The B.E. Journal of Macroeconomics Contributions Volume 11, Issue 1

2011

Article 42

The Price of Egalitarianism Yongsung Chang∗

∗ †

Sun-Bin Kim†

University of Rochester and Yonsei University, [email protected] Yonsei University, [email protected]

Recommended Citation Yongsung Chang and Sun-Bin Kim (2011) “The Price of Egalitarianism,” The B.E. Journal of Macroeconomics: Vol. 11: Iss. 1 (Contributions), Article 42. Available at: http://www.bepress.com/bejm/vol11/iss1/art42 c Copyright 2012 De Gruyter. All rights reserved.

The Price of Egalitarianism∗ Yongsung Chang and Sun-Bin Kim

Abstract Using a standard incomplete-markets model, we compute the welfare of two socioeconomic systems: laissez-faire and egalitarianism. The egalitarian system (in which after-tax wages are compressed) provides insurance against income risks but at the cost of inefficiency: it undermines productive workers’ incentives to work. When the stochastic process of idiosyncratic productivity shocks are calibrated to match the earnings inequality, the egalitarian society yields a much higher welfare as the insurance benefit dominates the efficiency loss. However, when the idiosyncratic productivity shocks are calibrated to capture the ex-post heterogeneity of earnings only, households are better off under laissez-faire if the labor supply is elastic enough. Transition between the two regimes is computed. When the wage compression is removed from the egalitarian steady state, the inequality emerges quickly and reaches its laissez-faire steady state in 20 years. KEYWORDS: egalitarianism, laissez-faire, welfare, income risks, efficiency

∗

We thank Romans Pancs, Josep Pijoan-Mas, Gianluca Violante, Fatih Guvenen, two anonymous referees, and seminar participants for valuable comments. Correspondence to Chang: Department of Economics, University of Rochester, Rochester, NY 14627, U.S.A. Emails: Chang: [email protected]. Kim: [email protected]. We acknowledge the support from the Korean National Research Foundation (NRF-2011-32A-B00028).

Chang and Kim: The Price of Egalitarianism

1

Introduction

A general equilibrium model with incomplete-markets and heterogeneous-agents (e.g., Bewley (1986), Aiyagari (1994), and Huggett (1995)) has now become a workhorse for macroeconomic analysis. Using this framework, we compute the welfare of the population in two polar socio-economic systems: laissez-faire and egalitarianism. The model economy extends Aiyagari’s (1994) model to endogenous labor supply (e.g., Pijoan-Mas (2006) and Chang and Kim (2007)). Workers are identical in preferences but face uninsurable individual productivity shocks and a borrowing constraint, which leads to a non-degenerate equilibrium distribution of earnings and wealth. In this environment workers have to insure themselves against future income uncertainty by working more—a mechanism emphasized by Pijoan-Mas (2006)—and saving more. An egalitarian progressive tax policy that equalizes aftertax wages provides an effective insurance against income risks.1 However, such a policy is associated with an efficiency loss, since it discourages highly productive workers’ incentives to work (e.g., Heathcote, Storesletten, and Violante (2008)). Our “laissez-faire” economy is calibrated to capture some of the salient features of the earnings and wealth distributions of the U.S. economy. For the benchmark economy (referred to as “Model I”), the magnitude of idiosyncratic shocks is calibrated to match the overall households earnings inequality in the PSID. When the egalitarian policy is adopted, the society yields a much higher average welfare than under laissez-faire: the insurance benefit dominates the efficiency loss. For example, when the elasticity of labor supply is equal to 1, average welfare under egalitarianism is higher than that under laissez-faire by 18% in consumptionequivalence units. While the elasticity of labor supply is crucial in the welfare cost-benefit analysis, egalitarianism consistently dominates laissez-faire for a wide range of elasticity of labor supply (between 0.25 and 4). In our model economy, workers are ex ante identical but ex post heterogeneous due to idiosyncratic productivity shocks. Not all cross-sectional variations in earnings are risks. Some of them may be foreseen by economic agents and reflect ex ante heterogeneity such as ability. We consider an alternative specification (referred to as “Model II”) where the stochastic process of idiosyncratic shocks are estimated by the wages of relatively homogeneous workers. Following Chang and Kim (2007), by restricting the data sample to a homogeneous group (households with heads who are high school graduates and whose age is between 35 and 55), we hope to capture only the ex post heterogeneity (risks). Under this specification, the 1 An extreme form of egalitarianism would be communism. For example, “The whole of society will have become a single office and a single factory with equality of labor and equality of pay,” from page 91 of The State and Revolution by V.I. Lenin.

