Macro Effects of Disability Insurance

Transcription

1 Macro Effects of Disability Insurance Soojin Kim Serena Rhee February 7, 2015 [Preliminary and Incomplete] Abstract This paper studies the aggregate implications of Disability Insurance (DI) in the labor market. To illustrate the macro effects of DI, we develop a general equilibrium model with workers who are heterogeneous with respect to age and skill. Increase in DI benefit reduces the labor supply of older workers by inducing early retirement. We show that the change in labor supply of older workers also indirectly affects the labor supply of younger workers when workers are imperfect substitutes in production. Using the cross-state variation in demographic composition, we estimate the elasticity of substitution across generations in the United States, quantify the direct and indirect effects of the DI policy, and study optimal design of it. JEL Codes: E6, J3 Keywords: Disability Insurance, Skill complementarity, Population aging Purdue University, 403 W. State Street, West Lafayette, Indiana soojink@purdue.edu. University of Hawaii at Manoa, 2424 Maile Way, Saunders Hall Room 542, Honolulu, Hawaii rhees@hawaii.edu.

2 1 Introduction Social Security Disability Insurance (DI) is a form of social protection providing insurance against health risks of individuals. It is one of the fastest growing social insurance programs in the United States with its total spending of $134 billion in In that year, the DI program provided benefits to 3.6% of the working-age population, which was a twofold increase from the 1980s. Recent empirical studies find that the DI program generates a significant disincentive to work. Autor and Duggan (2003) show that the fast increase in the number of DI recipients is related to the doubling of the labor force exit rate between 1984 and von Wachter, Song and Manchester (2011) study the earnings of the DI recipients compared to that of rejected DI applicants, and find a strong labor market attachment of rejected applicants. Similarly, French and Song (2014) and Maestas, Mullen and Strand (2013) both find strong and heterogeneous disincentives to work generated by the DI program. Facing an aging economy, the prevalence of near-retirement workers receiving DI has drawn attention from economists and policymakers interested in its potential effects on retirement timing. 1 Despite the progress made in empirical studies on labor supply decisions, there does not exist a general equilibrium analysis of the DI program that allows for possible interactions across generations. In this paper, we investigate the aggregate implications of the DI program. When heterogeneous workers are imperfect substitutes in production, the change in composition caused by DI can indirectly affect the labor supply decisions through changes in equilibrium wage. For instance, if young and old workers are imperfect substitutes, the early retirement of the old can lead to lower wages for the young, inducing behavioral changes in younger workers. Therefore, it is important to consider these general equilibrium effects in order to accurately assess the effectiveness and expected welfare gain of the DI program. Toward that goal, our first aim is to test whether the general equilibrium effects are present. Following the analysis by Munnell and Wu (2012), we use cross-state variation in the labor force composition to determine how changes in labor supply of older workers affects younger workers in the labor market. We extend their analysis by allowing for skill (education)-specific and industry-specific elasticities, and exploit micro-level data to measure the compositional externalities created by demographic changes in the labor force. Our second aim is to decompose the effects of DI on the labor market outcomes of the old and the young. We develop a general equilibrium model with workers who are heterogeneous with respect to age and skill level. Households are subject to health shocks and 1 A recent article published in The Economist ( Disability Insurance: Not Working, January 24, 2015) raises several concerns on the current DI system, the disincentive effects it creates and fiscal crisis the program is facing with the trust fund expected to be depleted by the end of

