Progressive Taxation and Risky Career Choices

Progressive Taxation and Risky Career Choices German Cubas and Pedro Silos Very Preliminary February, 2016 Abstract Occupations differ in their degree of earnings uncertainty. Progressive taxation provides insurance to risk-averse workers against adverse earnings outcomes. As a result, progressive tax systems distort the price of risk and influence the mobility and sorting of workers across occupations. This paper proposes a theory to understand the effect of the degree of tax progressivity on workers career choices when markets are incomplete. We quantify the distortion and we find that tax progressivity incentives young workers to take risk, thus partially completing the insurance markets. Hence, we provide a new perspective on the welfare cost of uninsurable earnings risk. To that end, we employ micro-data on occupational mobility and earnings from the United States and Germany to estimate a model of occupational choice and uninsurable earnings uncertainty. The model predicts that, as observed in the data, everything else equal, were US workers to face the relatively more progressive earnings tax function of Germany, a larger fraction of young workers will take risk and they will end up working into safer occupations. Key words: Labor Markets, Progressive Taxation, Occupational Choice, Incomplete Markets JEL Classifications: E21 D91 J31. Affiliation: University of Houston, Temple University, respectively. 1

1 Introduction This paper is a quantitative study of the effect of progressive income taxation on worker s occupational choice and mobility. When occupations differ in their degree of earnings risk, workers are risk averse, and opportunities to insure that risk are limited, a progressive tax system distorts the price of risk. This distortion leads to more risktaking on the part of young workers, more occupational mobility and consequently to larger safe occupations relative to the case of a linear tax. Much work has been devoted to constructing economic environments where income taxation affects the labor supply of individuals both at the extensive and intensive margin (see Rogerson (2006), Prescott (2004), Guner and Ventura (2012), among others). Little work has focused on the effect of the interplay between labor income risk and progressive taxation schemes on labor supply, exceptions are Acemoglu and Shimer (2000) and Conesa and Krueger (2006) which specifically analyze the insurance mechanism that is provided by a progressive tax system. To the best of our knowledge, the literature has not yet analyzed the interplay between labor income risk and progressive taxation and its effect on the career choice of individuals. As a first attempt, this paper poses and answers the following questions: Do occupations differ in the level of idiosyncratic labor income risk? Is there a negative correlation between the share of workers across occupations and the volatility of idiosyncratic labor earnings shocks? Is that correlation different when we look at countries with different progressivity of income taxes? How does the progressivity of the income tax schedule affects the price of risk and the allocation of workers across occupations? Is it quantitatively important? What are the welfare implications? We propose a new theory that allows us to analyze the interplay between labor income risk and progressive taxation and its effect on workers occupational choice and mobility. Specifically, we construct a life-cycle model where individuals earn labor and capital earnings but insurance opportunities against earnings risk are lim- 2

ited. Besides the standard consumption versus savings choice, individuals also have to decide the occupation or sector in which to supply their labor. Occupations differ in their degree of earnings variability. A government taxes earnings and it can do so with a more or less progressive tax function. As individuals are risk averse, the level of progressivity influences the amount of risk they are willing to bear. In our theory, a higher degree of progressivity is the same as lowering the risk aversion of workers thus an increase the progressivity of the tax schedule provides more insurance so workers have incentives to start their career in risky occupations. For this reason, more of them will end up switching to the alternative safer occupations, so, in equilibrium safe occupations are larger. In our quantitative analysis we begin by documenting new facts regarding earnings risk across 14 occupations in the US and Germany using comparable panel data. We use these two countries since, as showed in Guvenen and Ozkan (2014), they present substantial differences in the degree of progressivity of their tax schedule and so they serve as a natural starting point for our analysis. In both Germany and the US, the variation of the variance in the shocks to labor income across occupations is large, both when that variation is temporary as well as when it is permanent. In addition, by looking at the permanent shocks estimates, the US labor market is riskier than the German labor market. However, as for the transitory shocks, the US is safer on average, than Germany. The industries that are risky in the US are not generally risky in Germany in terms of the permanent shock which may reflect the differences in the labor market institutions between these two countries. However, the two countries look much similar in terms of the riskiness of their occupations in terms of the transitory shocks. In addition, the share of workers in safe occupations is larger in Germany than in US. Although overall occupational mobility is larger in the US than in Germany, interestingly, a larger proportion of young workers start their careers in risky occupations in Germany than in the US, which is what our theory predicts. Moreover, safer occupations are larger in Germany 3

