesfrom 1978 sectorIn the is relatively constant. The joint effect is a significant drop in the aggregate labor share in the to 2004.past This15 years, value labor’sis much sharehigher in than industry that in hasindustry kept anddecreasing services. Inwhereas the past that 15 years,in the labor’s services share sector is national income in recent years, which has provoked concerns and discussions in China. This is relatively constant. The joint effect is a significant drop in the aggregate labor share in the in industryconsistent has kept with decreasing the reported whereas 4 that percentage in the services point sectorreduction is relatively in average constant. wage’s The share joint from effect is national income in recent years, which has provoked concerns and discussions in China. This is a significant1995–2000 drop in tothe 2001–06 aggregate by labor ILO share (2008). in the Nevertheless, national income in light in recent of my years, new whichempirical has provoked findings in consistentsection with 2, the the reduction reported in 4 labor’s percentage share pointat the reductionpresent development in average stagewage’s seems share to frombe concerns1995–2000unavoidable and discussions to 2001–06 and in the China. turningby ILO This point (2008). is consistent should Nevertheless, be with coming the reported invery light soon. 4 ofpercentage myFigure new 7 point empiricalhas shownreduction findings such a in in averagesectionpossible wage’s 2, the sharetrend reduction from from 1995–2000 2003 in labor’s to 2004, to share 2001–06 although at the by I presentILO do not (2008). havedevelopment Nevertheless, the latest stagedata in tolight seems further of myto verify benew this unavoidable and the turning point should be coming very soon. Figure 7 has shown such a empiricalhypothesis. findings in section 2, the reduction in labor’s share at the present development stage seems to be possible trend Shastri from and 2003 Murthy to 2004, (2005) although provide I ado similar not have pattern the inlatest a considerable data to further drop verifyof wage’s this unavoidablehypothesis.share and in theorganized turning Indianpoint should industry be comingbetween very 1973 soon. and Figure 1997. 7 Duringhas shown this such period, a possible labor’s trend share in from 2003the to organized Shastri 2004, althoughand Indian Murthy I industrydo not(2005) have decreased provide the latest bya data similar 19 topercent, further pattern falling verify in a thisfrom considerable hypothesis. 51.7 percent drop to of 32.8 wage’s percent, shareas in shown organized in figure Indian 8. RUPE industry (2008) between points 1973 out that and National 1997. During Sample this Survey period, (NSS) labor’s of 2004–05 share in Shastri and Murthy (2005) provide a similar pattern in a considerable drop of wage’s share in the organizedshows a decline Indian in industry real wages decreased for urban by workers 19 percent, (male falling and female, from regular51.7 percent salaried to and32.8 casual) percent, organizedas shownover Indian the in industryNSSfigure (1999–2000). 8. between RUPE 1973 (2008) Wage and points levels1997. Duringoutof workers that this National period,are declining Samplelabor’s sharenot Survey only in the in (NSS) organizedthe unorganized of 2004–05 Indianshows industrysector a decline but decreased also in in real by the 19 wages organized percent, for falling urbansector. from workers Simultaneously 51.7 percent(male and to the 32.8 female,share percent, of regular profit as shown in salaried value in figure added and casual) in the overorganized the NSS sector(1999–2000). is found Wageto be rising. levels This of workers echoes aare report declining from the not National only in theCommission unorganized on 8. RUPE (2008) points out that National Sample Survey (NSS) of 2004–05 shows a decline in real sectorEnterprises but also in the Unorganizedorganized sector. Sector Simultaneously (NCEUS 2007). the The share wage of share profit in in my value organized added in the wagesorganized forindustrial urban sectorworkers sector is (male foundhas halvedand to female,be after rising. regular the This1980s. salaried echoes Although and a casual)report ILO overfrom (2008) the the NSSdoes National (1999–2000).not provide Commission India’s on WageEnterprises levelswage’s of workers share in the data,are Unorganized declining the average not Sector only real in wage (NCEUSthe unorganized growth 2007). rates sector Thefor the butwage periods also share in the1995–2000 in organized my organized and sector. 2001–07 are reported to be 1 percent and 1.6 percent respectively, significantly lower than the real GDP Simultaneouslyindustrial sectorthe share has of halved profit inafter value the added 1980s. in the Although organized ILO sector (2008) is found does to notbe rising. provide This India’s echoes wage’sgrowth share rates. data, I plot the inaverage figure real9 the wage labor’s growth share ratesof the for Indian the periodseconomy 1995–2000 since 1980, and which 2001–07 confirms such a declining trend. a reportare reportedfrom the Nationalto be 1 percentCommission and 1.6on Enterprises percent respectively, in the Unorganized significantly Sector (NCEUS lower than 2007). the real GDP Thegrowth wage share rates. in I myplot organized in figure industrial 9 the labor’ssector has share halved of theafter Indianthe 1980s. economy Although since ILO 1980, (2008) which does 3.3 The Second Grand Transformation: Toward the Postindustrial Society not confirmsprovide India’s such wage’s a declining share data, trend. the average real wage growth rates for the periods 1995–2000 and 2001–07Following are reported the to industrialization be 1 percent and process,1.6 percent modern respectively, services significantly begin to expand lower than simultaneously. the real GDP 3.3 TheFurthermore, Second Grandat a later Transformation: stage, the share of Towardthe services the sector Postindustrial will continue Society to expand at the growth rates.expense I plot of in industry. figure 9 Thisthe labor’s procedure share isof sometimesthe Indian economycalled deindustrialization. since 1980, which confirmsLabor’s sharesuch a will decliningFollowing trend. the industrialization process, modern services begin to expand simultaneously. Furthermore, at a later stage, the share of the services sector will continue to expand at the expense of industry. This procedure is sometimes called deindustrialization. Labor’s share will

10 3.3 The Second Grand Transformation: Toward the Postindustrial Society

Following the industrialization process, modern services begin to expand simultaneously. Furthermore, at a later stage, the share of the services sector will continue to expand at the expense of industry. This procedure is sometimes called deindustrialization. Labor’s share will keep increasing in this process. Ruiz (2005) presents a detailed analysis for both Spain and the United States from 1955 to 2005 regarding their sectoral value-added size, within-sector labor’s share, and aggregate labor’s share in the national economy. Figure 10 illustrates the evolution of the labor’s share relative to GDP per capita for Spain. In 1955, real GDP per capita in Spain was higher than US$4,000, past my first turning point of US$3,000 derived in section 2. So I think Spain from 1955 to 2005 is a good example to showcase the later stage of industrialization as well as deindustrialization. The Spanish aggregate labor’s share has kept increasing from 1955 to the 1980s. Interestingly, labor’s share in Spain fluctuated for a while in the 1990s and then started a downward trend. The PWT6.2 shows that Spain achieved a real GDP per capita level of US$15,000 in 1990. Therefore, the Spanish case is very consistent with my new panel econometric findings. Spain’s industrial sector was relatively stable at about 30 percent of GDP from 1955 to 1987; since then, it has dropped to about 20 percent, ending in 2005. Spain in 1959 had a relatively smaller services sector at 35 percent of the economy, whilst the United States in 1958 had already developed a services sector as large as 54 percent of the GDP. The share of the Spanish services sector has risen to 59 percent in 2005, which is comparable to the United States in the mid-1980s.

3.4 The Third (Ongoing) Transformation: Financialization and the Recent Rise of the Finance and Real Estate Sectors in Developed Countries

Many researchers have recognized the recent changes in labor’s share in the OECD countries, e.g., Blanchard (1997,1998), Caballero and Hammour (1998), Rodrik (1999), Acemoglu (2002, 2003), Blanchard and Giavazzi (2003), and Bentolila and Saint-Paul (2003). They have examined a variety of potential contributors behind this, including nominal macro factors, institutional differences, labor markets, biased technical change, and monopoly. I exploit the new EU KLEMS database to take a close look at the sectoral evolvement for the OECD countries (the industrial classification in the EU KLEMS is close to ISIC rev. 3). To mitigate short-term fluctuations, I compare the five-year average of 1975–79 period (denoted as 1975 for simplicity) with the 2000–2004 (simply put as 2000). I then average the 16 OECD countries that have data available for 1975–79. Table 4 shows a detailed decomposition of the main sectors. I separate the services sector into financial services and nonfinancial services because these two subsectors have behaved very differently. Column (1) shows the changes in the aggregate labor’s share. I