3 make endogenous labor supply decisions. Production takes heterogeneous labor as inputs, which are imperfect substitutes across generations and skills. Governments provide disability benefits to workers who are faced with an adverse health shock. Therefore, changes in the DI policy directly affects the labor supply decisions of the old more, as they are more susceptible to health shocks. Moreover, there exists an indirect effect: When the two generations are imperfect substitutes, a decrease in labor supply by the old changes the wage rate for the younger generation and their labor supply (macro effect). We then calibrate the model using the Survey of Income and Program and Participation (SIPP) and Health and Retirement Study (HRS) data. The key parameters of interest are the elasticities of substitution across age groups. We identify these elasticities under the assumption of the Constant Elasticity of Substitution (CES) production function following Card and Lemieux (2001) and Karabarbounis and Neiman (2014). Our calibrated model provides a coherent framework to study optimal design of DI policy, taking into account the general equilibrium effects. This paper serves as a starting point for analyzing government policies that affect generations differentially in the labor market. For example, the Americans with Disabilities Act (ADA), which prohibits discrimination of disabled workers in the labor market, disproportionately affects older workers. Another relevant policy is Social Security, which directly influences the decision to retire for workers in their early 60s. We believe this paper can be a stepping stone for future analyses on these important policies for a country facing an aging society. 1.1 Related Literature Starting with Bound (1989), many economists have studied the labor supply effects of disability insurance. Recently, Maestas, Mullen and Strand (2013) and French and Song (2014) use random assignment of disability examiners and judges to estimate the disincentive effects of disability insurance on labor supply of workers. Both papers find a strong disincentive effect of disability insurance. French and Song (2014) find that the receipt of benefits reduces labor supply of workers by 26 percentage points. Moreover, the magnitude of such effects are heterogeneous across degrees of disability. While these papers use econometric approach to study individual behavior, Kitao (2014) and Low and Pistaferri (2012) are among the few that develop a life-cycle model to analyze the effects of DI. Kitao (2014) focuses on the interaction between DI and unemployment insurance, as well as other policies, including Social Security and Medicare. By endogenizing the enrollment decision to various social programs and employment decision of households, she quantitatively shows the aggregate effects of 2

4 policy reforms. On the other hand, Low and Pistaferri (2012) focuses on the dynamics of the incentive and insurance tradeoff that DI creates. We also relate this paper to literature that studies the implications of imperfect substitutability across heterogeneous inputs in production. Among them, Card and Lemieux (2001) uses a Constant Elasticity of Substitution (CES) production function to explain college premia; Krusell et al. (2000) shows that capital-skill complementarity can explain the rise of the skilled labor and the skill premium; and Karabarbounis and Neiman (2014) estimates the elasticity of substitution between Information Technology (IT) and labor to explain the decline of the labor share. There are few papers that study the relationship between workers of different generations. In Gruber and Milligan (2010), youth (those aged between 20 and 24) and prime-aged (those aged between 25 and 54) unemployment drops when elderly (those aged 55-64) employment increases for males, and the effects are statistically significant for the prime-aged. Munnell and Wu (2012) uses state-year-age mortality rate as an instrumental variable to find that there is no evidence of crowd-out effect of young workers when the employment of old workers increases. Instead, they find that the increased employment of the old leads to increased employment of the prime-aged workers, implying that they might be complementary in production. This paper contributes to the DI literature by focusing on a different aspect from the previous papers: the possible intergenerational effects from the DI. We focus on the fact that older workers are more susceptible to health shocks, and thus more likely to receive DI benefits. In addition, the young and old have different skill sets and are heterogeneous inputs into production which are imperfectly substitutable. In such an economy, changes in government policies that disproportionately affect the old workers more (like the DI) can also affect young workers, through changes in the labor demanded by firms and equilibrium wages (the macro effect). We empirically show and quantitatively estimate the magnitude of the general equilibrium effects in this paper. The rest of the paper is organized as the following. In the next section, we provide an empirical analysis that test for the existence of the general equilibrium effect. We then present a simple model to illustrate the mechanism; and an enriched model for our quantitative analysis. In Section 4, we present our technique for identifying fundamental parameters of the economy, and present quantitative results in the following section. 3

