Taxation of Human Capital and WageInequality: A Cross-Country Analysis∗

Fatih Guvenen† Burhanettin Kuruscu‡ Serdar Ozkan§

October 6, 2009

Abstract

Wage inequality has been significantly higher in the U.S. than in continental Eu-ropean countries (CEU) since the 1970’s. Moreover, this “inequality gap” has furtherwidened during this period as the U.S. has experienced a large increase in wage in-equality, whereas CEU countries have seen only modest changes. This paper studiesthe role of labor income tax policies for understanding these facts. We begin by docu-menting two new empirical facts that link these inequality differences to tax policies.First, we show that countries with a more progressive labor income tax schedule havesignificantly lower before-tax wage inequality at different points in time. Second, pro-gressivity is also negatively correlated with the rise of wage inequality during thisperiod. We then construct a life cycle model in which individuals decide each periodwhether to go to school, to work, or to be unemployed. Individuals can accumulateskills either in school or while working. Wage inequality arises from differences acrossindividuals in their ability to learn new skills as well as from idiosyncratic shocks.Progressive taxation compresses the wage structure, thereby distorting the incentivesto accumulate human capital, in turn reducing the cross-sectional dispersion of wages.We find that these policies can account for half of the difference between the US andCEU in overall wage inequality and 76% of the difference in inequality at the upper end(log 90-50 differential). When this economy experiences skill-biased technical change,progressivity also dampens the rise in wage dispersion over time. The model explains42% of the difference in the total rise in inequality and 60% of the difference at theupper end.

∗First preliminary draft. For helpful early conversations on this project, we thank Daron Acemoglu,Richard Rogerson, and Tom Sargent. For useful comments and suggestions about this draft, we especiallythank Dirk Krueger and seminar participants at Columbia, Penn State, Texas A&M, Upenn, UniversidadCarlos III, Universite de Paris 1-Sorbonne, University of Oslo, Koc, Sabanci; conference participants at theCowles Foundation Summer Conference at Yale University, Heterogeneous-Agent Models in MacroeconomicsConference at the University of Mannheim, the SED conference, and the Midwest Macro Conference. MarinaMendes Tavares provided excellent research assistance. Guvenen acknowledges financial support from theUniversity of Minnesota Grant-in-Aid fellowship. All remaining errors are our own.†University of Minnesota and NBER; guvenen@umn.edu; http://www.econ.umn.edu/~guvenen‡UT-Austin; kuruscu@eco.utexas.edu; http://www.eco.utexas.edu/~kuruscu§University of Pennsylvania; ozkan@econ.upenn.edu; http://www.econ.upenn.edu/~ozkan

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1 Introduction

Why is wage inequality significantly higher in the United States (and the United Kingdom)than in continental European countries (CEU)? And, why has this “inequality gap” betweenthe US and CEU widened substantially since the 1970’s? (See Table I.) More broadly, whatare the determinants of wage dispersion in modern economies? How do these determinantsinteract with technological progress and government policies? The goal of this paper is toshed light on these questions by studying the impact of labor market (tax) policies on thedetermination of wage inequality, using cross-country data.

We begin by documenting two new empirical relationships between wage inequalityand tax policy. First, we show that countries with a more progressive labor income taxschedule have significantly lower wage inequality at different points in time. The measureof wages we use is “gross, before-tax, wages”1 and can, therefore, be thought of as a proxyfor the marginal product of workers. From this perspective, progressivity is associated witha more compressed productivity distribution across workers in an economy. Second, weshow that countries with a more progressive income tax have also experienced a smallerrise in wage inequality over time, and this relationship is especially strong for inequality atthe upper end of the distribution. This latter finding is intriguing because the substantialpart of the rise in wage inequality since 1980 has taken place above the median of thedistribution (see table II). Overall, these findings reveal a close relationship between wageinequality and progressive labor income taxes, which motivates our focus on tax policiesfor understanding differences in wage inequality. However, these correlations on their ownfall short of providing a quantitative assessment of the importance of the tax structure forwage inequality—e.g., what fraction of cross-country differences in wage inequality can beattributed to differences in tax policies? For this purpose, we build a model.

Specifically, we construct a life-cycle model that features some key determinants ofwages—most notably, human capital accumulation and idiosyncratic shocks. Here is anoverview of the framework. Individuals enter the economy with an initial stock of “humancapital” (skills, knowledge, etc.) and are able to accumulate more human capital over thelife cycle using a Ben-Porath (1967) style technology (which essentially combines learningability, time, and existing human capital for production). Individuals can choose to eitherinvest in human capital on-the-job up to a certain fraction of their time, or enroll in schoolwhere they can invest full time. We assume that skills are general and labor markets arecompetitive. As a result, the cost of on-the-job investment will be completely borne bythe workers, and firms will adjust the hourly wage rate downward by the fraction of time

1More precisely, wages are measured before-tax and also include employee and employer’s social securitycontributions as well as bonuses and over time pay when applicable. Therefore, they represent a fairly goodmeasure of the total monetary compensation of a worker.

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Table I: Log Wage Differential Between the 90th and 10th Percentiles

1978-1982 2001-2005 Changeaverage average

Denmark 0.76 0.97 0.20Finland 0.91 0.89 -0.01France 1.18 1.08 -0.10Germany 1.06 1.15 0.09Netherlands 0.94 1.06 0.12Sweden 0.71 0.83 0.12CEU 0.93 1.00 0.07UK 1.09 1.27 0.18US 1.34 1.57 0.23US-UK 1.21 1.42 0.21

invested on the job. Thus, the cost of human capital investment is the forgone earningswhile individuals are learning new skills.

We introduce two main features into this framework. First, we assume that individualsdiffer in their learning ability. As a result, individuals differ systematically in the amountof investment they undertake, and consequently, in the growth rate of their wages over thelife cycle. Thus, a key source of wage inequality in this model is the systematic fanning outof the wage profiles.2 Second, we allow for endogenous labor supply choice, which amplifiesthe effect of progressivity, a point that we return to shortly. Finally, for a comprehensivequantitative assessment, we also allow idiosyncratic shocks to workers’ labor efficiency, andalso model differences in the unemployment insurance and pension systems, which varygreatly across these countries.

The model described here provides a central role for policies that compress the wagestructure—such as progressive income taxes—because such policies hamper the incentivesfor human capital investment. This is because progressive taxes reduce (after-tax) wages atthe higher end of the wage distribution compared to the lower end. As a result, they reducethe marginal benefit of investment (the higher wages in the future) relative to the cost ofinvestment (the current forgone earnings), thereby depressing investment. Therefore, indi-viduals in an economy with a more progressive tax system will invest less in human capitaland, since higher ability individuals respond to incentives more, the before-tax wage (ie.,productivity) distribution will be more compressed. Furthermore, these effects of progres-sivity are compounded by differences in average labor income tax rates and endogenous

2Recent evidence from panel data on individual wages provide support for individual-specific growthrates in wages; see, for example, Guvenen (2007, 2009), Huggett, Ventura, and Yaron (2007), and Primiceriand van Rens (2009).

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Table II: Decomposing the Change in Log 90-10 Wage Differentials

Total Change Percentage due toin Log 90-10 Log 90-50 Log 50-10

CEU 0.07 91% 9%US-UK 0.21 70% 20%Difference 0.14 60% 40%

labor supply: the higher taxes in the CEU reduces labor supply—and, consequently, thebenefit of human capital investments—further compressing the wage structure.

The main quantitative exercise we conduct is the following. We consider the eightcountries listed in Table I, for which we have complete data for all the key variables ofinterest. We assume all countries to have the same innate ability distribution but alloweach country to differ in the observable dimensions of their labor market structure, such asin labor (and consumption) tax schedules, and in unemployment insurance and retirementbenefits systems. We then calibrate the model-specific parameters to the US data (inparticular, we match the log 90-10 wage differential in the US exactly) and keep theseparameters fixed across countries. The policy differences we consider explain about half ofthe observed gap in the log 90-10 wage differentials between the US and CEU in the 2000’s,and 76% of the wage inequality above the median (log 90-50 differential). When the Frischelasticity of labor supply is increased to 0.5 from its baseline value of 0.3, the model is ableto explain 60% of the log 90-10 differential and virtually all (97% to be exact) of the log90-50 differential observed in the data. The model explains only about 30% of the differencein the lower tail inequality between the US and CEU, which is perhaps not very surprisingsince the main human capital mechanism is likely to be more important for higher abilityindividuals and, therefore, above the median of the distribution. In contrast to the CEU,however, the United Kingdom turns out to be an outlier, in the sense that the model is leastsuccessful in explaining virtually any aspect of its data. We also provide a decompositionthat isolates the separate roles of differences in (i) average tax rates, (ii) progressivity, and(iii) pension and unemployment insurance systems. We find that progressivity is by far themost important component, accounting for about 65% of the model’s explanatory power,followed by benefits institutions (25%). Average tax rate differences are the least importantcomponent for wage inequality, accounting for the remaining 10%.

A contribution of the present paper that could be of independent interest is the derivationof country-specific effective labor income tax schedules, which is, to our knowledge, new tothis paper. As described in Section 2.2 and Appendix A.3, these are obtained by puttingtogether tax data from different OECD sources, and using a functional form that provides agood fit for this relatively diverse set of countries. These tax schedules allow us to measure

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the progressivity of the (effective) tax structure at different points in the income distribution.This is an essential ingredient in our analysis and could also be useful for studying otherquestions in the future.

An interesting question to consider is whether the widening of the inequality gap betweenthe US and the CEU since 1980 could also be explained by the same human capital channelsexamined above. One challenge we face in trying to answer this question is that the taxschedules described above are only available for the years after 2001 (because the detailedinformation from OECD sources for taxes is only available after that date) even though thetax structure has changed over time for several of the countries in our sample. Despite thiscaveat, we cautiously explore how much of the change in the US-CEU inequality gap canbe explained with fixed tax schedules.

As shown in Guvenen and Kuruscu (2007), the model described above with the Ben-Porath technology does not have a well-defined notion of returns to skill, which essentiallymeans that changes in the price of human capital (e.g., resulting from skill-biased technicalchange) has no effect on investment behavior. To circumvent this problem, in Section 6,we extend the human capital production technology to a two-factor structure along thelines proposed in that paper.3 Then, consistent with a large existing literature, we assumethat the main driving force for the rise in wage inequality was skill-biased technical change(SBTC), and we calibrate its magnitude from 1980 to 2003 so as to match the rise in theUS inequality during this period. Assuming the same technological change in all countries,the model explains about 40% of the observed gap in the rise in total wage inequality(log 90-10) between the US and CEU, and about 60% of the difference in the log 90-50differentials, during this time period. Thus, this exercise illustrates how government policiescan strongly influence the response of the economy to technological change by alteringindividuals’ incentives to undertake human capital investment, which keeps inequality low,but at the cost of lower aggregate output. To highlight this latter point, we briefly discussthe implications for some macro variables, such as GDP, hours, and so on.

Some previous papers have also examined the US-CEU differences in wage inequality,although using quite different techniques from the present paper; see, e.g., Blau and Kahn(1996); Kahn (2000), and Gottschalk and Joyce (1998). These papers mainly use regressionanalyses and conclude that unionization, centralized bargaining, and minimum wage laws

3Guvenen and Kuruscu (2009) has quantitatively studied a simplified version of this model—one thatabstracts from idiosyncratic shocks, endogenous labor supply as well as from all the institutional detailsstudied here—and applied it to the U.S. data. They concluded that even that stark version provides afairly successful account of several trends observed in the U.S. data since the 1970’s, including the rise inoverall wage inequality; the initial fall in the college premium in 1970’s and the subsequent strong increasein the next two decades; the rise in within-group wage inequality; the stagnation in aggregate productivitygrowth, and the small rise in consumption inequality despite the large rise in wage inequality. Here, webuild on this research by explicitly modeling labor market institutions and allowing for idiosyncratic shocksand endogenous labor supply to understand the role of tax policy for wage inequality.

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are important for understanding European wage inequality data. An important point tonote, however, is that these studies do not consider the role of progressive taxation in theirregression analyses. But as the empirical evidence we document in Appendix C shows,countries with more rigid institutions also have more progressive tax schedules, implyingthat this omission could attribute the effect of progressivity to these other institutions. Here,instead, by calibrating the model to the data, we circumvent this difficulty. Acemoglu (2003)is a notable exception in this literature in that he constructs a fully specified model to shedlight on the same question. He begins by observing that wage compressing institutions in theCEU could affect the incentives of firms (ie., innovators) such that they adopt technologiesthat are less skill biased than in the US. Therefore, in his model inequality would rise less inEurope because the rise in skill demand has been slower in that region. His paper raises aninteresting possibility and one that could potentially complement the mechanisms studiedin this paper.

In terms of methodology, this paper is also related to the recent macroeconomics lit-erature that has written fully specified economic models to address US-CEU differencesin the labor market outcomes, such as in unemployment rates and labor supply behavior.Prominent examples include Ljungqvist and Sargent (1998, 2008), and Hornstein, Krusell,and Violante (2007) who mainly focus on unemployment rates, and Prescott (2004), Oha-nian, Raffo, and Rogerson (2006), and Rogerson (2008) who study labor hours differences.Several of these papers rely on representative agent models, and are therefore naturallysilent on wage inequality; and those that do allow for individual-level heterogeneity do notaddress differences wage inequality.4 In terms of modeling choices, the closest framework toours is Kitao, Ljungqvist, and Sargent (2008), who study a rich life cycle framework withhuman capital accumulation, job search, and model the benefits system. Their goal is toexplain the different unemployment patterns over the life cycle in the US and Europe.