11 keep increasing in this process. Ruiz (2005) presents a detailed analysis for both Spain and the United States from 1955 keep increasing in this process. to 2005 regarding their sectoral value-added size, within-sector labor’s share, and aggregate Ruiz (2005) presents a detailed analysis for both Spain and the United States from 1955 labor’s share in the national economy. Figure 10 illustrates the evolution of the labor’s share to 2005 regarding their sectoral value-added size, within-sector labor’s share, and aggregate relative to GDP per capita for Spain. In 1955, real GDP per capita in Spain was higher than labor’s share in the national economy. Figure 10 illustrates the evolution of the labor’s share US$4,000, past my first turning point of US$3,000 derived in section 2. So I think Spain from relative to GDP per capita for Spain. In 1955, real GDP per capita in Spain was higher than 1955 to 2005 is a good example to showcase the later stage of industrialization as well as US$4,000, past my first turning point of US$3,000 derived in section 2. So I think Spain from deindustrialization. The Spanish aggregate labor’s share has kept increasing from 1955 to the 1955 to 2005 is a good example to showcase the later stage of industrialization as well as 1980s. Interestingly, labor’s share in Spain fluctuated for a while in the 1990s and then started a deindustrialization. The Spanish aggregate labor’s share has kept increasing from 1955 to the downward trend. The PWT6.2 shows that Spain achieved a real GDP per capita level of 1980s. Interestingly, labor’s share in Spain fluctuated for a while in the 1990s and then started a US$15,000 in 1990. Therefore, the Spanish case is very consistent with my new panel downward trend. The PWT6.2 shows that Spain achieved a real GDP per capita level of econometric findings. US$15,000 in 1990. Therefore, the Spanish case is very consistent with my new panel Spain’s industrial sector was relatively stable at about 30 percent of GDP from 1955 to econometric findings. 1987; since then, it has dropped to about 20 percent, ending in 2005. Spain in 1959 had a Spain’s industrial sector was relatively stable at about 30 percent of GDP from 1955 to relatively smaller services sector at 35 percent of the economy, whilst the United States in 1958 1987; since then, it has dropped to about 20 percent, ending in 2005. Spain in 1959 had a had already developed a services sector as large as 54 percent of the GDP. The share of the relatively smaller services sector at 35 percent of the economy, whilst the United States in 1958 Spanish services sector has risen to 59 percent in 2005, which is comparable to the United States had already developed a services sector as large as 54 percent of the GDP. The share of the in the mid-1980s. Spanish services sector has risen to 59 percent in 2005, which is comparable to the United States in the mid-1980s. 3.4 The Third (Ongoing) Transformation: Financialization and the Recent Rise of the Finance and Real Estate Sectors in Developed Countries 3.4 The Third (Ongoing) Transformation: Financialization and the Recent Rise of the Finance and Real Estate Sectors in Developed Countries Many researchers have recognized the recent changes in labor’s share in the OECD countries, e.g., Blanchard (1997,1998), Caballero and Hammour (1998), Rodrik (1999), Acemoglu (2002, Many researchers have recognized the recent changes in labor’s share in the OECD countries, 2003), Blanchard and Giavazzi (2003), and Bentolila and Saint-Paul (2003). They have e.g., Blanchard (1997,1998), Caballero and Hammour (1998), Rodrik (1999), Acemoglu (2002, examined a variety of potential contributors behind this, including nominal macro factors, 2003), Blanchard and Giavazzi (2003), and Bentolila and Saint-Paul (2003). They have institutional differences, labor markets, biased technical change, and monopoly. examined a variety of potential contributors behind this, including nominal macro factors, I exploit the new EU KLEMS database to take a close look at the sectoral evolvement for institutional differences, labor markets, biased technical change, and monopoly. the OECD countries (the industrial classification in the EU KLEMS is close to ISIC rev. 3). To I exploit the new EU KLEMS database to take a close look at the sectoral evolvement for mitigate short-term fluctuations, I compare the five-year average of 1975–79 period (denoted as the OECD countries (the industrial classification in the EU KLEMS is close to ISIC rev. 3). To 1975 for simplicity) with the 2000–2004 (simply put as 2000). I then average the 16 OECD mitigate short-term fluctuations, I compare the five-year average of 1975–79 period (denoted as countries that have data available for 1975–79. Table 4 shows a detailed decomposition of the 1975 for simplicity) with the 2000–2004 (simply put as 2000). I then average the 16 OECD main sectors. countries that have data available for 1975–79. Table 4 shows a detailed decomposition of the I separate the services sector into financial services and nonfinancial services because main sectors. these two subsectors have behaved very differently. Column (1) shows the changes in the contribution to I theseparate change the of services aggregate sector labor’s into share. financial Industry services reduced and nonfinancial the aggregate services labor’s because  these two subsectors have behaved very differently. Column (1) shows the changes in the aggregate labor’s share. I can see a 3.3 percent average reduction from 1975 to 2000. l i 1975, and share by 2.6 percent. Moreover, the effect of )1( , lv iti for industry dominates other effects.   This givesaggregate strong labor’ssupport share. that biased I can seetechnicalcan a 3.3 see percent achange, 3.3 percent average i.e., average labor-saving reduction reduction fromtechnical from 1975 1975 innovations to to 2000. 2000. l i 1975, and and l i 2000, represent represent the the deviation deviation of the sectoral labor’s share from the aggregate labor’s share in could have been the major cause of the decreaseof the sectoral in labor’s labor’s share from within the industry,aggregate labor’sas argued share by in year 1975 yearand 20001975 respectively. and 2000 respectively.The The further decomposition of the sectoral effects into Acemoglul i 2000, (2002, represent 2003). the deviation of the sectoral labor’s share from the aggregate labor’s share in )4(),3(),2(),1( follows the definitions in section 3.1. The sum of )4(),3(),1( , as shown in the further decomposition of the sectoral effects into (1), (2), (3), (4) follows the definitions in section 3.1. year During 1975 the and same 2000 period, respectively. the financial The furtherservices decomposition also had a significant of the sectoral impact effectson the into bottom row, illustrates the sectoral contribution to the change in labor’s share between 1975 and aggregate labor’s share)4(),3(),2(),1( follows by reducing the definitions it byThe 1.65 sum in percent. sectionof (1), (3),Notably, 3.1. (4), The as thisshownsum effect of in the mainly bottom )4(),3(),1( comes ,row, as shownillustrates from in thethe sectoral2000. contribution Although toagriculture the change has the lowest labor’s share, its relative size in the economy is very  bottom row, illustrates the sectoralin contributionlabor’s share between to the change1975 and in 2000. labor’s Although share betweenagriculture 1975 has the and lowest small labor’s (5.9 percentshare, its inrelative 1975 and down to 2.2 percent in 2000). Labor’s share in the financial the effect of sectoral size change )4( i  lv ,ti by -2.44 percent. That is, the financial sector 2000. Although agriculture has the lowest labor’s share, its relative size in the economy is very services sector is around 35 to 38 percent, which is more than 30 percent lower than the industry lessened the aggregate labor’s share mainlysize indue the to economy its relative is very size small expansion (5.9 percent in the in 1975 economy. and down I to 2.2 percent in 2000). Labor’s share small (5.9 percent in 1975 and down to 2.2 percent in 2000). Labor’s share in the financial and the nonfinance services. can see from the row  2000-1975 , inthe the value-added financial services share sector of the is financialaround 35 servicesto 38 percent, sector which is more than 30 percent lower than the services sector is around 35 to 38 percent, which is more than 30 percent lower than the industry From table 4, I can see agriculture in these developed countries has had a positive gained andin more the nonfinance than 10 percent services. from theindustry total economy and the nonfinancemainly at theservices. expense of the industry (–8.9 percent). Interestingly, the contributors in these two sectors are disparate: For industry, it is From table 4, I can see agricultureFrom in table these 4, Ideveloped can see agriculture countries in thesehas had developed a positive countries has had a positive contribution through within-sector change of labor intensity; for the financial sector, it is due to the relative increase of the value-added share in the toeconomy. the change of aggregate labor’s share. Industry reduced the aggregate labor’s share by 2.6 percent. . D To understand movements withinMoreover, the financial the effect services, of (1) vIi,t decompose li for industry it further dominates and showother effects. This gives strong support that the subindustry statistics in table 5. biased technical change, i.e., labor-saving technical innovations could have been the major cause of the Real estate activities (corresponding to the ISIC rev. 3 industrial code 70) have an extremely low value in terms of labor’s decreaseshare (6 in percent). labor’s share Moreover, within industry, the real as estate argued sector by Acemoglu is (2002, 2003). found to be the main cause of labor’s share dropDuring within the samethe financial period, the services financial (–1.84 services percent). also had a significant impact on the aggregate labor’s Once again, the expansion of the size of sharethe real by reducing estate sector it by 1.65 is the percent. dominant Notably, factor this that effect mainly comes from the effect of sectoral size  contributes to the drop in labor’s share, i.e.,change (4))4( i  lv ,ti by by –2.44 (–1.75 percent. percent). That is, the financial sector lessened the aggregate labor’s share In sum, sectoral analysis in this sectionmainly duegenerally to its relative confirms size expansion my previous in the findings economy. and I can see from the row D [1975–2000], the helps us to understand the disparate dynamicsvalue-added behind share these of the three financial types servicesof grand sector economic gained in more than 10 percent from the total economy transformations at different development stages. mainly at the expense of the industry (–8.9 percent). Interestingly, the contributors in these two sectors 4 EVIDENCE FROM THE ECONOMICare disparate: HISTORY For industry, it is through within-sector change of labor intensity; for the financial sector, it is due to the relative increase of the value-added sharecontribution in the economy. to the change of aggregate labor’s share. Industry reduced the aggregate labor’s Modern growth theory is largely built upon the empirical facts of the United Kingdom and the share by 2.6 percent. Moreover, the effect of )1( , lv iti for industry dominates other effects. United States since the beginning of the 20th Tocentury. understand Most movements of the recent within revisits the financial of the problemservices, I decompose it further and show the This gives strong support that biased technical change, i.e., labor-saving technical innovations on labor’s share only cover OECD countriessubindustry after WWII. statistics The in table earliest 5. GDP data available in the could have been the major cause of the decrease in labor’s share within industry, as argued by PWT is in 1950, when the United States had reached a per capita GDP level of US$11,233 and Real estate activities (corresponding to the ISICAcemoglu rev. 3 industrial (2002, code 2003). 70) have an extremely low the United Kingdom arrived at US$8,081. The economic development level of both the United value in terms of labor’s share (6 percent). Moreover, the real During estate sector the same is found period, to be the mainfinancial cause services also had a significant impact on the States and United Kingdom has been well above the first turning point of US$3,000. No wonder of labor’s share drop within the financial services (–1.84aggregate percent). labor’s Once share again, by the reducing expansion it ofby the 1.65 size percent.of Notably, this effect mainly comes from the relative constancy of labor’s share has been observed by many prominent researchers. In this  section, I will try to make use of the evidencethe real in estate the economicsector is the history dominant to factorexamine that whether contributesthe effect my to theof sectoraldrop in labor’s size change share, i.e., (4))4( i  lv ,ti by -2.44 percent. That is, the financial sector new empirical findings are equally applicable to these developed countries in an early stage of by (–1.75 percent). lessened the aggregate labor’s share mainly due to its relative size expansion in the economy. I development. In sum, sectoral analysis in this section generallycan confirms see from my the previous row findings and2000-1975 helps , theus value-added share of the financial services sector gained in more than 10 percent from the total economy mainly at the expense of the industry 4.1 The United Kingdom, 1500–2004 to understand the disparate dynamics behind these three types of grand economic transformations at (–8.9 percent). Interestingly, the contributors in these two sectors are disparate: For industry, it is different development stages. The first industrial revolution in human history originated in the United Kingdom in thethrough later partwithin-sector change of labor intensity; for the financial sector, it is due to the relative of the 18th century. As Landes (1969) summarizes, “… In the eighteenth century, a seriesincrease of of the value-added share in the economy. inventions transformed the manufacture of cotton in England and gave rise to a new mode or To understand movements within the financial services, I decompose it further and show production—the factory system … These improvements constitute the Industrial Revolution.”the subindustry statistics in table 5. Real estate activities (corresponding to the ISIC rev. 3 industrial code 70) have an extremely low value in terms of labor’s share (6 percent). Moreover, the real estate sector is found to be the main cause of labor’s share drop within the financial services (–1.84 percent). Once again, the expansion of the size of the real estate sector is the dominant factor that  contributes to the drop in labor’s share, i.e., )4(  lv ,ti by (–1.75 percent). 12 i In sum, sectoral analysis in this section generally confirms my previous findings and helps us to understand the disparate dynamics behind these three types of grand economic transformations at different development stages.

4 EVIDENCE FROM THE ECONOMIC HISTORY

Modern growth theory is largely built upon the empirical facts of the United Kingdom and the United States since the beginning of the 20th century. Most of the recent revisits of the problem on labor’s share only cover OECD countries after WWII. The earliest GDP data available in the PWT is in 1950, when the United States had reached a per capita GDP level of US$11,233 and the United Kingdom arrived at US$8,081. The economic development level of both the United States and United Kingdom has been well above the first turning point of US$3,000. No wonder the relative constancy of labor’s share has been observed by many prominent researchers. In this section, I will try to make use of the evidence in the economic history to examine whether my new empirical findings are equally applicable to these developed countries in an early stage of development.

4.1 The United Kingdom, 1500–2004

The first industrial revolution in human history originated in the United Kingdom in the later part of the 18th century. As Landes (1969) summarizes, “… In the eighteenth century, a series of inventions transformed the manufacture of cotton in England and gave rise to a new mode or production—the factory system … These improvements constitute the Industrial Revolution.” 4 Evidence from the Economic History

Modern growth theory is largely built upon the empirical facts of the United Kingdom and the United States since the beginning of the 20th century. Most of the recent revisits of the problem on labor’s share only cover OECD countries after WWII. The earliest GDP data available in the PWT is in 1950, when the United States had reached a per capita GDP level of US$11,233 and the United Kingdom arrived at US$8,081. The economic development level of both the United States and United Kingdom has been well above the first turning point of US$3,000. No wonder the relative constancy of labor’s share has been observed by many prominent researchers. In this section, I will try to make use of the evidence in the economic history to examine whether my new empirical findings are equally applicable to these developed countries in an early stage of development.

4.1 The United Kingdom, 1500–2004

The first industrial revolution in human history originated in the United Kingdom in the later part of the 18th century. As Landes (1969) summarizes, “… In the eighteenth century, a series of inventions trans- formed the manufacture of cotton in England and gave rise to a new mode or production—the factory system … These improvements constitute the Industrial Revolution.” Lindert and Williamson (1983) conducted the first rigorous economic analysis of the English worker’s living standards during the Industrial Revolution. Their new evidence endorsed an optimistic view of a rapid rise of the workers’ real wages. Recently economic historians have discovered new evidence supporting the viewpoint of real average wage stagnation relative to the output during the industrial revolution of the United Kingdom. Feinstein (1998) estimates that over about 80 years from 1770 to 1850, the increase in real earnings was less than 30 percent (his estimates were at 10 to 15 percent). Figure 11 (from Allen 2007) demonstrates an obvious lag between the real wage growth and output growth: The real wage index rose by only 12 percent between 1780 and 1840, while the output per worker rose by 46 percent. Allen (2007) also discusses the long-term evolution of the functional distribution of the British national income for the same period. As demonstrated by the dotted line in figure 12, the labor’s share dropped from above 60 percent at the end of the 18th century to below 50 percent in the middle of the 19th century, whereas the profit’s share increased from 20 percent to nearly 50 percent. “Engels’s pause” happened here, that is, the real wage lagged behind the rapid growth of output per worker. However, this “pause” changed dramatically from 1840 to 1900, during which the real wage increased by 123 percent and output per worker went up by only 90 percent. The U-Shape pattern in the movements of labor’s share during the British Industrial Revolution is consistent with my panel regression findings using modern-time data for a large number of countries

13 at various development levels. The United Kingdom transformed from a premodern agricultural society to an industrialized economy starting in the late 18th century in a similar way that many newly industrialized economies (NIEs) and developing countries have experienced about 200 years later, though it might have taken the United Kingdom a longer time to finish. According to Allen (2000), the share of labor force in UK agriculture went down from more than 70 percent in 1500 via 55 percent in 1700 to 35 percent in 1800. In 1850, agriculture of the United Kingdom employed one-quarter of the labor force (Clark and Werf 1998). Economic historians have debated for a long time about the timing of agricultural revolution in the United Kingdom as well as its relationship with the Industrial Revolution. The “revisionists” like Allen (1999) offer new evidence supporting an earlier occurrence of the agricultural revolution that can be dated back to the 1500s. They see the rise of agricultural productivity and output had facilitated the debouchment of the Industrial Revolution. In fact, this view echoes many prominent researchers in the growth and development literature, as by Jorgenson (1961, 1967), Matsuyama (1992), and most recently Gollin, Parente, and Rogerson (2002, 2007), who emphasize the importance of food problems and the essential effect of the agricultural revolution on releasing the much-needed resources to the juvenile modern economic sector. An up-to-date example is unquestionable impact of the green revolution on development. I will build a growth model in section 5 following this line of argument. Most recently, according to the EU KLEMS database, the United Kingdom reached its peak of labor’s share in 1975 at 70 percent. Using five-year averages, its share decreased from 67 percent (1975–79) to 63 percent (2000–2004). During the same period, its financial sector remarkably increased from 13 percent of GDP to 30 percent. The labor’s share within the financial sector went down from 51.7 percent to 46.9 percent, which is significantly lower than the aggregate labor’s share in the national economy. In short, the full development process of the first industrial economy in human history presents a perfect example of the cubic relationship between the labor’s income and the average income level.

4.2 The United States, 1790–1900

Is the United States special? A brief answer is no. My major data sources are the US Census Bureau (1975) and Carter et al. (2006), which cover a wide range of economic time series dating back to the colonial times. I illustrate the historical evolution of the American labor’s income and per capita GDP level in figure 13. To make the long-run data series consistent, I use the wage share in the national income as a proxy of labor’s share. In the beginning of these time series, the GDP per capita of the United States was at US$1,200 (in 2000 constant US dollars) in 1790, and then gradually rose to US$3,000 (the supposed turning point)

14 toward the end of the 1870s. The US economy experienced a phenomenal industrialization during the second half of the 19th century. In 1860, more than 60 percent of the total labor force was still employed on farms, which were producing 35 percent of the total GDP, and the per capita GDP level was at US$2,300. My calculation shows that the ratio of all workers’ wages to the GDP was around 70 percent then. Ten years later (in figure 13 I interpolate and connect 1860 and 1870 labor’s share points with a dotted line, due to the lack of data in between), this ratio went down to 60 percent ending in 1870. Labor’s share continued to decline to below 50 percent in 1880. From then on this downward trend was just reversed. In the next 10 years, from 1880 to the 1890s, the wage’s share in GDP gained 10 percent, gradually returning to 60 percent. In 1900 the share of farms’ value added in GDP decreased to 20 percent. Since 1900, the wage’s share in GDP has been stabilized at around 65 percent (except for the period of the Great Depression), during which time the Kaldor Fact had been generally applicable. Therefore, the United States was not very different from other countries in terms of the industrialization process, although the United States completed it in a faster pace than the United Kingdom and much earlier than most of the other countries. For the modern part of US economic development, a Solow growth model with a constant labor’s share of 65 percent could be a very good approximation of the real economy (good enough for modern economic analysis and forecast); however, when I need to seriously study the premodern and industrialization stages of the American economy, I probably cannot take the constancy of labor’s share for granted and might want to further scrutinize the historical data.

4.3 Japan, 1955–2000

Japan’s postwar economic development also defies the constancy of the labor’s share. I draw the Japanese labor’s share and real GDP per capita for the post WWII period in figure 14. In 1955, the labor’s share in the national income of Japan was as low as 44 percent, and its GDP per capita was at US$3,100, exactly surpassing the first turning point. In 40 years, Japan’s aggregate labor’s share had risen to 61 percent ending in 1998, according to the Japanese official sources. In addition, very comparable to other highly developed countries, the value-added share of Japan’s finance, insurance, real estate, and business services sector increased from 15 percent to 25 percent from the end of the 1970s to 2000.

4.4 Summary

The generalized fact of the cubic form movements in labor’s share is not only applicable to nowadays developing countries: It seems to describe a universal story of economic transformations, no matter when it happened, be it the late 1700s in the United Kingdom, the second half of 19th century in the United States, the 1950s through the 1970s in Japan, the 1970s through the 1990s in Korea, or the present in China and India.

