Accounting for the Kuznets Curve through Structural. Change

Transcription

1 Accounting for the Kuznets Curve through Structural Change Zhe Zhu University of Virginia December 18, 2017 Abstract I show a positive co-movement between the employment share of manufacturing sector and the Gini coefficient for income. In seven out of ten countries that have reliable long-term data, these two variables rise and fall together. I develop a model with heterogeneous agents in which demand-driven sectoral labor reallocation occurs alongside the evolution of inequality. When the industrialization process starts, the rising price of manufacturing goods relative to agricultural goods leads to and increase in the relative wage for manufacturing workers. Because labor is not freely mobile across sectors, income inequality increases due to a shortage of qualified labor in the high-wage manufacturing sector. After enough individuals acquire the skills to work in manufacturing and services, the relative wages in these sectors fall, reducing inequality. By adding a service sector to Kuznets conjecture and calibrating to Brazil from 1962 to 2010, this model produces a decline in manufacturing employment share, consistent with recent empirical findings in literature of structural change. A counterfactual analysis with reduced labor market friction generate a 20.7% decrease in income Gini coefficient from the benchmark calibration. JEL classification: O11, O41, J31, E24 Keywords: Kuznets Curve, structural change, income inequality, compensating wage differentials I am deeply indebted to my advisors Eric Young and Toshihiko Mukoyama for their constant support and invaluable advice. I am grateful to Latchezar Popov, Zachary Bethune, Sophine Osotimehin, and Leland Farmer for their insightful comments. I also benefitted from conversations with fellow graduate students at University of Virginia, participants in my practice job market talks, and participants at the Huskey Graduate Research Exhibition. All errors are mine. zz5vc@virginia.edu 1

2 1 Introduction Kuznets (1955) proposed a theory that during the process of economic development, the level of income inequality initially increases before reaching a peak, and subsequently decreases. Plotted on a graph with income per capita on the horizontal axis and Gini coefficient on the vertical axis, the Kuznets Curve exhibits an inverted U-shape pattern. 1 Barro (2000) tested this hypothesis using data compiled by Deininger and Squire (1996), and found that the Gini coefficient of household income rises with GDP per capita for values less than $1,636 (1985 U.S. dollars) and falls thereafter. In his paper, Kuznets highlighted the importance of structural change in shaping the Kuznets Curve. He conjectured that the pattern of inequality and growth is generated by the shift of labor from agriculture to manufacturing, or from rural to urban areas. In particular, workers are gradually reallocated into high-paying urban manufacturing sector. This movement initially creates a widening income inequality, and the trend declines when most workers have shifted to manufacturing. In theory, this two-sector model explains the Kuznets Curve perfectly. However, it is inconsistent with recent empirical findings on structural change. A large literature has documented a hump-shaped pattern in manufacturing employment shares for many upper-income countries. 2 In fact, just like Kuznets (1955), manufacturing employment shares were previously thought to increase monotonically. 3 It is only during the past half-century did de-industrialization start to emerge in developed countries. As is noted in Yi et al (2013), the current consensus is that structural change encompasses three distinct patterns: agriculture declines, services rise, and manufacturing follows a hump-shaped pattern 4. Figures 1 and 2 illustrate these patterns in Brazil and 1 The validity of Kuznets Curve had been debated in earlier research. Recent research has generally converged to support Kuznets theory: see Barro (2000) for example. Empirical literature focusing on this topic is discussed in much greater detail in the Appendix. 2 For example, see Yi et al (2013). 3 Early empirical research shows that along the development path, employment share in manufacturing increases while the counterpart in agriculture decreases, see for example, Clark (1957), Kuznets (1957, 1966), and Chenery and Syrquin (1975). This finding is constrained by the development process, as most countries have not yet entered post-industrialization. 4 Recent research documents these patterns, see Maddison (1991) and Buera and Kaboski (2009, 2012) for example. 2

3 Japan. 5 Both countries see dramatic expansion of service sector employment, which account for more than 60% of total employment. On the bottom of both figures, manufacturing employment shares show a clear hump. Previous theoretical work provides various explanations of the Kuznets Curve, but none of this work relates it to structural change across agriculture, manufacturing, and services. Lindert (1986) proposed a mechanism that is the most similar to Kuznets conjecture. He used a data set of England from 1670 to 1911 to argue that the inverted U-shape pattern of wealth inequality resulted from the falling importance of land, which was a crucial factor in agricultural production. But he did not consider the service sector, either. I construct a three-sector model with heterogeneous agents. Structural change is driven by Stone-Geary preferences based on the framework of Kongsamut et al (2001). This non-homothetic utility function produces a gradual demand shift from agricultural consumption to manufacturing, then service consumption. Following Aiyagari (1994), I introduce incomplete markets and heterogeneous agents with idiosyncratic shocks to labor efficiencies. This setting provides a within-sector wage inequality across sectors, which helps generate a smooth Kuznets Curve along the transition. To generate wage inequality across sectors, I assume a heterogeneous sector-specific human capital. Agents cannot work in manufacturing or services unless they have sector-specific skills. This friction impedes the free mobility of labor across sectors, thus creating wage gaps. By adding services into the model economy, I am able to produce labor reallocations consistent with the three patterns shown in figures 1 and 2. On top of Kuznets conjecture, my model produces a declining share of manufacturing employment following the initial rise. In addition, I can capture the massive expansion of services. In the development process, as soon as agents obtain skills, they enter the high-paying manufacturing sector; when the number of qualified workers becomes large enough, the premium of working in manufacturing shrinks, whereas the higher income elasticity of demand in services causes the relative price of service goods to increase, resulting in and increase in the relative wage in services as well. Workers are then attracted into services from manufacturing, generating a decline in manufacturing employment share and a rise in services employment share. 5 More countries can be found in Appendix, Figures A1 A4. 3