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welfare results can be reversed if the labor supply is elastic enough. The laissezfaire economy yields a higher welfare if the elasticity of labor supply is larger than 1.8. However, even in this case the welfare cost of egalitarianism is fairly small, since the insurance benefit nearly offsets the efficiency loss. Egalitarianism creates a trade off: insurance benefit versus efficiency loss. This trade-off is numerically decomposed by studying an efficient allocation under an economy with complete capital markets (which is referred to as a “complete markets” economy). When the complete set of contingent claims is available, workers effectively eliminate income risks by trading contingent claims. The welfare gap between the “complete markets” and “laissez-faire” economy reflects the welfare gain from eliminating income risks. The welfare gap between the “complete markets” and “egalitarian” economy reflects the efficiency cost from distorting labor supply because income risks are completely eliminated in both economies.2 For example, in Model I (large risks) the above mentioned 18% welfare gain of egalitarianism consists of a 31% welfare gain from the insurance benefit and a 13% efficiency loss from distorting labor effort. We also compute the equilibrium transition path between regimes. Including the transition period does not alter our welfare results substantially because the transition occurs rapidly in our model economies. Starting with an egalitarian steady state, when the wage compression is removed, individual households have to accumulate more assets as a measure of precaution. According to our simulation, inequality emerges quickly as the Gini coefficient of wealth distribution rises from 0 to 0.3 in 5 years after abolishing the wage compression. The economy approaches the laissez-faire steady state in 20 years. The closest to our study is Pijoan-Mas (2006), who first analyzes the welfare cost of market incompleteness in an Aiyagari model with endogenous labor effort. While both models share the incomplete-markets economy setting, we are interested in comparing the egalitarian and laissez-faire economies, whereas he is mainly interested in the welfare cost of market incompleteness (complete versus incomplete markets). We also provide a comparison with complete markets. As noted above, this allows us to decompose the welfare cost of egalitarianism into the insurance benefit (laissez-faire vs. complete markets) and the efficiency loss (egalitarian vs. complete markets). The remainder of the paper is organized as follows. Section 2 lays out a benchmark model economy with incomplete capital markets and uninsurable income risks. In Section 3, the laissez-faire version of the model is calibrated to the 2 Utility

is assumed to be separable between consumption and leisure. Thus, under the complete markets economy, workers supply labor effort according to their realized productivity: the most productive worker works the most and the least productive worker supplies the least amount of labor.

http://www.bepress.com/bejm/vol11/iss1/art42 DOI: 10.2202/1935-1690.2243

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Chang and Kim: The Price of Egalitarianism

U.S. economy. We then compute the egalitarian policy that compresses after-tax wages in this economy. We compare the steady states of the two regimes as well as the transition between them. Section 4 summarizes the results.

2

Model

The benchmark economy extends Aiyagari’s (1994) model to one with endogenous labor supply (e.g., Pijoan-Mas (2006) and Chang and Kim (2006, 2007)). There is a continuum (measure one) of workers who have identical preferences and face uninsurable idiosyncratic productivity shock x, which follows a Markov process with a transition probability distribution function πx (x |x) = Pr(xt+1 ≤ x |xt = x). A worker is assumed to have separable preferences over consumption ct and hours worked ht : 1+1/γ

u(ct , ht ) =

h ct1−σ − 1 −B t 1−σ 1 + 1/γ

(1)

Workers trade claims for physical capital, at , which yields the real rate of return rt . Capital markets are incomplete. Physical capital is the only asset available to workers, and workers face a borrowing constraint: at ≥ a for all t. The representative firm produces output according to a constant-returns-toscale Cobb-Douglas technology in capital, K (which depreciates at rate δ each  t period), and effective units of labor, Lt (= ht xt dμ), where μ is the distribution of workers defined over asset holdings at and productivity xt :3 Yt = F(Lt , Kt ) = Ltα Kt1−α . Without tax, a worker earns wt xt ht , where wt is the wage rate per effective unit of labor. For simplicity, the individual state, represented by his asset holdings and productivity (a, x), is public knowledge (known to the government) and the government imposes a tax rate (subsidy rate if negative), −∞ < τ(at , xt ) < 1, on  wages where after-tax earnings are 1 − τ(at , xt ) wt xt h(at , xt ).4 The government is assumed to balance its budget: 

τ(at , xt )wt xt h(at , xt )dμ(at , xt ) = 0.

3 This

implicitly assumes that workers are perfect substitutes for each other. While this assumption abstracts from reality, it greatly simplifies the labor-market equilibrium. 4 Starting with equal assets, the tax dependent only on realized productivity (i.e., τ = 1 − 1/x) is enough to equalize the after-tax earnings for all.

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The individual worker maximizes his lifetime utility: ∞

max∞ E0 ∑ u(ct , ht )

{ct ,ht }t=0

t=0

subject to   ct = (1 + rt )at + 1 − τ(at , xt ) wt xt h(at , xt ) − at+1 and at+1 ≥ a. It is convenient to write the value function for a worker in recursive form:      V (a, x) = max u(c, h) + β E V (a , x )|x  c,a ,h

  subject to c = (1 + r)a + 1 − τ(a, x) wxh(a, x) − a and a ≥ a. The intertemporal first-order condition (i.e., Euler equation) is:   (2) c(a, x)−σ = β E (1 + r)c(a , x )−σ |x The intratemporal first-order condition (i.e., the optimal labor supply function) is:   Bh(a, x)1/γ c(a, x)σ = 1 − τ(a, x) wx (3) A stationary equilibrium consists of a value function, {V (a, x)}; a set of decision rules for consumption, asset holdings, and labor supply, {c(a, x), a (a, x), h(a, x)}; aggregate inputs, {K, L}; factor prices, {w, r}; and an invariant distribution of workers μ(a, x) such that: 1. Individuals optimize: Given w and r, the individual decision rules c(a, x), a (a, x), and h(a, x) solve V (a, x). 2. The representative firm maximizes profits: wt = αk1−α

(4)

rt + δ = (1 − α)k−α

(5)

where k = K/L. 3. The goods market clears: 

   a (a, x) + c(a, x) dμ = F L, K + (1 − δ )K.

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Chang and Kim: The Price of Egalitarianism

4. The factor markets clear: L=



xh(a, x)dμ(a, x),

K=



adμ(a, x).

5. Individual and aggregate behaviors are consistent: For all A0 ⊂ A and X 0 ⊂ X,   μ(A0 , X 0 ) =

A0 ,X 0

A ,X

1a =a (a,x) dπx (x |x)dμ da dx .