Finally, a number of recent papers share some common modeling elements with oursbut address different questions from the present paper. Important recent examples includeKrebs (2003), Caucutt, Imrohoroglu, and Kumar (2006), Huggett, Ventura, and Yaron(2007), and Erosa and Koreshkova (2007). Krebs (2003) studies the impact of idiosyncraticshocks on human capital investment and shows that reducing labor income risk can in factincrease growth, in contrast to the incomplete markets literature without human capital,which typically reaches the opposite conclusion. Caucutt, Imrohoroglu, and Kumar (2006)develop an endogenous growth model with heterogeneity in income. They show that areduction in the progressivity of tax rates can have positive growth effects even in situationswhere changes in flat rate taxes have no effect. Another important contribution is Huggett,

4A notable exception is Hornstein, Krusell, and Violante (2007), who do study the implications of theirframework for wage inequality, but conclude that it does not generate much wage dispersion or differencesin wage inequality across countries, despite having many successful implications for unemployment ratesand the labor share.

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Ventura, and Yaron (2007), who study the distributional implications of the Ben-Porathmodel and estimate the sources of lifetime inequality using US wage data. Finally, theinteraction of human capital investment and progressive taxes is also present in Erosa andKoreshkova (2007), who investigate the effects of replacing the current U.S. progressiveincome tax system with a proportional one in a dynastic model. They find a large positiveeffect on steady state output, which comes at the expense of higher inequality. Whileour paper has many useful points of contact with this body of work, to our knowledge thecombination of human capital accumulation, ability heterogeneity, progressive taxation, andendogenous labor supply is new to this paper, as is the attempt to explain cross-countryinequality facts in such a framework.

The next section starts with a stylized model to explain the various channels throughwhich tax policy affects wage inequality. It then explains how the country-specific taxschedules are estimated and uses the estimates to document some empirical links betweentaxes and inequality. Sections 3 and 4 describe the main model and the parametrization.Section 5 presents the cross-sectional quantitative results and sensitivity analyses. Section6 extends this model to examine the evolution of inequality over time. Section 7 concludes.

2 US versus CEU: Differences in Empirical Trends

In this section, we document two new empirical relations between wage inequality and theprogressivity of the tax policy. Although what is meant by progressivity is well-understoodas a qualitative concept,5 the precise empirical measure of progressivity we focus on issuggested by the model studied here. To this end, we begin with a stylized version of themore general model studied in Section 3 that illustrates the key mechanisms at work andwill allow us to define different measures of progressivity subsequently used in documentingthe empirical facts. We then discuss how the tax schedules are derived for each country andpresent the empirical findings in Section 2.3.

2.1 Model 0: Intuition in A Stylized Framework

Consider an individual who derives utility from consumption and leisure and has access toborrowing and saving at a constant interest rate, r. Let β be the subjective time discountfactor and assume β(1 + r) = 1. Each period individuals have one unit of time endowmentthat they allocate between leisure and work (n ∈ [0, 1]). While working, individuals can

5The Britannica Concise Encyclopedia defines progressive taxes as “tax levied at a rate that increasesas the quantity subject to taxation increases.” Similarly, the American Heritage Dictionary defines it as“..increasing in rate as the taxable amount increases.”

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accumulate new human capital, Q, according to a Ben-Porath style technology. Specifically,Q = Aj (hin)α where h denotes the individuals’ current human capital stock, i denotes thefraction of working time (n) spent learning new skills, and Aj is the learning ability ofindividual type j. We assume that skills are general and labor markets are competitive. Asa result, the cost of human capital investment is completely borne by workers, and firmsadjust the hourly wage rate downward by the fraction of time invested on the job (equation(2)). Finally, labor earnings are taxed at a rate given by the average tax function τn(y)

and the corresponding marginal tax rate function is denoted by τ(y). Putting these piecestogether, the problem of a type j individual can be written as:

maxcs,as+1,is

S∑s=1

βs−1u(cs, 1− ns)

s.t

cs + as+1 = (1− τn(ys))ys + (1 + r)as

hs+1 = hs + Aj (hsisns)α (1)

ys = PHhs(1− is)ns (2)

Using the fact that Qjs = A (hsisns)

α, the “cost of investment” (ie., hsisns) can be writtenas: Cj(Qj

s) = (Qs/Aj)

(1/α), which will play a key role in the optimality conditions below.Now, it is useful to distinguish between two cases.

Inelastic Labor Supply. First, suppose that labor supply is inelastic, in which casens = 1. The optimality condition for human capital investment is (assuming an interiorsolution):

(1− τ(ys))C′j(Q

js) =β(1− τ(ys+1)) + β2 (1− τ(ys+2)) + ...+ βS−s (1− τ(yS)). (3)

The left hand side is the marginal cost of investment, whereas the right hand side is themarginal benefit, which is given by the present discounted value of net wages in all futuredates earned by the extra unit of human capital. Notice that both the marginal cost andbenefit of investment take into account the marginal tax rate faced by the individual. Tounderstand the effect of taxes, first consider the case when taxes are flat-rate, ie, τ ′(y) ≡ 0.In this case, all terms involving taxes cancel out and the FOC reduces to:

C ′j(Qjs) =β + β2 + ...+ βS−s.

Thus, flat-taxes have no effect on human capital investment. This is a well-understood

8

insight that goes back to at least Heckman (1976) and Boskin (1977).6

Now consider progressive taxes, ie., τ ′(y) > 0. We rearrange equation (3) to get:

C ′j(Qjs) =β 1− τ(ys+1)

1− τ(ys)︸ ︷︷ ︸Progressivity discount

+ β2 1− τ(ys+2)

1− τ(ys)︸ ︷︷ ︸...

+ ...+ βS−s1− τ(yS)

1− τ(ys)︸ ︷︷ ︸Progressivity discount

. (4)

As long as the individual’s earnings grow over the life cycle and the tax structure isprogressive, all tax ratios on the right hand side will be smaller than one, which will depressthe marginal benefit of investment, and in turn dampen human capital accumulation. Thus,each of these tax ratios can be thought of as capturing the progressivity discount thateffectively reduces the value of a higher wage earnings in the future when compared tothe forgone lower wage earnings today. Therefore, each ratio provides a key measure ofthe distortion created by progressive taxes. To draw an analogy to the taxation literature(c.f. Prescott (2004), Ohanian, Raffo, and Rogerson (2006), etc.) it is more convenient tofocus on a closely related measure—what we refer to as the progressivity wedge—which isessentially one minus the progressivity discount, or:

PW (ys, ys+k) ≡ 1− 1− τ(ys+k)

1− τ(ys)=τ(ys+k)− τ(ys)

1− τ(ys).

A progressivity wedge of zero corresponds to flat taxes and the distortion grows withthe value of the wedge.7 To understand the effect of progressive taxes on wage inequal-ity, first note that the distortion created by progressive taxes differs systematically acrossability levels. At the low end, individuals with very low ability whose optimal plan involveno human capital investment in the absence of taxes, would experience no wage growthover the life-cycle, and therefore, no distortion from progressive taxation. At the top end,individuals with high ability whose optimal plan involves low wage earnings early in lifeand high earnings later will face very large wedges, which will dampen their investmentbehavior. Thus, progressivity will reduce the cross-sectional dispersion of human capital,and consequently, the wage inequality in an economy, even with inelastic labor supply.8

6With pecuniary costs of investment, flat-taxes can affect human capital investment, as shown by Kingand Rebelo (1990) and Rebelo (1991). Similarly, Lucas (1990) shows that flat-taxes can have a negativeimpact on human capital investment when labor supply is elastic. Trostel (1993) contains a nice summaryof the history of thought on the effects of taxation in human capital models.

7It is easy to see that in a model with retirement (as in the next section), a redistributive the pensionsystem will have an effect that would work very similarly to progressive income taxation. The same is truefor the unemployment insurance system, which dampens the incentives to invest, although this is likely tobe more important at the lower end of the income distribution. We study both in the full model below.

8Notice that the price of human capital PH does not appear in any version of the FOC displayed above,the implication being that it has no effect on the amount of investment undertaken by individuals. This is

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Endogenous Labor Supply. Second, consider now the the case with elastic labor supply.The FOC can be shown to be:

C ′j(Qjs) =β 1− τ(ys+1)

1− τ(ys)ns+1 + β2 1− τ(ys+2)

1− τ(ys)ns+2 + ...+ βS−s

1− τ(yS)

1− τ(ys)nS, (5)

where now the marginal benefit accounts for the utilization rate of human capital, whichdepends on the labor supply choice. (For derivation, see Appendix A.1). Now, once again,let us consider the effect of flat rate taxes. The intra-temporal optimality condition impliesthat labor supply choice depends on the tax rate and the level of human capital. Forexample, assuming a separable power utility function we get: (1−ns)−γ = PHhs (1− τ) c−σs .Therefore, a higher level of tax depresses labor supply choice (as long as the income effect isnot too large), which then reduces the marginal benefit of human capital investment, whichreduces the optimal level of human capital. But labor supply in turn depends on the level ofhuman capital, which further depresses labor supply, the level of human capital, so on andso forth. Therefore, with endogenous labor supply, even a flat-rate tax does have an effect onhuman capital investment, and this effect can be large because of the amplification describedhere. Furthermore, it is also clear that restrictions imposed on maximum labor supply (suchas the 35 hour workweek law implemented in France for several years during the 2000’s)will also depress human capital accumulation and compress the wage distribution. (Thisillustrates a situation where unions can affect inequality at the upper end—by restrictinglabor hours thereby depressing human capital investment at the top.)

Because average labor hours differ significantly across countries and over time (c.f.,Prescott (2004), Ohanian, Raffo, and Rogerson (2006)), it is also useful to consider thissecond measure of wedge that takes into account each country’s utilization rate of its humancapital—relative to the average country in the sample—in addition to its tax structure.Formally, for country i, what we now call the progressivity wedge*, is defined as:

PW ∗i (ys, ys+k) = 1− 1− τ(ys+k)

1− τ(ys)

(ninALL

), (6)

where ni is the hours per person in country i and, similarly, nALL is the average of hoursacross all countries in the sample. Notice that because of the rescaling by nALL, if a countryhas a sufficiently high average labor hours and low progressivity, this wedge measure canbecome negative (e.g., the US). Therefore, this new measure is defined relative to a givensample of countries, but is still informative about the relative return to human capitalwithin a group of countries, which is the focus of this paper.

problematic, especially because our goal is to study the impact of skill-biased technical change that raisesthe value of human capital. When we move on to the full model below, we are going to consider a differenttechnology for human capital accumulation that circumvents this problem.

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Table III: Tax Function Parameter Estimates

τ(y/AW ) = a0 + a1(y/AW ) + a2(y/AW )φ

Country: a0 a1 a2 φ R2

Denmark 1.4647 −.01747 −1.0107 −.15671 0.990Finland 1.7837 −.01199 −1.4518 −.11063 0.999France 0.5224 .00339 −.24249 −.41551 0.993Germany 1.8018 −.01708 −1.3486 −.11833 0.992Netherlands 3.1592 −.00790 −2.8274 −.03985 0.984Sweden 9.1211 −.00762 −8.7763 −.01392 0.985UK 0.5920 −.00390 −.32741 −.30907 0.989US 1.2088 −.00942 −.94261 −.10259 0.993

To summarize, the basic model studied here implies that countries with a more progres-sive tax system will have a lower (before-tax) wage inequality. Furthermore, it will becomeclear below that these countries will experience a smaller rise in wage inequality in responseto SBTC.

2.2 Deriving the Country-Specific Tax Schedules

For each country, we follow the same procedure described here. First, the OECD web siteprovides a tax calculator that estimates the total labor income tax for all income levelsbetween 1/2 of average earnings (hereafter, AW ) to two times AW. The calculator takesinto account several types of taxes (central government, local and state, social securitycontributions made by the employee, and so on) as well as many types of deductions andcash benefits (children exemptions, deductions for taxes paid, social assistance, housingassistance, in-work benefits, etc.).9 Using this tool, we calculate the average labor incometax rate, τ(y), for 50%, 75%, 100%, 125%, 150%, 175% and 200% of AW. One possibleapproach would be to approximate these data points with a flexible functional form, whichcan then serve as the average tax schedule for the relevant country. It turns out howeverthat this approach does not always produce sensible results for the tax schedule for incomelevels much beyond 200% of AW, which is relevant when individuals solve their dynamicprogram. Fortunately, there is another piece of information available from OECD thatallows us to overcome this difficulty. Specifically, we also have the top marginal tax rateand the top bracket corresponding to it for each country. As described in more detail in the

9Non-wage income taxes (e.g. dividend income, property income, capital gains, interest earnings) andnon-cash benefits (free school meals or free health care) are not included in this calculation. Anothernotably absent component is the social security contributions made by the employer.