5 2 Empirical Analysis 2.1 Aggregate Trends In this section, we document aggregate trends in the DI program and its beneficiaries. Figure 1: Social Security Disabled Beneficiaries Note: Chart 2 from the Annual Statistical Report on the Social Security Disability Insurance Program (2013). Figure 1 plots the number of Social Security disabled beneficiaries from 1970 to As is clear from the Figure, there has been a steady increase in the number of DI beneficiaries. The increase has accelerated since the 1984, the year in which Social Security Disability Benefits Reform Act was passed. The Act liberalized the screening process of the applicants, which, according to the analysis by Autor and Duggan (2006) contributed to the rise in the beneficiaries. In 2013, DI program provided benefits to 3.6% of the working-age population for disabled workers only. If one includes disabled adult children and widow(er)s, the share increases to more than 4%. The number of enrollments are only expected to increase with the aging of the baby boomers and more general trends of population aging. Since older workers are more likely to have a disability, vast majority of the DI beneficiaries are those who are relatively old. In Figure 2, we document the age composition of disabled workers. Since the mid-1990s, the proportion of beneficiaries who are 45 years or older has been steadily increasing. However, between the early 1980s and the mid-1990s, we see a decreasing share of older workers receiving benefits. Given that the demographic composition has been changing over the same period of time, it is essential to control for it. In Figure 3, we document DI beneficiary-population ratio by age group. We see that the hump-shaped age composition disappears as we control for the demographic changes. In the 4

6 Figure 2: Age Composition of Disabled Workers Note: Authors calculation based on the Annual Statistical Report on the Social Security Disability Insurance Program (2013, Table 19). beginning of 1980s, only 7.2% of workers aged between 55 and 64 received DI benefits, but there was a steady increase in this ratio. By 2013, 12.6% of workers in their late 50s and early 60s received DI benefits, which is a 5 percentage point increase in 30 years. These aggregate trends show us the fast increase in the DI program, and that the DI disproportionately affects the relatively old workers more. 2.2 Empirical Evidence of Macro Effects In this section, we empirically test and measure the effect of changes in the supply of older workers on labor market outcome of young workers. Changes in the population s age composition may have indirect effects on labor market outcomes by affecting age-specific (within-group) wages and employment. A higher share of older workers in the labor force might be related to higher unemployment among the young, when the two types of labor are imperfectly substitutable. Our first goal is to conduct an empirical analysis to identify and measure this component. The main empirical analysis for testing and measuring the indirect effect relies on crossstate differences in the age composition of the labor force and the consequent variation in labor market outcomes. The goal is to figure out what would happen to the labor market outcomes of a worker if he were to be transferred to a location with an older population. To that end, we compute the aggregate and age-specific wage and employment rate for 5

7 Figure 3: Recipients to Population Ratio by Age Group Note: Authors calculation based on the Annual Statistical Report on the Social Security Disability Insurance Program (2013, Table 19) and the Census Bureau s Population Estimates Program. each state using the Current Population Survey (CPS). The sample size of the CPS is too small at the state level to yield reliable estimates of age-specific mobility. To have sufficient precision, we focus on three age groups: individuals between the ages of 25 and 44, 45-54, and those older than 55 but younger than 65. We refer to these groups as young workers (Y ), middle-aged workers (M), and old workers (O). The main empirical specification looks at how the labor performance of young workers in state s and year t depends on the shares of the labor force older than 40, share j st, j {M, O}: log labor_outcome = α s + β t + γ 1 log share M st + γ 2 log share O st + ε st, (1) where α s and β t denote state and time fixed effects, respectively. Following Shimer (2001), we first estimate the above equation with Ordinary Least Squares regression (OLS) and later with lagged birthrates as an instrument that accounts for the variation in the age composition. More specifically, our instrument in state s and year t is defined as the sum of all birthrates in state s from year t 39 to t 25. Lagged birthrates help us to control for the possible endogeneity of the age structure because the lagged birthrates affect the current demographic structure, but are not associated with the current economic status of state s. The instrument turns out to do a good job of inducing variation in the age composition. Our coefficients of interest are γ 1 and γ 2, as they represent the effects of demographics on labor market outcomes of young workers. Tables 1 and 2 report the empirical results from 6