compared to the US which is also a prediction of our theory. 2 Career Choice and Progressive Taxation: A Canonical Model 2.1 Environment The economy is populated by a continuum of workers who provide labor services to finance the purchase of a consumption good. Individuals live for two periods and may choose to work in either of two occupations, labeled occupations 1 and 2. Each individual productivity in occupation j is denoted by z j and it is an i.i.d. draw from the normal distribution F(z j ). The two occupations differ in their degree of earnings risk; the higher risk is reflected in a larger dispersion of the productivity distribution. Without loss of generality assume that occupation 2 is riskier than occupation 1. Specifically, denote the variance of the distribution of the log of productivity z j in occupation j by σ 2 j and let σ 2 2 = ασ2 1 with α > 1. Individuals do not observe the productivity shock before entering in the occupation. Immediately after making that choice, they observe the level of productivity and produce, get paid, and consume the final good. After the initial period they have an option to switch and face a random productivity shock in the alternative occupation. After the switching decision has been made, no more switches are possible. Workers are risk averse and they order amounts of consumption c according to u(c) = c 1 γ /(1 γ). The amount of effective labor supplied by a worker in occupation j is e z j. The supply of a unit of effective labor is compensated at a rate w j. Denoting the total amount of effective labor in occupation j by N j, final output Y is produced according to, Y = N θ 1 N1 θ 2. (1) 4

The zero-profit-condition for the firm implies w 1 = θn θ 1 1 N 1 θ 2 and hence w 2 = 1 θn θ 1 N θ 2. Finally, a government taxes workers earnings using a polynomial tax function. The revenue collected is wasted. Specifically, the after-tax earnings for a worker in occupation j with pre-tax earnings equal to e z j w j are a(e z j w j ) b. The parameter a drives the scale of the tax function while b drives the curvature. It is changes in b that reflect changes in progressivity. A higher b implies less progressivity; b = 1 implies a linear tax. 2.2 Individual Decision Problem The value functions now read: V 1 = and, V 2 = [ (aw1 e z 1) b] 1 γ 1 γ [ (aw2 e z 2) b] 1 γ 1 γ [[ (aw1 e z 1) b] 1 γ [ (aw2 e z 2) b] 1 γ ] df(z 1 )+ max, df(z 1 γ 1 2 ) df(z 1 ) γ (2) [[ (aw2 e z 2) b] 1 γ [ (aw1 e z 1) b] 1 γ ] df(z 2 )+ max, df(z 1 γ 1 1 ) df(z 2 ) γ (3) Entry Decision Individuals decide to start the labor career in the occupation that yields the highest utility: j = argmax{v 1,..., V 2 }. (4) Optimal Switching Policies Once a worker has observed the productivity in the initially chosen occupation, he has the opportunity to switch. Since utility is an increasing (and continuous) function of the productivity draw, there is cutoff point in the productivity support below which the worker decides to switch. For occupation 5

j, this cutoff (z j ) is defined as: [a(w j e z j ) b] 1 γ 1 γ = [ a(w j e z ) b] 1 γ df 1 γ j (z) (5) The cut-off productivity level equalizes the value of staying in j and enjoying a productivity z j, to the expected value of switching to the alternative occupation (labeled j). We can simplify further: ( ) b(1 γ) wj e z j = (e z ) b(1 γ) df j (z). (6) w j Notice that the right-hand side is the expectation of a log-normal with an underlying normal distribution with mean (1 γ)b0.5σ 2 j and variance equal to (1 γ) 2 b 2 σ j 2. Using standard properties the cutoff productivity for a worker starting in occupation j is, z j = [ log(w j ) log(w j ) ] 0.5σ j 2 [1 b(1 γ)]. (7) The cut-off value is lower if either the coefficient of relative risk aversion γ is higher, or if the tax system becomes less progressive (a higher b). Note that for a given level of γ, a lower b is akin to lowering the overall level of risk aversion. 2.3 Allocation of Workers Let z j be the standardized cutoff level; that is, z j = z j +0.5σ2 j σ j. Using the standard notation of Φ for the normal cumulative density function, we now define the sizes of the two occupations, L 1 and L 2. To calculate the size of an occupation, we add the number of individuals who begin their career in that occupation and decide to stay, plus those who start in the alternative occupation but end up switching. From this accounting of worker flows, and letting µ denote the mass of workers who initially 6