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Figure 1: Estimated Average Tax Rate Functions, Selected OECD Countries, 2003

0 1 2 3 4 5 6 7 8 9

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

UNITED STATES

Data: AverageLabor Income Tax RateFitted Function

0 1 2 3 4 5 6 7 8 9

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

GERMANY

0 1 2 3 4 5 6 7 8 9

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Multiples of Average Earnings (In Respective Country)

FINLAND

R2:0.993

R2:0.992

R2:0.999

Appendix, we use this information to generate average tax rates at income levels beyondtwo times AW. Then, we fit the following smooth function to the available data points:10

τ(y/AW ) = a0 + a1(y/AW ) + a2(y/AW )φ.

The parameters of the estimated average tax functions for all countries are reported inTable III, along with the R2 values. Although the assumed functional form allows for variouspossibilities, all fitted tax schedules turn out to be increasing and concave in the relevant

10We have also experimented with a variety of different functional forms in addition to this one, includinga popular specification proposed by Guoveia and Strauss (1994), which is commonly used in the quantitativepublic finance literature (c.f, Castañeda, Díaz-Giménez, and Ríos-Rull (2003), Conesa and Krueger (2006),and the references therein). Because we estimate tax schedules for a number of different countries with verydifferent progressivity structures, we found the functional form used here to provide the best fit across theboard, as can be seen from the high R2 values in Table III.

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Figure 2: Progressivity Wedges At Different Income Levels: 1− 1−τ(k×0.5)1−τ(0.5)

for k = 2, 3, .., 6.

0.5 1 1.5 2 2.5 3 3.50

0.05

0.1

0.15

0.2

0.25

0.3

0.35

y/AW

DENFIN

FRA

GER

NET

SWE

UK US

regions (up to 10 times AW). The lowest R2 is 0.984 and the mean is 0.991 indicating afairly good fit. In figure 1 we plot the estimated functions for three countries: one of the twoleast progressive (United States), the most progressive (Finland), and one with intermediateprogressivity (Germany).

Figure 2 plots the progressivity wedges for the eight countries in our sample. Specifically,each line plots PW (0.5, 0.5k) for k = 1, 2, ..., 6, which are essentially the wedges faced by anindividual who starts life at half the average earnings in that country and looks towards aneventual wage level that is up to six times his initial wage. As seen in the figure, countries areranked in terms of their progressivity, probably consistent with one could anticipate: the USand the UK have the least progressive tax system, whereas Scandinavian countries have themost progressive one, with larger continental European countries scattered between thesetwo extremes. The differences also appear quantitatively large (although a more preciseevaluation needs to await the full-blown model in Section 3): for example, a young workerwho earns half the average wage today and aims to earn twice the average wage (k = 4)in the future loses about 13% of his before-tax wage in the US and the UK comparedto 27% in Denmark and Finland. These differences grow with the ambition level of theindividual, dampening the incentives for human capital investment especially at the top ofthe distribution.

13

Figure 3: Progressivity Wedge and the Log 90-10 Wage Dispersion in 2003. Awedge of zero corresponds to flat taxation (no distortion) and progressivity increases along thehorizontal axis. The wedge measure used corresponds to PW(0.5,2.5) as defined in the text.

0.1 0.15 0.2 0.25 0.30.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

Progressivity Wedge

Log

90−

10 W

age

Diff

eren

tial

Corr = −0.83

DEN

FIN

FRA

GER

NET

SWE

UK

US

Regression Line

2.3 Taxes and Inequality: Cross-Country Empirical Facts

As explained above, the average labor income tax schedule in 2003 has been estimated foreach of the eight countries listed in Table I. Using these schedules, we normalize AW ineach country to 1 and focus on the progressivity wedge between half the average earningsand 2.5 times the average earnings: PW (0.5, 2.5). Similarly, when we calculate PW ∗ for agiven country, we use the average hours per person in that country between 2001 and 2005for ni in equation (6), and the average of the same variable across all countries for nALL.

The wage inequality data come from the OECD’s Labour Force Survey database andare derived from the gross (i.e., before tax) wages of full-time, full-year (or equivalent)workers.11 This is the appropriate measure for the purposes of this paper, as it more closely

11The definition of gross wages is given in footnote 1. An exception to this definition is France, for whichwage earnings are net of employee social security contributions. Also, in contrast to the other countries inthe sample France excludes “agricultural and general government workers and household service workers”from its samples when reporting wage data. Despite these caveats we are including France in our samplebecause it is not clear how much these differences affect the final wage inequality numbers. To get anidea, we have compared the wage inequality figures from our main data to another source for France, alsoprovided in the OECD Labour Force Survey (reported as the GAE0 variable), which includes all workersand reports gross wages, but is only available from 2002 to 2005. At least during this period, the two datasources agree extremely well, which in reassuring. Other issues regarding data comparability and detailsare provided in the Appendix.

14

Table IV: Cross-Correlation of PW (k,m) and Log 90-10 Wage Differential

1980k↓

m→ 1.0 1.5 2.0 2.5 3.0

0.5 0.82 0.85 0.86 0.87 0.881.0 0.87 0.87 0.87 0.861.5 0.86 0.84 0.792.0 0.76 0.65

20030.5 0.73 0.77 0.80 0.83 0.851.0 0.81 0.84 0.87 0.891.5 0.87 0.88 0.882.0 0.87 0.82

corresponds to the marginal product of each worker (and, hence, her wage) in the model.The fact that the inequality data pertains to before tax wages is important to keep in mind;if it were after-tax wages, the correlation between the progressivity of taxes and inequalitywould be mechanical and therefore not surprising at all.

Figure 3 plots the relationship between before-tax log 90-10 wage inequality and pro-gressivity wedge in the 2000’s. Countries with a smaller wedge—meaning a less progressivetax system and therefore smaller distortion in human capital investment—have a higherwage inequality. The relationship is also quite strong with a correlation of 0.83. Repeatingthe same calculation using the utilization adjusted wedge (PW ∗) yields a correlation of0.75. Both of these relationships are consistent with the simple human capital model withprogressive taxes presented above.

Moreover, this strong relationship is also robust to using wedges calculated from dif-ferent parts of the wage distribution. This can be seen in table IV, which reports thecorrelation between the log 90-10 differential and PW (k,m) as k and m are varied over awide range. The same table also reports the correlation using the log 90-10 wage differentialin 1980’s in each country, even though the wedges are still the ones obtained using the 2003tax schedules. Surprisingly, the correlation is as strong as before even in this case. Oneinterpretation of this finding is that even though the tax schedules for each country mayhave changed over time, the relative ranking of the progressivity within this group mightnot have changed significantly, which in turn generates the same kind of inequality rankingin 1980. (Indeed the correlation between the log 90-10 wage differential in 2003 and 1980is 0.87).

We next turn to the change in inequality over time. Figures 4 and 5 plot the progres-sivity wedge* versus the change in the log 90-50 and 50-10 wage differentials, respectively.

15

Figure 4: Progressivity Wedge* and Change in Log 90-50 Differential: 1980 to2003. The wedge measure for country i is PW ∗i (0.5, 2.5) as defined in equation (6). As before,progressivity increase along the horizontal axis.

−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Progressivity Wedge*

Cha

nge

in L

og 9

0−50

Wag

e D

iffer

entia

l: 19

80−

2003

Corr = −0.86

DEN

FIN

FRA

GER

NET

SWE

UK US

Data

Regression Line

Countries with a more progressive tax system in 2000’s have experienced a smaller risein wage inequality since 1980’s. The relationship is especially strong at the top of thewage distribution and weaker at the bottom: the correlation between progressivity andthe change in the 90-50 differential is remarkably strong (−0.86), whereas the correlationwith the 50-10 differential is much weaker (only −0.36); see figures 4 and 5). This resultis consistent with the idea that the distortion created by progressivity is likely to be feltespecially strongly at the upper end where human capital accumulation is an importantsource of wage inequality, but less so at the lower end of the wage distribution where otherfactors, such as unionization, minimum wage laws, etc. could be more important.

Finally, Table V gives a more complete picture of the differences between the two defi-nitions of wedges. First, the top panel reports the correlation of each wedge measure withlog wage differentials. For example, the upper most left cell shows the correlation betweenPW (0.5, 2.5) and the log 90-10 differential, which is the same information illustrated beforein figure 3. Other cells report information not seen in the previous figures. For example, oneconclusion that comes out of this table is that the adjustment for utilization rates throughlabor hours makes little difference in the correlations in year 2003, but a somewhat largerdifference (reduction) in the correlations in year 1980. However, with either measure, pro-gressivity is negatively correlated with inequality even when one focuses on different partsof the distribution.

16

Figure 5: Progressivity Wedge* and Change in Log 50-10 Differential: 1980 to2003. See figure 4 for notes.

−0.1 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

−0.15

−0.1

−0.05

0

0.05

0.1

Corr = −0.36

DEN

FIN

FRA

GERNET

SWE

UK

US

Progressivity Wedge*

Cha

nge

in L

og 9

0−50

Wag

e D

iffer

entia

l: 19

80−

2003

Data

Regression Line

This picture changes somewhat when we turn to the change in inequality over time(bottom panel). Now the simple wedge measure has a rather low correlation with log wagedifferentials (the strongest is with log 90-50 and that is −0.39). However, adjusting for hoursper person increases these correlations significantly to −0.63 for the log 90-10 differential,and to −0.86 for the log 90-50 differential (which is plotted in figure 4). We conclude thatthe relationship between the wedge measures and cross-sectional inequality is quite robustindependently of the wedge measure used, as well as what initial or final income level ischosen. The change in inequality over time is somewhat more sensitive to the adjustmentby hours per person. Since our full model includes a labor supply choice, this measure willbecome the most relevant measure, as we shall see when we move to the full-blown modelin the next section.

3 Model 1: For Cross-Sectional Analysis

The model we use for the cross-sectional analysis is a richer version of the basic frameworkpresented in Section 2.1. Each individual has one unit of time in each period, which she canallocate to three different uses: work, leisure, and human capital investment. Preferences

17

Table V: Correlation Between Progressivity Measures and Wage Dispersion

Measure of Wedge:PW (0.5, 2.5) PW ∗(0.5, 2.5)

Log wage differentials Year: 200390-10 −.83 −.7590-50 −.84 −.7350-10 −.73 −.67

Year: 198090-10 −.87 −.5190-50 −.74 −.3850-10 −.88 −.57

Change from 1980 to 200390-10 −.11 −.6390-50 −.39 −.8650-10 .14 −.36

over consumption, c, and leisure time, 1− n, are given by this common separable form:

u(c, n) = log(c) + ψ(1− n)1−ϕ

1− ϕ. (7)

If an individual chooses to work, as before, she can allocate a fraction (i) of her workinghours (n) to human capital investment. However, more realistically, we now assume thati ∈ [0, χ] where χ < 1. An upper bound less than 100% on on-the-job investment can arise,for example, because the firm incurs fixed costs for employing each worker (administrativeburden, cost of office space, etc.), or due to minimum wage laws. Individuals can invest full-time by attending school (i = 1) and enjoy leisure for the rest of the time. Thus, the choiceset for investment time is: i ∈ [0, χ]∪1, which is non-convex when χ < 1. Finally, humancapital depreciates every period at rate δ < 1. Except for the differences described here,the human capital accumulation process is the same as the stylized framework described inSection 2.1.

As before, human capital is produced according to a Ben-Porath technology: Q =

Aj (hin)α. A key parameter in this specification is Aj, which determines the productivity oflearning. The heterogeneity in Aj implies that individuals will differ systematically in theamount of human capital they accumulate, and consequently, in the growth rate of theirwages over the life cycle. This systematic fanning out of wage profiles is the major sourceof wage inequality in this model. Also, as can be seen from the optimality conditions (forexample, (5)), the price of human capital has no effect in this model other being a scalingfactor. Thus, for simplicity we set PH = 1 in the rest of the cross-sectional analysis.

18

An individual may choose to be unemployed at age s, ns = 0, in which case she receivesunemployment benefit payments as specified below. Individuals retire at age R and receiveconstant pension payments every year until they die at age T. The benefits system isdescribed in more detail below.

3.1 Idiosyncratic Shocks and Earnings

Individuals receive idiosyncratic shocks to the efficiency of the labor they supply in the mar-ket. Specifically, when an individual devotes ns(1−is) hours producing for his employer, hiseffective labor supply becomes εns(1− is), where the ε shocks are generated by a stationaryMarkov transition matrix Π(ε′ | ε) that is identical across agents and over the life cycle.The observed total wage income of an individual of type j who receives a shock ε is

yjs ≡ εhjsnjs(1− ijs) = εhjsn

js︸ ︷︷ ︸

Potential earnings

− ε× hjsnjsijs︸ ︷︷ ︸,Cost of investment

(8)

where εhjsnjs is the “potential earnings” of an individual—that is, the income an individualwould earn if he spent all his time on the job producing for his employer. Therefore, wageincome can be written as the potential earnings minus the “cost of investment,” which issimply the forgone earnings while individuals are learning new skills. Finally, the hourlywage rate is given by

wjs = yjs/njs = εhjs − εhjsijs = εhjs − εC(Qj

s)/njs

where C(Qjs) is the opportunity cost of investment as before. Because here we also have

idiosyncratic shocks, the total cost of investment also depends on these efficiency shocks.