8 the two specifications. Table 1: OLS Regression Coefficient Standard Error 95% Confidence Interval middle-aged old Note: Table 1 shows the OLS regression result: We regresse employment rate of young workers in age between 25 and 45 with population share of the middle-age (45 54) and the old (55 65). As seen in Table 1, the increase in the share of middle-aged and old workers has significant effect on the employment of young workers. The effect is still quite robust when we use the IV specification (Table 2). Table 2: IV Regression Coefficient Standard Error 95% Confidence Interval middle-aged old Note: Table 2 shows the IV regression resut of equation 1. We plan to extend our empirical analysis by accounting for industry specific coefficients across age groups. This extension is important as different industries and occupations require different types of skills in their production, and the changes in DI enrollment has risen more rapidly among workers with low education and who are engaged in manual tasks. We also use Survey of Income and Program Participation (SIPP) data to control for individual characteristics in order to measure the indirect effects of demographic compositional change. 3 The Model We now proceed to build a structural model that helps us decompose the direct and indirect effects caused by the changes in the labor force composition, caused by the DI program. Before we describe the full model, we provide a very simple model to illustrate our mechanism. 3.1 A Simple Model In this section, we aim to show how young workers behaviors change when the old workers reduce their labor supply, under different substitutability assumptions in the production function. 7

9 Consider a model with two types of workers, i {L, H}. Production takes place using a Constant Elasticity of Substitution production function Y = (θ L L ρ + θ H H ρ ) 1 ρ, where ε = 1, is the elasticity of substitution between L and H, with ρ (, 1]. When 1 ρ ρ = 1, the inputs are perfect substitutes. Two inputs are gross substitutes (ε > 1) when ρ > 0, and gross complements (ε < 1) when ρ < 0. A special case is when ρ = 0, where the production function reduces to Cobb-Douglas. The workers in the model have utility over consumption (c) and leisure (1 l) represented by u(c, l) = c1 σ 1 1 σ ψ l 1+ 1 ν i 1 + 1, ν where σ represents risk aversion, ψ i, the type-specific disutility of work, and ν, the Frisch elasticity of labor supply. Assume that the worker lives for one period and consumes his income, i.e., c = w i l i. In equilibrium, the wages of each worker type are given by w L = θ L (θ L L ρ + θ H H ρ ) 1 ρ 1 L ρ 1 w H = θ H (θ L L ρ + θ H H ρ ) 1 ρ 1 H ρ 1, and the workers optimal labor supply choices are l i = ( ) ν 1 w 1 σ σν+1 i. ψ i In the following, we show how the equilibrium changes when ψ H increases. We interpret such a change as type-h worker s outside option increasing, due to a more generous disability insurance, for example. L and H are perfect substitutes: ρ = 1. We first consider the case in which workers are perfect substitutes. Then, as is clear from the equilibrium conditions, wage rates for L and H are independent of each other, at θ L and θ H. Therefore, as ψ H increases, labor supply of H decreases, but labor supply of L is constant: there is no general equilibrium effect. L and H are imperfect substitutes: ρ < 1. Now, a higher ψ H (disutility of work) not only changes the decision of H workers, but also that of L workers through changes in the 8