15 nowadays developing countries: It seems to describe a universal story of economic transformations,nowadays developing no matter countries: when Itit seemshappened, to describe be it the a lateuniversal 1700s story in the of United economic Kingdom, the secondtransformations, half of 19th no centurymatter when in the it United happened, States, be theit the 1950s late 1700sthrough in thethe 1970sUnited in Kingdom, Japan, the the 1970s throughsecond half the of1990s 19th in century Korea, in or the the United presentnowadays States, in China thedeveloping and1950s India. throughcountries: the It seems1970s to in describe Japan, athe universal 1970s story of economic through the 1990s in Korea, or the presenttransformations, in China and no India. matter when it happened, be it the late 1700s in the United Kingdom, the nowadays developing countries: It seems to describe a universal story of economic second half of 19th century in the United States, the 1950s through the 1970s in Japan, the 1970s transformations, no matter when it happened, be it the late 1700s in the United Kingdom, the nowadays developing countries:through the It seems 1990s toin describeKorea, or a theuniversal present story in China of economic and India. second half of 19th century in the United States, the 1950s through the 1970s in Japan, the 1970s 5 TOWARD A GROWTHtransformations, MODEL no matter OF whenUNBALANCED it happened, be TRANSFORMATION it the late 1700s in the United Kingdom, the 5 TOWARD A GROWTH MODEL OF UNBALANCEDthrough TRANSFORMATION the 1990s in Korea, or the present in China and India. 5 Tow ard a Growthsecond Mod halfel of of 19thUnb centuryalanc ine dthe T rUnitedansfor States,ma ttheion 1950s through the 1970s in Japan, the 1970s

In this section, I buildthrough a neoclassical the 1990s in two-sectorKorea,5 TOWARD or the growth present A GROWTH model in China based andMODEL India.on CES OF productionUNBALANCED function. TRANSFORMATION In thisThisIn section,this model section, I buildintends I abuild neoclassical to explaina neoclassical two-sector the nonlinear two-sector growth and model growthnonmonotonous based model on CES based productionmovements on CES function. ofproduction labor’s This share function. 5 TOWARD A GROWTH MODEL OF UNBALANCED TRANSFORMATION modelduringThis intends model long-run to intendsexplain growth, the to nonlinearexplain especially the and nonlinear nonmonotonousduringIn this structural and section, nonmonotonous movements transformations. I build a ofneoclassical labor’s movements Ishare take two-sector during the of firstlabor’s long-run growth grand share model based on CES production function. during long-run growth,5 TOWARD especially A GROWTH duringThis structural modelMODEL intends transformations. OF UNBALANCEDto explain the Inonlinear take TRANSFORMATION the andfirst nonmonotonous grand movements of labor’s share growth,transformation especially during as my structural baseline transformations. case and build I take an explicitthe first modelgrandIn this transformation to section, explore I buildthe as mechanism amy neoclassical baseline behind two-sector growth model based on CES production function. transformation as my baseline case and duringbuild anlong-run explicit growth, model especially to explore during the structuralmechanism transformations. behind I take the first grand this important structural change, i.e., from the premodern agriculturalThis model intendssociety to to explain the industrial the nonlinear and nonmonotonous movements of labor’s share case thisand importantbuild an explicit structuralIn model this section,change, to explore I i.e.,build the from mechanismatransformation neoclassical the premodern behind two-sector as thismy agricultural baselineimportant growth case modelstructural society and basedbuild tochange, theanon explicitCES industrial i.e., production model to function. explore the mechanism behind economy. during long-run growth, especially during structural transformations. I take the first grand This model intends to explainthis important the nonlinear structural and change,nonmonotonous i.e., from movements the premodern of labor’s agricultural share society to the industrial from economy. the premodern agricultural society to the industrial economy. transformation as my baseline case and build an explicit model to explore the mechanism behind during long-run growth,economy. especially during structural transformations. I take the first grand this important structural change, i.e., from the premodern agricultural society to the industrial 5.1 Consumer’s Problemtransformation as my baseline case and build an explicit model to explore the mechanism behind 5.1 Consumer’s Problem economy. 5.1 C onsumer’s Problemthis important structural change, i.e., from the premodern agricultural society to the industrial 5.1 Consumer’s Problem I specify the consumer’seconomy. preference structure in terms of Engel’s law, one of the most robust I specify the consumer’s preference structure in terms of Engel’s5.1 Consumer’s law, one Problemof the most robust I specifyempirical the consumer’s findings preference in economics. structure Recent in termsI specifyformulations of Engel’s the consumer’s law, along one ofthis preference the line most include robust structure Kongsamut,empirical in terms of Rebelo, Engel’s law, one of the most robust andempirical Xie (2001), findings and5.1 in Gollin, Consumer’seconomics. Parent RecentProbleme, andempirical formulationsRogerson findings (2007). along in economics.I thistake linea preference includeRecent formulations Kongsamut, form very alongclose Rebelo, this to line include Kongsamut, Rebelo, findings in economics. Recent formulations along this line include Kongsamut,I specify theRebelo, consumer’s and Xie preference (2001), structure in terms of Engel’s law, one of the most robust and Xie (2001), and Gollin, Parente, andand Rogerson Xie (2001), (2007). and Gollin, I take Parente, a preference and Rogerson form very (2007). close I take to a preference form very close to and Gollin,Gollin, Parente,Parente, and and Rogerson Rogerson (2007). (2007). I take Typical a preference infinite-lived form veryempirical closehouseholds to Gollin,findings have Parente, in preferenceseconomics. and Recent as formulations along this line include Kongsamut, Rebelo, Gollin, Parente, andI specify Rogerson the consumer’s (2007). TypicalGollin, preference Parente, infinite-lived structure and Rogerson in households terms of(2007). Engel’s have Typical law, preferences oneinfinite-lived of the as most households robust have preferences as (11), and Xie (2001), and Gollin, Parente, and Rogerson (2007). I take a preference form very close to Rogerson(11), (2007). Typicalempirical infinite-lived findings households in economics.(11), have preferences Recent formulations as (11), along this line include Kongsamut, Rebelo, Gollin, Parente, and Rogerson (2007). Typical infinite-lived households have preferences as  and Xie (2001), and Gollin, Parente, and Rogerson (2007). I take a preference form very close to t  (11),   Gollin,tt ),( dtmaueU Parente, and Rogerson (2007).t Typical infinite-lived households have preferences as 0 t  tt ),( dtmaueU (11)  tt ),( dtmaueU (11) 0 0 (11),  t  tt ),( dtmaueU (11) 0  t  tt ),( dtmaueU (11)  0      at ,    at ,  t aaif   t  aaif   1a ,   mau tt ),(  t    (12) mau tt ),(   1    (12)  mt 1 t aaif mt 1        a , mau tt ),(  m111 a    1 a   t  aaif   t t ? aaif   t ?aaif   t   mau tt ),(   1   (12)  1 a  mt 1  t ? aaif    at ,  aaif   1  a   t  t ?aaif  mau tt ),(   1    (12) mt 1 Consumption is composed of two goods, which are both in per capita terms, the Consumption is composed 1 ofa two goods, which are both in per capita terms, the Consumption is composed of two goods, whicht ?aaif are both in per capita terms, the traditional Consumption is composed of twotraditional goods, whichagricultural are both goods in Consumption aper and capita the modern terms, is composed goodsthe ofm two (composed goods, which of manufactures are both in perand capita terms, the agriculturaltraditional goods agricultural a and the modern goods goodsa and m (composed the modern of manufacturesgoods m (composed and traditional of manufactures services). This andis traditional agricultural goods a and thetraditional modern services).goods m Thistraditional (composed is a simplified agricultural of manufactures version goods of thea andEngel’s the modernlaw, combining goods m a subsistence (composed of manufactures and traditional services). This Consumption is a simplified is levelcomposed version of food ofof consumptionthetwo Engel’sgoods, which law,and a are combiningstandard both in constant per a subsistencecapita relative terms, risk the aversion (CRRA) preference. a simplifiedtraditional version services). of the ThisEngel’s is law, a simplified combining versiona subsistence of the level Engel’s oftraditional food law, consumption combiningservices). and This a a subsistence standardis a simplified version of the Engel’s law, combining a subsistence level of food consumptiontraditional and agricultural a standard goods constant a and relative the modern risk goodsaversion m (CRRA) (composed preference. of manufactures and  level of food consumption and a standard constant relative risk aversion (CRRA) preference. constantlevel relative of food risk consumption aversiontraditional (CRRA and services).) preference. a standard ThisBefore Before isconstant a simplified a a threshold threshold relative version a riskis is reached, reached,of aversion the Engel’s which which (CRRA) islaw, is the the combining subsistence preference.subsistence a subsistence level, all household consumption is Before a threshold a is reached, which is the subsistence level, all household consumption is level of food consumption and a standard constant relative risk aversion (CRRA) preference. level,Before all household a threshold consumption a is reached, is concentrated whichconcentrated in is agricultural the subsistence in goods. agricultural Beforelevel,After the goods. alla threshold thresholdhousehold After thea isconsumption isthreshold reached, reached, whicha isis reached, is the subsistence consumption level, of all household consumption is     consumptionconcentrated of agricultural in agriculturalBefore goods a threshold is goods. kept at After a. is reached,the threshold which isa the concentrated is subsistencereached, consumption inlevel, agricultural all household ofgoods. consumption After the threshold is a is reached, consumption of  agricultural goods is kept at a . concentrated in agricultural goods. After the threshold a is reached, consumption of agricultural goods concentratedis kept at a in. agricultural goods. After the thresholdagricultural a goods is reached, is kept consumption at a . of 5.2 Producer’s agricultural Problem goods is kept at a . 5.2 Producer’s Problem agricultural goods is kept at a . 5.2 Producer’s Problem 5.2 Producer’s Problem There5.2 are Producer’s two production Problem sectors in the economy:There the agriculturalare two production sector and sectors the inmodern the economy: sector. Due the to agricultural sector and the modern sector. 5.2 Producer’s ProblemDue to nonlinearity of the utility function and limited agricultural productivity in the premodern nonlinearity of the utility function and limited agricultural productivityThere in the are premodern two production era, all sectors labor in the economy: the agricultural sector and the modern sector. There are two production sectors in the era,economy: all labor the is employedagricultural in agriculture. sector and With the modernthe improvement sector. of agricultural technology, a Due to nonlinearity of the utility function and limited agricultural productivity in the premodern is employedThereDue to are nonlinearityin agriculture.two productionThere ofWith the are the sectorsutility two improvement production functionin the economy: ofsectorsand agricultural limited in thethe agriculturaleconomy:technology, the a sectorproductivitymodernagricultural and sector the sector in can modern the growand premodern the sector. modern sector. era, all labor is employed in agriculture. With the improvement of agricultural technology, a era,Due allto nonlinearitylabor is employedDue of tothe nonlinearity inutility agriculture. function of the With utilityand thelimited function improvement agricultural and limited of productivityagricultural productivity technology,in the premodern in athe premodern by absorbing the released labor from agriculture. My framework is purely neoclassical and assumes equal era, all labor is employedera, all labor in agriculture. is employed With in agriculture. the improvement With the improvement of agricultural of agricultural technology, technology, a a marginal productivity of labor across sectors. I adopt CES production functions for the two sectors. For simplicity, I assume Hicks-neutral technologies. Population dynamics are also assumed away.

16 nowadays developing countries: It seems to describe a universal story of economic transformations, no matter when it happened, be it the late 1700s in the United Kingdom, the second half of 19th century in the United States, the 1950s through the 1970s in Japan, the 1970s through the 1990s in Korea, or the present in China and India.