3.2 Government: Taxes and Transfers

Unemployment and Pension Benefits. The unemployment benefit system is modeledso as to capture the salient features of each country’s actual system in a relatively parsimo-nious manner. For computational reasons, we make some simplifying assumptions to theactual systems implemented by each country.12 Specifically, if a worker becomes unemployedat age s, the initial level of the unemployment payment she receives is an increasing functionof her years of work before becoming unemployed, denoted by m, and also (typically) de-creases with the duration of the unemployment spell. The precise nature of the dependence

12Solving the present model for a single country and a single parametrization takes more than 12 hoursfor the US and up to 40 hours for some countries (such as Denmark) on a state of art workstation. Thismakes calibration very time consuming, which is why we try not to add any more state variables, whichwould be required to model the benefits systems in more detail.

19

on past service and the duration of the unemployment spell varies by country, which willbe incorporated during calibration. Finally, in most countries the replacement rate fallswith the level of pre-unemployment income, which is also partly captured here. Φ(y∗,m, s)

denotes the unemployment benefit function of an s year old individual who has worked atotal of m years before becoming unemployed (at age s − m). Although, in reality, un-employment payments depend on the pre-unemployment earnings, making this dependenceexplicit will add (some measure of) past earnings as an additional state variable into analready demanding (and non-convex) computational problem. Thus, we simplify the prob-lem by assuming that Φ instead depends on y*, which is the income the individual wouldhave earned in the current state if he did not have the option of receiving unemploymentinsurance. For the precise problem that yields y∗, see Appendix A2.

After retirement individuals receive constant pension payments every period. Essen-tially, the pension of a worker with ability level j depends on the average lifetime earningsof workers with the same ability level (denoted by yj) as well as on the number of yearsthe worker has been employed up to the retirement age (denote it by mR) subject to amaximum years of contribution, m. The pension function is denoted as Ω(yj,mR).13

The Tax System and the Government Budget. The government imposes a flat-rateconsumption tax, τc, as well as a potentially progressive labor income tax, τn(y).14 The col-lected revenues are used for three purposes: (i) to finance the benefits system, (ii) to financegovernment expenditure, G, that does not yield any direct utility to consumers (either dueto corruption or waste), and (iii) the residual budget surplus or deficit is distributed in alump-sum fashion, denoted Tr, to all households regardless of employment status.

3.3 Individuals’ Dynamic Program

Individuals are able to trade a full set of one-period Arrow securities a(ε′ | ε) that pays oneunit of consumption good when the shock is ε′ next period and today’s shock is ε. The priceof each Arrow security is denoted by q(ε′ | ε).

Individuals cannot accumulate human capital while unemployed.15 The problem of ans-year old individual with ability Aj (we suppress ability type for clarity), who has worked

13In reality, pension payments depend on the workers’ own earnings history, but modeling this explicitlyalso adds an extra state variable, which this simplified structure avoids.

14Because capital is mobile internationally, it is harder to justify using country-specific tax rates on capitalincome, unlike for labor and consumption, which are almost always taxed at destination (or the countryof residence of the worker). In particular, the mobility of capital implies the equalization of after-tax ratesacross countries of comparable assets. For these reasons, we abstract from capital income taxes.

15Notice that if an individual chooses to go back to school after losing her job, she is considered a studentand not as unemployed.

20

form years, entered the period with h units of human capital and a units of Arrow securitiesand has observed shock ε is given by:

V (h, a,m; ε, s) = maxc,n,i,a′(ε′)

[u(c, n) + β

∑ε′

Π(ε′ | ε)V (h′, a′(ε′),m′; ε′, s+ 1)

]s.t

(1 + τc)c+∑ε′

q(ε′ | ε)a′(ε′) = (1− τn(y))y + a+ Tr

y = [εh(1− i)︸ ︷︷ ︸]nw

In + Φ(y∗,m, s)︸ ︷︷ ︸UI Benefits

(1− In) (9)

h′ = (1− δ)h+ A(hni)α, l′ = (1− δ)lm′ = m+ In

i ∈ [0, χ] ∪ 1

where In is an indicator function that is equal to 1 if the agent is working in that periodand 0 if he is unemployed; and y∗ is defined above.

The solution to problem (9) gives a set of functions V (h, a,m; ε, s), c(h, a,m; ε, s),a′(h, a,m; ε′, ε, s), n(h, a,m; ε, s), m′(h, a,m; ε, s), Q(h, a,m; ε, s), and implied wage earn-ings y(h, a,m; ε, s). We will need these expressions in the definition of equilibrium below.

After retirement, individuals receive a pension and there is no human capital investment.Since there is no uncertainty during retirement, a riskless bond is sufficient for smoothingconsumption. Therefore, the problem of a retired agent at age s > R can be written as16

WR(a, yj,mR; s) = maxc,a′

[u(c, n) + βWR(a′, yj,mR; s+ 1)

](10)

s.t

(1 + τc)c+ qa′ = (1− τn(ys))ys + a+ Tr

ys = Ω(yj,mR).

Definition 1 A stationary recursive competitive equilibrium for this economy is a set ofequilibrium decision rules c(x), n(x), Q(x), i(x) and a′(ε′, x); and value functions, V (x)

and WR(x), for working and retirement periods respectively, where x = (h, a,m; ε, s, j)

(notice the inclusion of j into this vector); and a time-invariant measure Λ(x) such that16Notice that because the pension payments explicitly depend only on yj and mR, these are the only

two variables we need to keep track of in the individuals’ problem. However, in the specification of theequilibrium, we also need to identify the fraction of agents in state (h, a,m; ε, R − 1, j)—since mR in turndepend on this full state vector—to determine the total social security payments made by the government.

21

1. Given the labor income tax function, τ(y), consumption tax, τc, and government policyfunctions, Φ and Ω; individuals solve problems in (9) and (10).

2. The government budget balances:17

∫x(:,s≤R)

τn(y(x))y(x)I(n(x) > 0)dΛ(x) +

∫x

τcc(x)dΛ(x) = G+ Tr

+

∫x(:,s≤R)

Φ(y∗(x),m, s)I(n(x) = 0)dΛ(x)

+T∑s=R

∫x(:,s=R−1)

Ω(yj,mR(x))dΛ(x).

The first term in the government’s budget is the total tax revenue from labor incomecollected from all agents who are working and younger than retirement age.18 Similarly, thesecond term is the total tax revenue from the consumption tax, but it is collected from allagents including the retirees. On the right hand side, the pension payments only depend ona worker’s ability through yj and the number of years she worked until retirement (mR(x)),which in turn depends on the full state vector x at age R − 1. Therefore, we integrate thepension payments over the full state vector x conditioning on age R− 1 and then sum thesame amount over all ages greater than R to find total pension payments.

4 Quantitative Analysis

In this section, we begin by discussing the parameter choices for the model. Our basiccalibration strategy is to take the United States as a benchmark and pin down a number ofparameter values by matching certain targets in the US data.19 We then assume that othercountries share the same parameter values with the US along unobservable dimensions (suchas the distribution of learning ability), but differ in the dimensions of their labor marketpolicies that are feasible to model and calibrate (specifically, consumption and labor incometax schedules, the retirement pension system, and the unemployment insurance system).

17The notation x(:, s ≤ R) indicates that the integration is taken over the entire domain of variables instate vector x, except for s which is restricted to the specified range. Others are defined analogously.

18The pension and unemployment benefit functions are written as paying after-tax income, so they arenot taxed again.

19Taking the US as the benchmark country to pin down unobservable parameters is also motivated bythe fact that its economy is subject to much less of the labor market rigidities compared to CEU—suchas unionization, and other distorting institutions—that are not modeled in our framework. Therefore, itprovides a better laboratory for determining the unobservable parameters than other countries where thesedistortions could be more important for wage determination.

22

We then examine the differences in economic outcomes—specifically in wage dispersion,output, and labor supply—that are generated by these policy differences alone.

4.1 Calibration

A model period corresponds to one year of calendar time. Individuals enter the economy atage 20 and retire at 65 (S = 45). Retirement lasts for 20 years and everybody dies at age85. The net interest rate, r, is set equal to 2%, and the subjective time discount rate is setto β = 1/ (1 + r).20 The curvature of the human capital accumulation function, α, is setequal to 0.80 broadly consistent with the existing empirical evidence. Higher values of thisparameter have sometimes been estimated in the literature (cf. Heckman (1976), Heckman,Lochner, and Taber (1998), Kuruscu (2006)). Such values generate a stronger response ofhuman capital investments to changes in the environment (such as changes in technologyand differences in progressivity, among others) and, consequently, increase the explanatorypower of the model. Therefore, in our baseline calibration, we opt for this lower and moreconservative value for α.

Utility function. The utility function we use (given in (7)) has two parameters to cal-ibrate: the curvature of leisure, ϕ; and the utility weight attached to leisure, ψ. Theseparameters are jointly chosen to pin down the average hours worked in the economy, aswell as the average Frisch labor supply elasticity. We assume that each individual has 100hours of discretionary time per week (about 14 hours a day) and taking a 40 hours per weekas the average labor supply for employed workers in the US, implies that individuals work40% of their available time: n = 0.4. With power utility, the Frisch elasticity of labor isequal to 1−n

n1ϕ. Because of heterogeneity across individuals, labor supply (n) varies in the

population, so there is a distribution of Frisch elasticities. We simply target the Frisch elas-ticity implied by the average labor hours, n. The empirical target we choose is 0.3, whichis consistent with the empirical estimates surveyed by Browning, Hansen, and Heckman(1999), which range from zero to 0.5. Domeij and Floden (2006) argue that the previous es-timates might be biased downward due to ignoring borrowing constraints and suggest usingvalues near the upper end of this range. While it is common to use higher elasticity valuesin representative agent macro studies (e.g., Prescott (2004) among many others), values of0.5 or lower are also more common in quantitative models with heterogeneous agents (c.f.,Heathcote, Storesletten, and Violante (2008), Erosa, Fuster, and Kambourov (2009)). Aswill become clear below, a higher Frisch elasticity improves the performance of our model,so in our baseline case we choose the relatively conservative value of 0.3.21 In the sensitivity

20This interest rate should be thought of as the “after-tax” rate since we do not model taxes on savingsexplicitly.

21With our baseline calibration, the Frisch elasticities in the population range from 0.25 to 0.39.

23

analysis, we will experiment with both a higher Frisch elasticity of 0.5 and a case withouthours choice (i.e, a 0-1 choice).

Distributions: Learning Ability, Initial Human Capital, and Shocks. Recall thatagents have two individual-specific attributes at the time they enter the economy: learn-ing ability and initial human capital endowment. We assume that these two variablesare jointly uniformly distributed in the population and are perfectly correlated with eachother.22 While the assumption of perfect correlation is made partly for simplicity, a strongpositive correlation is plausible and can be motivated as follows: The present model is inter-preted as applying to human capital accumulation after age 20 and by that age high-abilityindividuals will have invested more than low ability individuals, leading to heterogeneity inhuman capital stocks at that age, which would then be very highly correlated with learn-ing ability. Indeed, Huggett, Ventura, and Yaron (2007) estimate the parameters of thestandard Ben-Porath model from individual-level wage data, and find learning ability andhuman capital levels at age 20 to be strongly positively correlated (corr: 0.792). Mak-ing the somewhat stronger assumption of perfect correlation allows us to collapse the twodimensional heterogeneity in Aj and hj0 into one, speeding up computation significantly.

Therefore, this jointly uniform distribution of (Aj, hj0) yields four parameters to becalibrated. It turns out that the mean value of raw labor, E

[hj0], is a scaling parameter

and is simply set to a computationally convenient value, leaving three parameters thatneed to be pinned down: (i) the cross-sectional standard deviation of initial human capital,σ(hj0), (ii) the mean learning ability, E [Aj], and (iii) the dispersion of ability, σ (Aj) . The

idiosyncratic shock process, ε, is assumed to follow a first order Markov process, with twopossible values, 1− γ, 1 + γ, and a symmetric transition matrix:

Π =

[p 1− p

1− p p

].

This structure yields two more parameters, γ and p, to be calibrated—for a total of 5parameters. Finally, because there is measurement error in the individual-level wage data,we add a zero mean iid disturbance to the wages generated by the model. Notice that thisshock is different from the idiosyncratic shocks as it does not affect individuals’ optimalchoices at all.

22We prefer the uniform distribution over a Gaussian distribution because it has a bounded support soinitial human capital and ability can be ensured to be non-negative. Another choice would be a log normaldistribution but most empirical measures of ability find it more closely approximated by a symmetricdistribution, unlike a log normal one. It will turn out, however, that the wage distribution generated bythe model will be closer to log-normal with a longer right tail (more consistent with the data), due to theconvexity arising from the human capital production function.

24

Data Targets. Our calibration strategy is to require that the wages generated bythe model be consistent with micro-econometric evidence on the dynamics of wages foundin panel data on US households. Specifically, these empirical studies begin by writing astochastic process for log wages (or, sometimes, labor earnings) of the following generalform:

log wjs =[aj + bjs

]︸ ︷︷ ︸systematic comp.

+ zjs + εjs︸ ︷︷ ︸stochastic comp.

zjs = ρzjs−1 + ηjs

where wjs is the “wage residual” obtained by regressing raw wages on a polynomial in age;the terms in brackets, [aj + bjs], capture the individual-specific systematic (or life cycle)component of wages that result from differential human capital investments undertaken byindividuals with different ability levels, and zjs is a first order autoregressive process withinnovation ηjs. Finally, εjs is an iid shock that could capture classical measurement error thatis pervasive in micro data and/or purely transitory movements in wages. For concreteness,in the discussion below, we refer to the first two terms in brackets as the “systematiccomponent” and to the latter two terms as the “stochastic component” of wages.