10 wage rates. However, the direction of the change in labor supply of L is determined by the relative magnitude of income and substitution effects. In order to illustrate this point, we show how the equilibrium changes for σ = 0.5, σ = 1, and σ = 2. When σ = 1, income and substitution effects cancel out (labor supply is independent of wage), whereas income effect dominates for σ = 2, and substitution effect dominates for σ = 0.5. Figure 4 represents the labor supply of H workers in equilibrium. Labor supply of H is not only determined by ψ H but also w H, except for the case in which σ = 1. Thus, we can think of σ = 1 as representing the disincentive effect purely from ψ H, while the others reflect changes in the equilibrium wage given in Figure 5. As a comparison point, we provide the equilibrium wage of H workers when inputs are perfect substitutes (ρ = 1), in which case wage is independent of the labor supply. Figure 4: Labor Supply of H Workers Figure 5: Wage Rate of H Workers Note: In this specification, we let θ L = θ H = 0.5, ν = 1.5, and ψ L = 1. When L and H are perfect substitutes, ρ = 1. For imperfectly substitutable case, we use ρ = 0.5, which implies the elasticity of substitution of 2. Now, we explore the equilibrium wage of L workers and their labor supply responses in Figures 6 and 7. In contrast to the case in which ρ = 1, when ρ < 1, equilibrium wage of L workers decreases when labor supply of H decreases. And depending on the magnitude of income and substitution effects, L workers either increase, decrease, or do not change their labor supply. Similar to the case in which both goods are perfect substitutes, when income and substitution effects cancel out, labor supply of L is unaffected. If the substitution effect is dominating, decrease in labor supply of H also lowers the labor supply of L (which would be consistent with our empirical results). On the other hand, if income effect is dominating, the opposite happens. This effect is what we call, the indirect effect on young workers caused by policies that distort behaviors of old workers. Note that when the two inputs are perfect substitutes, L worker s choices are not affected. In most standard macro models, age groups are assumed to be perfectly substitutable (while we often capture imperfect substitutability across skill levels). In such class of models, we cannot capture the indirect effect from changes in 9

11 Figure 6: Wage Rate of L Workers Figure 7: Labor Supply of L Workers Note: In this specification, we let θ L = θ H = 0.5, ν = 1.5, and ψ L = 1. When L and H are perfect substitutes, ρ = 1. For imperfectly substitutable case, we use ρ = 0.5, which implies the elasticity of substitution of 2. demographic composition of the labor force. Figure 8: Aggregate Productivity Note: In this specification, we let θ L = θ H = 0.5, ν = 1.5, and ψ L = 1. When L and H are perfect substitutes, ρ = 1. For imperfectly substitutable case, we use ρ = 0.5, which implies the elasticity of substitution of 2. Y Labor productivity is defined as l L +l H, output per worker. Finally, we compare the efficiency cost from the changes in ψ H, measured by the labor Y productivity, (Figure 8). Efficiency of labor decreases, and the magnitude depends l L + l H on labor supply responses by both types of workers (driven by σ). Another feature to note is the lower labor productivity when σ = 1. Even though both workers do not change their labor supply in response to wages (similar to ρ = 1), there is still aggregate efficiency cost (which does not exist under perfect substitutes). With this simple example, we demonstrated the macro effects from changes in labor force composition, when workers of different age groups are imperfect substitutes. Now, we 10

12 present our full model, in which households make labor supply decisions and production takes heterogeneous labor across ages and skills as inputs with a CES technology. 3.2 Quantitative Model Demographics. Households start their lives at age 25, and we model the choices of households until they are 62. Technology. A single consumption good is produced using labor as inputs. We model imperfect substitutability across skill (education) and age groups, following Card and Lemieux (2001). There are two skill levels high school graduates and college graduates supplied by different age groups. Within a skill level, age groups are imperfect substitutes, modeled by the standard constant elasticity of substitution (CES) function. We define and ( L = α Lj L η j ( H = α Hj H η j j j ) 1 η ) 1 η, where L j and H j are high school and college graduate labor supplied by age j, and L and H are their aggregates. The efficiency of workers of age group j with skill i {L, H} is denoted by α ij, and η ( < η 1) controls the elasticity of substitution across different age groups. The elasticity of substitution under the CES is ε A = 1 1 η. If ε A > 1 (or η > 0), age groups are gross substitutes, while if ε A < 1 (or η < 0), the two are gross complements. A special case is when η = 1, which implies that age groups are perfect substitutes. For our analysis, ε A is a key parameter of interest. Whether ε A is less than 1 (imperfect substitute) and the magnitude of it determines the magnitude of macro effects from the DI. Given L and H, the aggregate output is again determined by a CES production function, Y = (θ L L ρ + θ H H ρ ) 1 ρ, where ρ ( < ρ 1) determines the constant elasticity of substitution between the two skill levels. We denote the elasticity of substitution between skill levels by ε S = 1 1 ρ. 2 2 This is our benchmark specification of the production function. For a more flexible analysis, we can allow 11