Following Aiyagari and McGrattan (1998), social welfare is defined as:5 W = ∞

V (a, x) = E0 ∑ β t=0

 t



V (a, x)dμ(a, x),

c(at , xt )1−σ − 1 h(at , xt )1+1/γ −B . 1−σ 1 + 1/γ

This is the utilitarian social welfare function that measures ex ante welfare in the steady state—i.e., the welfare of an individual before the realization of initial assets and productivity, which is drawn from the steady-state distribution μ(a, x). The average welfare of the laissez-faire economy is compared to those under egalitarianism. Specifically, we ask how much consumption a consumer in the egalitarian economy has to be compensated to be indifferent to living in the laissez-faire economy. This compensating differential Δ is computed by:  1−σ   ∞ 1+1/γ (1 + Δ)c (a , x ) − 1 (a , x ) h t t 1 t t 1 −B E0 ∑ β t dμ1 (at , xt ) 1−σ 1 + 1/γ t=0    ∞ 1−σ − 1 1+1/γ (a , x ) (a , x ) h c t t t t 0 0 −B dμ0 (at , xt ) = E0 ∑ β t 1−σ 1 + 1/γ t=0 (6) where c0 , h0 , and μ0 are consumption, labor supply, and the steady-state distribution under laissez-faire and c1 , h1 , and μ1 are those under egalitarianism (or complete markets). A positive Δ implies that the average welfare of households is higher under laissez-faire, and a negative Δ implies that a household is worse off under laissez-faire. 5 This

measure of social welfare or its variants have been widely used in the literature. Examples include Domeij and Heathcote (2004), Young (2004), Pijoan-Mas (2006), Heathcote, Storesletten and Violante (2008) and Rogerson (2009). Detailed justifications for this welfare measure are provided in Aiyagari and McGrattan (1998).

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3

Quantitative Analysis

3.1

Calibration

The parameters of the model economy are chosen to match some key aspects of the U.S. economy. The unit of time is a year. Individual productivity x is assumed to follow an AR(1) process: ln x = ρx ln x + εx , where εx ∼ N(0, σx2 ). A sizeable literature has estimated this process using wages from panel data, including, Floden and Linde (2001), French (2005), Chang and Kim (2007), and Heathcote et al. (2008). While there are differences in the estimate on the magnitude of the shocks, the consensus is that these shocks are large and persistent. Our benchmark model (referred to as Model I) adopts a persistence value of ρx = 0.92 used in Floden and Linde (2001) and Pijoan-Mas (2006). For the magnitude of shocks, σx = 0.3 is used to match the Gini coefficient of the cross-sectional earnings distribution in the PSID sample (see details below).6 Workers are not allowed to borrow: a = 0. The labor-income share, α, is 0.64, and the annual depreciation rate of capital, δ , is 10%. In our benchmark calibration, the elasticity of labor supply, γ, is 1. This value is larger than the typical micro estimate (e.g., MaCurdy, 1981). However, considering that typical micro estimates do not reflect the extensive margin of labor (i.e., the labor-market participation decision), it is desirable to use a larger value. For example, Heckman and MaCurdy (1980) find that the elasticity of labor supply of female workers can be as large as 5 when participation decisions are taken into account. In a recent study in which the human capital investment part of compensation was taken into consideration, Imai and Keane (2004) estimate that the elasticity of labor supply for males is 3.7. Since the elasticity of labor supply is important for the household’s ability to insure against fluctuations in productivity, we consider a wide range of γ, between 0.25 to 4, which constitutes the lower and upper bound estimates in the literature. Given the above parameter values, the preference parameter for the disutility from working, B, is chosen such that average hours worked are 0.33 in the steady state. According to Juster and Stafford (1991), a typical married couple in the Michigan Time Use Survey spend about one-third of their discretionary time working for paid compensation. We choose the time discount factor β so that the real rate of return to capital is 4% in the steady state (e.g., Kydland and Prescott (1982)). There is no tax in the benchmark “laissez-faire” economy. Due to precautionary savings, the steady-state interest rate is 4%, while the assumed subjective time discount rate is 8% (β = 0.9258). Finally, the relative risk aversion σ = 1.3 6 This

is somewhat larger than Floden and Linde’s estimate of σx = 0.21.

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Chang and Kim: The Price of Egalitarianism

is chosen so that there is zero cross-sectional correlation between wage and hours in the steady state as in Heathcote et al. (2008) and Pijoan-Mas (2006). Table 1 summarizes the parameter values of the benchmark model economy. Table 1: PARAMETERS OF THE B ENCHMARK E CONOMY Parameter α = 0.64 δ = 0.1 a=0 γ =1

Description Labor share in production function Capital depreciation rate Borrowing constraint Labor-supply elasticity

Model I ρx = 0.92 σx = 0.3 β = 0.9258 B = 10.0 σ = 1.3

Persistence of idiosyncratic productivity S.D. of innovation to idiosyncratic productivity Discount factor Disutility from working Relative risk aversion

Model II ρx = 0.78 σx = 0.27 β = 0.9404 B = 34.5 σ = 2.8

Persistence of idiosyncratic productivity S.D. of innovation to idiosyncratic productivity Discount factor Disutility from working Relative risk aversion