We begin with the i.i.d shock in the specification and assume that it corresponds tothe measurement error in the wage data. This is consistent for example with Guvenenand Smith (2009), who find the majority of transitory variation in wages to be due tomeasurement error. Based on the results of the validation studies from the US wage data,23

we take the variance of the measurement error to be 10% of the true cross-sectional varianceof wages in each country, which yields σ2

ε = 0.034 for the United States.

We then choose the following five data moments to pin down the five parameters iden-tified above:

1. the mean log wage growth over the life cycle (which is informative about E(Aj))

2. the cross-sectional dispersion of wage growth rates, σ2(bj) (which is informative aboutσ(Aj))

3. the cross-sectional variance of the stochastic component (which is informative aboutγ), and

4. the average of the first three autocorrelation coefficients of the stochastic componentof wages (which is informative about p)

23For an excellent survey of the available validation studies and other evidence on measurement error inwage and earnings data, see Bound, Brown, and Mathiowetz (2001).

25

Table VI: Baseline Parametrization

Parameter Description Valueϕ Curvature of utility of leisure 5.0 (Frisch = 0.3 )ψ Weight on utility of leisure 0.20α Curvature of human capital function 0.80S Years spent in the labor market 45T Retirement duration (years) 20r Interest rate 0.02β Time discount factor 1/(1 + r)χ Maximum investment time on the job 0.50δ Depreciation rate of skills (annual) 1.5%

E[hj0]

Average initial human capital (scaling) 4.95Parameters calibrated to match data targetsE [Aj] Average ability 0.190

σ(hj0)/E[hj0]

Coeff. of variation of initial human capital 0.076σ [Aj] /E [Aj] Coeff. of variation of ability 0.408γ Dispersion of Markov shock 0.23p Transition probability for Markov shock 0.90

5. the log 90-10 wage differential in the population (which, together with the previousmoments, is informative about σ(hj0)).

The target value for the mean log wage growth over the life cycle (i.e., the cumulative growthbetween ages 20 and 55) is 45%. This number is roughly the middle point of the figuresfound in studies that estimate life-cycle wage and income profiles from panel data sets suchas the Panel Study of Income Dynamics (see, for example, Gourinchas and Parker (2002),Davis, Kubler, and Willen (2006), Guvenen (2007)). The second data moment is the cross-sectional variance of wage growth rates, σ2(bj). The estimates of this parameter are quiteconsistent across different papers, regardless of whether one uses wages or earnings (which isnot always the case for some other parameters of the income process). For example, usingmale hourly earnings data, Haider (2001) estimates a value of 0.00043 and using annualearnings data he estimates it to be 0.000041. Baker (1997, Table 4, rows 6 and 8) usesan annual earnings measure and estimates values of 0.00031 and 0.00039 in the two mostclosely related specifications to the present paper, whereas Guvenen (2009) finds a valueof 0.00038, again using male annual earnings data. Finally, Guvenen and Smith (2009)estimate a process for household annual earnings and obtain a value of 0.00035. We takeour empirical target to be 0.00040, which represents an average of these available estimates.

The next two moments are included to ensure that the model is consistent with somekey statistical properties of the stochastic component of wages in the data. These moments

26

are (i) the unconditional variance of the stochastic component, (zs + εs), as well as (ii) theaverage of its first three autocorrelation coefficients. The empirical counterparts for thesemoments are taken from Haider (2001) (which is the only study that estimates a processfor hourly wages and allows for heterogeneous profiles). The figure for the unconditionalvariance can be calculated to be 0.109 using the estimates in Table 1 of his paper.24

The reason we match the average of the first three autocorrelation coefficients is becauseHaider (2001) estimates an ARMA(1,1) process whereas in our model we employ a slightlymore parsimonious structure with an AR(1) process plus an iid shock. This latter formula-tion is more popular among calibrated macroeconomic models because it requires one fewerstate variable in the dynamic programming problem while still capturing the dynamics ofwages quite well. Nevertheless, because our formulation of the stochastic component is dif-ferent, it is not possible to exactly match each autocorrelation coefficient in the ARMA(1,1)specification, which is why we match the average of the first three. From Haider’s estimatesthis value is calculated to be 0.33.25

Our fifth, and final, moment is the log 90-10 wage differential in the entire populationin year 2003. Adding this moment ensures that the calibrated model is consistent withthe overall wage inequality in the US in that year, which is the benchmark against whichwe will measure all other countries. The empirical target value is 1.57 (from the OECD’sLabour Force Survey data). Table VII displays the empirical values of the five momentsas well as their counterparts generated by the calibrated model. As can be seen here allmoments are matched fairly well, some are matched exactly.26 One point to note is thateven though the average of the first three autocorrelation coefficients is pretty low (0.33),recall that the stochastic component includes measurement error as well, which is iid. TheMarkov shocks to human capital, which approximate the AR(1) process in the data, havea first order annual autocorrelation of 0.80 (implied by p = 0.90 shown in Table I).

Before we conclude this discussion a remark is in order. A caveat to the empiricalcounterparts of the first four moments mentioned above is that these are taken from studiesthat either use data on males or households, because the counterparts of these moments forfemale workers is almost impossible to find in the literature due to the difficulties involvedwith the extensive margin of labor supply for females. In contrast, the wage inequality data

24Over the sample period, the average innovation variance is estimated to be 0.074, the AR coefficient is0.761 and the MA coefficient is −0.42. Using these parameters the unconditional variance is 0.109.

25Even though the calibration matches the average of the autocorrelation coefficients quite well (tableVII: 0.33 in the data versus 0.34 in the model), as explained above, each coefficient cannot not matchedexactly. But they are not too different either: 0.48, 0.33 and 0.20 in the model compared to 0.42, 0.32, and0.24.

26Because the moments chosen are typically non-linear functions of the underlying parameters we cal-ibrate, having five moments and five parameters does not guarantee that all moments will be matchedexactly. Considering this, the close correspondence is an encouraging sign that the model is flexible enoughto generate wage dynamics similar to that observed in the data.

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Table VII: Empirical Moments Used for Calibrating Model Parameters

Moment Data ModelMean log wage growth from age 20 to 55 0.45 0.46Cross-sectional variance of wage growth rates 0.00040 0.00040Cross-sectional variance of stochastic component 0.109 0.107Average of first three autocorrelation coeff. of stochastic component 0.33 0.34Log 90-10 ratio in 2003 1.57 1.58

we examine pertains to all workers in the economy—so includes female workers. It is notclear, however, how important this discrepancy is because our main focus is on the cross-sectional log 90-10 wage differential and along this dimension male data agrees with dataon all individuals quite well: for example, in the US Current Population Survey data, thelog 90-10 differential for males is 1.61 between 2001-2003 and it is 1.60 for all individuals.Similarly, the log 90-50 differential is 0.81 for males and 0.80 for all individuals. There aresome differences in the change in inequality over time (1980-2003): inequality rises by 33log points for males compared to 26 log points for all individuals, which is mainly due tothe closing gender wage gap during period.27

Unemployment and Pension System. Within the general structure described for thepension and UI systems, there is a great deal of variation across countries in the parame-ters that control the generosity, the duration, and the insurance component of the benefitssystem. For example, among the countries in our sample, individuals in Denmark andNetherlands receive the largest pension payments after retirement with the present value ofretirement wealth for the average individual exceeding half a million US dollars, whereas theUS and the UK have the lowest pension entitlements—less than six times average annualearnings in each respective country (and less than half the wealth in Denmark and Nether-lands).28 We provide the exact formulas for each country and discuss the specifics in moredetail in Appendix B. Finally, the calibration of G, the surplus wasted by the governmentis challenging due to the difficulty in obtaining reliable estimates of this magnitude. In thebaseline case, we assume no surplus is wasted, i.e., G ≡ 0; instead the government rebatesback all the surplus to households in a lump-sum fashion (Tr). We examine the sensitivityof our results to this assumption in Section 5.3.

27The source for these statistics is Autor, Katz, and Kearney (2008), whose authors kindly provided uswith their data.

28Of course, these countries also differ in the amounts of taxes they collect to finance the retirementsystems, so these numbers should not necessarily be interpreted as the generosity of one system versus theother.

28

Consumption Taxes. The average tax rate on consumption is taken from McDaniel(2007), who provides estimates for 15 OECD countries for the period 1950 to 2003. Themethodology used by the author is basically to calculate the total tax revenue raised fromdifferent types of consumption expenditures and to divide this by the total amount of cor-responding expenditure. Among the countries we study here, Denmark is the only countrythat McDaniel (2007) does not provide an estimate for. We set Denmark’s consumptiontax rate equal to that of Finland, which has a comparable value added tax rate.29

4.2 Life Cycle Profiles for Wage, Earnings, and Hours

Before concluding this section, it is useful to briefly examine if the calibrated model producesplausible behavior over the life cycle for wages, earnings, as well as labor hours comparedto the US data. Figure 6 displays the relevant graphs, which are computed using 10,000simulated life cycle paths for individuals drawn from the joint distribution of (Aj, hj0). Thetop panel of 6 plots the mean log hours of employed workers. As can be seen here, theaverage hours is close to the chosen target of 0.40 and displays little trend over the lifecycle. In the US data, average hours rises up to about age 25 and then remains fairly flatfor about 30 years (about until age 55), after which point it starts declining until retirement(cf., Erosa, Fuster, and Kambourov (2009), figure 2). Although the model does not capturethe rise in hours in the first 5 years of the life-cycle, the flat hours profile during most ofthe working life is well-captured by the model. Hours also decline in the model especiallyafter age 50, although not by as much as in the data. Some of the decline in the data couldbe due to health shocks or partial early retirement, which are not allowed for in our model.

The dashed lines around the mean profile show the 2 standard deviation bands of thehours distribution in the population, which shows a small rise in hours dispersion over thelife cycle. More precisely, the variance of log hours goes up by 1.6 log points, which isfairly small compared to the mean hours of 0.40. Again, this is broadly consistent with thefindings of Erosa, Fuster, and Kambourov (2009) (figure 9, 10), who document a fairly flatvariance profile for hours with a rise only after mid 40’s. Although, naturally, there is fairamount of noise in their data source (the Panel Study of Income Dynamics) that makes aprecise statement difficult, the rise in dispersion they find appears to be somewhat largerthan what is generated by our model. This can be fixed here by increasing the Frisch laborsupply elasticity, which is an exercise we will conduct later below.

The middle panel Figure 6 plots the mean log wages and earnings over the life-cycleapproximated by a cubic polynomial in age, as commonly done in the literature. Themodel reproduces the well-known hump-shape in wages and earnings. In particular, mean

29We have also experimented with setting Denmark’s rate equal to Sweden’s, but this had a very minoreffect on the results.

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Figure 6: Life Cycle Profiles of Wages, Earnings, and Hours

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log wage grows by about 45% (as calibrated) and peaks at around age 50 and then declinesby about 20% until retirement age. Mean log earnings follows a similar pattern, but declinesby about 5% more than the wage profile which is due to the fall in labor supply later in life,seen in panel (a). The only notable difference from the US data is perhaps that wages andearnings grow somewhat more slowly when individuals are in their 20’s, but this period ofthe life cycle is always difficult to interpret due to schooling, part time jobs, etc., so this isprobably not a major drawback.

Finally, the lower panel plots the variances of log wages and earnings, which both rise ina convex fashion up to 55 and then grow more slowly. The variance of earnings grow fasterthan that of wage due to the fact that hours dispersion rises over the life cycle. Guvenen(2009) constructs the empirical counterpart for earnings from the PSID and finds this profileto rise from about 0.20 to 0.73 from age 22 to 62. In the model the variance rises fromabout 0.15 to 0.75 from age 20 to 65, which is fairly consistent with this empirical evidence.The only notable difference perhaps is that Guvenen (2009) finds the profile to be slightlyconvex throughout the life cycle (see his figure 4), whereas, in our model, this convexity isstronger earlier in the life cycle and tapers off after age 55.

Overall, with the five empirical moments we targeted, the model appears to generate lifecycle behavior—both in terms first and second moments—that is broadly consistent withthe data, which is encouraging for the cross-country comparisons we undertake next.

5 Cross-Sectional Results

In this section, we begin by presenting the implications of the calibrated model for the cross-country wage inequality at a point in time. We then provide decompositions that illustratethe separate roles of progressivity, average tax rates, and other labor market institutions(pension and unemployment insurance systems) on these results. We also perform sensitivityanalyses with respect to key parameters and conduct some welfare experiments.

5.1 The Cross-Section in the 2000’s

First, figure 7a plots the log 90-10 wage differential for each country in the data against thevalue implied by the model. The correlation between the simulated and actual data is 0.86,suggesting that the model is able to capture the relative ranking of these eight countries interms of overall wage inequality observed in the data. A natural concern, of course, is thatwith eight data points, a seemingly high correlation can be driven by a few outliers with noobvious pattern among the rest of the data points. As seen in the figure, however, this isnot the case: most of the countries line up quite nicely along the regression line.

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Figure 7: Wage Inequality in Eight OECD Countries: Benchmark Model versus Data

(a) Log 90-10 Wage Dispersion

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Table VIII: Measures of Wage Inequality: Benchmark Model versus Data

Log 90-10 Log 90-50 Log 50-10Data Model % explained % explain. % explain.