4 I also show a co-movement between manufacturing employment share and Gini coefficient of income. These two variables both follow a hump shape in the development process, and I find that they rise and fall together. Figures 3 and 4 show the co-movement of the Gini coefficient and manufacturing labor share in Brazil and Japan. 6 Both countries show inverted U-shape curves, and the peaks of these curves occur at almost the same time, only three to four years apart. Benchmark calibration of my model captures this co-movement. The mechanism behind the co-decline part of the model is explained by inter-industry compensating wage differentials. Time series data show that in many countries, wages from agriculture, manufacturing, and services are never equal. For example, US manufacturing wage has been consistently higher than the other two sectors for a long time. If a wage gap exists in the steady state, there has to be some underlying mechanism that compensates for the low-paying jobs in agriculture or services. A vast literature in labor economics documents the existence of compensating wage differentials 7. Krueger and Summers (1988) find a substantial dispersion in wages across industries. Recent empirical work by Gittleman and Pierce (2012) adds other payments and benefits to wages in the calculation, and they find an even greater inter-industry differential. My model assumes a disutility in both agriculture and manufacturing. If workers decide to join agriculture or manufacturing labor force, they will be compensated with a higher wage. This mechanism generates wage differences even in the steady state. In the transition path, income inequality initially increases due to higher wage in manufacturing. It subsequently declined because workers shift to lower-wage services from manufacturing. Apparently, the assumption of compensating wage differential is crucial in generating declines in both manufacturing employment and Gini coefficient. I calibrate the preference parameters to US industry level price indices and US consumption expenditure shares from 1962 to Technological parameters are calibrated matching time series of Brazilian national account data from IBGE (Instituto Brasileiro de Geografia e Estatstica), 6 Figure A5 12 in appendix documents eight more countries. In seven out of the ten countries, the two curves show co-movement. Developed economies generally experienced decline in both inequality and manufacturing employment share. The developing countries, however, mainly went through simultaneous increase. This coincides with discussion in Yi and Zhang (2013). 7 This question has been an important one in labor economics for many decades. Slichter (1950) was among the first to address it. Subsequent contribution by Krueger and Summers (1987), Dickens and Katz (1987a,b), and Abowd and Kramarz (1999) are foundations of this theory. 4

5 within the time frame of 1962 to By careful calibration of initial distribution of skills and wealth, the model produces co-moving hump shapes for both income Gini coefficient and manufacturing employment share. Two main forces are driving the decline of manufacturing employment share and income Gini coefficient: the high relative wage in manufacturing sector and the shift of demand towards service consumption. For developing countries that are industrializing and experiencing rising income inequality, my model predicts that they can foresee the coming turning point in both inequality and deindustrialization. For developed countries, my model does well in depicting the trend in manufacturing employment share, but not in the Gini coefficient. Piketty (2013) and many other papers have documented a steady increase in income inequality over the last four decades in the United States, but in my model income inequality eventually shrinks. My explanation is that my model does not attempt to account for the contribution of tax schedules on disposable income. According to the most recent work of Hubmer et al (2017), by far the most important driver of this wave of rising inequality in the U.S. is the significant drop in tax progressivity starting in the late 1970s. They also show earnings inequality falls short of accounting for the data. Their finding is consistent with Aghion and Bolton (1997) s trickle-down theory wealth may trickle down from the rich to the poor and produce a Kuznets Curve. This effect will be hampered if redistributive policies are less progressive. Piketty (2013) s theory of unbalanced growth rate of wages and capital returns 8 cannot account for a significant amount of data, either. I conduct a counterfactual analysis with reduced labor friction. In particular, I increase the speed of manufacturing-specific skill acquisition. This exercise reduces the highest point of income Gini coefficient by 20.3% compared to the benchmark. The turning point of the hump also comes earlier than the benchmark. With accelerated transition into manufacturing, wage dispersion is not as large as the benchmark calibration, therefore income is more equally distributed. In another policy experiment, I calibrated my model to US data from 1950 to Model produces a co-decline in manufacturing employment and income Gini coefficient. I shut down the skill acquisition process and re-run the transition. The distribution of sector specific skills is now 8 An earlier paper, Williamson (1985) had the same argument. 5