Table 2 reports the cross-sectional dispersions of wealth and earnings from the data and models. According to the PSID all households (those whose household head is between ages 18 and 65), the Gini coefficients of wealth and earnings are 0.75 and 0.41, respectively. In our Model I, these values are, respectively, 0.67 and 0.40 in the data. While the model does well to match the earnings inequality, it cannot generate enough inequality in the cross-sectional wealth distribution, especially at the right tail. (See below for a detailed comparison of the wealth distribution between the model and data.) It is well known that a standard model with idiosyncratic income risks cannot generate highly concentrated wealth at the top 5% or 1% as we see in the data. Published by De Gruyter, 2011

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Table 2: C ROSS -S ECTIONAL D ISTRIBUTION

Wealth Gini Earnings Gini Corr(wage, hours)

PSID All

Model I

PSID HS

Model II

0.75 0.41 0.00

0.67 0.40 0.00

0.53 0.31 0.19

0.48 0.30 0.19

Notes: The Gini coefficients for earnings are based on non-zero earnings only. “PSID HS” are those for households whose heads are between ages 35 and 55 and have 12 years of education. In order to assess the insurance benefit of an egalitarian policy, it is desirable for the model economy to properly capture income risk. In our model economy, workers are ex ante identical but ex post heterogeneous due to idiosyncratic productivity shocks. While the AR(1) process adopted above captures earnings inequality across households, not all variations in earnings are risks. Some of them may reflect ability difference, i.e., ex ante heterogeneity. Following Chang and Kim (2007), we consider an alternative specification (which is referred to as “Model II”) where the stochastic process of idiosyncratic productivity shocks reflects ex-post heterogeneity: ρx = 0.78 and σx = 0.27. These values are estimated by the wage dynamics from arguably ex ante homogeneous workers by restricting the data sample to households with heads who are high school graduates and between ages 35 and 55 as of 1983 (1984 survey). This sample is denoted as “PSID High-School Households.”7 By restricting the sample to relatively homogeneous households, we hope to capture only the ex post heterogeneity (risks). The other parameters are identical to those in Model I except for B, β , and σ , which are re-calibrated to match the average hours of work (0.33), rate of return (4%), and correlation between hours and wages (0.19 for this sample in the PSID). In our quantitative analysis below, we will present the results from both Model I and Model II. 7 The

AR(1) process of the wage residual (after controlling for sex, age, and age-squared) is estimated using Heckman’s (1979) maximum-likelihood estimation procedure. We correct for a sample selection bias because the productivity (wages) of workers who did not work is not reported. Time effects (aggregate business-cycle effect) are controlled by annual dummies. See Chang and Kim (2007) for details.

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3.2

Cross-sectional Distributions of Earnings and Wealth

Since the model deals with idiosyncratic productivity, it is desirable for the model economy to possess a reasonable degree of heterogeneity. We report the crosssectional distribution of earnings and wealth of the benchmark economy and compare them to those in the data. Figure 1 shows the Lorenz curves of earnings and wealth distributions from three data sources (Survey of Consumer Finances (SCF), PSID, and “PSID HS”) and the two model specifications (Model I and Model II). The SCF statistics are based on D´ıaz-Gim´enez, Quadrini, and R´ıos-Rull (1997). The PSID statistics reflect household wealth (in the 1984 survey), including the net worth of houses, other real estate, vehicles, farms and businesses owned, stocks, bonds, cash accounts, and other assets. The statistics of “ PSID HS (High School)” are those of households with heads whose education level is 12 years and whose age is between 35 and 55. As the figures show, the model does well in matching the Lorenz curves of earnings except near zero. Note that while the PSID include workers with zero earnings, all workers in our models worker positive hours. For the wealth distribution, there is a noticeable discrepancy between the model and the data, as the model fails to generate highly concentrated wealth at the top. Figure 1: L ORENZ C URVES OF E ARNINGS AND W EALTH Earnings

Wealth

100

100 o

o

45 Model I Model II PSID HS PSID All SCF

90

80

90

80

70

70

60

60

50

50

40

40

30

30

20

20

10

10

0

0

20

40

45 Model I Model II PSID HS PSID All SCF

60

80

100

0

0

20

40

60

80

100

Notes: “PSID HS” are those for households whose heads are between 35 and 55 years old and have 12 years of education.

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Table 3: C HARACTERISTICS OF W EALTH D ISTRIBUTION

1st

2nd

Quintile 3rd 4th

5th Total Gini

Survey of Consumer Finances Share of wealth -.39 1.74 5.72 13.43 79.49 Group avg/pop avg -.02 .09 .29 .67 3.97 Share of earnings 7.05 14.50 16.48 20.76 41.21

100 0.78 1 100 0.63

PSID: All Households Share of wealth Group avg/pop avg Share of earnings

-.52 .50 5.06 18.74 76.22 -.02 .03 .25 .93 3.81 7.51 11.31 18.72 24.21 38.23

100 0.75 1 100 0.41

PSID: High School Share of wealth Group avg/pop avg Share of earnings

1.03 7.07 13.01 21.10 57.76 0.05 0.36 0.64 1.06 2.97 14.29 14.67 20.08 25.07 25.86

100 0.53 1 100 0.31

Model I Share of wealth Group avg/pop avg Share of earnings

0.01 1.55 7.53 21.20 69.71 0.00 0.08 0.38 1.06 3.48 9.29 15.86 19.29 23.92 31.65

100 0.67 1 100 0.40

Model II Share of wealth Group avg/pop avg Share of earnings

1.10 6.87 15.11 26.39 50.53 0.06 0.34 0.75 1.32 2.53 19.25 20.88 20.86 20.18 18.83

100 0.48 1 100 0.30

Notes: The SCF statistics are based on D´ıaz-Gim´enez, Quadrini, and R´ıos-Rull (1997). The PSID statistics reflect the household wealth and earnings in the 1984 survey. The statistics of “High School” are those for households with heads whose education level is 12 years and whose age is between 35 and 55.