Level ∆ from US Level ∆ from US (d)/(b)(a) (b) (c) (d) (e) (f) (g)

Denmark 0.97 0.60 1.20 0.38 63 93 37Finland 0.89 0.67 1.26 0.33 49 77 27France 1.08 0.49 1.44 0.14 30 74 12Germany 1.15 0.41 1.29 0.29 71 79 59Netherlands 1.06 0.50 1.35 0.23 46 63 30Sweden 0.83 0.73 1.28 0.30 42 69 20CEU 1.00 0.57 1.30 0.28 49% 76% 27%UK 1.27 0.29 1.51 0.07 22 1 49US 1.57 0.0 1.58 0.00 –

Similarly, Figure 7b plots the log 90-50 wage differential for each country in the dataagainst the predicted value by the model. The correlation between the actual and simulateddata is even higher—0.88—for the log 90-50 wage differential. The correlation of the sim-ulated and actual log 50-10 wage differential on the other hand is somewhat lower at 0.63(figure 7c). Thus, the model does a better job in matching the relative ranking of countriesfor the upper end wage inequality. This finding is consistent with the idea that progressivetaxation affects the human capital investment of high-ability individuals more than othersand, therefore, the mechanism is more relevant for the upper end of the wage distribution.

While these figures and correlations reveal a clear qualitative relationship, they do notallow us to quantify how important taxation is for cross-country differences in inequality.For this, we turn to table VIII. The first column reports the level of the log 90-10 wagedifferential in the data for all countries. The second column expresses the same informationfor each country as a deviation from the US, which is our benchmark country. For example,in Denmark the actual log 90-10 differential is 0.97, which is 60 log points lower than thatin the US. The third and fourth columns display the corresponding statistics implied bythe calibrated model. Again, for Denmark, the model generates a log 90-10 differential of1.20, which is 38 log points below the corresponding figure implied by the model for theUS (1.58). Therefore, the model explains 63% (= 38/60) of the difference in the log 90-10differential between the US and Denmark, reported in column (e). Similar comparisonsshow that the model does quite well in explaining the level of wage inequality in Germany(41 log points lower than the US inequality in the data versus 29 log points lower in themodel) but does poorly in explaining the UK (29 log points difference in the data versus 7log points in the model). Inspecting column (e), shows that the fraction explained by the

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model ranges from 30% for France to 71% for Germany. Averaging this figure across allCEU countries show that the model explains 49% of the actual gap in inequality betweenthe US and CEU in 2003.

To get a better idea about which part of the wage distribution is better captured bythe model, the next two columns display the same calculation performed in column (e),but now separately for the log 90-50 (f) and 50-10 (g) differentials. Inspecting these twocolumns, it becomes apparent that for all CEU countries the model explains the upper tailinequality much better than the inequality at the lower end. For example, for Denmark, themodel explains 93% of the log 90-50 differential while only generating 37% of the log 50-10differential. In fact, the model explains at least 63% of the upper tail inequality for all CEUcountries, averaging 76% across all countries, whereas it explains on average only 27% ofthe log 50-10 differential. Among the CEU countries, Germany is the one best explainedby the model overall: a healthy 79% of the upper tail and 59% of the lower tail inequalityis generated by the model. The model does poorly in explaining the lower tail inequalityin France (12%). Recall however, the wage data for France differs from other countries inthat their sample excludes public sector workers and the wage measure is net of employeesocial security contributions. It is not clear if these differences could have to do with thevery low explanatory power of the model for this country. Finally, a notable exception tothese generally strong findings is the UK, which is an important outlier: the model explainsalmost none of the difference between the UK and US at the upper tail (1% to be exact)whereas it explains 49% of the inequality at the lower end. As we shall see below, we foundUK to be an outlier along most dimensions this paper attempts to explain and the leastwell-understood economy when viewed through the lens of this model.

Finally, it is of interest to ask if the calibrated model is broadly consistent with thedistribution of wage inequality between the upper and lower tails in each region. As seen inTable IX, when the data for all CEU countries are aggregated, 57% of the log 90-10 wagedispersion in this region is located above the median and 43% is below the median. Thisratio is very well matched by the model, even though moment from the CEU is used in thecalibration. Turning to the US, the upper tail inequality as a fraction of total is slightly lowerthan the CEU, at 53%. The model somewhat overstates the inequality at the upper tail(59%) compared to the US data, but the difference does not seem too substantial, especiallysince none of these aspects of inequality have been directly targeted in our calibration.

5.2 Understanding the Roles of Progressivity, Average Tax Rates,and Benefits Institutions

The baseline model incorporates several differences between the labor market policies ofthe US and the CEU—differences in pension systems, unemployment insurance systems,consumption taxes, as well as differences in both the progressivity and the average rate

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Table IX: Wage Dispersion in the Upper and Lower Tails: Model versus Data

Total 90-10 % 90-50 % 50-10CEU Data 1.00 57.1% 42.9%

Model 1.30 56.5% 43.5%US Data 1.57 53.1% 46.9%

Model 1.58 58.9% 41.1%

implied by the income tax systems. It is, therefore, instructive to isolate the roles playedby each of these components for the results presented in the previous section. To this end,we conduct two decompositions. First, we assume that continental Europe has the samepension and unemployment insurance systems (together referred to as “benefits institutions”)and the same consumption tax as the US, but each country retains its own income taxschedule as in the baseline model. This experiment quantifies the explanatory power of themodel that is coming from the income tax system alone versus the role of other institutions.In the second experiment, we go one step further in understanding the role of incometaxes, and assume that all countries have the same average income tax rates as the US, thesame benefits institutions and consumption taxes as the US, but each country keeps theprogressivity of its income tax schedule used in the baseline model. This experiment isolatesthe role of progressivity alone in explaining cross-country differences in wage inequality.There are several non-trivial issues to deal with in conducting these experiments which wenow discuss in more detail.

The first experiment is relatively straightforward. One issue to notice is that when weset each country’s benefits system equal to that in the US, this leads to a change in the gov-ernment’s budget balance. First, because benefits are more generous in continental Europe,setting them to the US values reduces the expenditures of the government. But, second,because wages and labor supply are also endogenous, the change in the benefits systemalso affects human capital accumulation and labor supply, and therefore the revenues alsochange. Therefore, an important question is whether or not we should let the governmentbudget to re-balance after the experiment (which will affect the lump-sum amounts receivedby individuals, creating an income effect) or not (and simply keep the same lump-sum asin the baseline case). We have conducted this experiment both ways and found only quan-titatively minor differences (available upon request), so here we only report the case wherethe government budget is rebalanced and the lump-sum amount is re-adjusted.

Table X, column 2, reports the results. In the top panel, the correlations between thedata and model are all lower than in the baseline case, but the difference is relativelysmall for the log 90-10 differential (goes from 0.86 to 0.75) and even smaller for the upperand lower end inequality (going from 0.88 and 0.63 down to 0.83 and 0.62 respectively).Turning to panel B, which reports the fraction of US-CEU difference explained by the

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Table X: Decomposing the Effects of Progressivity, Average Taxes, and Labor Market In-stitutions

Benchmark Labor Income Tax Progressivity aloneDifference from Benchmark: (1) (2) (3)Progressivity — — —Average Income Taxes — — set to USBenefits institutions — set to US set to USConsumption tax — set to US set to US

A. Correlation Between Data and Model90-10 0.86 0.75 0.8090-50 0.88 0.83 0.8750-10 0.63 0.62 0.60

B. Fraction of US-CEU Difference Explained by Model90-10 0.49 0.37 0.3390-50 0.76 0.57 0.4850-10 0.27 0.20 0.20

model, again the explanatory power goes down, this time a bit more. For example, for theoverall inequality, the explained fraction goes from 0.49 down to 0.37. Therefore, taxes aloneaccount for about 75% (= 37/49) of overall inequality difference, and the benefits systemand consumption taxes account for the remaining 25%. Interestingly, this is almost exactlythe same fraction explained by taxes versus other institutions for the upper and lower tailinequality (0.57/0.76 = 0.75 and 0.20/0.27 = 0.74). The bottom line is that with incometaxes alone, the model generates close to 60% of the wage inequality differences above themedian, and more than a third of the difference in overall wage inequality, between the USand CEU.

We now go one step further and investigate if the power of taxes come from differencesin average tax rates across countries, or whether they result from the differences in theprogressivity structure. In other words, if continental Europe differed from the US onlyin the progressivity of its labor income tax system, but had the other features of its labormarket policies identical to the US—including the same average tax rate on labor income—how much of the differences in wage inequality found in the baseline model would stillremain? To answer this question, we proceed as follows. First, we need to be careful abouthow we adjust the average tax rate to the US level, because many plausible modificationsto the tax structure will simultaneously affect the progressivity (as measured, for example,by the wedges). We show in Appendix A.3 how the average tax rate can be adjusted toany desired rate without affecting the progressivity of the tax system (which is less trivialthan it might first appear). Then, using these hypothetical tax schedules we solve each

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country’s problem assuming that all countries have identical labor market policies (set tothe US benchmark) and their tax schedules generate the same average tax rate as in the USwhen using individuals’ choices made using US’s original tax schedule. As before, we solvea fixed-point problem in the lump-sum amount such that the government budget balanceswith the new structure in place.

Panel A displays the effect of progressivity on the correlation between the data andthe model. For the log 90-10 wage differential, the correlation in the baseline case was0.86, whereas progressive taxes alone generate a correlation of 0.80 (which is incidentallyhigher than the correlation with full tax schedules used in column 2). Thus, qualitatively,differences in progressivity captures a substantial part of the differences across countriesin wage inequality. This is even more striking in the second row, which reports the log90-50 differential. The baseline correlation is 0.88; incorporating progressivity alone, andignoring all other differences across countries generates a correlation that is only slightlylower—0.87. A similar finding is observed at the lower tail where the correlation changesvery little from the baseline.

As before, in panel B, we report what fraction of the explained variation is due toprogressivity alone and what fraction is due to other differences, including the differencesin average tax rates. Comparing columns 1 and 3, we see that progressivity alone explains33% of the difference in the log 90-10 differential between the US and CEU and 48%of the difference in the log 90-50 differential. Expressing this as a fraction of the totalvariation explained in the baseline model, progressive taxes are responsible for 68% of theexplanatory power of the model for the log 90-10 differential. Comparing this to the totaleffect of taxes, which was calculated to be 75% above, it becomes clear that progressivityis the key component of the income tax system that is responsible for understanding wageinequality differences. A similar fraction—63% (= 0.48/0.76)—explained by progressivityat the upper tail and lower tail: 75% (= 0.20/0.27).

Finally, the baseline model explains almost 100% of the differences in the GDP perworker differences between the US and CEU (last row of the table). Taxes alone account for74% of the explanatory power of the model, and progressivity accounts for 56%. Therefore,thinking of GDP per worker as a proxy for average wages, we find that average taxes becomemore important when it comes to explaining the first moment of wages.

Overall, we conclude that the benefits system and consumption taxes together are re-sponsible for about a quarter of the explanatory power of the model for wage inequality.Somewhat surprisingly, this explanatory power does not vary too much between the upperand lower end inequality. One could have conjectured that some of these institutions pro-vide insurance at the lower end, and therefore, these institutions might have a larger impactin that range, but we do not see that. One possible explanation is that with human capitalaccumulation the distorting effect of these policies are more important than their insurance

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Table XI: Effect of Labor Supply Elasticity on Wage Inequality Differences

Frisch = 0.5 Discrete hours: n ∈ 0, 0.40Log 90-10 Log 90-50 Log 50-10 Log 90-10 Log 90-50 Log 50-10

(a) (b) (c) (d) (e) (f)Denmark 84 1.22 48 46 47 47Finland 62 96 36 34 41 28France 39 97 16 15 32 9Germany 85 95 68 45 39 56Netherlands 54 78 30 28 34 24Sweden 53 92 24 25 32 20CEU 62% 97% 33% 32% 38% 28%UK 32 -10 86 25 0 56

effects and individuals with high ability respond more strongly to distortions in the returnsto human capital, which makes these institutions affect the upper end inequality as well.

The more important finding however is the role of progressivity, which for all practicalpurposes is the key component of the income tax structure for understanding wage inequalitydifferences. Average tax rates differences are the least important among the three types ofpolicy differences we examine in this paper.

5.3 Sensitivity Analysis

We now conduct sensitivity analyses with respect to some key parameters of the model. Webegin with the Frisch labor supply elasticity and consider two, somewhat extreme, cases:(i) high elasticity where Frisch = 0.5, and (ii) the case without continuous hours choice:n ∈ 0, 0.40. As a third, and last, exercise, we examine the role of the assumption wemade in the benchmark model regarding how the surplus (or deficit) in the government’sbudget is distributed to households, namely that it is rebated back in a lump-sum fashion,which implies that government expenditures are perfect substitutes for private consumption.Instead, here, we assume that half of the budget surplus in each country is wasted and yieldsno utility to individuals. This is also likely to be an extreme assumption, but is useful toillustrate whether the results are sensitive to this scenario. In every exercise below, themodels are recalibrated to match the same five targets in Table VII.