6 fixed at the 1950 levels, which reduces much of the labor reallocation in the transition path. I find that with a less significant structural transformation, Gini coefficient in 2010 is 6.0% higher than benchmark model result. My research fits into a large literature of structural change. There has long been a discussion of the driving forces behind labor reallocation. Kongsamut et al (2001) and Ngai and Pissarides (2007) are the core contributions in their own respective strands. Ngai and Pissarides (2007) assume TFP growth rates are different across sectors. This price effect approach will produce a constant manufacturing employment share, which cannot account for the hump shape. I employ estimation methodologies used in Herrendorf et al (2013) and Herrendorf et al (2015) to calibrate preference and production parameters in my model. Their conclusion also provided supportive evidence for my assumption of equalized capital share of income. The rest of this paper is organized as follows. In Section II I formally present the model. Section III explains the mechanism to generate a Kuznets Curve along with structural change in detail. Then I discuss compensating wage differentials in Section IV. Section V provides a benchmark model calibrated to US data, and a counterfactual analysis based on that. Section VI concludes. 2 Model 2.1 Production There are 3 production sectors: agriculture, manufacturing, and services, with products denoted A, M, and S respectively. All these sectors use capital and labor in production. Capital is produced in manufacturing sector. All sectors share a common growth rate of TFP, but the levels of productivity are different. The production functions are: A t = η A t F A (K A t, N A t, L t ), M t + I t = η M t F M (K M t, N M t ), 6

7 S t = η S t F S (K S t, N S t ), where K i t and N i t are the capital and labor used in producing goods i. η A t, η M t, η S t are sectoral TFP levels. Investment goods I t is produced in manufacturing sector and invested to capital in next period: I t = K t+1 K t + δk t. Kongsamut, Rebelo, and Xie (2001) use labor augmenting technology to generate a generalized balanced growth where agricultural labor shifts to services. In another word, their model delivers structural change and balanced growth at the same time. Notice in my model growth is generated by TFP growth. Under this assumption the model converges to a balanced growth path with constant labor shares. The labor reallocation process happens during the transitions. When computing the model, I assume Cobb-Douglas form of production function across three sectors, so essentially, neutral technology and labor augmenting technology are interchangeable. 2.2 Households There is a continuum of heterogeneous households, indexed by i [0, 1]. The preferences are displayed by a Stone-Geary utility function, as in Kongsamut, Rebelo, and Xie (2001): U(a t, m t, s t ) = [(a t ā) ρ m γ t (s t + s) θ ] 1 σ 1. 1 σ This utility function drives the structural change by the non-homotheticity among demand for goods from different sectors. This coincides with Engel s Law the share of food consumption will decrease as household s income increases. ā can be viewed as subsistence level of food consumption, and s can be interpreted as home services. Households are heterogeneous in two dimensions: labor efficiency and sector-specific human capital. Labor efficiency follows the pattern in Aiyagari (1993), individuals randomly draw work efficiency units in each period. For heterogeneity in the sector-specific human capital, I use the 7

8 simplest setting that an individual either has the ability to work in the sector or not. Therefore, this human capital measure takes the value of 0 or 1. I assume that everyone is initially endowed with the ability to work in agriculture, but not necessarily in manufacturing or services. Agents get draws to become capable of working outside of agriculture. To make things more clear, I further assume the acquisition of ability is permanent. For instance, once a worker draws 1 for the manufacturing sector, he will be capable of working in manufacturing forever. In addition, an individual is allowed to work in only one sector in each period, the labor endowment is not separable among sectors. Labor efficiency for an individual at time t is denoted as n t, i.i.d over time, with a support [n min, n max ]. I denote sector-specific abilities as h A t, h M t, and h S t. According to the assumptions, h A t = 1 for every individual, for all time; h M 1 = 0 and h S 1 = 0 for all individuals, and from period 0 they started to be randomly selected to possess the ability to enter other sectors. Moreover, since the acquisition is permanent, if h M t = 1, then h M t+1 = 1, if h S t = 1, then h S t+1 = 1. An example of one individual s career ability evolution is shown below: Compensating Wage Differentials Figures 5 and 6 show the relative wage pattern in the United States. Manufacturing jobs almost always pay more than the other two sectors. This relative level of wages may not hold for all countries, but the fact is that in many countries, wages from these three sectors are never equal. In order to account for this wage difference, I incorporate compensating wage differentials in my model. The assumption here is that workers prefer service jobs as a result of the non-pecuniary benefits. A large labor economics literature has documented the existence of this compensating effect, and interpreted this effect as working environments, job security, and benefits, etc. I assume workers get a larger utility if they work in services than in manufacturing. The relative utility 8

9 levels of working in agriculture and manufacturing is ambiguous, it will be calibrated in the model. I write the value functions as the following: V (k, n, h M, h S ) = max{v A (k, n, h M, h S ), V M (k, n, h M, h S ), V S (k, n, h M, h S )} V A (k, n, h M, h S ) = V M (k, n, h M, h S ) = V S (k, n, h M, h S ) = max {Q AU(a, m, s) + βe[v (k, n, h M, h S )]} {k,a,m,s} max {U(a, m, s) + βe[v {k,a,m,s} (k, n, h M, h S )]} max {Q SU(a, m, s) + βe[v (k, n, h M, h S )]} {k,a,m,s} Note that Q A and Q S are scaling factors. Following the assumption that service jobs are more favorable, we can infer that Q S > 1. Benchmark calibration at the steady state shows Q A < 1. This means that agricultural jobs are the least favorite among the three, and service jobs are always preferred. Under this parameterization, the decline in agricultural employment is driven by two factors: non-homothetic utility and largest utility discount for agricultural workers. This parameterization ensures manufacturing sector pays the highest wage among three sectors. Households own risk-free assets. I normalize the price of manufacturing goods to 1, and express the relative price of agricultural goods and services goods by P A t can be formally written in recursive form as: and P S t. The household s problem max E 0 [ V (k0, n 0, h M 0, h S 0 ) ] The choice variables are the sector to work at in each period t, consumption goods {a t, m t, s t } t=0, and asset for next period {k t+1 } t=0. Household s budget constraint in period t depends on her choice of sectoral work. Given h i t = 1, i {A, M, S}, if household decides to work in sector i, her budget constraint can be written as P A t a t + m t + P S t s t + k t+1 (1 + r t+1 )k t + n t w i t. 9