5 TOWARD A GROWTH MODEL OF UNBALANCED TRANSFORMATION

In this section, I build a neoclassical two-sector growth model based on CES production function. This model intends to explain the nonlinear and nonmonotonous movements of labor’s share during long-run growth, especially during structural transformations. I take the first grand modern sectormodern can grow sector by can absorbing growtransformation by the absorbing releasedmodern as my thelabor baselinesector released from can agriculture.case labor grow and from by build absorbing Myagriculture. an framework explicit the My released model is framework to labor explore fromis the agriculture. mechanism My behind framework is modern sector can grow by absorbing the released laborpurely from neoclassical agriculture.purelymodern neoclassicaland sector My assumes framework can grow thisand equal importantassumes by is marginal absorbing equalpurely structural productivity themarginal neoclassical released change, productivityof labor labori.e., and from assumesacross of theagriculture. laborsectors. premodernequal across marginalI adoptMy sectors.agricultural framework CES productivity I adopt society is CES of to labor the acrossindustrial sectors. I adopt CES purely neoclassical and assumes equal marginal productivityproduction of functionslaborproductionpurely across neoclassical for functions sectors.the two economy.and Isectors. foradopt assumes the CES twoFor simplicity,equalsectors.production marginal For Ifunctions simplicity,assume productivity Hicks-neutral for I assumethe oftwo labor Hicks-neutralsectors. technologies. across For sectors. simplicity, technologies. I adopt I assume CES Hicks-neutral technologies. production functions for the two sectors. For simplicity,Population I assume dynamicsPopulationproduction Hicks-neutral are dynamicsfunctions also technologies. assumed forare thealso away. two assumed sectors.Population away. For dynamics simplicity, are I assumealso assumed Hicks-neutral away. technologies. Population dynamics are also assumed away. Population dynamics5.1 are Consumer’s also assumed Problem away. 5.2.1 The5.2.1 Agricultural5.2.1 The The Agricultural Agricultural Sector Sandector theSector and Premodern the and5.2.1 Premodern the The PremodernSociety Agricultural Societ y Society Sector and the Premodern Society 5.2.1 The Agricultural Sector and the Premodern Society 5.2.1 The AgriculturalI specify Sector the andconsumer’s the Premodern preference Society structure in terms of Engel’s law, one of the most robust The production function for the agricultural sector is modeled by (13), in a CES form. Two factors are The productionThe function production for functionthe empiricalagricultural for the findings sectoragriculturalThe production inis economics.modeled sector function by is Recent(13),modeled forin formulations athe byCES agricultural(13), form. in a alongTwo CES sector thisform. isline modeledTwo include by Kongsamut, (13), in a CES Rebelo, form. Two The production function for the agricultural sector is modeledrequired byThe (13), forproduction in the a CESproduction: functionform. landTwo for N theand agriculturallabor L . The sector elasticity is modeledof substitution by (13), between in a landCES and form. labor Two factors are requiredfactors arefor requiredthe production:and for Xiethe landproduction:(2001), factorsN and and a landGollin, arelabor requiredN Parente,L anda . The forlabor elasticityandthe Lproduction:Rogersona . The of elasticitysubstitution (2007). land ofNI take substitution and a laborpreference La . The form elasticity very close of substitutionto factors are required for the production: land N andbetween labor L inlanda . agricultureThebetweenfactors and elasticity labor are landis s requiredin , ofandaagriculture constant substitution laborGollin, for Accordingthein is agriculture Parente, production:  , a betweento constant andthe is seminal land Rogerson land., a AccordingN workconstant and and (2007). laborof laborArrow. to Accordingin Typicalthe agricultureetL aal.seminal. The(1961), infinite-lived toelasticity worktheis as wellseminal of, aasof constant households thesubstitution work recent .of According have preferences to the seminal as work of between land and labor in agriculture is  , a constant. Accordingbetween to the land seminal and laborwork inof agriculture is  , a constant. According to the seminal work of Arrow etempirical al. Arrow(1961), findings et as al. well (1961), of asDuffy the(11), as recent welland Papageorgiou as empirical theArrow recent findings(2000), et empirical al. (1961),and of Duffy Antrasfindings as well (2004),and of asPapageorgiou Duffy Ithe can recent assume and Papageorgiou empirical (2000),the elasticity findings of (2000), of Duffy and Papageorgiou (2000), Arrow et al. (1961), as well as the recent empirical findingsand Antras of Duffy (2004),andArrow Antras and Iet can Papageorgioual. (2004), assume(1961), I asthecan well (2000),elasticity assume as the theand of recent elasticitysubstitution Antras empirical (2004), of issubstitution belowfindings I can 1,assume ofespecially is Duffy below the and elasticity1, for especially Papageorgiou countries of substitution for countries (2000), is below 1, especially for countries substitution is below 1, especially for countries at the stage of transformation from the agricultural society and Antras (2004), I can assume the elasticity of substitutionat the stage is belowofatand transformationthe Antras 1,stage especially (2004),of transformation from forI can countriesthe assume agricultural tfrom theat the elasticity societyagriculturalstage of ofto transformation substitutionthe society modern: to isthe from below modern: the 1,).1,0[ agricultural especially   ).1,0[ for society countries to the modern:   ).1,0[  tt ),( dtmaueU (11) ).1,0[ at the stage of transformation from the agricultural society to tothe theat modern: modern:the stage  of transformation).1,0[ . 0 from the agricultural society to the modern:   ).1,0[       1   1     1 1  1  1     1     1   1  NAY   L ])1([ (13)   1 aa  NAY   La ])1([ (13)  1  1  aa aa  NAY  a1   La 1 ])1([  (13)  NAY    L  ])1([  1 (13)  NAY    L  ])1([  1 (13) aa a aa a     at ,  aaif  Agricultural t technology grows at exogenous speed g , Agricultural Agriculturaltechnology growstechnology at exogenous growsmau tt ),(   at speed1 exogenous ga , speed  (12)g , a mt 1 a Agricultural technology grows at exogenous speed g , AgriculturalAgricultural technology technology grows at grows exogenous at1 exogenous speed a g , speed ga , a  a t ?aaif       A tg Aa A a tg tg a a a  (14) a tg (14) ,  eAAg (14) , ataa 0,, , eAAg ataa 0,,  eAAg Consumption (14) is composedataa 0,, of two goods, which are both in per capita terms, the Aa a tg Aa ataa 0,, a tg ,  eAAg (14) Aa A ,  eAAg (14) Aa ataa 0,, a ataa traditional0,, agricultural goods a and the modern goods m (composed of manufactures and Aa Aa traditional services). This is a simplified version of the Engel’s law, combining a subsistence 5.2.2 The Modern Sector, Grand Transformation,5.2.2 The and Modern Modern Sector, Economic Grand Growth Transformation, and Modern Economic Growth 5.2.25.2.2 The The Modern Modern Sect or,levelSector, Grand of foodGrand Transf consumption ormation,Transformation, andand Moderna standard and ModernEconomic constant Economic G relativerowth riskGrowth aversion (CRRA) preference. 5.2.2 The Modern Sector, Grand Transformation, and Modern5.2.2 Economic The Modern Growth Sector, Grand Transformation, and Modern Economic Growth  After the threshold of agriculturalBefore aconsumption threshold a is is reached reached, at time which T, the is themodern subsistence sector emerges level, andall household consumption is  After the thresholdAfter the of thresholdagricultural of consumptionagriculturalAfter consumption a the is reached threshold a at is timeof reached agricultural T , theat time modern consumption T , sectorthe modern a is sector reached at time T , the modern sector After the threshold of agricultural consumption a isemerges reached someand at emergesAfter timesome portion the Tportion ,andof thresholdthe the somemodern oflabor the portion concentratedofforce labor sectoragricultural starts forceof theto mitigatestartsin emergeslabor consumption agricultural to force to mitigate andthe starts modernsome goods. a to to isportionthe mitigatesector. reachedAfter modern The ofthe toatthe factorthresholdsector. thetime labor modern marketTThe force, thea factorsector. always starts ismodern reached, clears toThe sectormitigate tofactor consumption to the modern of sector. The factor emerges and some portion of the labor force starts to mitigate to emergesthe modern and sector. some portionThe factor of the labor force starts to mitigate to the modern sector. The factor modern sector canmarket grow always getby (15).marketabsorbing clears l = always L to /the Lget, andreleased clears(15). l = toL labor get/ L. aa (15). /fromLLl , andmarket agriculture. always/ LLl mm , and/ MyLLl clears. framework to get/ LLl (15).. is aa / LLl , and mm / LLl . marketa alwaysa clearsmagricultural tom get (15). goods is aa kept/ LLl , atand a . mm / LLl . market always clears to get (15). purelyaa / LLl neoclassical, and  mm and/ LLl assumes. market equal always marginal clears productivity to get (15). of labor aa / acrossLLl , and sectors. mm I /adoptLLl . CES production functionsll for 1 the (15) two sectors. For simplicity, I assumell ma Hicks-neutral 1 (15) technologies. ma la + lmll ma =  1 1(15) (15) 5.2 Producer’s Problem ll ma  1 (15) Population dynamics are also assumedll ma  1 (15)away. N N N Because Because the Becausequantity the quantity theof Thereland quantityof land is are almost is ofalmosttwo land productionfixed, fixed, is almost Because L is issectors thusfixed, thus the approximately approximately inquantity the is economy:thus of constant. approximately land constant. theis Ialmost agriculturalwill I normalize will constant.fixed, sector L I iswill andthus the approximately modern sector. constant. I will 5.2.1 The AgriculturalN Sector and the Premodern Society NL Because the quantity of land is almost fixed, is thus approximately Because constant. the quantity I will of land is almostN fixed, is thus approximately constant. I will L N N Due to nonlinearitynormalize of the utility to be function 1L in the andfollowing limited analysis. agricultural productivity in the premodern normalizeto beLnormalize 1 toin bethe 1 following in the to following beanalysis. 1 in the analysis. following analysis.L N NL era, all labor is employed in agriculture. With the improvement of agricultural technology, a normalize L to be 1 in the following analysis. normalize L to be 1 in the following analysis. The productionThe function modern for sectorthe agricultural utilizes capital sector Kis modeled and LaborThe by modern(13),L , following in sectora CES utilizesform.a CES Two capital-form (16), K and Labor Lm , following a CES -form (16), TheThe modern modern sector sector utilizesutilizes capital capital K and K Labor andm LaborLm , following Lm , following a CES -form a (16),CES -form (16), The modern sector utilizes capital Kfactors and Labor are required Lm , following for the production:The a CES modern-form land sector (16), N utilizes and labor capital La .K The and elasticity Labor ofLm substitution, following a CES -form (16),       1   1     1 1   1  1     1 between land and labor in agriculture is , a constant 1 .  According 1 to the seminal work of  KAY   L ])1([ (16)   1 (16) mm  KAY   Lm ])1([ (16)  1  1  mm mm  KAY  m1   Lm 1 ])1([  (16)    1 Arrow et al. (1961), as well as the recent empirical findings  of1 Duffy and Papageorgiou (2000), mm  KAY   Lm ])1([ (16) mm  KAY   Lm ])1([ (16) and Antras (2004), I can assume the elasticity of substitution is below 1, especially for countries    at the stage of transformation is thee from is elasticity the the elasticity isagricultural the of ofelasticitysubstitution substitution society of insubstitution in tothe the the modernmodern modern: in sector,sector, isthe the modern elasticity  ).1,0[ sector,. I normalize ).1,0[ ofI substitutionnormalize   the price).1,0[ theI innormalize of pricethe agricultural modern of the pricesector, of ).1,0[ I normalize the price of  is the elasticity of substitution in the modern sector,   ).1,0[ I normalize is the elasticity the price of substitution of in the modern sector,   ).1,0[ I normalize the price of agricultural goods p  ,1 with p denotingagricultural the price of goods modern pa goods ,1 withrelative p to denoting the the price of modern goods relative to the agriculturala goods pa  ,1 with p denoting the price of modern goods relative to the goods pa = 1, with p denoting the price of modern goods relative to the agricultural goods. The modern agricultural goods pa  ,1 with p denoting the price 1 of modernagricultural1 goods relative goods to pthea  ,1 with p denoting the price of modern goods relative to the agricultural goods.  1 The modern sector technologyagricultural follows goods. (17), The modern sector technology follows (17), aa  NAY sector Lagriculturala ])1([ technology (13) goods.follows The(17), modern sector technology follows (17), agricultural goods. The modern sector technology follows (17), agricultural goods. The modern sector technology follows (17), 

Am tg Agricultural technology grows at exogenous speed m ga , , mmm 0,  eAAg (17) (17) Am  A  a a tg Modern goods are either consumed or invested, whilst agricultural goods are used only , ataa 0,,  eAAg (14) Aa for consumption. Thus I have (18) and (19),

 1  1   5.2.2 The Modern Sector, Grand Transformation,  and1 Modern Economic Growth a  NA  a ])1([  LaL (18)

  After the threshold of agricultural consumption 1 a  is1 reached at time 17T , the modern sector      1   emerges and some portion of mthe laborKA force starts tom mitigate])1([ to the modernKKML ttt (19) sector. The factor market always clears to get (15).  aa / LLl , and  mm / LLl . Moreover, I assume there is a very small amount of capital k0 available at time T . ll ma  1 (15) 5.3 Competitive Equilibrium Because the quantity of land is almost fixed, N is thus approximately constant. I will Analysis of the premodernL stage is easy because only agricultural goods are produced and N normalize L to be 1 in theconsumed. following Ianalysis. limit my discussion of the dynamic optimization problem to the period after the

The modern sector utilizes capitalmodern Keconomy and Labor starts L(atm , timefollowing T ). Thena CES from-form (18), (16), I can derive (20),

 1  1   1      1   1 mm  KAY   LAma ])1([ (16)  a ])1([  al (20)

 is the elasticity of substitution From (20)in the I canmodern derive sector, the dynamics   ).1,0[ ofI normalizethe share of the labor price allocated of to agriculture over time (21), which is solely determined by the technology parameter in agriculture. Therefore, I agricultural goods pa  ,1 with p denoting the price of modern goods relative to the treat la and lm as exogenous variables. agricultural goods. The modern sector technology follows (17),  1  1      a       Aa  l ,ta    (21)  1   

Applying the market clearing condition (15) to (19) and (21), I get (22),

   1  1  1   mt  kAk t  )1( m   kml tt (22)

 Therefore, the optimal sequence of choices is { ,km tt } Tt ,

  m1 1   max e   Tt )(  t  dta (23)  0   km },{ Tttt  1 

subject to the constraint condition (22), (15) and (21).  