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Table 3 summarizes more detailed information on wealth and earnings. For each quintile group of the wealth distribution, we compare wealth share, the ratio of group average to economy-wide average, and the earnings share. Clearly, both the SCF and PSID all households exhibit much more skewed distributions of wealth. The top 20% of families owen 79.5% and 76.2% of total wealth in the SCF and PSID all households, respectively (only 57.7% in the PSID HS). According to Model I, the richest 20% own 70% of total wealth, well short of those in the SCF or PSID all households. If we focus on only the ex-post heterogeneity, Model II’s distributions line up well with the data (PSID HS Households). In both Model II and PSID HS, the poorest 20% own virtually nothing. The PSID HS sample found that households in the 2nd, 3rd, 4th, and 5th quintiles own 7.07, 13.01, 21.10, and 57.76% of total wealth, respectively, while, according to Model II, they own 6.87, 15.11, 26.39, and 50.33%, respectively. The average wealth of those in the 2nd, 3rd, 4th, and 5th quintiles is, respectively, 0.36, 0.64, 1.06, and 2.97 times larger than that of a typical household, according to the PSID HS. These ratios are 0.34, 0.75, 1.32, and 2.53, according to Model II. While the models cannot generate a highly concentrated wealth distribution at the top 5% or 1%, they reproduce the ex-post dispersion of earnings and wealth that are comparable to those seen in the data.

3.3

Steady-State Comparisons: Laissez-faire vs. Egalitarianism

We investigate the welfare consequence of an egalitarian policy that eliminates income risks by compressing the after-tax wages. In this section, we compare the steady states of the laissez-faire and egalitarian economies, and in the next we consider the transition dynamics between the two regimes. It is straightforward to see that under the tax policy τ(a, x) = 1 − 1x , after-tax wages, hours, and earnings of all workers become identical, given the same asset holdings. Then, the wealth distribution at the steady state becomes degenerate and the equilibrium allocation is identical to that under the representative agent model with the mean productivity, x = 1. This is the steady state of the egalitarian society considered.8 Table 4 compares the steady-state aggregate hours, capital, output, consumption and social welfare under the egalitarian tax policy in Model I (with γ = 1). Looking at the laissez-faire steady state in the first column, note that the efficiency labor units (0.334) are not so different from the hours worked (0.333). This is due to a near zero correlation between hours and wages—i.e., labor supply is not systematically correlated with productivity. The second column reports aggregate 8 One can view this as a steady state after the “revolution” by which all assets are confiscated and re-distributed equally across households and the wage compression is imposed at the same time.

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Table 4: S TEADY-S TATE C OMPARISONS

Relative to Egalitarian

Relative to Complete Markets

0.333 0.334 1.462 0.569 0.422

2.1 % 2.4 % 51.8 % 18.1 % 9.6 % - 18.4 %

42.2 % - 20.6% 17.7% - 8.5% - 15.0% - 31.1%

0.333 0.340 1.488 0.579 0.430

- 2.0 % 0.0 % 27.1 % 8.9 % 3.8 % -2.0 %

11.7 % - 4.7 % 21.2 % 3.9 % - 1.0 % - 28.0 %

Laissez-faire Model I Labor Hours Efficiency Units Capital Output Consumption Social Welfare Model II Labor Hours Efficiency Units Capital Output Consumption Social Welfare

Notes: Welfare is computed based on Equation (6). quantities under the “laissez-faire” steady state relative to those under the egalitarian wage compression. Aggregate hours worked under laissez-faire are higher than those under egalitarianism by 2.1%. The labor input measured in efficiency units is larger than that of the egalitarian economy by 2.4%. Aggregate capital is 51.8% higher, reflecting a strong motive for precautionary savings against a large income risk. Output and consumption are 18.1% and 9.6% higher, respectively, than those in the egalitarian steady state. In terms of average welfare, households are worse off in the laissez-faire economy. According to our compensating differential measure, households are willing to sacrifice up to 18.4% of their consumption to stay in the egalitarian steady state than to be in the laissez-faire steady state. The egalitarian tax policy presents a trade-off between the benefit of insurance against income risks and the efficiency loss from distorting labor effort. In order to decompose this trade-off, we compute the equilibrium under complete cap-