10 2.4 Equilibrium Definition: the recursive competitive equilibrium of the model economy consists of prices { P A, P M, P S, w A, w M, w S, r }, value function V (n, k, h M, h S ), optimal decision rules {g i (n, k, h M, h S ), i = k, a, m, s}, capital and labor distribution of households, x(k, n, h M, h S ), sectoral aggregate capital stock K A, K M, K S and aggregate labor supply N, such that: 1. Households optimization: Given prices, the value function V is a solution to the agent s optimization problem, and g i s are the associated optimal decision rules. 2. Firm s optimization: Prices satisfy the following marginal conditions: r = P A η A F A K(K A, N A ) = η M F M K (K M, N M ) = P S η S F S K(K S, N S ), w A = P A η A F A N (K A, N A ), w M = η M F M N (K M, N M ), w S = P S η S F S N(K S, N S ), 3. Aggregation: Aggregate capital stock and labor supply are consistent with the stationary distribution, or: K A + K M + K S = kdx, N A + N M + N S = x x ndx, 3 Dynamics The heterogeneity setting combined with the fact that sectoral job selection is a choice variable make it impossible for us to fully exhibit the dynamic pattern by analytical solutions. However, by some basic intuition and derivation from the equilibrium conditions, we can at least take a first look before the model is computed numerically. 10

11 Marginal product of capital will be equal across sectors because of the unique interest rate, therefore we have P A t η A t F A 1 (K A t, N A t, L t ) = η M t F M 1 (K M t, N M t ) = P S t η S t F S 1 (K S t, N S t ) = r t, t. (1) Along with the market clearing condition for capital, we can pin down K A t, K M t, and K S t. Also from the firm s profit maximization problem we can derive relationships between sectoral wages and prices: P A t η A F A 2 (K A t, N A t, L t ) = w A t ; (2) η M F M 2 (K M t, N M t ) = w M t ; (3) P S t η S F S 2 (K S t, N S t ) = w S t. (4) Then we derive the first order conditions for the household s maximization problem: for a t : for m t : ρ[(a t ā) ρ m γ t (s t + s) θ ] σ (a t ā) ρ 1 m γ t (s t + s) θ = λ t P A t ; (5) γ[(a t ā) ρ m γ t (s t + s) θ ] σ (a t ā) ρ m γ 1 t (s t + s) θ = λ t ; (6) for s t : θ[(a t ā) ρ m γ t (s t + s) θ ] σ (a t ā) ρ m γ t (s t + s) θ 1 + µ t = λ t P S t ; (7) The nonnegativity constraint only applies to s t because a t and m t are necessities defined by the utility function 9. for k t : λ t = βλ t+1 E(1 + r t+2 ); (8) 9 In fact, all through the discussion I assume the income level is high enough to support A t > Ā and M t > 0. If the income level is too low to satisfy these conditions, the individual will consume nothing to get the highest possible utility, which is a trivial scenario. 11

12 3.1 Structural Change I first show the dynamics of sectoral labor allocation. As is mentioned before, structural change is driven by the non-homotheticity of the preferences. We see this from equations (5)-(7). Positive amount of a t and m t have to be ensured. In particular, a t > ā has to be satisfied first. When facing a tight constraint, the priority is to keep alive with food consumption. The first part on the left hand side of equation (7) is the marginal utility obtained from one unit of services consumption. At a low level of income, household is not able to afford high level of consumption of any good. Because of the existence of home services, s, the marginal utility of services is relatively small compared to agriculture and manufacturing (note that 0 < ρ, γ, θ < 1). The threshold for individual to start consuming services is when the per dollar marginal utility of agriculture and manufacturing both fall below the marginal utility created by home services. We can express the threshold conditions as: ρ[(a t ā) ρ m γ t s θ ] σ (a t ā) ρ 1 m γ t s θ P A t < θ[(a t ā) ρ m γ t s θ ] σ (a t ā) ρ m γ t s θ 1 P S t (9) γ[(a t ā) ρ m γ t s θ ] σ (a t ā) ρ m γ 1 t s θ < θ[(a t ā) ρ m γ t s θ ] σ (a t ā) ρ m γ t s θ 1 P S t (10) further simplification yields: P S t s θ < P A t (a t ā) ρ (11) P S t s θ < m t γ (12) only when both (11) and (12) are satisfied, the individuals start to consume positive services. After S t becomes positive, we can drop the nonnegativity constraint, equalizing the per dollar marginal utilities across all sectors. The optimal composition of consumption is given by: 12