Am m tg Am  m tg   ,, mmm 0,  eAAg (17) (17) Am mmm 0, tg Am m tg Am AAmm , m tg  eAAg m tg (17) , mmm 0,   eAAg (17) , A mmm 0, ,eAAg (17)mmm 0, eAAg (17) A AAm m Modernm goods are either consumed or invested, whilst agricultural goods are used only for Modern Modern goodsgoods areare eithereither consumedconsumed oror invested,invested, whilstwhilst agriculturalagricultural goodsgoods areare usedused onlyonly for consumption. Thus I have (18) and (19), Modernconsumption.for consumption. goods Modern Modern Modern Thus are eitherI goodsgoodsgoodshave Thus consumed(18) are areareI haveand eithereithereither (19), (18) or consumedconsumedconsumed invested,and (19), orororwhilst invested,invested,invested, agricultural whilstwhilstwhilst agriculturalagriculturalagriculturalgoods are used goodsgoodsgoods only areareare usedusedused onlyonlyonly for consumption. Thus I have (18) and (19), for consumption.for consumption. Thus I have Thus(18) andI have (19), (18) and (19),  1  1   1 1 1 a  NA   a ])1([  1  LaL (18) a     a   (18) a NA  1 a1 ])1([   LaL 1  1  1   1   11    1  1   a  NA    1  a ])1([  1  LaL (18) (18) a  NA aa  NA a ])1([   LaL aa (18)])1([  LaL (18)   1  1    1  1 1 m  KA   m ])1([  1  KKML ttt (19)  KA  1   1 ])1([    KKML (19) m  1 m1   ttt     1   1  1 1   1  1    m  KA    1  m ])1([  1  KKML ttt (19) (19) m  KA mm  KA m ])1([  mm ])1([  KKML ttt (19)  KKML ttt ttt (19) Moreover, I assume there is a very small amount of capital k0 available at time T . Moreover, Moreover, I assume I there assume is a verythere small is a amountvery small of capital amount k0 available of capital at time k0 T available. at time T . Moreover, Moreover, II assumeassume therethere isis aa veryvery smallsmall amountamount ofof capitalcapital k 0 available available atat timetime T .. Moreover, I Moreover,assume there I assume is a very there small is a amount very small of capital amount k of0 availablecapital k 0at0 time available T . at time T . 5.3 5.3Competitiv Competitivee Equilibrium Equilibrium 5.3 Competitive Equilibrium 5.3 CompetitiveAnalysis5.3 Competitiveof Equilibrium the premodern Equilibrium stage is easy because only agricultural goods are produced and consumed. I Analysis of the premodern stage is easy because only agricultural goods are produced and consumed. I limit my discussion of the dynamic optimization problem to the period after the Analysislimit of consumed.AnalysistheAnalysis my premodern discussion ofof I the thelimit of stage premodernpremodern the my dynamic is discussion easy stagestage optimizationbecause isofis easyeasythe only dynamic problembecausebecause agricultural to optimizationonlyonly the agriculturalperiodagriculturalgoods afterare problem producedthe goodsgoods modern to are arethe and economy produced producedperiod afterstarts andand the modern economy starts (at time T ). Then from (18), I can derive (20), consumed.(at Itimemodernconsumed.consumed. limit T ).my Theneconomy discussion II limitlimit from starts mymy(18), of discussiondiscussion I(atthe can timedynamic derive ofTof (20), ). thethe optimizationThen dynamicdynamic from (18),optimizationoptimization problem I can toderive theproblemproblem period (20), toto after thethe periodperiodthe afterafter thethe modern economy starts (at time T ). Then from (18), I can derive (20), modern economymodern starts economy (at time starts T ). (at Then time from T ). (18), Then I fromcan derive (18), I(20), can derive (20),  1   1 1    1  Aa  a ])1([  al  (20)(20) Aa a1 ])1([  al  (20)  1     1   1  11 Aa   1  a  ])1([  1  al (20) (20) Aa  Aaa a ])1([   al (20)aa ])1([  al (20) From From (20)(20) II cancan derivederive thethe dynamicsdynamics ofof thethe shareshare ofof laborlabor allocatedallocated toto agricultureagriculture overover timeFrom (21), (20) which I can derive is solely the dynamics determined of the by share the technologyof labor allocated parameter to agriculture in agriculture. over time Therefore,(21), I Fromtime (20) (21), I From From Fromcan which derive (20)(20)(20) is I II the solelycancancan dynamics derivederivederive determined thethethe of dynamicsdynamicsdynamics the by share the ofoftechnologyofof thethethelabor shareshareshare allocated parameter ofofof laborlaborlabor to allocatedallocatedallocatedagriculture in agriculture. tototo over agricultureagricultureagriculture Therefore, overoverover I l l whichtimetreat is solely (21),la and determinedwhich lm is as solely byexogenous the determinedtechnology variables. parameter by the technology in agriculture. parameter Therefore, in Iagriculture. treat a and m Therefore, as I time (21), whichtreattimetime (21),(21),isla solely and whichwhich determinedlm isis as solelysolely exogenous determinedbydetermined the variables. technology byby thethe parametertechnologytechnology in parameterparameter agriculture. inin agriculture.Therefore,agriculture. I Therefore, Therefore, II  exogenoustreat lvariables.a and and 1 l m as as 1exogenousexogenous variables.variables. treat l andtreat l asla exogenous and1 lm as variables.1 exogenous variables. a m  a   m   a     a   1  1  A  1  1  1  A1a  1    1   Aa     l   a    (21)  a  l ,ta   Aa    (21) (21)   l ,ta   Aaa    A  Aa1   a  l   1  (21)   l ,,ta ta  (21)  (21)(21) (21) l ,ta l ,ta  1   1  11       Applying Applying thethe marketmarket clearingclearing conditioncondition (15)(15) toto (19)(19) andand (21),(21), II getget (22),(22), Applying Applying Applying the market thethe clearing marketmarket condition clearingclearing (15)conditioncondition to (19) (15) (15)and (21),toto (19)(19) I get andand (22), (21),(21), II getget (22),(22), Applying the Applying market clearing the market condition clearing (15) condition to (19) (15)and (21),to (19) I get and (22), (21), I get (22),        1  1 1  1  1  1  mt  kAk t   )1( m    kml tt (22)       mt  kAk t 1 )1( m 1  1 kml tt (22)        1 1  1  1 11  1 1  1  mt  kAk t    )1( m   kml tt (22) (22) mt  kAk t )1( m  kml tt (22) mt  kAk t mt  )1( kAk t m   )1(  mkml tt  (22)  kml tt (22)   Therefore, the optimal sequence of choices is { ,km tt } Tt , Therefore, the optimal sequence of choices is { ,km tt } Tt ,   Therefore, Therefore, thethe optimaloptimal sequencesequence ofof choiceschoices isis {{ ,,km tt } Tt ,, Therefore, Therefore, the Therefore, optimal the optimal sequencethe optimalsequence of sequencechoicesof choices is isof { choices,km tt } isTt {,, ,km tt tt } Tt Tt , 1  1     Tt )( m 1     Tt )( mt 1  max e Tt )(  t1  dta (23) max 0e   1    dta (23) km },{  01  1    km },{ Tttt 0   Tt )( )( m1t 1    Tt )( Tttt mt  1 Tt )(  m1tt 1  (23) max e     dta (23) (23) max max 0 e     dta (23)  e km },{ Tttt 0  dta   (23)  km },{ 0 km km },{ },{ Tttt 0  1  Tttt Tttt 1  1  subject to the constraint condition (22), (15) and (21). subject to the constraint condition (22), (15) and (21). subject to thesubjectsubject constraint toto thethe condition constraintconstraint (22), conditioncondition (15) and (22),(22), (21). (15)(15) andand (21).(21).

18 Then ThenI Then Then provide III provideprovideprovide an analytical ananan analyticalanalyticalanalytical solution: the solution:solution:solution: current-value thethethe current-valuecurrent-valuecurrent-value Hamiltonian, Hamiltonian,Hamiltonian,Hamiltonian, Then Then II provideprovide anan analyticalanalytical solution:solution: thethe current-valuecurrent-value Hamiltonian,Hamiltonian, Then I provide an analytical solution: the current-value Hamiltonian,  1   1  1  1   m 1 1  1  1 1  mt1 1  1 1 1   mt 1  11 11 1   mkH ),,(  m1t 1  mt  kA t  )1( m 11  kml tt  (24) (24) mkH ),,( t  mt  kA t )1( m  kml tt  (24) t  mt  t  1 m 1  tt   mkH ),,(  m1 1  mt  kA t )1( m 1  kml tt  (24) mkH ),,(  1t   mt  kA t1 )1( m1   kml tt  (24) (24)   m11  mt  t  m  1   tt  mkH ),,( 11t   mt  kA t  )1( m  kml tt  (24) mkH ),,(  1  mt  kA t )1( m   kml tt  (24) 1   with the state variable k , control variable m , and current-value costatem. variable . The withwith the state the statevariable variable k, control k ,,variable controlcontrol m variablevariable, and current-value m ,, andand costatecurrent-valuecurrent-value variable costatecostate The variablenecessaryvariable conditions.. The The with the state variable k ,, controlcontrol variablevariable m ,, andand current-valuecurrent-value costatecostate variablevariable .. The The are,necessarywithnecessary the state conditionsconditions variable are,are, k , control variable m , and current-value costate variable . The necessary conditions are, necessary conditions are,      m ),,( mmkH  tt  0 (25) (25) (25) m ),,( mmkH  tt tt  0 (25) m ),,( mmkH tt tt  0 (25) (25) m ),,( mmkH  tt  0 (25) m ),,( mmkH tt  0 (25) 1     11    11 11     11   11   11   11   11  k mkH (),,( Amt   )1(   kl tm 11   111 )    tt (26) k mkH (),,( Amt  )1(  kl tm    ) tt (26) k mt   tm 11   tt k mkH (),,( Amt   )1( kl tm 11 )   tt (26) k mkH (),,( Amt   )1(  kl tm 11    )    tt (26) (26) (26) k mt  tm   tt 1 k mkH (),,( Amt   )1(  kl tm   )   tt (26) k mkH (),,( Amt   )1( kl tm  )   tt (26)   Tt )( lim   Tt )( )(  ke  0 (27) lim   Tt )( )(  ke tt tt  0 (27) (27) tlimt    Tt )(  ke tt  0 (27) (27) limt     ke tt tt  0 (27) limtt  Tt )( ke tt 0 (27) (27) limt   ke tt  0 (27) t  The The The optimaloptimaloptimal consumptionconsumptionconsumption ofofof thethethe modernmodernmodern goodsgoodsgoods followsfollowsfollows thethethe EulerEulerEuler equationequationequation (28),(28),(28), The The optimaloptimal consumptionconsumption ofof thethe modernmodern goodsgoods followsfollows thethe EulerEuler equationequation (28),(28), The optimal The optimal consumption consumption of the modern of the goods modern follows goods the followsEuler equation the Euler (28), equation (28),   m t 1 m tt 1   (28) mtt 1 r  )( (28) (28) mt 1 r  )( (28) (28) mt  r )( (28) mtt 1 r  )( (28) (28) mtt  r  )( (28) mt  mt  wherewhere rr is is is thethethe realrealreal interestinterestinterest rate.rate.rate. wherewhere r is ther real is is interestthethe realreal rate. interestinterest rate.rate. where r is the real interest rate.   1     11   11 11     11 t  11   11 t  11   11  t Am   )1(     kl tm 11   111 (29) t Am  )1(  kl tm   (29) t m   tm 11    (29)  Am   )1(  kl tm 11 (29) t Am   )1(    kl tm 11    (29) (29)  m  tm   t   1 tt Am  )1(  kl tm   (29) tt Am   )1(  kl tm  (29) t t 5.45.4 DynamicsDynamics ofof labor’slabor’s shareshare 5.4 5.4Dynamics Dynamics of labor of labor’s’s share share 5.4 Dynamics of labor’s share I will examine the evolution of labor’s share within these growth dynamics. The labor’s share in I will examine the evolution of labor’s share within these growth dynamics. The labor’s share in I willagricultureI willexamine examine the is evolution calculated the evolution of labor’sas (30), of share labor’s within share these within growth these dynamics. growth The dynamics. labor’s share The in labor’sagriculture share in agricultureI will examine is calculated the evolution as (30), of labor’s share within these growth dynamics. The labor’s share in is calculatedagriculture as (30), is calculated as (30), agriculture is calculated  as (30), 11 1   11 )1(   La  )1(  La1 SLa  1 )1(   La1 1 (30) (30) La   1 a  1 (30) SLa   1 )1(  La  1 SLa   N 11 )1(  L11 (30) (30) (30) S   N 1 )1(  La )1(  La1 (30) La  N  )1(   La SLa   N 1 )1(  La1 (30)  N  )1(  La  N )1(  La In In thethe premodernpremodern society,society, allall laborlabor isis employedemployed inin agricultureagriculture toto meetmeet thethe subsistencesubsistence In the Inpremodern In In thethethe premodernpremodernpremodern society, all society,society,society, labor is allall allemployed laborlaborlabor isisis in employedemployedemployed agriculture in ininto agricultureagricultureagriculturemeet the subsistence tototo meetmeetmeet needs, thethethe subsistencesubsistencesubsistence so needs, so In thea premodernLL .. II cancan getget society, (31),(31), all labor is employed in agriculture to meet the subsistence needs, so In thea premodern LL . I can get society, (31), all labor is employed in agriculture to meet the subsistence La =needs, L. I can so get (31),a  LL .. II cancan getget (31),(31), needs, so a  LL . I can get (31), needs, so a  LL . I can get (31), 1  1 SLa premodern,  1 11 (31) (31) (31) SLa premodern,   1 (31) La premodern,  1 N  SLa premodern,   N 11 (31) (31) S  )1( 1   NL  (31) La premodern, )1(    NL  1 SLa premodern,  )1(   NL 1 (31) )1(   NL   )1(   L  Equation Equation (31)(31) showsshows thatthat thethe laborlabor shareshare SLa in in thethe premodernpremodern eraera isis invariant.invariant. Equation (31) shows that the labor share SLa in the premodern era is invariant. Equation Equation (31)(31) showsshows thatthat thethe laborlabor shareshare SLa in in thethe premodernpremodern eraera isis invariant.invariant. Equation (31) shows that the labor share SLa in the premodern era is invariant. Equation (31) shows that the labor share SLa in the premodern era is invariant.