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ital markets, where the complete set of contingent claims is available. Under complete capital markets, the efficient allocation is achieved as workers supply hours according to their realized productivity. Consumption is equalized for all workers (under the separable utility between consumption and leisure) and the hours of work are determined by the intratemporal optimality condition in (3). The welfare gap between the “complete markets” and the “egalitarian” economy reflects the efficiency cost from distorting labor supply because income risks are completely eliminated in both economies. The welfare gap between the “complete markets” and benchmark “laissez-faire” economy reflects the welfare gain from eliminating income risks because neither economy is subject to distortion of labor effort other than precautionary motives. While workers save and work more in the incomplete markets economy (Pijoan-Mas (2006)) out of a precautionary savings motive, such distortion is due to a lack of insurance. Thus, the welfare gap between “complete markets” and “laissez-faire” economies is interpreted as an insurance benefit. The last column of Table 4 reports the aggregate quantities of “laissez-faire” relative to the “complete markets” economy. Workers, on average, work 42.2% more hours in the laissez-faire economy, whereas the labor input measured in efficiency units is 20.6% smaller in the laissez-faire economy because highly productive workers supply many more hours under the complete-markets economy (efficient allocation). Due to precautionary savings, capital is substantially (by 17.7%) higher in the laissez-faire economy. Output and consumption are lower (by 8.5% and 15.0%, respectively) in the laissez-faire economy. Compared to the completemarkets economy, households are substantially worse off under laissez-faire. The households in the complete-markets economy are willing to forgo up to 31.1% of their consumption not to live in the laissez-faire economy. This amount of consumption reflects the insurance benefit from complete insurance against income risks. While households are substantially worse off under laissez-faire according to Model I where the stochastic process of productivity shocks is calibrated to match the overall earnings inequality in the data, our welfare results may overstate insurance benefits because some cross-sectional variations in earnings reflect ability rather than risks. To address this issue, we consider an alternative specification that captures ex-post heterogeneity only. In Model II, a much smaller idiosyncratic productivity shock estimated from the arguably ex-ante homogeneous “PSID HighSchool Households” is used (ρx = 0.78 and σx = 0.27). The bottom half of Table 4 reports the same steady-state comparison for Model II (with γ = 1). First, note that the aggregate efficiency unit of labor input is now 0.34 (slightly higher than the average hours) due to a small but positive (0.19) cross-sectional correlation between wages and hours. Aggregate hours of work in the laissez-faire economy are lower than those in the egalitarian economy Published by De Gruyter, 2011

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by 2.0%, whereas the efficiency unit of labor is almost the same. Capital, output, and consumption are higher in the laissez-faire economy as in Model I. Households are only slightly worse off under laissez-faire. It would require an increase in consumption of 2% to make a household in the laissez-faire society at least as happy as the average household in the egalitarian society. Again, the last column reports the aggregate quantities of the laissez-faire economy relative to those in the “complete markets” economy. Workers on average work 11.7% more hours in the laissezfaire economy, whereas the labor input measured in efficiency units is 4.7% lower in the laissez-faire economy. Capital is higher in the laissez-faire economy because of precautionary savings. Output is slightly higher but consumption is lower. Households in the complete-markets economy are willing to sacrifice up to 28% of their consumption to stay in the complete-markets steady state in comparison to the laissez-faire steady state.9 The elasticity of labor effort is an important factor that affects the ability of households to intertemporally substitute hours in response to stochastic variation in productivity over time. In our benchmark calibration, an elasticity of 1 is used. We re-do our analysis with a wide range of labor supply elasticities (from 0.25 to 4). These values constitute the lower and upper bounds of labor supply elasticities in the literature. When a different elasticity of labor supply is used, we re-calibrate the preference parameters B and β so that average hours worked and the real interest rate in the steady state are identical across economies. Specifically, for each value of γ, values for the parameter for the disutility from working B and the discount factor β are chosen to obtain aggregate hours of 0.33 and a real interest rate of 4% under laissez-faire.10 As Table 5 shows, a higher value of γ (less painful to supply additional hours) requires us to lower the value of B (disutility from working) to yield the same average hours in the steady state. Since an elastic labor supply (a higher value of γ) yields higher output and capital, a smaller discount factor (β ) is required to obtain the same equilibrium interest rate. Figure 2 exhibits the welfare of the laissez-faire economy relative to that of the egalitarian economy for various values of γ. As expected, laissez-faire performs 9 The comparison of the incomplete-markets economy relative to the complete markets in Pijoan-

Mas (2006) falls in between our Model I and Model II. For example, he finds that average hours are higher by 15.2% in the incomplete markets economy whereas the efficiency unit of hours is lower by 4.7%. Capital and output are higher by 22.8% and 4.4%, respectively. Consumption and average welfare are lower by 0.6% and 16%, respectively. This is due to the size of idiosyncratic shocks. Model I uses the same persistence (ρx ) but a larger standard deviation of innovations (σx ). Model II uses smaller values for both persistence and the standard deviation of innovations. 10 Here, in order to isolate the effect of the elasticity of labor supply, we did not vary σ to match the cross-sectional correlation between hours and wages. In Model I, the cross-sectional correlation is almost independent of γ: it varies from -0.02 (γ = 0.25) to 0.04.(γ = 4). In Model II, the correlation varies from 0.03 (γ = 0.25) to 0.24.(γ = 4), not very far from what we see in the data (0.19).

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Chang and Kim: The Price of Egalitarianism

Table 5: C ALIBRATED VALUES OF B AND β γ

UNDER VARIOUS

.25

.5

1.0

2.0

4.0

269 .9308

30.0 .9289

10.0 .9258

5.78 .9214

4.41 .9165

980 .9414

107 .9415

34.5 .9404

19.0 .9372

13.8 .9322

γ

Model I B β Model II B β

Notes: Given the labor-supply elasticity (γ), we choose the parameter for the disutility from working (B) and the discount factor (β ) to yield the average hours worked of 0.33 and real rate of return of 4% in the laissez-faire steady state. Figure 2: W ELFARE OF L AISSEZ - FAIRE RELATIVE TO E GALITARIAN 5 Model I Model II 0

% in consumption

5

10

15

20

25

0

0.5

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1

1.5 2 2.5 Labor supply elasticity (J)

3

3.5

4

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better as the elasticity of labor supply increases. When labor supply is elastic, workers can more easily take advantage of high-productivity opportunities. In Model I where households face larger idiosyncratic risks, the laissez-faire consistently performs worse than the egalitarian economy regardless of γ. However, in Model II where households are subject to small idiosyncratic risks, laissez-faire outperforms the egalitarian economy as long as γ is greater than 1.8.11