choose occupation 1, the total mass of workers in occupation 1 is, L 1 = µ(1 Φ( z 1 ))+(1 µ)φ( z 2 ), (8) and similarly for occupation 2, L 2 = (1 µ)(1 Φ( z 2))+µΦ( z 1 ). (9) The amount of labor in efficiency units in both occupations is found by aggregating the respective productivities of workers in each occupation. For occupation 1, the total labor input is defined as, N 1 = µ e z df 1 (z)+(1 µ)φ( z z1 2 ) e z df 1 (z). (10) Since ez df 1 (z) = ez df 2 (z) = 1, then N 1 = µ e z df 1 (z)+(1 µ)φ( z z1 2 ). (11) Analogously the amount of efficiency units of labor in occupation 2 is, N 2 = (1 µ) e z df 2 (z)+µφ( z z2 1 ) (12) The previous two expressions can be further simplified to, 1 and N 1 = µφ(σ 1 z 1 )+(1 µ)φ( z 2 ), (13) N 2 = (1 µ)φ(σ 2 z 2 )+µφ( z 1 ). (14) 1 From the properties of the truncated log-normal, we know that if z j N( 0.5σj 2, σ2 j ), then (see Johnson, Katz, and Balakrishnan (1995), p. 241): E(e z j z j > z j ) = Φ(σ j z j )/(1 Φ( z j )). Since E(e z j z j > z j ) = z e z df j (z) j 1 Φ( z j ), then z e z df j (z) = Φ(σ j z j ). j 7

2.4 Tax Progressivity and Allocations How does the level of tax progressivity influence the sorting of workers in the decentralized economy? Note that a decrease in b increases both z 1 and z 2. Intuitively, a more progressive tax system makes taking a bet more attractive. In our environment this translates into workers more willing to switch occupations after they have observed the technology shock. However, the increase in z1 is larger because α is greater than 1. To illustrate with several figures some of the outcomes of the model, we provide a simple numerical simulation. 2 In Figure 1 we display the cutoff productivity values z1 and z 2. The riskier occupation 2 with respect to occupation 1 (the larger the α) the smaller the cutoff productivity values. In this case, more workers want to try in occupation 2 in order to get a good shock. At the same time, the higher the variance, more workers are going to switch to occupation 1. For workers that decided to enter in occupation 1 (the safe occupation) the riskier the alternative the less attractive it is for the marginal worker and so more workers will decide to stay in that occupation. This will make that N 1 goes up and since we have decreasing returns on each type of labor, w 1 will go down. This general equilibrium effect will make that more workers that entered occupation 2 decide to stay there and so the cutoff value goes down and in equilibrium N 2 goes up If we fix α and we increase the progressivity of the tax schedule by lowering b, then the cutoff levels for both occupations rises. Conditional on entry, a more progressive tax schedule provides more insurance so workers have incentives to switch to the other occupation. In addition, Figure 2 shows that the more progressive the tax system the less workers start in occupation 1 since they have incentives to take more risk in occupation 2. 2 The coefficient of risk aversion is set to 2 and the variance of occupation 1 is normalized to 1.5. We let α vary between 1 and 3, and provide results for three different values of b: 0.1, 0.5, and 0.9. 8

In addition, for the same level of progressivity, as α increases the number of entrants in occupation 2 increases since workers want to take the risky bet in the labor market. Lastly, Figure 3 shows the size of occupation 1 in equilibrium. As α increases, more workers start in occupation 2 and so more of them are going to change occupations and this make occupation 1 larger in equilibrium. For a fix α the more progressive the tax system, again the more entrants in occupation 2 and the larger occupation 1 in equilibrium. Thus, even though, providing insurance through the tax system give incentives to take more risk, it then make the safe industry larger and at the same time it spurs selection. 3 Risk in the Labor Market In this section, we briefly describe our data set. Then we document the differences the risk workers face in different industries both in Germany and the US. We do this by estimating the labor earnings processes and the properties of the shocks faced by workers in different industries. Second, we characterize and estimate the empirical relation between the share of workers and the degree of uncertainty in earnings across industries for both countries. 3.1 Data Our goal is to analyze the empirical relationship between the progressivity of the tax schedule and the occupational choice of individuals. Germany and US present very different tax schedules and so serve as natural experiment to address our research question. In addition, there exist comparable panel data that allows us to contrast the labor markets of these two countries in many dimensions. Specifically, we use the comparable versions of the PSID for the US and the SOEP for Germany provided by the Cross-National Equivalent File 1970-2009 at Ohio State University. I contains equivalently defined variables for a set of developed countries, 9