19  N   N  N N Moreover, this shareMoreover, is a function this Moreover,of share theMoreover, landis a functionthisper capitashare this of share iswhen the a function land is a functionper of capita ),1,0( theL of land when the per land  ScapitaLa perpremodern, capita when),1,0(  when.  S ),1,0(  ),1,0( L . S SLa premodern,  .  . Equation (31) shows that the labor share SLa in the premodern eraL is invariant.La Moreover,premodern, L this shareLa premodern, That is, land-abundant countries will haveThat relatively is, land-abundant high labor’s countries share in will national Nhave relativelyincome. high labor’s shareNN in national income. Moreover, this shareThat is,is aland-abundant functionis a Moreover,functionThat of is, the of land-abundantcountries thelandthis land shareper per willcapita iscapita haveacountries function when when relatively will of the have high land),1,0( relatively labor’s  per capita share Shigh when in labor’s national  .share. That income.),1,0( inis,NN nationalland-abundant  Sincome.  . Moreover,Moreover, this this share share is is a a function function of of the the land landL per per capita capitaLa when whenpremodern,  ),1,0( ),1,0( ),1,0( LL    SSLaLa premodern, premodern, ... After the modern sector After starts, the modern labor’s sector share After starts,in the agriculture modern labor’s sector sharebecomes instarts, agriculture (32), labor’s becomesshare in agriculture (32), becomesLL (32),LaLa premodern, premodern, That is, land-abundant countries will have After relatively the modern high sector labor’s starts, share labor’s in national share inincome. agriculture becomes (32), countriesThatThat is, willis, land-abundant land-abundanthave relatively high countries countries labor’s willsharewill haveinhave national relatively relatively income. high high labor’s labor’s share share in in national national income. income. After the modern sector starts, After After labor’s thethe share modernmodern in agriculture sectorsector starts,starts, becomes labor’slabor’s (32), shareshare inin agricultureagriculture becomesbecomes (32),(32), 1 1 After the After After modern1 the the modern1sectormodern starts, sector sector labor’s starts, starts, share labor’s labor’s in agriculture share share in inbecomes agriculture agriculture (32), becomes becomes (32), (32), SLa  1 (32)  SLa  1 (32)  SLa SLa 1 (32) 1 (32)     )1( la )1(   l )1(   )1( l   la 1 a 11 a S  1 (32)  1 La SLaLa  11 (32) (32)(32)  SSLaLa 11 (32) (32) )1(   l    a )1( )1( )1(      lllaa Similarly, labor’s share Similarly, in the labor’smodern Similarly, )1( share sector Similarly, lin a labor’sais, the modernlabor’s share shareinsector the in modernis, the modern sector sector is, is, Similarly, labor’s share in the Similarly, Similarly,modern sector labor’slabor’s is, shareshare inin thethe modernmodern sectorsector is,is, 1  1  Similarly, Similarly, Similarly, labor’s1 share labor’s labor’s1 in the share share modern in in the thesector modern modern is, sector sector is, is, S  1 (33) S  1 (33) Lm SLm  S  Lm1 (33) 1 (33) 1la  Lm 1la  1la  1la  )1(   k      )1(   k  1 )1( k  )1( 1 k  S   (33) 11  Lm 1 SLm  11 (33) (33) 1l  SLm  1 (33) (33) a SLmLm 11lla 1 (33)   11l al   )1( k  )1( )1(    k aa   )1( )1(     kk   The aggregate labor The share aggregate in the national Thelabor aggregate Theshare income aggregate kin the labor national can laborshare be representedshare inincome the innational the bynational can incomesectoral be represented income  can  be by can represented sectoral be represented by sectoral by sectoral value-added composition, as defined by value-added(34) – (35), composition, as defined by (34) – (35), The aggregatevalue-added labor share composition,value-added in the national as composition, defined income by (34)as defined can– (35), be by represented (34) – (35), by sectoral  The aggregate The The The aggregate aggregateaggregate labor share labor laborlabor in the share shareshare national in inin the thethe income national nationalnationalf can income incomeincome be represented  can can can by be bebe sectoral represented representedrepresented value-added by byby sectoral sectoralsectoral value-added composition, as definedvalue-added by (34) composition, – (35), as defined by (34) – (35),  pYSYS mLmaLa Ya value-addedvalue-added Ya composition, composition,  pYSYS as mLmaLa as defined definedYa by by (34) (34) – – (35), (35),Ya   S composition,S pYSYS mLmaLa  as defined)1( (34)Ya pYSYS by mLmaLa (34) – (35),YYa aS S Ya  )1( (34)   La Lm SLa SLm SLa )1( La (34)SLm  Lm )1( (34)  pYY ma Y Y  pYY ma Y Y  pYSYS YpYY ma YpYY Yma YY Y mLmaLa a a    pYSYS mLmaLa Yaa Yaa   S S  )1(  (34)pYSYS pYSYS mLmaLa mLmaLa YYaa YYaa La  Lm SLaLa SLmLm   )1( )1( (34) (34)  pYY Y  Y SSLaLa SSLmLm  )1( )1( (34) (34) (34) ma pYY ma Y Y  pYY pYY ma ma YY YY 1 1 1 1 1 1 1 1  1  1  1  1 A  )1(  )1(   la  A   )1(  )1(   la  a A  )1(  )1(  a la  )1(   l a Aa )1(  a  p  1 (35)p  1 (35) p  1p  1 1 (35)  1 (35) 1  1 11 11 1  1 A   )1(  1  1  1 111 11  1 m  A lm  )1(  A A m )1( )1(   11lm   A  )1(  m)1(   la  m lm   )1(    llm    11 a )1(     Aa  )1( )1(  )1(  )1(  laa       kt AAa )1(     )1( )1( k   )1( )1(    llaa  kt p  p  1aa (35) t  kt 1 (35)  p     1 (35) (35) pp1  1   11 11 (35) (35) A   )1(   11 m  lm  Am   )1( )1( ll 11  11 AAm   )1( )1(  mml   )1(   k  mm  )1(    lmm    t )1( k     )1( )1(     kktt       kt t  The relative price of The the relativemodern price goods The of relative to The the the modernrelative agricultural price ofpricegoods the goodsof modernto the the modern agriculturalp goods is determined goods to the goods toagricultural the by p agricultural is determined goods goods p by is determinedp is determined by by (35). (35). The relative(35). price of the(35). modern goods to the agricultural goods p is determined by The relative The The The relative relative relativeprice of price pricetheprice modern of ofof the thethe goods modern modernmodern to the goods goodsgoods agricultural to toto the thethe agricultural agriculturalgoodsagricultural p is determined goods goodsgoods bypp (35). is is is determined determineddetermined by byby  1     (35).       1 (35).(35).   1 1 1   1 (35).(35).   1   1 Y Aa   la Y])1([   Aa     la ])1([ a Ya Ya Aa a Alaa ])1([ la ])1([           1   1  1 (36) 1   1  (36)1  (36)     11    1   1 11  1 1 (36)  1  (36) 1    1   1    1 Y A  ])1([  kApl Y  A11   l ])1([   1  ])1([ 11 11 1 kApl    1 l ])1([ a Y a A mY  A l ])1([ ])1([ a  m ])1([ kApl a    lmkApl ])1([ 11   l ])1([ m Ya aa Ya aaa m Aaaa   m   llaa m])1([ ])1([ m  YYaa AAaa   llaa ])1([ ])1([  1  a   1 1  1  (36) 1 1  (36) (36)      1    1 1 1  11 11 1 11 11 11 (36) (36) Y A  ])1([ Y  kApl    l ])1([ 11         11 a a YY m AAaa    aa m])1([ ])1([ ])1([ m  kApl kApl     lllm ])1([ ])1([ ])1([ I can see from (32) that with theA developmentaa I can see ofa athefrom])1([ modern (32) thatm msector withkApl lthe development, labor’slmm share])1([ of in the modern sector l  , labor’s share in I can see I fromcan see I(32) canfrom thatsee (32) fromwith that the(32)with development thethat development with the of development theofa the modern modern ofsector sector the modern la ,, labor’slabor’s sector share sharela in ,agriculturein labor’sa share in agriculture S increases monotonously.agriculture However, S according increases to (33), monotonously. labor’s share However, in the according to (33), labor’s share in the La agricultureS S increasesLaagriculture increases monotonously. Smonotonously. increasesLa However, monotonously. However, according according to (33), However, labor’s to (33), shareaccording labor’s in the modernto share (33), in sectorlabor’s the is determinedshare in the I can see from (32) thatLa with the I I cancan development seeseeLa fromfrom (32)(32) of the thatthat modern withwith thethe sector developmentdevelopment la , labor’s ofof thethe share modernmodern in sectorsector lla  ,, labor’slabor’s shareshare inin  I I can can see see from from (32) (32) that that with with the the development development of of the the modern modern sector sector llaa , ,labor’s labor’s share share in in 1 la   1la a 1 la 1 la  modernagriculture sector isS determinedmodern increases sector by bymonotonously. kis ::determined whenwhenmodern the the laborHowever, labor sectorby allocated allocated is : according determinedwhen to the tothe modernthe tolabor by modern(33), sectorallocatedk labor’s: sector 1 ltosharea  the 1 , andinlmoderna thek ,  ,,sector thethe labor’s labor’s 1 incomel income   , share share in  the La agriculturemodern sector SLaLa is increases increasesdeterminedk monotonously.monotonously. by k : when However,However, the labor according accordingallocated toto the(33),(33), modern labor’slabor’sa sector shareshare inin1 thethela  , agricultureagriculture SSLaLa increases increases monotonously. monotonously. However, However, according according to to (33), (33), labor’s labor’s share share in in the the  1la 11ll and k , the labor’sand incomek  , sharethein the labor’s inmodern themodern incomemodern sector sector Sshare sectorLm can in S demonstrate LmStheLm can modern can demonstrate demonstrate 1a aal nonmonotonoussector Sa nonmonotonousa nonmonotonous can feature, demonstrate which feature, is adecided nonmonotonous which by the is relativedecided by the relative modern sector is determined bymodernand k: whensector, the the labor’sis determinedlabor income allocated by share to1 l a theain: when the modern modern theLm laborsector sector allocated 1 SlaLm   to can , the demonstrate modern sector a nonmonotonous 1l   , modernmodernk sector sector is is determined determined by by kk ::: when whenwhen the thethe labor laborlabor allocated allocatedallocated to toto the thethe modern modernmodern sector sectorsector 11lllaa     , , feature, which is decided by themovement relative movement ofmovement k and l . Otherwiseof of kk and and I can ll .only .Otherwise Otherwisekk see monotonous I I can can only only dynamics see see monotonous (including the dynamics possibility (including of aa the and k  , the labor’sfeature, income which share feature,is decided kin thewhich bymodern themis decided relative sector bymovementS themm canrelative demonstrate of movementk and lam nonmonotonous .of Otherwise k and Ilm can. Otherwise only see I can only see andand kk,, , the thethe labor’s labor’slabor’s income incomeincome Lm share shareshare in inin the thethe modern modernmodern sector sectorsector SSLmLm can can can demonstrate demonstratedemonstrate a aa nonmonotonous nonmonotonousnonmonotonous monotonous dynamics (including the possibilitypossibility of of constancy) constancy) in inthe the aggregate aggregate labor’s labor’s share share LmLm during economic transformation. feature, which ismonotonous decided byconstancy) thedynamicsmonotonous relative in the(including movement aggregate dynamics the labor’s of (includingpossibility k share and duringl theof. Otherwiseconstancy) possibilityeconomic Itransformation. inofcan theconstancy) only aggregate see in labor’sthe aggregate share labor’s share feature,feature,feature, which whichwhich is isis decided decideddecided by byby the thethe relative relativerelativem movement movementmovement of ofof kk and and and lllm .. . Otherwise OtherwiseOtherwise I II can cancan only onlyonly see seesee during economic transformation.during economic feature,during transformation. economicwhich In is an decided transformation. alternative by the way, relative the evolution movement of of the k aggregate and lmm. labor’sOtherwise income I can share only insee national monotonous dynamics (includingmonotonousIn anthe alternative possibility dynamics way, of theconstancy) (including evolution inof the the possibility aggregateaggregate labor’s of labor’s constancy) income share share in thein national aggregate income labor’s can beshare In an alternative way, In thean alternative evolutionmonotonous monotonousincome In of way,an thedynamics dynamicsalternativecan theaggregate be evolution described (including (including way, labor’s of the as the evolutionthe (37),incomethe aggregate possibility possibility share of labor’sthe in of of aggregatenational constancy) constancy) income labor’s share in in the the inincome aggregate aggregatenational share labor’s labor’s in national share share during economic transformation.describedduring as economic (37), transformation. income can be describedincome as can(37), be during duringdescribed economic economic as (37), transformation. transformation. In an alternative way, theincome evolution can be of described the aggregate as (37), labor’s income share in national In In In an anan alternative wLalternativealternative way, way,1way, the thethe (37) evolution evolutionevolution of ofof the thethe aggregate aggregateaggregate labor’s labor’slabor’s income incomeincome share shareshare in inin national nationalnational income can be described as (37),incomeincome  cancan bebe describeddescribed asas (37),(37), wL 1 (37)wL incomeincome1 wLcan can be (37)be described described 1 1 krKwL as as (37) r(37), (37),         w r r r  1 krKwL  w  1 krKwL    wL 1 (37) wLw 1 1krKwL w (37) (37)      wLwL  11 (37) (37) r   r  1 krKwL    rr w  1 krKwL   wrw  11 krKwL krKwL  ww 20 N Moreover, this share is a function of the land per capita when  ),1,0( L   SLa premodern,  . That is, land-abundant countries will have relatively high labor’s share in national income. After the modern sector starts, labor’s share in agriculture becomes (32),

1 SLa  1 (32)  )1(   la

Similarly, labor’s share in the modern sector is,

1  SLm  1 (33) 1la  )1(   k 

The aggregate labor share in the national income  can be represented by sectoral value-added composition, as defined by (34) – (35),

 pYSYS mLmaLa Ya Ya   SLa SLm  )1( (34)  pYY ma Y Y

1 1    1 Aa  )1(  )1( la  p  1 (35) A   )1( 1  1 m  )1(   lm     kt 

The relative price of the modern goods to the agricultural goods p is determined by (35).

 1      1 Ya Aa la ])1([   1   1  1  (36)   1    1 Y Aa  a ])1([ m  kApl   lm ])1([

I can see from (32) that with the development of the modern sector la  , labor’s share in

agriculture SLa increases monotonously. However, according to (33), labor’s share in the

1la modern sector is determined by k : when the labor allocated to the modern sector 1la   ,

and k  , the labor’s income share in the modern sector SLm can demonstrate a nonmonotonous

feature, which is decided by the relative movement of k and lm . Otherwise I can only see monotonous dynamics (including the possibility of constancy) in the aggregate labor’s share during economic transformation. In an alternative way, the evolution of the aggregate labor’s income share in national income can be described as (37),