13 P A t (a t ā) ρ = m t γ = P t S (s t + s) θ (13) Notice that the most important dynamic pattern is about the labor shift along with development. In this model, in particular, we care about labor reallocation along the transition path. We have to analyze the income effect of demand of different goods. First we investigate the early stage of development. The argument above shows that for now we can ignore the services because nothing is spent on that sector. Suppose individuals face fixed income every period, denoted by I t : P A t a t + m t = I t, we can easily derive the consumption of each good: a t = ρ γ + ρ I t p A t + γ γ + ρā, m t = γ γ + ρ (I t P A t ā). This simple example allows us to figure out the income effect. When I t increases, the change in relative expenditure depend on ρ, γ. If γ > ρ, clearly the relative expenditure of manufacturing goods will increase. Previous research on structural change provides calibration of these parameters. Caselli and Coleman II (2001), in a two sector Stone-Geary utility function without services, use US consumption data from 1959 to 1996 to calibrate ρ = 0.01 and γ = Echevarria (1997) uses international data from 34 countries to calibrate these parameters for a slightly different utility function, her results are ρ = 0.19, γ = 0.36, and θ = Even though this set of parameters does not show a huge gap between manufacturing goods and agriculture goods as in Caselli and Coleman II (2001), γ is still substantially larger. Based on these calibrated results, we are confident to say that the manufacturing expenditure will rise faster with increase in income. As income increases along with development, the income share of manufacturing expands, demand for labor in this sector also increases. By assumption of the sectoral specific human capital, acquisition of manufacturing skills is slower than service abilities, therefore there is a shortage of labor supply in 13

14 manufacturing. This imbalance between supply and demand will push up the wage rate. Individuals who get the draws to qualify for manufacturing jobs will choose to reallocate themselves into the high-paying manufacturing sector. This process is the structural change in the early stage of development. Now we turn to the later stage of development. Again we will use the fixed income example to demonstrate the income effect. When the economy is richer, services can no longer be excluded from discussion. Now we have P A t (a t ā) ρ = m t γ = P t S (s t + s) θ and Solving this system of equations, we get: P A t a t + m t + P S t s t = I t a t = ρ I t + Pt S s + (1 ρ)ā, Pt A m t = γ(i t + P S t s P A t ā), s t = θ I t Pt A ā (1 θ) s. Pt S This set of equations again enables us to check the dynamic pattern of sectoral employment. There are two main forces in this stage. The first force is the rise of services. As mentioned before, Echevarria (1997) provides calibrated result that θ = 0.45 > γ = 0.36 > ρ = The services enjoys the largest share in preferences. The mechanism is as follows: individuals will first satisfy the needs of food to prevent starving; after some level of income is reached, they turn to manufacturing because manufacturing goods delivers higher marginal utility when they are not hungry; the third level living standard will allow them to enjoy the highest satisfaction from services. The income effect will increase the relative expenditure on services in the later stage of development. Therefore we will see the expansion of services sector, labor will be allocated to 14

15 produce services goods. The second force is the decline in wage premium in manufacturing. As we progress to the second stage of development, the share of individuals who qualify for manufacturing jobs will be constantly increasing to a certain point where the wage in manufacturing is no longer the highest. The services sector will enjoy the highest wage rate, causing the manufacturing workers to reallocate themselves into services once they are endowed with the ability to work in services. Hence, the later stage of development features a decline in labor shares in both agriculture and manufacturing, and a rise in services. In order to show this in a simulated time series, careful calibration is required since the structural change is a result of interaction of a lot of prices. I discuss the calibration in detail in next section. Combining the early and later stage of development, this model is able to generate a sectoral labor reallocation pattern with declining agriculture, inverted U-shaped manufacturing, and rising services. Because the prices play a key role in determining the expansion and contraction of sectors, we have to be careful about calibrating the model to match the data. 3.2 Inequality The other dynamic pattern we are interested in is the evolution of inequality. With the first order conditions, we can now use comparative statics to take a first look at this process. From equations (2)-(4) we can write the relative wage of manufacturing and services to agriculture as: w M t w A t = η MF2 M (Kt M, Nt M ) η A F2 A (Kt A, Nt A, L t ) 1 P A t (14) wt S wt A = η SF2 S (Kt S, Nt S ) η A F2 A (Kt A, Nt A, L t ) P S t P A t (15) Notice that on the right hand side of equations (14) and (15), 1 P A t and P S t P A t are the relative price of manufacturing goods and services goods. Holding other variables constant, the relative wages in manufacturing and services are increasing functions of relative prices in respective sectors. Previous analysis already described the mechanism of Stone-Geary utility function: the relative demand of manufacturing and services will gradually increase, push up the relative prices of these 15

16 goods. By (14) and (15), relative wage outside agriculture will increase, qualified workers will quit agriculture jobs to pursue higher wages. Since the majority of labor force still works in agriculture sector, the minority takes larger and larger share of the economy s total income, income inequality will consequently rise. But the rising trend cannot last forever, because as more workers master skills for other sectors during the development process, wage gap is gradually eliminated. Income inequality then decreases, producing a Kuznets curve. 4 Benchmark Model Results For benchmark calibration, I take Brazil from 1962 to 2010 as the target. As illustrated in figure 4, Brazil has entire humps for both curves, naturally it is the best experiment field. TFP grows at same rate across three sectors and the rate g is constant. Production functions are assumed to be Cobb-Douglas across all three sectors, with same capital share of income α. This assumption is reasonable and it simplifies model computation 10. Herrendorf et al (2015) find that different capital shares of income across sectors do not catch too much of the structural change in the US. There are six parameters in the Stone-Geary utility function to calibrate. Since Brazil does not have very reliable data source on expenditure shares before 1989, I calibrate these preference parameters to US from 1962 to Essentially, I am assuming households from Brazil and US share a same utility function. It is no harm to make this assumption, and the benefit is that these parameters can be calibrated with complete data. I adopt a discrete choice framework in computation to smooth value functions and decision rules. This will greatly speed up model solution. In particular, I add a transitory shock ɛ that is drawn from G(ɛ) which is assumed to be a type 1 extreme value distribution with scale parameter 1/α ɛ. An individual s recursive decision problem is then given by V (k, n) = max{v A (k, n) + ɛ A, V M (k, n) + ɛ M, V S (k, n) + ɛ S } 10 Using same capital shares of income is that in every period of transition, there exists a relationship P Aη A w 1 α A = P Sη S w 1 α S When computing the transition, I can use this relationship to infer the implicit capital and labor distribution across sectors. Instead of solving a system of nonlinear equations, essentially I solve a system of linear equations.. 16