3.4

Transition Dynamics from Egalitarian to Laissez-Faire

We now consider the transition from the egalitarian to the laissez-faire economy. When the economy moves from the egalitarian to the laissez-faire steady state, the average household accumulates additional capital for precautionary reasons. By and large, however, including the transition period does not alter our welfare results substantially because the transition occurs rapidly in our model economies. Our simulation indicates that the model economy reaches its laissez-faire steady state in 20 years. The economy is assumed to be at the egalitarian steady state in year 0, where asset holdings are equal across households and wages are compressed. In year 1, the wage compression is removed.12 Figure 3 shows the transition from egalitarian to laissez-faire in Model I (with γ = 1). We normalize the values of aggregate capital, output, consumption, labor input, and wages to those of the egalitarian steady state. When the wage compression is removed, households begin to accumulate savings as a precautionary measure against income risks. Accumulation of aggregate capital results in a decline of the rate of return to capital. The wage rate increases given the complementarity between capital and labor. As households anticipate a rising wage over time, hours worked initially decline. However, labor measured in efficiency units rises 11 Heathcote,

Storesletten, and Violante (2008) analyze the trade-off from an equal-wage policy in a quantitative model. In order to obtain a transparent analytical solution, they abstract from capital. 12 Alternatively, one can investigate a transition from the laissez-faire to the egalitarian economy. In this case, however, the transition from the laissez-faire to the “equal-asset” egalitarian steady state is not guaranteed unless an additional assumption is made about how the assets are re-distributed. Since the introduction of the egalitarian tax policy eliminates idiosyncratic income risks, individuals do not accumulate assets for precautionary motives. Then from an individual’s perspective, asset holdings are perceived as one of the ex ante heterogeneous characteristics from which interest payment (rt a0 ) serves as an additional resource for consumption. Individuals choose different consumption and work hours depending on asset holdings. Hence, the evolution of the asset distribution over the transitional periods critically depends on the shape of the asset distribution at the time of the switch. If assets are not equal at the introduction of wage compression, the transition will end up with an equilibrium that is different from the “equal-asset” egalitarian steady state. One possible way to guarantee the “equal-asset” egalitarian steady state is to confiscate all assets and re-distribute them equally. Then, the transition is essentially similar to that of a representative-agent model.

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Chang and Kim: The Price of Egalitarianism

Figure 3: T RANSITION FROM E GALITARIAN TO L AISSEZ - FAIRE (M ODEL I) 1.15

1.6 Capital Output Consumption

1.5 1.4

Hour Efficiency Unit

1.1

1.3

1.05

1.2

1

1.1 0.95

1 0.9

0

10

20 year

30

40

0.1

0.9

0

10

20 year

30

40

1.2 Interest Rate

Wage

0.09

1.15

0.08 1.1 0.07 1.05 0.06 1

0.05 0.04

0

10

20 year

30

40

22

0.95

0

10

20 year

30

40

0.7 Average Welfare

Gini (Wealth) Gini (Earnings)

0.6

23

0.5 24

0.4

25

0.3 0.2

26 27

0.1 0

10

20 year

30

40

0

0

10

20 year

30

40

Welfare 0 1st percentile 20th 50th 80th 99th

10 20 30 40 50

0

10

20 year

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30

40

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Figure 4: T RANSITION FROM E GALITARIAN TO L AISSEZ - FAIRE (M ODEL II) 1.3

1.1 Capital Output Consumption

1.25 1.2

1.06

1.15

1.04

1.1

1.02

1.05

1

1

0.98

0.95

0

10

20 year

30

Hour Efficiency Unit

1.08

40

0.075

0.96

0

10

20 year

30

40

1.1 Interest Rate

0.07

Wage

0.065

1.05

0.06 0.055 1

0.05 0.045 0.04

0

10

20 year

30

40

69.5

0.95

0

10

20 year

30

40

0.5 Gini (Wealth) Gini (Earnings)

Average Welfare

70

0.4

70.5 71

0.3

71.5

0.2

72 0.1

72.5 73

0

10

20 year

30

40

0

0

10

20 year

30

40

Welfare 20 1st percentile 20th 50th 80th 99th

40 60 80 100 120

0

10

20 year

30

40

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Chang and Kim: The Price of Egalitarianism

initially as workers with high productivity tend to work more to accumulate assets. (Also, the lack of capital in the beginning of the laissez-faire economy requires a stronger substitution in labor supply.) Thus, the gap between hours worked and efficiency units of labor is large in the beginning. The average welfare decreases over time. Surprisingly, inequality emerges rapidly. For example, the Gini coefficient of wealth increases from 0 to 0.3 in 5 years. It reaches 0.65 in 15 years, close to its steady-state value. The panel at the bottom of the figure shows the distribution of welfare (value functions at that point in time) of the 1st, 20th, 50th, 80th, and 99th percentile of wealth distribution over time.13 As the figure shows, in 15 years, the dispersion in welfare is already close to its laissez-faire steady state. In 20 years, the economy almost completes its transition to the laissez-faire. Figure 4 shows the transition of Model II. Overall, the dynamics are similar to those of Model I. However, there is a notable difference. Hours worked do not drop as much as in Model I. In Model I, the average hours worked significantly decreases immediately after the wage compression is removed, while the efficiency unit of labor increased significantly. This implies that workers in an economy with larger idiosyncratic shocks have a stronger incentive to intertemporally substitute their hours. Workers with high idiosyncratic productivity supply the majority of labor inputs, and at the same time, workers with low idiosyncratic productivity tend to choose leisure over work and wait for the next good draw. This makes the average welfare during the transition better than that at the new steady state in Model I. However, when idiosyncratic shocks are small as in Model II, workers on average work longer hours to accumulate assets and self-insure against income shocks since the gains from waiting for an extremely good productivity shock are small. This makes average welfare during the transition worse than that at the new steady state (laissez-faire) in Model II. Finally, Figure 5 summarizes the welfare of the laissez-faire economy relative to that of the egalitarian economy when the transition (from egalitarian to laissez-faire) is included. Qualitatively, the welfare comparison is, by and large, similar to that based on steady states because the transition is rapid. However, as was explained above, considering the transition makes the laissez-faire economy worse off in Model II. In sum, the egalitarian dominates the laissez-faire regardless of the elasticity of labor supply considered (0.25 ≤ γ ≤ 4) in Model I. In Model II, however, people are willing to move to the laissez-faire economy if labor supply is highly elastic (γ > 3). 13 Specifically,