wL 1 (37)    (37) rr r Set  k   r . I will analyze the dynamics of  in the following discussions. Set  k  wr .. I I1 willwillkrKwL analyzeanalyzew thethe dynamicsdynamics ofof  in in thethe followingfollowing discussions.discussions. r r   wr  SetSet k k w .w Set. I will I will analyze analyzek wrr . Ithe willthe dynamics dynamicsanalyze theof of dynamics in in the the followingof following in thediscussions. discussions. following discussions. Set  k   w .. I I willwill analyzeanalyze thethe dynamicsdynamics ofof  in in thethe followingfollowing discussions.discussions.  wr   SetSet  k  w .I will I will analyze analyze the dynamicsthe dynamics (38) (38) of k in of the  following in the followingdiscussions. discussions.  k r w (38)        k   r (38) (38) w (38)       (38) (38)  kk   r r k ww r w    k rr  w (38)  kk  r r kk ww rr  ww (38)  k r  w Wage w k is is derivedderivedr asas inin (39),(39),w WageWage ww is is derivedWage derived asw as in is in (39),derived (39), as in (39), WageWage ww is is isderived derivedderived as in asas (39), inin (39),(39), 11 11 111 Wage w is derived as in (39), 1   1  1 1   1     1   1 1 1 1 ktt 11     k    1  Aw  )1()1(      kt 11 11 (39) (39) m        Aw m  k kt  )1()1(    kt    1 (39)  t  lm   1  1 Aw Aw  Aw )1()1( )1()1(        )1()1(   (39) (39)  lk mt    (39) m m Aw m     )1()1(     lmt   (39) (39)  Aw m l l )1()1(  lkt   (39)  Aw  m m  )1()1(    lm   (39) m   m     lm   In In combinationcombination withwith (21),(21), thethe wagewage levellevel w (relative (relative toto thethe agriculturalagricultural goodsgoods price)price) isis  In In combination combination In combination In with combination with (21), (21),with the (21), the withwage wagethe (21),wage level level thelevel w wagew w (relative (relative (relative level to to to w thethe the (relativeagricultural agricultural agricultural to goodsthe goods goodsagricultural price) price) price) is also is goods is price) is also exogenously In In combinationcombination determined withwith (21),(21), by thetheA wagewage and alevellevel over w time. (relative (relative toto thethe agriculturalagricultural goodsgoods price)price) isis also exogenously determined by Aa and and a over over time.time. also exogenously In combination determined with (21), bya Athea wage and alevel over w time. (relative to the agricultural goods price) is alsoalso exogenously exogenouslyexogenously determined determinedInterest Interestdetermined raterateby by by A raA a is is and and and calculatedcalculated a over over overa time. asastime. time. (40),(40),  also exogenously Interest rate determined r is calculated by Aa as and and (40), a over over time.time. Interest Interest also Interestrate rate exogenously r Interest r rate is is calculatedr calculatedis ratecalculated determined r as isas as (40),calculated (40),(40), by Aa as and (40), a over time. Interest Interest raterate r is is calculatedcalculated11 asas (40),(40), 11 111 Interest rate r is calculated1   1 as (40),  1 1   1   1  11  1 1 ktt 11     k    1   Ar     )1(    kt 11 11 (40) (40) m        Ar m k kt   )1(   kt    1 (40)  t  lm  1   1 (40) Ar    Ar   )1(        )1(  (40) kmt   (40) Ar m m )1( m    (40) l mt   Ar m   )1(   lk   (40) (40)    lmlm     mt     Ar m     )1(   lm   (40)   l     m   Hence Hence II getget (41),(41), Hence Hence I HencegetI get (41), (41), HenceI get (41), I get (41), Hence Hence II getget (41),(41), 11 11 111 Hence I get (41),   11  kktt 1  1   1 1 k   1  1  )1(    ktt         1   1 1 1 ll 1    1 )1(   m  11 11 kt 1   )1( lk    t     kt kt    lmt 11  1     k     k    11 1   k   kt 11 (41) (41) )1( )1(   tt     )1(   lkkt    1 tt      l t          kt  lm m kkmt 11   k  kt  k  (41) (41)   1  t   )1(    t   1kt t1  t l t  1 1 )1( lk   1 lm       k     )1(   lkmkttt 1     (41)k  km   (41) k k 1   11 l k k 1   (41) l t  t t 1 t    )1(   lm  tt   1 t lmt    )1( k        k  )1( l       k  k t   llmt 11  k    (41) (41) 11 1 tt t 11mm  l lm1 tt lkmt    )1(  )1(      )1(  lkkt     m   1  k  lm lm  mt 1  1  k  ll (41)   t     )1(   l   t  m     lmkt     1   )1(     1 lm   lm  So the So Sodynamics thethe dynamicsdynamics of k are, ofof  are, are,   So So the the dynamics dynamics So theof of dynamics are, are, of  are,  So So thethe dynamicsdynamics ofof  are, are,  So the dynamics of  are,      1  llm 1 k  1 lm (1 )1   k (42) (42) (42)  11l l 11 1 klkm (1 )1  k (42) m m  llm  k ( ( )1 1 )1  llm (42) (42)( 1 )1  k (42) m ( )1   (42) (42) lmlm   1klklmm 1 kk llm ( )1  k (42) lm  k Because Because Because mlabor’s share labor’slabor’s is, shareshare is,is, Because Because labor’s labor’s Because share share is,labor’s is, share is, Because Because labor’slabor’s shareshare is,is, 1 Because labor’s share is,   1 (43) (43) (43) 11   1 (43)  (43) (43)  11 (43) 11   11 (43) (43)  1 (43) To 1make To To labor’s makemake share labor’slabor’s constant, shareshare I constant,constant, must have II (44), mustmust havehave (44),(44), To To make make labor’s labor’s To sharemake share constant,labor’s constant, share I Imust must constant, have have (44), (44),I must have (44), To To11 makemake labor’slabor’s shareshare constant,constant, II mustmust havehave (44),(44), 111  lk  To1 make (44) (44) labor’s share constant, I must have (44), 1 1  mt  1 (44) lk mt   (44)  11   111  lk mt lk mt  (44) (44) lk mt 11 (44)  lk mt  1 (44) (44) mt 1  lk mt  (44)

21 From (21), I can see that the employment share in the agricultural and modern sectors is only determined by the technology growth rate in agriculture, with the neoclassical assumption. Labor’s share will evolve in different patterns under the following two conditions:

 1 1    lk mt    0: labor’s share will increase from t

 1 1    lk mt    0: labor’s share will decrease from t

The intuition behind these dynamics is, if the agriculture releases more labor than the modern sector can easily absorb, the wage rate will be brought down relatively. In the beginning of modern economic take-off, capital is comparatively rare, thus demanding higher return. However,k will keep growing and finally labor turns out to be the relatively scarce factor. This will reverse the downward trend in the movements of labor’s share in the economy.

5.5 A Simple Simulation

In this section, I conduct a simple calibration and simulation for the above-discussed growth model. As an important example, I try to test whether a nonmonotonous pattern of movement in labor’s share could really emerge from my proposed model during the British Industrial Revolution. My model-based simulation tracks quite well with the empirical evidence provided by Allen (2007). The proposed multi- sector CES growth model is helpful for understanding the nonlinearity in the movements of labor’s share during economic transformations. The details of simulation will be provided later.

6 Conclusions

In this paper I present a new set of evidence to characterize the long-run evolvement of labor’s share accompanying the modern economic development. The movements of labor’s share demonstrate a nonlinear and nonmonotonous pattern after the debut of the modern economic sector. I summarize this as a generalized fact that labor’s share tracks a cubic relationship with the economic development level, due to the grand economic transformations. I have further explored the evidences from economic history and confirmed this generalized relationship is also applicable to the earlier development stage of the United Kingdom and the United States, whose contemporary economic time series (summarized by the Kaldor fact) inspired the standard modern growth theory. The Kaldor fact however can be seen as a special case focusing on the relatively stable portion upon the long cubic curve. The mainstream Cobb-Douglas class growth models are not able to capture the nonmonotonous pattern in the labor’s share movements, while my proposed two-sector CES-form model is qualified for explaining this dynamics. Calibration and simulation based on the proposed growth model fit the historical facts fairly well.

22 References Acemoglu, Daron. 2002. Directed Technical Change. The Review of Economic Studies 69, no. 4: 781–809 (October). Acemoglu, Daron. 2003. Labor- And Capital-Augmenting Technical Change. Journal of the European Economic Association 1(1): 1–37. Acemoglu, Daron, and Veronica Guerrieri. 2008. Capital Deepening and Non-balanced Economic Growth. Journal of Political Economy 116, no. 3. Allen, Robert C. 1999. Tracking the Agricultural Revolution in England. The Economic History Review 52, no. 2: 209–235 (May). Allen, Robert C. 2000. Economic structure and agricultural productivity in Europe, 1300–1800. European Review of Economic History 4(01): 1–25 (April). Allen, Robert C. 2007. Engel’s Pause: A Pessimist’s Guide to the British Industrial Revolution. Economics Series Working Paper 315. University of Oxford: Department of Economics. Antras, Pol. 2004. Is the US Aggregate Production Function Cobb-Douglas? New Estimates of the Elasticity of Substitution. Contributions to Macroeconomics 4(1): article 4. Arrow, K. J., H. B. Chenery, B. S. Minhas, and R. M. Solow. 1961. Capital-Labor Substitution and Economic Efficiency. Review of Economics and Statistics 43(3): 225–250. Ashton, Thomas S. 1948. The Industrial Revolution, 1760–1830. Oxford: Oxford University Press. Bai, Chongen, and Zhenjie Qian. 2009. Factor Distribution in the National Income: The Story behind the Statistics. Economic Research (Jing Ji Yan Jiu). Barnes, Sebastian, Simon Price, and Maria Sebastia-Barriel. 2008. The elasticity of substitution: evidence from a UK firm-level data set. Bank of England working paper 348. London: Bank of England. Barro, Robert J., and Jong-Wha Lee. 2000. International Data on Educational Attainment: Updates and Implications. Harvard CID Working Paper no. 042 (April). Bentolila, Samuel, and Gilles Saint-Paul. 2003. Explaining Movements in the Labor Share. Contributions to Macroeconomics 3(1): article 9. Bernanke Ben S., and Refet S. Gurkaynak. 2001. Is Growth Exogenous? Taking Mankiw, Romer and Weil Seriously. National Bureau of Economic Research Macroeconomics Annual. Blanchard, Olivier. 1997. The Medium Run. Brookings Papers on Economic Activity 2: 89–158. Blanchard, Olivier. 1998. Revisiting European Unemployment: Unemployment, Capital Accumulation and Factor Prices. National Bureau of Economic Research Working Paper no. 6566. Blanchard, Olivier, and Francesco Giavazzi. 2003. Macroeconomic Effects Of Regulation And Deregulation In Goods And Labor Markets. The Quarterly Journal of Economics 118(3): 879–907 (August). Caballero, Ricardo J., and Mohamad L. Hammour. 1998. Jobless growth: appropriability, factor substitution, and unemployment. Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 48(1): 51-94 (June). Carter, Susan B., Scott Sigmund Gartner, Michael R. Haines, Alan L. Olmstead, Richard Sutch, and Gavin Wright, eds. 2006. Historical Statistics of the United States: Millennial Edition. New York: Cambridge University Press.

23 Caselli, Francesco, and Wilbur John Coleman II. 2001. The US Structural Transformation and Regional Convergence: A Reinterpretation. Journal of Political Economy 109(3): 584–616 (June). Clark, Gregory, and Ysbrand Van Der Werf. 1998. Work in Progress? The Industrious Revolution. The Journal of Economic History 58(03): 830–843 (September). Duffy, John, and Chris Papageorgiou. 2000. A Cross-Country Empirical Investigation of the Aggregate Production Function Specification. Journal of Economic Growth 5(1): 87–120 (March). Feinstein, Charles H. 1998. Pessimism Perpetuated: Real Wages and the Standard of Living in Britain during and after the Industrial Revolution. The Journal of Economic History 58(03): 625–658 (September). Galor, Oded, and David Weil. 2000. Population, technology, and growth: From Malthusian stagnation to the demographic transition and beyond. American Economic Review 90: 804–828. Gollin, Douglas. 2002. Getting Income Shares Right. Journal of Political Economy 110(2): 458–474 (April). Gollin, Douglas, Stephen L. Parente, and Richard Rogerson. 2002. The Role of Agriculture in Development. The American Economic Review 92(2): 160–164 (May). Gollin, Douglas, Stephen L. Parente, and Richard Rogerson. 2007. The food problem and the evolution of international income levels. Journal of Monetary Economics 54(4): 1,230–1,255 (May). Hansen, Gary D., and Edward C. Prescott. 2002. Malthus to Solow. American Economic Review 92(4): 1,205– 1,217 (September). ILO (International Labor Organization). 2008. Global Wage Report 2008–09: Minimum wages and collective bargaining: Towards policy coherence. Jorgenson, Dale W. 1961. The Development of a Dual Economy. Economic Journal 71(282): 309–334. Jorgenson, Dale W. 1967. Surplus Agricultural Labor And The Development Of A Dual Economy. Oxford Economic Papers no. 3 (November). Landes, David S. 1969. The Unbound Prometheus: Technological Change and Industrial Development in Western Europe from 1750 to the Present. Cambridge, MA: Cambridge University Press. Leontief, Wassily. 1964. International Factor Costs and Factor Use. American Economic Review 54: 335–345. Lindert, Peter H., and Jeffrey G. Williamson. 1983. English Workers’ Living Standards during the Industrial Revolution: A New Look. The Economic History Review 36, no. 1: 1–25. Kaldor, Nicholas. 1957. A model of economic growth. The Economic Journal67(268): 591–624. Keynes, John M. 1939. Relative Movements of Real Wages and Output. The Economic Journal XLIX: 48–49. Kongsamut, Piyabha, Sergio Rebelo, and Danyang Xie. 2001. Beyond Balanced Growth. Review of Economic Studies LXVIII: 869–882. Kuznets, Simon. 1955. Economic Growth and Income Inequality. American Economic Review 45: 1–28. Kuznets, Simon. 1959. Quantitative Aspects of the Economic Growth of Nations: IV. Distribution of National Income by Factor Shares. Economic Development and Cultural Change 7(3): 1–100. Kuznets, Simon. 1973. Modern Economic Growth: Findings and Reflections. American Economic Review 63(3): 247–258 (June). Lewis W. A. 1954. Economic development with unlimited supplies of labor. The Manchester School 22(2): 139–191 (May).

24 Matsuyama, Kiminori. 1992. Agricultural productivity, comparative advantage, and economic growth. Journal of Economic Theory 58(2): 317–334. NCEUS (National Commission on Enterprises in the Unorganized Sector). 2007. Financing of Enterprises in Unorganized Sector (April). Ngai, Rachel L., and Christopher A. Pissarides. 2007. Structural Change in a Multisector Model of Growth. American Economic Review 97(1): 429–443 (March). Ranis, Gustav, and John C. H. Fei. 1961. A theory of economic development. American Economic Review 51: 533–565 (September). RUPE (Research Unit for Political Economy). 2008. India’s Runaway Growth: Distortion, Disarticulation, and Exclusion. No. s 44–46. Rodrik, Dani. 1999. Democracies Pay Higher Wages. Quarterly Journal of Economics (August). Ruiz, Garrido C. 2005. Are Factor Shares Constant? An Empirical Assessment from a New Perspective. Working paper available at http://www.eco.uc3m.es. Salhofer, Klaus. 2000. Elasticities of Substitution and Factor Supply Elasticities in European Agriculture: A Review of Past Studies. Discussion paper no. 83-W-2000. Shastri Rahul, and Ramana Murthy. 2005. Declining Share of Wages in Organised Indian Industry (1973–97): A Kaleckian Perspective. Industrial Organization 0504020, EconWPA. Solow, Robert M. 1957. Technical change and the aggregate production function. Review of Economics and Statistics 39: 312–320. Solow, Robert M. 1958. A skeptical note on the constancy of relative shares. American Economic Review 48(4): 618–631. Solow, Robert M. 2008. Introduction. Journal of Macroeconomics 30(2): 601–603 (June). Subramanian, Arvind. 2008. What Is China Doing to Its Workers? The Business Standard http://www. petersoninstitute.org/publications/opeds/oped.cfm?ResearchID=885. US Census Bureau. 1975. Historical Statistics of the United States, Colonial Times to 1970. Young, Andrew T. 2006. One of the Things We Know that Ain’t So: Is US Labor’s Share Relatively Stable, not Relatively Stable. Journal of Macroeconomics (May).