17 where the conditional value function is given by V i (k, n, h M, h S ) = max {Q iu(a, m, s) + β {k,a,m,s} V (k, n, h M, h S, ɛ)dg(ɛ)} is the value associated with a specific choice of sector i A, M, S, and Q A > Q S > Q M = 1. Given the above specification, I can write probabilities for each discrete choice of sectors P r(i k, n) = exp{α ɛ V i (k, n)} j {A,M,S} exp{α ɛv j (k, n)} and expected value V (k, n) = γ E α ɛ + 1 α ɛ ln( where γ E = is Euler s constant. i {A,M,S} exp{α ɛ V i (k, n)}) The benefit of applying discrete choice literature to my model is it great reduces kinks in both value functions and decision rules. Now every choice is chosen with a positive probability, instead of choosing the maximum value with probability 1. It is also easy to match the fact that workers will choose the largest value function. Scale parameter α ɛ can be adjusted to make sure the largest value will be chosen with a very close to 1 probability. 4.1 Parameter Values Table 1 shows the parameters values I chose. I set σ to be 1, so the utility function now takes the form of natural logarithm. For the other five preference parameters, I follow Herrendorf et al (2013) s method using a different time span to estimate them. Q A, Q S, π A, and π S are calibrated from the model. The first two govern the relative wage, so they are calibrated from a steady state computation. The latter two govern the speed of ability acquisition and model convergence, they are calibrated in the transition. Note that to account for the relative wage between manufacturing and service jobs, Q S is set to be larger than 1 in every set of parameters. For simplicity, I set relative TFP levels η A and η S to their average levels, data source of these two parameters 17

18 are from Penn World Table. 4.2 Co-movement Figure 7 illustrates model result from benchmark calibration. The result shows a clear comovement of manufacturing employment share and income Gini coefficient. To match the initial level of manufacturing employment, I assume that in the initial distribution of skills, only 17.5% of households are able to work in manufacturing. This ensures that we observe the rising part of both curves. In terms of matching data, as shown in Figure 8, income Gini coefficient in the model changes more drastically than in the data. This is due to a higher intra-sectoral inequality setting. This can be controlled by labor efficiency shocks. However, to match both ends of the transition, the highest point of income Gini is higher than data. Figure 9 shows the employment shares in the data and in the model. All three sectors are matched with good fit. Three distinct trends are captured by the model as well. 5 Counterfactual Analysis 5.1 Faster Industrialization In this section I perform a simple experiment on the benchmark to examine the effect of reducing labor friction. In particular, I increase the speed of manufacturing skill acquisition. There are two possible effects. One, with a faster transition into industrialized economy, income distribution is higher than benchmark. The magnitude of this effect depends on the level of compensating wage differentials in services. When there is a large compensating wage, services will start to grow earlier, thus keeping manufacturing employment from uncontrolled increase. Two, with faster skill acquisition, supply of manufacturing workers is larger, therefore reducing the wage gap between manufacturing and agriculture. In this sense, the initial income inequality will be lower. I now set π M to be 0.012, and keep π S unchanged. Figure 10 depicts the resulting manufacturing employment share and income Gini coefficient. Apparently, this change generates a higher manufacturing share 18

19 with a faster transition, but income Gini will be lower at its maximum point. Compared to the benchmark calibration, income Gini decreases from 0.87 to 0.69 in the counterfactual. Figure 11 serves as an illustration of comparison among data, benchmark model, and counterfactual analysis. In terms of matching data, Gini coefficient in the counterfactual analysis matches better at high levels of inequality, but falls much faster than data in the decreasing episode. Figure 12 depicts this trend. Figure 13 shows model fit for employment shares. This counterfactual model still provide a qualitatively correct match to data. According to this result, the effect of larger supply of manufacturing workers dominates the effect of larger manufacturing employment shares. Figure 14 provides a clear explanation of the mechanism. With increased skill acquisition speed in manufacturing, there will be sufficient supply of manufacturing workers. Wages in agriculture and services catch up faster with manufacturing wage. This effectively reduces initial wage dispersion and inequality. The policy implication is clear. Policies targeted at accelerating industrialization create a faster and larger manufacturing work force, but alleviate rising income inequality. 5.2 United States I run another calibration to US data from 1950 to The transition in US is very different from Brazil. Figure 15 shows the sectoral employment shares in the model versus in the data. Generally, model provides a good fit and exhibit the correct trends. One may notice that manufacturing labor share does not show an increase phase over the chosen period. This is true in US data. Kuznets theory may apply to development process that starts from an agricultural economy. However, United States in 1950 is already a highly industrialized country. There is evidence that US had a hump shape in manufacturing employment share 11. I do not use data earlier than 1950 because Gini coefficient is not recorded very accurately back then. 11 See Yi and Zhang (2013) for example. 19