among them, the Panel Study of Income Dynamics (PSID) of the US, and the German Socio-Economic Panel (SOEP) of Germany. PSID The PSID data are drawn from the PSID-CNEF files. The PSID started in 1968 collecting information on a sample of roughly 5,000 households. Of these, about 3,000 were representative of the US population as a whole (the core sample), and about 2,000 were low-income families (the Census Bureau s SEO sample). Thereafter, both the original families and their split-offs (children of the original family forming a family of their own) have been followed. It is annual until the 1997 wave when it became biannual. In the empirical analysis we use data on individuals in the period 1970-2007. SOEP The SOEP data are drawn from the SOEP-CNEF files. The German Socio- Economic Panel (SOEP) is a wide-ranging representative longitudinal study of private households, located at the German Institute for Economic Research, DIW Berlin. Every year, there were nearly 15,000 households, and about 25,000 persons sampled. The data provide information on all household members, consisting of Germans living in the Old and New German States, Foreigners, and recent Immigrants to Germany. The Panel was started in 1984. In the empirical analysis we use data on individuals in the period 1984-2012. For both data sets, we focus on working-age individuals, aged 22-66. We drop those that are not employed and the self-employed, those who do not report earnings, education or hours worked as well as individuals with less than 8 years of consecutive data. In the PSID-CNEF individuals are classified into occupations according to ISCO- 68 and industries according to a 34 industry classification provided by the CNEF. After constructing the panel of individuals and re-grouping the data into 14 occupations, we end up having data for labor earnings per hour, employment status, age, education level, industry, occupation and gender. 10

3.2 Labor Income Shocks The first step in our analysis computes earnings variability at the individual level with a regression approach used extensively in the literature. We proceed by estimating a fixed effects model for each occupation j in our sample. Given a panel of N individuals for whom we measure earnings (and other variables) over a period of time T, we assume that (log) earnings per hour for individual i, of age h, in occupation j at time t, y j iht can be modeled as y j iht = f(x j iht, Θ)+ỹj iht (15) The first component in this specification, f, is a function of observables and parameters Θ that captures the life-cycle component of earnings that is common to all workers. X j iht is a vector of observables that includes a cubic polynomial in age, marital status, gender, education, year and industry. By estimating this regression by OLS we obtain the residual income, u j iht, which we assume can be decomposed into a fixed effect α j i, an AR(1) component and a transitory component: u j iht = αj i + ηj ih + ωj ih (16) ω j ih = ρj ω j ih 1 + ǫj ih (17) where α j N(0, σj,α 2 ), ηj N(0, σj,η 2 ), ǫj N(0, σj,ǫ 2 ), are i.i.d random variables. α j i is an occupation-individual-specific fixed effect that captures the variation in initial conditions such as innate ability. variance σ 2 j,η earnings. ω j ih η j ih is a fully transitory component with that encompasses both measurement error and temporary changes in is the persistent component of idiosyncratic income at age h that captures lasting changes in earnings. Each period, the individual is hit by a persistent shock of size ǫ j ih. The magnitude of this shock is governed by the variance σ2 j,ǫ and 11

the extent to which it lasts is determined by the parameter ρ j. What is important in our paper is that these variances are occupation-specific. The rich panel structure of the PSID and SOEP allows us to observe individuals of a given age at different points in time and thus at a given year we observe individuals of different ages. We follow the standard estimation strategy in the literature and use an equally weighted minimum distance estimator. We choose the parameters in order to minimize the distance between theoretical moments obtained from the above income process and sample moments. Specifically, we use the empirical variance-covariance terms over age obtained from of residual earnings. Following this procedure we end up with estimates of σj,η 2, σ2 j,α, σ2 j,ǫ and ρj, for each of the 14 occupations for Germany and US. Tables 1 and 2 shock the estimates values for the parameters of the income processes of each occupation for both countries. As it can be observed there are substantial differences in the income process workers face depending upon the occupation they have chosen to supply labor to. For instance US sales workers face much more permanent risk than Teachers. Clerical workers face almost no transitory risk but high permanent risk. We also find substantial crosscountry differences. On average, the US is riskier than Germany. However, there are occupations in the US that safer than in Germany and viceversa. For instance, in the case of the permanent shock US is safer in Technicians and Professionals, Administrative and Managerial Workers, Other Administrative Workers and Catering, Cooks, Maids and related, but much riskier in the rest of the 14 industries. Although, in our quantitative analysis we take these differences as exogenous, they surely reflect differences in the labor markets of these countries and they will have non/trivial consequences in the workers careers choice as well as they consumption and saving behavior. 12