25 Appendix

Table A1 Labor’s share and real GDP per capita, 1950–2003 Commodity exporters removed (1) (2) (3) (4) (5) (6) Variables Yearly, FE Yearly, FE 5Y Avg, FE 5Y, FE 5Y, FE 5Y, FE –274.8*** –301.5*** –235.4*** –245.7*** –18.54** –751.0* 1n(rgdpch) (34.47)* (33.70)* (70.21)* (68.57)* (8.753) (589.4) 30.98*** 33.95*** 26.59*** 27.59*** 1.202** 118.9* [1n(rgdpch)]2 (3.960)* (3.872)* (8.173)* (7.986)* (0.512)* (105.0) –1.141*** –1.248*** –0.979*** –1.009*** –8.243* [1n(rgdpch)]3 (0.151)** (0.147)** (0.315)** (0.308)** (8.250) 0.212* [1n(rgdpch)]4 (0.241) –0.110*** –0.111*** Year (0.0168)* (0.0365)* 840.2*** 1140*** 726.0*** 978.2*** 116.0*** 1795 Constant (99.32)* (103.2)** (199.6)** (206.7)** (38.15)* (1230) Observations 2037 2037 463 463 463 463 R2 0.100 0.063* 0.087 0.064 0.062 0.089 # Countries 101 101 101 101 101 101

*** p < 0.01, ** p < 0.05, * p < 0.1 Notes: Robust standard errors in parentheses. The removed commodity exporters: BHR BRN QAT TTO ARE OMN GAB SAU DZA KAZ NGA YEM MNG VEN IRN ZMB CHL NOR AZE MOZ BOL RUS CIV BLR. Source: Author’s calculations.

26 Table A2 Labor’s share and development with standard controls, 1950–2003 Five-year panels with country and time FE, commodity exporters removed (1) (2) (3) (4) (5) –349.0*** –348.2*** –437.9*** –438.8*** –814.1*** 1n(rgdpch) (92.41)* (91.82)* (96.72)* (96.90)* (122.5)** 40.19*** 40.02*** 50.98*** 51.07*** 92.56*** [1n(rgdpch)]2 (10.95)** (10.88)** (11.49)** (11.51)** (14.17)** –1.521*** –1.514*** –1.950*** –1.953*** –3.475*** [1n(rgdpch)]3 (0.430)** (0.427)** (0.451)** (0.452)** (0.544)** –2.480* –3.660* –3.228* –3.453* –6.362* 1n(School Year) (2.013) (2.072) (2.163) (2.243) (3.345) 1.770** 1.343* (1.373) 2.187** [1n(School Year)]2 (0.809)* (0.848) (0.853) (1.093)* 0.153** 0.159** 0.153** 0.157** 0.108** Investment (0.0867) (0.0862) (0.0891) (0.0898) (0.0870) –0.0281 0.309** 0.501* 0.539* 0.186* Population growth (0.559) (0.576)* (0.602) (0.611) (0.582) –0.0428* –0.0409* –0.00624 Institution (0.0428) (0.0391) (0.0373)* –0.00773* –0.0164* Openness (0.0200)* (0.0193) –1.074*** 1n(inf lation) (0.335)** 1042*** 1041*** 1280*** 1283*** 2414*** Constant (258.5)*** (256.8)*** (269.6)*** (270.2)*** (352.8)*** Observations 388 388 368 368 351 R2 0.118 0.132 0.151 0.152 0.257 # Countries 81 81 78 78 74

*** p < 0.01, ** p < 0.05, * p < 0.1 Notes: Robust standard errors in parentheses. The removed commodity exporters are the same as in table A1. Source: Author’s calculations.

27 Table 1 Correlation between the operating surplus of private unincorporated enterprises (OSPUE) and naive definitions (1) (2) (3) Variables Correlation Pooled Panel, FE LaborShare 0.629*** 1.108*** Naive 0.737 (0.0332)* (0.0252)* 27.40**** 4.288*** Constant (1.766)** (1.219)** Observations 855 855 R2 0.543 0.709 # Countries 61

*** p < 0.01, ** p < 0.05, * p < 0.1 Note: Robust standard errors in parentheses. Source: Author’s calculations.

Table 2 Labor’s share and real GDP per capita, 1950–2003 (1) (2) (3) (4) (5) (6) Variables Yearly, FE Yearly, FE 5Y Avg, FE 5Y, FE 5Y, FE 5Y, FE –283.8**** –311.2**** –249.0**** –262.7*** –14.41** –832.6**** 1n(rgdpch) (34.10)** (33.39)** (69.14)** (67.65)* (8.640) (588.2)*** 32.21*** 35.26*** 28.35*** 29.78*** 0.972* 132.6**** [1n(rgdpch)]2 (3.909)* (3.827)* (8.022)* (7.853)* (0.499) (104.6)*** –1.196*** –1.306*** –1.052*** –1.099*** –9.238* [1n(rgdpch)]3 (0.148)** (0.145)** (0.308)** (0.302)** (8.199) 0.239* [1n(rgdpch)]4 (0.239) –0.104*** –0.124*** Year (0.0151)* (0.032)** 861.1**** 1149*** 757.4**** 1046*** 95.54** 1970 Constant (98.52)** (101.6)* (197.2)*** (203.7)* (38.08)* (1229) Observations 2406 2406 552 552 552 552 R2 0.088 0.056 0.087 0.066 0.062 0.089 # Countries 123 123 123 123 123 123

*** p < 0.01, ** p < 0.05, * p < 0.1 Note: Robust standard errors in parentheses. Source: Author’s calculations.

28 Table 3 Labor’s share and development with standard controls, 1950–2003 Five-year panels with country and time fixed effects Variables (1) (2) (3) (4) (5) –351.8*** –357.4**** –439.6**** –439.3*** –746.7***** 1n(rgdpch) (87.53)* (87.13)** (91.48)** (91.71)* (115.6)***** 40.92*** 41.56*** 51.63*** 51.59*** 85.12**** [1n(rgdpch)]2 (10.33)** (10.28)** (10.82)** (10.84)** (13.28)*** –1.567*** –1.594*** –1.996*** –1.994*** –3.208*** [1n(rgdpch)]3 (0.403)** (0.401)** (0.423)** (0.424)** (0.506)** –3.722** –5.007*** –4.682** –4.633** –6.353*** 1n(School Year) (1.750)* (1.845)** (1.911)* (2.034)* (2.773)** 1.633** 1.233** 1.229* 1.837*** [1n(School Year)]2 (0.775)* (0.808)* (0.812) (1.010)** 0.134** 0.144* 0.128** 0.127* 0.0802** Investment (0.0750) (0.0748) (0.0773) (0.0781) (0.0763)* 0.0619 0.357** 0.520** 0.514* 0.0305** Population growth (0.537) (0.552)* (0.574)* (0.582) (0.567)** –0.0320* –0.0324 0.00167* Institution (0.0377) (0.0380) (0.0371)* 0.00140 –0.00691* Openness (0.0193) (0.0189)* –1.078*** 1n(inf lation) (0.293)** 1042*** 1057*** 1276*** 1275*** 2214*** Constant (245.9)*** (244.8)*** (256.1)*** (256.8)*** (334.6)*** Observations 440 440 420 420 402 R2 0.107 0.119 0.135 0.135 0.221 # Countries 92 92 89 89 85

*** p < 0.01, ** p < 0.05, * p < 0.1 Note: Robust standard errors in parentheses. Source: Author’s calculations.

29 Figure 1 Labor’s share and real GDP per capita

Source: Author’s calculations.

30 Table 4 Evolution in the sectoral labor’s share, OECD: 1975–2000

Labor’s share Agriculture Industry Financial svc Nonfinance svc blah (A, B) (C, D, E, F) (J, K) (G, H, I, L–Q) (1) (2) (3) (4) (5) Lshare VA Lshare VA Lshare VA Lshare VA 1975–1979 Avg 58.9 18.10 5.9 64.0 36.3 35.60 16.2 69.6 41.5 2000–2004 Avg 55.6 23.80 2.2 56.0 27.4 38.60 26.7 67.6 43.6 D [1975–2000] –3.3 5.70 –3.7 –8.0 –8.9 3.00 10.5 –2.1 2.1 li , 1975 –40.74 5.12 –23.26 10.75 li , 2000 –31.75 0.43 –17.00 11.98 . (1) vi , t Dli –2.9 0.34 –2.90 0.48 –0.86 . (2) vi , t li , t 0.1 –2.41 1.86 –3.77 4.47 . (3) Dvi Dli 0.8 –0.21 0.71 0.31 –0.04 . (4) Dvi li , t –1.2 1.51 –0.46 –2.44 0.23 (1) + (3) + (4) –3.3 1.64 –2.64 –1.65 –0.67

Notes: Lshare denotes labor’s share (percent); VA: the share of sectoral value-added in GDP (percent). Letters in brackets following sector names correspond to the industrial code of ISIC rev. 3. Source: EU KLEMS database.

Table 5 Decomposing changes within the financial sector, OECD: 1975–2000 Financial Real estate, renting and Real estate intermediation (J) business activities (K) (ISIC rev. 3: 70) (1) (2) (3) Lshare VA Lshare VA Lshare VA 1975–1979 Avg 56.6 5.1 27.2 11.2 6.9 6.6 2000–2004 Avg 54 6.7 34.2 20.1 6.1 9.9 D [1975–2000] –2.7 1.6 7 8.9 –0.8 3.4 li , 1975 –2.23 –31.71 –52.00 li , 2000 –1.61 –21.38 –49.54 . (1) vi , t Dli –0.13 0.79 –0.05 . (2) vi , t li , t –0.11 –3.54 –3.41 . (3) Dvi Dli –0.04 0.63 –0.03 . (4) Dvi li , t –0.04 –2.82 –1.75 (1) + (3) + (4) –0.21 –1.41 –1.84

Note: Column (3), the real estate sector (ISIC rev. 3: 70) is a subsector of column (2) (ISIC rev. 3: K). Source: EU KLEMS database.

31 Figure 2 Evolution of labor’s share, 1970–2000

80 75 70 65 19801985 1990 1995 60 1975 2000 55 50

45 1985 19801990 40 19952000 35 30 25 20 15 10

Labor's share in percent 5 0 2500 7500 12500 17500 22500 27500 0 5000 10000 15000 20000 25000 30000 Real GDP per capita (2000 constant dollars)

1970–74 1980–84 1990–94 2000–04 China India

Source: Author’s calculations.

Figure 3 Cross-country comparison of the labor’s share, 1970–74 average

70 GBR USA CAN DEU DNK 60 IRL FIN ZAF ESP ISL FRA NOR AUS LUX NLD MLT BEL NZL TGO ZWE ITA MUSJAM SDN JPN 50 TTO PRT STP CRI PNG KEN JOR

COL VEN 40 PER CHL BWA KOR DZA MYS CIV GRC BOL GAB ECU 30 BEN CMR Labor's share in percent 20 THA

2500 7500 12500 17500 22500 0 5000 10000 15000 20000 25000 Real GDP per capita (2000 constant dollars)

Labor's share Predicted labor's share

Source: Author’s calculations.

32 Figure 4 Cross-country comparison of the labor’s share, 1980–84 average

70 SWE

GBR FRA DNK DEU USA IRL AUT FIN NLDCAN CHN BEL 60 NZL ZWE JPN AUS ZAF ESP NOR SWZ MLT ITA ISL LUX PRT FJI TTO 50 JAM HUN HKG LKA MUS KORJOR CRI SLB COL KENIND BWA PNG CHL VEN 40 SDN BOL GRC MYS NGA MEX PER 30 CMR ECU BFA THA

Labor's inshare percent

BEN BDIRWA 20 SLE

2500 7500 12500 17500 22500 0 5000 10000 15000 20000 25000 Real GDP per capita (2000 constant dollars)

Labor's share Predicted labor's share

Source: Author’s calculations.

Figure 5 Cross-country comparison of the labor’s share, 1990–94 average

80 MKD

SWE EST ANT GBRFIN CANDNK CHE DEU USA CHN CUB FRA DJI TWN BENLDL ISL 60 ZAF PRT ESP JPN AUS AUT NOR HND NZL PANCRI TTOKOR MLT IRL ITA HKG RUS BHS LKA NAM SVK MUS KEN JOR TURTUN IND PNGZWE ARG BHR BOL NIC BRA DOM COL CHL KWT 40 BWA CIV PRY MEXVEN GRC DZA OMN CMR MAC SEN PHL THA PER IRN ARE 20 NGABEN SLE ECU TZA

0 Labor's inshare percent

-20 2500 7500 12500 17500 22500 27500 0 5000 10000 15000 20000 25000 30000 Real GDP per capita (2000 constant dollars) Labor's share Predicted labor's share

Source: Author’s calculations.

33 Figure 6 Cross-country comparison of the labor’s share, 2000–2004 average

70 SWE ANT ISL CHE HRV DNK SVN ISR GBR USA FRA ESP DEU NLDCAN 60 PRT JPNBEL AUT SLE HND CHN BLR EST FIN AUS HKG RUS MKD CRI ZAF MLT UKR NOR PAN TWN CYP KEN HUN KOR 50 NZL SGP CZE ITA ARM CHL CUB SVK BHS MDA JOR BRA POLLVALTU IRL TUR NAM TUN MUS BOLNIC PRY DOMBGR MAC 40 IND FJI COLKAZ GRC BHR GTM MEX TTO THAVEN MNG KGZ EGY SAU KWT 30 MOZ PHL OMN PER BWA ARE TCD CIV BFA AZE DZAIRN SEN TJKCMR PNG QAT 20 LSO NER NGA

Labor's inshare percent 10 TZA

0 2500 7500 12500 17500 22500 27500 32500 37500 0 5000 10000 15000 20000 25000 30000 35000 40000 Real GDP per capita (2000 constant dollars) Labor's share Predicted labor's share

Source: Author’s calculations.

Figure 7 Labor’s Share of China, 1978–2004

Note: Data of Labor’s Share from Bai and Qian (2009); Real GDP from PWT6.2

34 Figure 8 Wage share in organized Indian manufacturing, 1973–97

Source: Shastri and Murthy (2006).

Figure 9 Labor’s Share of India, 1980–2007

Note: Labor’s Share from National Sources; Real GDP from PWT6.2

35 Figure 10 Labor’s Share of Spain, 1955–2005

Source: Data of Labor’s Share from Ruiz (2005); Real GDP from PWT6.2

Figure 11 British wage and GDP since the Industrial Revolution

Source: Allen 2007.

36 Figure 12 Historical factor shares, the United Kingdom: 1770–1913

Source: Allen 2007.

Figure 13 Labor’s Share of the United States, 1850–2000

Note: Data from Historical Statistics of the United States 37 Figure 14 Labor’s Share of Japan, 1955–2003

Source: Labor’s Share from Official Sources; Real GDP from PWT6.2

38