20 5.2.1 Inequality Figure 16 shows Gini coefficient from data and model. Apparently model cannot even catch the obvious trend that US income gap has been steadily rising since the 1970s. Here I only look at the contribution of structural change on income inequality, so this model is abstracted from many factors that can influence Gini coefficient. In addition, Gini coefficient in my model is decided by several conditions. One is initial distribution of asset holdings among households. A more skewed distribution will generate a higher Gini coefficient. Second condition is the choice of Q A and Q S, the utility-compensating parameters for agricultural and service workers. If these numbers are large, the model will compensate this utility difference with a wider gap between sectoral wages, thus creating a larger inequality. The third condition is the value of π M and π S, the ability acquisition speeds. If workers learn skills fast, earnings inequality will not have a very substantial increase at all. As I have previous mentioned, the main force that drives income inequality in my model is earnings differences. Wealth inequality, or asset positions, is not an emphasis in this paper. The general consensus on the reason for US income inequality rising from 1970s is unequal asset positions. Return on asset and education premium are the main forces behind this wave of rising income inequality. Since my model does not account for these facts, the model generated Gini coefficients cannot match data very well Co-movement Figures 17 shows co-movement data and model results from model. Apparently, US data cannot tell the same story in figures 3 and 4, but results from my model seem to deliver a consistent story with figures 3 and 4, there is decline in both manufacturing labor share and Gini coefficient. Again, increasing inequality in US since the 1970s is a well known fact, and my model apparently does not provide the underlying reasons for this trend. 20

21 5.2.3 Fixed Skill Distribution I run an experiment where I shut down the skill acquisition channel. This will greatly reduce the magnitude of labor reallocation. It will not stop reallocation completely because the initial distribution is set so that 70% of the workers can work in services, and 47% can work in manufacturing. There will not be a change in this composition, but there will be some degree of labor reallocation. Figure 19 illustrates the implied structural change. Now there is a lower bound for agricultural employment share, since there are a certain number of workers who cannot leave agriculture.shifts into manufacturing and services both slow down. Wage rates in manufacturing and services are higher than the benchmark calibration. This is because the relative price is higher in these two sectors because of limited supply of labor. Figure 20 shows the implied Gini coefficient. Income inequality still declines in general, but slower than before. This is due to the fixed number of agricultural workers. In an environment where these workers can acquire skills to enter services, inequality will decrease because service wage is in between agricultural wage and manufacturing wage. It fills in the gap between high income earners and low income earners. The last period Gini coefficient is 6.0% higher than benchmark calibration. 6 Conclusion Kuznets Curve is an old hypothesis, I still find it interesting because some developing countries are currently experiencing a fast growth accompanied with rising inequality. Kuznets had his own conjecture for the underlying mechanism of his curve, however this conjecture has not been formally presented. The contribution of this paper is to create a link between manufacturing employment share and inequality level. I find that in the development process, there is positive correlation between manufacturing employment share and Gini coefficient. The theoretical framework has some explanatory power for the positive correlation, and the numerical results from Brazil is consistent with my hypothesis. Counterfactual analysis for developed economies shows that structural change, in particular, declining manufacturing employment, has an effect of 21

22 reducing income inequality. 22

23 Appendix A. Data Sources and Definitions A1. Sectoral Definition In this paper, I use GGDC 10-sector database as the main source for sectoral employment shares. Agriculture sector includes only itself. Manufacturing in this paper means manufacturing, mining, and construction. All other are services utilities, trade services, transport services, business services, and personal services. Government services is excluded. A2. Preference Parameters To estimate preference parameters, I follow Herrendorf et al (2013) s method. I apply the final consumption expenditure definition of consumption goods. I particularly use Table and Table from BEA s NIPA data. A2. Production Functions The steady state is defined to match 2010 data. In computation, I also use asymptotic convergence to assume ā = c = 0 in the steady state. Therefore, I can infer 2010 relative TFP levels for each sector using relative prices and relative wages. By cross checking BLS major sector multifactor productivity data and Inklaar and Timmer (2012), I am able to compute quantity index for each sector, and then use weighted average to calculate price indexes for agriculture, manufacturing, and services as the only three sectors in the economy. Capital share of income α is assumed to be This has become the new standard measure of capital share of income since the heated discussion of decline in labor share of income. 23