4 Quantitative Model 5 Concluding Remarks 13

References Acemoglu, D., and R. Shimer (2000): Productivity gains from unemployment insurance, European Economic Review, 44(7), 1195 1224. Conesa, J. C., and D. Krueger (2006): On the optimal progressivity of the income tax code, Journal of Monetary Economics, 53(7), 1425 1450. Guner, Nezih, K. R., and G. Ventura (2012): Taxation and Household Labour Supply, Review of Economic Studies, 79(3), 1113 1149. Guvenen, Fatih, K. B., and S. Ozkan (2014): Taxation of Human Capital and Wage Inequality: A Cross-Country Analysis, Review of Economic Studies, 81, 818 850. Prescott, E. C. (2004): Why do Americans work so much more than Europeans?, Quarterly Review, (Jul), 2 13. Rogerson, R. (2006): Understanding Differences in Hours Worked, Review of Economic Dynamics, 9(3), 365 409. 14

Figures -0.04-0.06 z 1,z 2-0.08 b=0.1 b=0.5 b=0.9-0.10 1.0 1.5 2.0 2.5 3.0 α Figure 1: The figure plots the cutoff values for occupation 1 (solid lines) and occupation 2 (dash-dotted lines) as a function of the dispersion in risk (α). The different colors represent different degrees of progressivity (blue: low; green: medium; red: high). 15

0.54 0.53 Size Occ. 1 0.52 b=0.1 b=0.5 b=0.9 0.51 0.50 1.0 1.5 2.0 2.5 3.0 α Figure 2: The figure plots total size of occupation 1 as a function of the dispersion in risk (α). The different colors represent different degrees of progressivity (blue: low; green: medium; red: high). 0.50 0.45 Entrants Occ. 1 0.40 0.35 b=0.1 b=0.5 b=0.9 0.30 0.25 1.0 1.5 2.0 2.5 3.0 α Figure 3: The figure plots the mass of entrants in occupation 1 as a function of the dispersion in risk (α). The different colors represent different degrees of progressivity (blue: low; green: medium; red: high). 16

Tables Table 1: Estimates for US Occupation σǫ 2 ση 2 ρ σα 2 1 Technicians and Professionals 0.0042 0.0539 0.9841 0.0685 2 Teachers 0.0070 0.0429 0.9626 0.0097 3 Other Professionals and Technical Workers 0.0228 0.0875 0.9477 0.0454 4 Administrative and Managerial Workers 0.0176 0.0292 0.9942 0.0000 5 Clerical and Related Workers 0.0416 0.0000 0.1400 0.0717 6 Other Administrative Workers 0.0055 0.0238 0.9493 0.0249 7 Sales Workers 0.0642 0.0219 0.8262 0.0000 8 Catering, Cooks, Maids and related. 0.0210 0.0495 0.7569 0.0000 9 Cleaners, Barbers, Hairdressers and related. 0.0508 0.0000 0.1014 0.0653 10 Protective Service Workers. 0.0098 0.0235 0.9470 0.0000 11 Production Workers. 0.0307 0.0000 0.7833 0.0501 12 Other Production Workers 0.0203 0.0145 0.8411 0.0456 13 Transport Operators. 0.0098 0.0242 0.8025 0.0933 14 Other Operators 0.0392 0.0054 0.8562 0.0000 17

Table 2: Estimates for Germany Occupation σǫ 2 ση 2 ρ σα 2 1 Technicians and Professionals 0.0105 0.0667 0.9679 0.0004 2 Teachers 0.0040 0.0485 0.9534 0.0209 3 Other Professionals and Technical Workers 0.0117 0.0414 0.9379 0.0338 4 Administrative and Managerial Workers 0.0496 0.0262 0.7801 0.0000 5 Clerical and Related Workers 0.0013 0.0350 1.0000 0.0261 6 Other Administrative Workers 0.0147 0.0354 0.9046 0.0175 7 Sales Workers 0.0191 0.0498 0.5852 0.0869 8 Catering, Cooks, Maids and related. 0.0242 0.0305 0.4564 0.0488 9 Cleaners, Barbers, Hairdressers and related. 0.0398 0.0714 0.4241 0.0356 10 Protective Service Workers. 0.0061 0.0305 0.9460 0.0263 11 Production Workers. 0.0037 0.0248 0.9585 0.0510 12 Other Production Workers 0.0091 0.0000 0.9280 0.0188 13 Transport Operators. 0.0052 0.0270 0.7583 0.0372 14 Other Operators 0.0007 0.0471 1.0000 0.0466 18