5.3.1 Effect of Labor Supply Elasticity

Frisch Elasticity = 0.5. We begin by setting ϕ = 3.0, which implies a Frisch elasticityof 0.5. We then recalibrate the five parameters discussed in Section 4.1 to match the same

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five moments reported in Table VII. Table XI reports the counterpart of the analysis weconducted for the benchmark model and reported in Table VIII. It basically quantifies howmuch of the US-CEU differences observed in the data can be explained by this model withhigh Frisch elasticity. Comparing the two tables makes it clear that the model’s explanatorypower has improved across the board. Now the model can explain 62% of the US-CEUdifference in the log 90-10 wage differentials (compared to 49% in the benchmark case) anda remarkable 97% of the upper tail inequality (from 76% before). The improvement in thelog 50-10 differential is more modest, going up to 33% from 27% in the benchmark case.

So what is the drawback then of this alternative calibration? In fact, not too much. Onenotable shortcoming compared to the benchmark case is that because hours and wages arestrongly correlated in this model, a higher Frisch elasticity implies that the rise in earningsinequality is significantly higher than the rise in wage inequality over the life cycle. It is notclear how important this shortcoming is though. One possible fix would be to add preferenceshocks to the value of leisure (similar to the route taken by Heathcote, Storesletten, andViolante (2008), but also allow the value of leisure to change stochastically). This wouldreduce the wage-hours correlation and fix this problem without probably affecting the mainresults. In this paper, we have not pursued this approach of introducing more heterogeneityinto an already rich and complex model and, instead, opted for the more conservative lowerFrisch elasticity figures for our baseline model.

Discrete Hours Choice: Full-Time Work versus Unemployment. To better un-derstand the role of continuous labor hours choice, we now examine another case whereworkers can only choose between full time employment at fixed hours (n = 0.40) and un-employment. The utility function is as in the baseline case with a Frisch elasticity of 0.3 forall individuals in all countries (since the experiment eliminates hours per person differencesby assumption). The results are reported in the last three columns of Table XI. Withoutthe amplification provided by endogenous labor supply—and the resulting dispersion inhours both within each country and across countries—the explanatory power of the modelfalls and, in some cases, it falls significantly. For example, the model explains 32% of thedifference in the log 90-10 differential, compared to 49% in the benchmark case, and 62% inthe high Frisch case. For the upper end inequality, the difference is even larger: the modelnow explains 38%, half of the baseline value, and also much lower than the 97% in the highFrisch case. The difference is much smaller in the lower tail however, where the explainedfraction slightly rises to 28% from 27% in the baseline, and is only a bit lower than 33% inthe high Frisch case. Overall, these findings underscore the importance of the interaction ofendogenous labor supply choice with progressive taxation for understanding wage inequalitydifferences across countries, especially above the median of the distribution.

39

Table XII: Effect of How Government Expenditures Effect Utility

G = Tr = 0.5× Gov’t SurplusLog 90-10 Log 90-50 Log 50-10

(a) (b) (c)Denmark 63 90 38Finland 49 75 29France 30 71 14Germany 69 75 60Netherlands 45 59 31Sweden 42 67 23CEU 49% 73% 29%UK 21 0 49

5.3.2 Wasteful Government Expenditures versus Transfers

The last case we examine concerns the way the budget surplus is used by the government.In the baseline model, the surplus was rebated back to households in a lump-sum fashion,essentially assuming that government expenditures are perfect substitutes for private con-sumption. To examine if our results are sensitive to this assumption, we solve the modelwith the same parametrization as the baseline but now assume that half of the governmentsurplus is wasted: G = Tr, and each component equals half of the government’s surplus(i.e., tax revenues minus benefits payments). As seen in Table XII, qualitatively it reducesthe explanatory power of the model in some cases for the log 90-10 and 90-50 differentials,and increases for the 50-10 differential. However, quantitatively, the effect is very minimalacross the board. (In fact, in some cases, due to rounding no effect is visible when comparingthese results to the benchmark case in Table VIII.)

5.4 Other implications

While the main focus of this paper is to understand differences in wage inequality, themodel also make predictions for some other variables and how they differ across the USand the CEU. We now discuss these briefly (Table XIII). Notice that the first two columnsreport variables only as ratios. This is because for GDP per worker the levels are notinformative (and not comparable to data counterpart); and for hours per worker, the modelwas calibrated to match the US data exactly (n = 0.40), so, again, there is no informationin levels.

The model does a good job of matching GDP per worker differences: in the data, theCEU has a GDP per worker that is 23% lower than that of US, which is almost exactly

40

Table XIII: Some Key Variables in the CEU and in the US: Model vs Data,2001-2005

GDP/ Worker Hours/Worker Unemp. Rate EducationalAttainment

US/CEU US/CEU CEU US CEU USData 0.77 0.82 7.4% 5.5% 27.8% 38.0%Model 0.77 0.91 7.5% 5.7% 21.5% 37.9%

matched by the model. The UK on the other hand is again an outlier (not in the table).In the model, UK’s GDP per worker is only 1.4% lower while it is 24% lower in the data.Turning to hours per worker, the CEU is 19% below the US in the data. The modelcaptures half of this difference and generates a 9.5% lower hours per worker for the CEU.Since we allow for unemployment and model the differences in the UI benefits system, it isalso of interest to examine the implications of the model along this dimension. Somewhatsurprisingly, the average unemployment rate in the model is quite close to the data bothfor the US and the CEU. Again, the UK is an outlier, where the model generates anunemployment rate of 9.3% compared to only 4.8% in the data. Finally, the model alsodoes well in accounting for the educational attainment rate30 for the US, but underestimatesit for the CEU (21.5% compared to 27.8% in the data). Of course, in our model, educationis currently treated in a simple manner—as an option for accumulating human capital fulltime with the same production function used for on the job training—so these comparisonsshould be taken with a grain of salt. A more thorough modeling of the differences informal education between the US and Europe is a difficult problem, but also a potentiallyinteresting and fruitful direction to extend the current model, which we intend to undertakein future work.

6 Inequality Trends Over Time: 1980-2003

As discussed above, the one factor Ben-Porath model studied so far does not have a well-defined notion of returns to skill. The price of human capital, PH , is simply a scalingfactor and has no effect on any implications of the model (which is why we normalized itto 1 above). This is an important shortcoming when the goal is to study the changes inhuman capital behavior over time in response to, for example, skill-biased technical change.Guvenen and Kuruscu (2009) proposed a tractable way to extend the Ben-Porath modelthat allows for a notion of returns to skill and, therefore, generates responses to a chance

30This is defined as in Autor, Katz, and Kearney (2008): the fraction of population aged 24-65 who havecompleted 2 years of college education or more.

41

in the price of human capital. We now describe the necessary modifications to the modelpresented above.

6.1 Model 2: An Extended Framework

Human Capital Accumulation. Suppose that individuals now have two factors of pro-duction: they begin life with an endowment of “raw labor” (i.e., strength, health, etc.),which is constant over the life cycle but, as before, they are also able to accumulate humancapital over the life cycle. Let lj denote raw labor of an individual of type j.31 Raw laborand human capital command separate prices in the labor market, and each individual sup-plies both of these factors of production at competitively determined wage rates, denotedby PL and PH , respectively. Individuals begin their life with zero human capital (that is,hj0 ≡ 0 for all j) and each period produce new human capital, Qj, according to the followinggeneralized Ben-Porath technology:

Qj = Aj((θLl

j + θHhj)ijnj

)α. (11)

Notice that we now allow both factors of production to also affect learning. The mo-tivation for this specification is that an individual’s physical capacity (health, strength,stamina, etc) is also likely to affect her productivity in learning in addition to her abilityand existing human capital stock. Furthermore, Guvenen and Kuruscu (2009) show thatthis specification generates many plausible implications for the behavior of wages in the USsince the 1970’s, which is another motivation for adopting this formulation. Finally, bothraw labor and human capital depreciate every period and we assume that this happens atthe same rate δ.

Idiosyncratic Shocks and Earnings. With this new two-factor structure, the observedtotal wage income of an individual is given by

yjs ≡ ε[PLl

j + PHhjs

]njs(1− ijs) = ε

(PLl

j + PHhjs

)njs︸ ︷︷ ︸

Potential earnings

− ε(PLl

j + PHhjs

)njsi

js︸ ︷︷ ︸,

Cost of investment

(12)

where now the potential earnings of an individual is given by [PLεl + PHεhjs]n

js. Similarly,

the hourly wage rate is given by

wjs = yjs/njs = ε

(PLl

j + PHhjs

)− εC(Qj

s)/njs

31The dependence of raw labor on j makes clear that although raw labor, it can vary across individuals,albeit in a way that is perfectly correlated with ability. We will provide justification for this structure inthe calibration section.

42

where C(Qjs) ≡ (PLl

j + PHhjs)n

jsijs is the opportunity cost of investment (unadjusted for

the idiosyncratic shock) for this model.

Skill-Biased Technical Change. The two factor structure introduced above breaks theneutrality of the human capital investment with respect to change in the price of humancapital PH . In particular, now a rise in PH increases investment, even when PL is fixed.Before delving into the analysis of the model, it is useful to step back and understandthis point more clearly. To this end, we make some assumptions that yield an analyticalexpression for the optimality condition: we set χ ≡ 1, eliminate the benefits system (Ω ≡ 0

and Φ ≡ 0), and set the idiosyncratic shocks to their mean value. For simplicity (althoughnot necessary), let us also assume δ = 0. Finally, we assume PH/PL = θH/θL, whichessentially means that the relative price of human capital to raw labor is the same as theirrelative productivity in the human capital function. While this assumption is not necessaryfor quantitative results, we make in the rest of the paper because it simplifies the solutionof the model substantially.32 Under these assumptions, the first order condition is:

C ′j(Qjs) =θHβ

1− τ(ys+1)

1− τ(ys)ns+1 + β2 1− τ(ys+2)

1− τ(ys)ns+2 + ...+ βS−s

1− τ(yS)

1− τ(ys)nS (13)

The key observation is that optimal investment, Qjs, now does depend on the level of

θH , unlike in the optimality conditions of the standard Ben-Porath model given in (4) and(5) above, where PH did not appear at all. This is because, in our two-factor model, theopportunity cost of investment depends on the prices of both raw labor and human capital(see equation (2)), whereas the marginal benefit is only proportional to the price of humancapital. As a result, a higher level of θH (for example, due to SBTC) increases the marginalbenefit more than the marginal cost, resulting in higher investment. This feature is animportant difference between the current framework and the standard Ben-Porath model.

6.2 Quantitative Results

Calibration. There are some new parameters that need to be calibrated. Except thosediscussed here, all parameters values are kept at the same values given in table I. Animportant point to note is that for the cross-sectional analysis of the previous section, theextended model of this section would have precisely the same implications as the one factorBen-Porath model used above. This is because θH and θL are constant at a point in timeand their values can be normalized to generate exactly the same behavior observed before.33

32See Guvenen and Kuruscu (2009) for further discussion of this point.33In other words, we could have used the more general model since Section 3, but chose to work with the

simplest model for transparency of results.

43

Table XIV: Rise in Wage Inequality, 1980-2003: Model versus Data. The model iscalibrated to match the 23 log points rise in the log 90-10 differential for the US from 1980 to 2003.

Change in Log Wage DifferentialsLog 90-10 = Log 90-50 + Log 50-10

CEU Data Level 0.070 0.063 0.007% 91% 9%

Model Level 0.175 0.134 0.041% 100% 77% 23%

US Data Level 0.230 0.160 0.070% 70% 30%

Model Level 0.241 0.192 0.050% 100% 79% 21%

Difference Data: Level 0.160 0.097 0.063% 60% 40%

Model Level 0.0674 0.058 0.009% 87% 13%

% Explained 42% 60% 14%

This implies that with proper choices of θL and θH and the distribution of lj, we do nothave to recalibrate any other parameter and can still obtain exactly the same results foryear 2003 as before. This is the route that we follow below.

Specifically, we have eliminated the initial human capital stock by setting hj0 ≡ 0, butinstead introduced raw labor. We make the same assumptions for raw labor as we madeearlier about hj0. That is, we assume that lj is uniformly distributed and is perfectlycorrelated with Aj. We also assume that θH = θL = 1 in 2003. With this assumption weuse the same mean value and coefficient of variation for lj as we did for hj0 in Table I

For examining the change in inequality over time, we choose the change in SBTC, i.e.,∆ log (θH/θL), to match the the log 90-10 wage differential of 1.34 in 1980 which implies anincrease of 0.24 in the log 90-10 wage differential from 1980 to 2003. The implied change∆ log (θH/θL)=0.236.

Results. With this calibration, wage inequality rises by 0.175 in CEU during the sametime, compared to the 0.070 rise in the data (first column of table XIV). These resultssuggest that differences in labor market policies can generates about 42% (= (0.241 −0.175)/(0.230− 0.070)) of the widening in the inequality gap between CEU and US duringthis time period.

Another dimension of the rise in wage inequality is seen in table II and replicated incolumns 2 and 3 of the last table. The substantial part of the rise in 90-10 differential in

44

the CEU has been at the top: the 90-50 differential is responsible for 91% of the total risein the 90-10 differential during this period, whereas only 9% is at the lower end. A similaroutcome, somewhat less extreme, is observed in the US where 70% of the rise in the log90-10 differential is due to the 90-50 differential. The model generates a similar picture:about 77% of the rise in the CEU and 79% in the US is due to the 90-50 differential.