24 Appendix B: Computation Strategy The algorithm follows the steps below: 1. Set 2010 as the steady state, and asymptotically assume ā = c = 0. This gives me constant expenditure shares across goods. Further, I can pin down P A t and P S t by price indexes I constructed using BLS dataset. Relative TFP levels can be obtained from BLS data as well. The questions break down into computing {r, w A, w S }. Parameters that have to be calibrated are {α ɛ, Q A, Q S }. These three parameters are time-invariant, so they don t have to be calibrated during transition. 2. Now with the steady state as the last period of transition, I try to find an origin where the transition path starts. I choose the starting point where the average income is very low. At this stage, I assume a log-normal distribution of initial wealth in 4 different groups of workers. They are in 4 groups because there are only 4 types of skill distribution: A,AM,AS,AMS. I assume these log-normal distributions have different means. Along with the assignment of probability on each type, I can use the 1950 Lorenz curve to calibrate these 4 means. 3. Once we find out an origin and the destination, we can simulate the transition path. First I guess a transition path of prices {r t, Pt A, Pt M, Pt S } 240 t=0, deduce the other prices and aggregate variables on a sectoral level. This forms a whole series of variables on a path. Then use this series and the balanced growth path obtained from step 1, use backward recursion on the value functions to back out the decision rules series, and integrate with stationary distribution. Compare the two series. Update the guess if the guess and the implied series do not agree. When the two series converge, the transition dynamics are simulated. Unlike step 1, in this step to solve the dynamic programming problem, simple grid search combined with local optimization is necessary. The choice variable where to work is dependent on the relative wages and the sector-specific human capital. When the good draw happens and the individual is allowed to enter high paying sectors, the value function has a higher slope. When optimizing, we have to watch out for the kink on value functions. The non-concavity of value functions thus prevent us from using local optimization. Fortunately, extreme value distribution solves this problem. Policy functions should be everywhere differentiable. 24

25 Appendix C: Kuznets Curve: Literature at a Glance First endeavor to validate Kuznets Curve generally focuses on individual countries. Only stylized facts are required, no estimation is necessary. Historical evidences found from developed countries seem to support the hypothesis. Williamson (1985) shows that in Britain the income Gini coefficient rose from in 1823 to in 1871, then decreased to in For Germany, Dumke (1991) finds the income share of the top 5 percent increased from 28.4 percent in 1880 to 32.6 percent in 1900, then fell to 30.6 percent in 1913, and Kraus (1981) finds the same share dropped to 6.2 percent in For France, according to Morrison (1991, 1997), the income share of the top decile reached the peak at around 50 percent in 1870, then reduced to 45 percent in 1890, further reduced to 36 percent in Sweden also experienced the Kuznets Curve type of inequality evolution as noted by Soderberg (1987, 1991). More recent experiences from developing countries show mixed evidences. For example, Brazil and Colombia generally fit into the Kuznets Curve pattern. The East Asian Miracle countries (Korea, Taiwan), however, did not experience the Kuznets Curve, despite the fact that they experienced rapid growth after WWII. Table 2 and 3 show Gini coefficients in Brazil and Taiwan. As a result of the conflict in evidences found from different individual countries, cross country evidence started to be intensively investigated. As is noted by Barro (2000), early empirical work confirms the Kuznets hypothesis with data through 1970s (see Ahluwalia (1976a, 1976b)), but the evidence has weakened ever since (see Anand and Kanbur (1993), Deininger and Squire (1996, 1998)). Barro (2000) uses a new data set and finds that the evidence did not weaken, Gini coefficient rises with GDP per capita for values less than $1636 (1985 U.S. dollars) and falls thereafter. Galbraith and Kum (2002) find the industrializing countries generally support Kuznets hypothesis. Huang and Lin (2007) use a semiparametric Bayesian inference strategy and discover an inverted -shape instead of an inverted U-shape. But this is approximately in line with Kuznets theory. 25

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29 Figure 1: Employment Shares in Japan Figure 2: Employment Shares in Brazil 29

30 Figure 3: Comovement of manufacturing employment shares and Gini coefficient Figure 4: Comovement of manufacturing employment shares and Gini coefficient 30

31 Figure 5: Sectoral Wages in US: Figure 6: Agriculture and Service Wages Relative to Manufacturing Wages 31

32 Figure 7. Entire hump shape for both manufacturing employment share and Gini coefficient 32

33 Figure 8. Gini coefficient: Model vs. Data 33

34 Figure 9. Employment Shares 34

35 Figure 10. Counterfactual: Comovement 35

36 Figure 11. Comovement: Data vs. Model vs. Counterfactual 36

37 Figure 12. Counterfactual: Gini Coefficient 37

38 Figure 13. Counterfactual: Employment Shares 38

39 Figure 14. Relative Wages: Counterfactual vs Benchmark 39

40 0.9 Figure 8. Sectoral employment shares: model vs. data ashare:data ashare:model mshare:data mshare:model sshare:data sshare:model year Figure 15. US employment shares: model vs data 40

41 Figure 16. US Gini coefficient: model vs data 41

42 Gini MSHARE Figure 16. US Gini coefficient: model vs data 42

43 0.9 Figure 7. Relative wages amwage:model amwage:data smwage:model smwage:data year Figure 18. Relative Wages 43

44 Figure 19. Employment shares: data vs. benchmark model vs. restricted model 44

45 Figure 20. Gini coefficient: benchmark model vs. restricted model 45

46 parameter value calibration method β 0.99 Standard discount factor δ Standard depreciation rate σ 1.0 Fixed at 1 ρ 0.02 Match US expenditure share and relative prices γ 0.15 same as above Ā 0.4 same as above S 1.12 same as above g TFP growth rate α s average capital share Guerriero (2012) Q A 0.4 calibrated from steady state Q S 2.1 same as above α ɛ 1.32 same as above π M model calibration in transition π S same as above table 1: parameter values 46

47 Appendix D: Supplemental Diagrams Data Source for Figure A1-A4: Groningen Growth and Development Center 10 Sector Database. Figures A1-A4: ITALY, KOREA, SPAIN, AND TAIWAN. 47