these values are ExV (a, x) at the corresponding percentile of μ(a) at time t.

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Figure 5: W ELFARE TION I NCLUDED

OF

L AISSEZ - FAIRE

RELATIVE TO

E GALITARIAN : T RANSI -

5 Model I Model I (w/ transition) Model II Model II (w/ transition) 0

% in consumption

5

10

15

20

25

4

0

0.5

1

1.5 2 2.5 Labor supply elasticity (J)

3

3.5

4

Summary

Egalitarianism is popular because it provides insurance against bad outcomes in the market despite its efficiency loss from distorting working incentives. Using a workhorse model with incomplete-markets, the welfare cost of egalitarianism (wage compression) is computed. When the idiosyncratic income shocks are calibrated to match the overall cross-sectional earnings inequality in the data, the egalitarian society yields a much higher average welfare, since the insurance benefit dominates the efficiency loss. However, when the idiosyncratic income risks are calibrated to capture only the ex post heterogeneity in wages, the welfare results can reverse if the labor supply is elastic enough. However, even with an elasticity of labor supply 4, the utilitarian social welfare cost of egalitarianism is only 6% in consumption-equivalence units. We find that the transition between the regimes is rapid. When the wage compression is removed , inequality emerges quickly. The Gini coefficient of crosssectional wealth distribution rises from 0 to 0.3 in 5 years and approaches its laissezhttp://www.bepress.com/bejm/vol11/iss1/art42 DOI: 10.2202/1935-1690.2243

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Chang and Kim: The Price of Egalitarianism

faire steady state in 20 years. However, this transition can be painful. Households are exposed to income risks and they have to accumulate additional wealth to selfinsure against future uncertainty in the market. Our finding of a small welfare cost of egalitarianism in a workhorse model is puzzling. We suspect that a standard heterogeneous-agents model may understate the welfare cost of an egalitarian society for the following reasons. Variation in income at the individual level is not all risk. A lot of it may be foreseen by economic agents and probably reflect ex ante heterogeneity. If so, the insurance benefit of egalitarianism in our benchmark model may be overstated. Perhaps the true cost of egalitarianism lies in the distortion in the growth core of such variables as innovation and human capital accumulation or in a moral hazard problem with private information, both of which the standard model abstracts from. Nevertheless, we think that the standard incomplete-markets model can be extended to address the quantitative issues arising from various socio-political systems.

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Floden, Martin, and Jesper Linde, (2001) “Idiosyncratic Risk in the United States and Sweden: Is There a Role for Government Insurance?,” Review of Economic Dynamics, 4(2), 406-437. French, Eric, (2005) “The Effects of Health, Wealth, and Wages on Labor Supply and Retirement Behavior,” Review of Economic Studies, 72 (2), 395-427. Heathcote, Jonathan, Kjetil Storesletten, and Giovanni L. Violante (2008) “Insurance and Opportunities: A Welfare Analysis of Labor Market Risk,” Journal of Monetary Economics, 55(3), 501–525. Heckman, James J. (1979) “Sample Selection Bias as a Specification Error,” Econometrica, 47(1), 153-161. Heckman, James J., and MaCurdy, Thomas E. (1980) “A Life-Cycle Model of Female Labour Supply,” Review of Economic Studies 47(1), 47-74. Huggett, Mark (1996) “Wealth Distribution in Life-Cycle Economies,” Journal of Monetary Economics 38(3), 469-94. Imai, Susumu, and Michael P. Keane (2004) “Intertemporal Labor Supply and Human Capital Accumulation,” International Economic Review 45(2), 601-641. Juster, F. Thomas, and Frank P. Stafford (1991) “The Allocation of Time: Empirical Findings, Behavior Models, and Problems of Measurement,” Journal of Economic Literature 29(2), 471-22. Kydland, Finn, and Edward Prescott (1982): “Time to Build and Aggregate Fluctuations,” Econometrica, 50(6), 1345-1370. Lenin, V. I., The State and Revolution (Classic, 20th-Century, Penguin). MaCurdy, Thomas E. (1981): “An Empirical Model of Labor Supply in a Life Cycle Setting,” Journal of Political Economy, 89(6), 1059-1085. Pijoan-Mas, Josep (2006) “Precautionary Savings or Working Longer Hours?” Review of Economic Dynamics, 9(2), 326–352. Young, Eric R. (2004), “Unemployment Insurance and Capital Accumulation,” Journal of Monetary Economics, 51(8), 1683–1710.

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