7 Conclusion

In this paper, we have studied the impact of progressive labor income taxation on wageinequality when a major source of wage dispersion is human capital accumulation. Tounderstand the main mechanisms and their quantitative importance, we have examined theinequality differences between the US and the CEU countries, which differ significantly intheir income tax structures as well in other dimensions of their labor market institutions.We found that the policy and institutional differences we model can explain at least halfof the total wage dispersion between the US and CEU and three-quarters of the dispersionabove the median of the distribution. The model explains much less—about 30%—of thedifferences below the median, which seems plausible since differences in human capital isunlikely to be an important source of wage inequality for individuals in this income range.Unionization and wage setting institutions (collective bargaining, etc.) are probably moreimportant for the lower tail.

We also showed that among the many policy differences between the US and CEU, themost important for wage inequality is the progressivity of the income tax system, which isresponsible for about 2/3 of the model’s explanatory power. This is followed by the benefitssystem (25%), and average income taxes, which is the least important (10%). Prescott(2004) and Rogerson (2008), among others, have shown that average income taxes are im-portant for understanding differences in average hours between US and Europe. Combiningour findings with theirs, it seems that the differences in the mean of taxes explain differ-ences in the means across these regions, whereas differences in the dispersion of tax ratesacross households explain differences in dispersion of wages. We also found endogenouslabor supply to play an important amplification role for wage inequality when interactedwith progressivity. When this channel is shut down by assuming constant hours, the model’sexplanatory power falls significantly. In contrast, if one is willing to accept a higher averageFrisch elasticity (of 0.5), the model is able to explain 60% of total inequality differences andalmost all differences in the upper tail. Finally, we have also investigated if the differentialrise in wage inequality between these two regions could be explained by the channels ex-plored here. The answer is a qualified yes: even when we use fixed tax schedules (derivedfrom 2003 data), the model explains about 40% of the differences in the rise in wage dis-

45

persion between the US and CEU and 60% of the differences in the upper tail from 1980 to2003. [Discuss Welfare Experiment]

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A Appendix: Key Derivations and Definitions

A.1 Derivation of the optimal investment condition (equation (13))

Here we derive the optimal investment condition in the most general framework studies inthis paper (equation (13) in Model 2). The optimality conditions presented earlier in thepaper ((3), (4), and (5)) can all be obtained as special cases of this formulation.

Under the assumptions stated in Section 6 (i.e., setting χ ≡ 1, eliminating unemploymentbenefits and pension payments (Ω ≡ 0 and Φ ≡ 0), and setting idiosyncratic shocks to theirmean value) the problem of the agent is given by

V (h, a, s) = maxcs,ns,Qs

u((1 + r)as + ys(1− τ(ys))− as+1, 1− n)

+ V (hs+1, as+1, s+ 1)

subject to

ys = (θLl + θHhs)ns − C(Qs)

Note that total tax liability of the agent is given by yτ(y). The derivative of tax liabilitywith respect to y gives the marginal tax rate. Thus, τ(y) = τ(y) + yτ ′(y). Using thisexpression, we obtain the following FOC’s for this problem:

(ns) : (θLl + θHhs) (1− τ(ys))u1(cs, 1− ns) = u2(cs, 1− ns)(as) : u1(cs, 1− ns) = βV2(hs+1, as+1, s+ 1)

(Qs) : C ′(QS) (1− τ(ys))u1(cs, 1− ns) = βV1(hs+1, as+1, s+ 1)

Envelope conditions are:

(as) : V2(hs, as, s) = (1 + r)u1(cs, 1− ns)(hs) : V1(hs, as, s) = ns (1− τ(ys))u1(cs, 1− ns) + ns+1βV1(hs+1, as+1, s+ 1)

Using the envelope conditions we obtain

50

C ′(Qs) (1− τ(ys)) = θHns+1(1− τ(ys+1))βu1(cs+1, 1− ns+1)

u1(cs, 1− ns)︸ ︷︷ ︸1

1+r

+

θHns+1(1− τ(ys+1))β2u1(cs+2, 1− ns+2)

u1(cs, 1− ns)︸ ︷︷ ︸1

(1+r)2

+ ....

Then the following conditions give the interior solution to consumer’s problem (where β =

1/(1 + r)):

(θLl + θHhs) (1− τ(ys))u1(cs, 1− ns) = u2(cs, 1− ns),u1(cs, 1− ns) = β(1 + r)u1(cs+1, 1− ns+1),

and

C ′j(Qjs) =θHβ

1− τ(ys+1)

1− τ(ys)ns+1 + β2 1− τ(ys+2)

1− τ(ys)ns+2 + ...+ βS−s

1− τ(yS)

1− τ(ys)nS,

which is equation (13).

A.2 Definition of y∗ introduced in Section 3.2

Recall that y∗ was defined in Section 3.4.1 as “the income an individual would receive in aeconomy identical to the present model, except that the unemployment insurance was setto zero. Mathematically, the definition is therefore:

y∗ = h(1− i∗)n∗

51

where n∗ and i∗ are given by the solution to the problem below

(c∗, n∗, i∗, a′∗(ε′)) = arg maxc,n,i,a′(ε′)

[u(c, n) + β

∑ε′

Π(ε′ | ε)V (ε′, a′(ε′), h′,m+ 1; s+ 1)

]s.t.

(1 + τc)c+∑ε′

q(ε′ | ε)a′(ε′) = (1− τn(y))y + a+ Tr

y = [εh(1− i)]nh′ = (1− δ)h+ A(hin)α, l′ = (1− δ)li ∈ [0, χ].

A.3 Deriving Tax schedules with Different Progressivity but SameAverage Tax Rate

To compute the contribution of the tax progressivity to differences in inequality, we pro-ceed as follows. First, we assume that all other policies, consumption tax, unemploymentinsurance and social security systems in CEU are the same as in the US. We also adjust thelabor income tax schedule in each European country so that the average tax on labor income(total tax revenue from labor income divided by total labor income) is the same as in theUS. Thus, the only difference between the US and CEU is the differences in progressivity.We assume that the lump-sum transfers adjust to balance budget.

To change average tax rates in Europe without changing progressivity we conduct thefollowing procedure. Let τi(y) be the marginal tax rate in country i for income level y.We would like to obtain a new tax schedule τ ∗i (y) with the same progressivity but with adifferent level. Thus we need to have

1− τ ∗i (y′)

1− τ ∗i (y)=

1− τi(y′)1− τi(y)

for all y and y’.

Rewriting this we obtain

1− τ ∗i (y′)

1− τi(y′)=

1− τ ∗i (y)

1− τi(y)for all y and y’.

Letting this ratio to be equal to a constant k the new tax schedule τ ∗ is obtained by thefollowing expression:

1− τ ∗i (y) = k(1− τi(y)) for all y.

52

Let the average tax rate be

τi(y) = a0 + a1y + a2yφ.

The marginal tax rate isτi(y) = a0 + 2a1y + a2(φ+ 1)yφ.

To have a new tax schedule τ ∗(y) which has a different average tax rate but has thesame progressivity we need to have

1− τ ∗i (y) = k(1− τi(y)).

Solving for τ ∗(y), we get

τ ∗i (y) = 1− k + k[a0 + 2a1y + a2(φ+ 1)yφ

].

Sinceyτi(y) =

∫ y

0

τi(x)dx,

we can solve for the average tax rate τ ∗i (y) as

τi∗(y) = 1− k + k[a0 + a1y + a2y

φ] = 1− k + kτi(y). (14)

This expression gives us the new average tax rate schedule that we feed into the model.We choose k so that the average labor income tax rate in country i is equal to the averagelabor income tax rate in the US.

B Pension and Unemployment Benefits Systems

Pension System. The details of the pension benefits system for OECD countries usedin this paper are taken from the OECD publication entitled “Pensions at a Glance: 2007.”The specific numbers used below are from Table I.2 and the unnumbered table of page 35of that document. Further details of these pension systems including the number yearsrequired to qualify for full benefits, and so on, are described more fully on pages 26-35 ofthe same document.

Let yj be the lifetime average of net (after-tax) labor earnings of all individuals withability level j; and let y be the same variable averaged across all ability levels. Finally, recallthan mR is the total number of years a worker has been employed up to the retirement age,

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Table A.1: Pension System Formulas

a b Ranges Ceiling for PensionableIncome (as % of AW)

DEN 0.371 0.528 all —FIN 0.011 0.695 all —FRA 0.141 0.484 all 300%GER -0.004 0.621 if yj ≤ 1.5y

0.927 if yj > 1.5y 150%NET 0.005 0.928 all —SWE -0.021 0.735 all 367%UK 0.257 0.154 if yj ≤ y 115%

0.315 0.096 if y < yj ≤ 1.5y0.396 0.042 yj > 1.5y

US 0.168 0.355 all 290%

and let m be the maximum number of years of work that an individual can accumulateretirement credits in a given country.

The net retirements earnings of individual with ability j is given as:

Ω(yj,mR) = min

(1,mR

m

)[ay + byj

]The first term approximate the credit accumulation process whereby individuals qualifyfor full retirement benefits after working a certain number of years and only qualify forpartial pensions if they retire before that. We set m equal to 40 years for all countries.Different countries differ mainly in the value of the coefficients a and b. Broadly speaking,a determines the “insurance” component of retirement income, because it is independent ofthe individual’s own lifetime earnings, whereas b captures the private returns to one’s ownlifetime earnings. In this sense a retirement system with a high ratio of a/b provides highinsurance but low incentives for high earnings and vice versa for a low ratio of a/b. Inspectingthe coefficients in the table shows that there is a very wide range of variation across countries.Finally, some countries have a ceiling on pensionable income and entitlements, which is alsoreported in Table A.1.

UI System. OECD provides data on unemployment benefits that would be paid to aqualifying person at different points during the unemployment spell: (i) in the first monthafter the worker becomes unemployed, (ii) and after 5 years of long-term unemployment,which we will refer to as initial UI and final UI benefits respectively. An individual with

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Table A.2: Unemployment Insurance Formulas

a b UI Ranges of IncomeDEN 0.173 0.258 0.53 if y ≤ 0.75y

0.367 if y > 0.75yFIN 0.285 0.100FRA 0.010 0.392 2.24GER 0.091 0.253 0.90NET 0.205 0.246 1.13 if y ≤ 1.25y

0.513 if y > 1.25ySWE 0.145 0.375 if y ≤ 0.75y

0.338 0.118 if 0.75y < y ≤ y0.456 if y > y

UK 0.301US 0.045 0.420 if y ≤ y

0.465 0.61 if y > y

gross earnings y, who has been employed for m years prior to becoming unemployed willreceive and initial UI of:

Φ(y,m, s) = min(

1,m

mUI

) [ay + byj

]As before, mUI denotes the minimum number of years required to receive full UI benefits

and partial benefits are received in case of unemployment before then. We set mUI to 20years for all countries. UI benefits are assumed to decline (every year) linearly betweenthe rates provided by OECD for initial and final UI levels. There is also an upper level ofunemployment insurance denoted by UI in some countries.

Initial UI: Initial phase of unemployment but following any waiting period. No socialassistance "top-ups" are assumed to be available in either the in-work or out-of-work sit-uation. Any income taxes payable on unemployment benefits are determined in relationto annualised benefit values (i.e. monthly values multiplied by 12) even if the maximumbenefit duration is shorter than 12 months.

Final UI: These are “after tax” and including unemployment benefits, social assistance,family and housing benefits in the 60th month of benefit receipt. For married couples thepercent of AW relates to one spouse only; the second spouse is assumed to be "inactive"with no earnings in a one-earner couple and to have full-time earnings equal to 67% ofAW in a two-earner couple. Children are aged 4 and 6 and neither childcare benefits norchildcare costs are considered.

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Table A.3: Correlation between Different Labor Market Institutions

Union density Union coverage Centralization & Coordination PWUnion coverage 0.49 1C&C 0.57 0.75 1PW 0.88 0.75 0.78 1PW* 0.81 0.85 0.69 0.93

C Progressivity versus Other Labor Market Institutions

Table A.3 reports the cross-correlations between different aspects of labor market insti-tutions in a country and the progressivity of its income tax structure. The progressivitymeasures we use are PW and PW* defined in the text. The labor market institutions areunion density, union coverage rate, and C&C (Centralization & Coordination score). All threedefinitions are explained in more detail below. All three variables are measured in a waythat higher numbers indicate more deviation from a free market economy. The main find-ing is that both measures of progressivity are strongly positively correlated with all threelabor market institutions. Therefore, countries that have a more unionized labor force withstronger centralized bargaining are also those that have a more progressive labor incometax system. To our knowledge, this finding is new to this paper.

Definition of Labor Market Institutions.

Union density is typically measured by the percentage of wage-and salary-earners that areunion member in terms of the total workforce. In many countries, mandatory and vol-untary extension mechanisms extend the results of collective agreements between unionsand employers to non-unionised workers and firms, which is termed union coverage. Thus,union coverage, tells potentially more about the actual influence of the trade unions in wagebargaining than union density. Centralization measures the institutional level at which ne-gotiations take place: for example, wage bargaining at firm- or plant-level (decentralisedbargaining), industry-level (bargaining at the intermediate level), and countrywide level(centralised bargaining). In many countries, informal networks and intensive contacts be-tween social partners coordinate the behaviour of trade unions and employers’ associations.Examples are the leading role of a limited number of key wage settlements in Germany,and the active role of powerful employer networks in Japan. Therefore, not only the formaldegree of centralisation matters, but also the degree of informal consensus seeking betweenbargaining partners. This is generally called the level of coordination. The C&C score is anindex that increases with the level of centralization and coordination.

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