13 Endowments and Preferences. Households are endowed with one unit of time that they can devote to work (l) or leisure (1 l). They have preferences over consumption and leisure over their life-cycle, and their lifetime utility is represented by E ] β j u(c j, 1 l j ), [ j=j j=1 where c j and 1 l j denote consumption and leisure when the household is in age group j. We model both the extensive and intensive margin of labor supply, and therefore, l j [0, 1]. Households are also endowed with health status h j, which affects their labor productivity. There is an exogenous health distribution for the newly born, denoted by f(h 1 ), where h 1 [ h, h ]. Health status follows a Markov chain with exogenous transition probabilities given by π(h j+1 h j ). A household with skill i, age j, and health h earns a total labor income of y ij w ij hl, where w ij is the wage rate per efficient unit of labor provided by a worker of skill i and age j. Government Policies. individuals. 3 In our model, the government provides DI benefits to qualified The government determines a health threshold, h DI ( h, h ) and provides a payment of d(y ij ) to households whose health falls below the threshold and do not work. We assume that the disability insurance payment is a function of the household s market labor income, y ij. Under the current DI system in the United States, disability insurance payments are determined by the worker s Average Indexed Monthly Earnings (AIME), which is the average of the worker s 35 highest annual earnings. Since earnings are persistent, we simplify the policy so that we do not need to keep track of the history of income for each household. These expenditures are funded by taxing labor income of households at rate τ, and the government balances the budget. Financial Market. Financial markets are incomplete. Each period, households can trade risk-free bonds and face borrowing constraints with a borrowing limit of A. The interest rate on risk-free bonds is exogenously given (r) and constant over time. for skill- and industry-specific elasticity of substitution for age (ε A ) and elasticity of substitution across skill groups (ε S ). 3 We abstract from Social Security. While Social Security is an important determinant for the timing of retirement, Social Security incentives are mostly at work when workers are in their early 60s (there are clear peaks in the retirement decisions of the old at 62, the early retirement age, and at 65, the normal retirement age). In this paper, we would like to focus on the disincentives to work created by Disability Insurance for workers before the early retirement age. 12

14 Household Problem. At the beginning of period, households are indexed by their skill i {L, H}, age group j {1, 2,..., J}, health status h, and asset a. They make consumption (c), saving (a ), and labor supply (l) decisions. Their optimization problem is represented by the following. V (i, j, h, a) = max c,l,a u(c, 1 l) + β h π(h h)v (i, j + 1, h, a ) (2) s.t. c + a = (1 τ)y ij + (1 + r)a, if l > 0 c + a = d(y ij ) + (1 + r)a, if l = 0 and h < h DI y ij = w ij hl c 0, l [0, 1] a A Labor income of a household is denoted by y ij, which consists of w ij, the wage rate per effective unit of labor, h, health, and l, labor supply of the household. Those households whose health status falls below the threshold h DI can choose to exit the labor force and receive disability payments. Note that if the worker s health improves, he can always come back to labor market. For simplicity, we do not explicitly model the DI application process. Therefore, workers with low (enough) health automatically qualifies for DI payments when he is not working. 4 Households have savings technology that yields an interest rate of r, which we assume are exogenous and constant over time. Equilibrium. Now, we define a competitive equilibrium. Denote the state variables of each household by s (i, j, h, a), and their distribution, by Φ (s). Definition. Given a government policy { h DI, d( ) }, a competitive stationary equilibrium is a set of value functions V (s), policy functions {c (s), l (s), a (s)}, labor demand for firms {L j, H j } j {1,...,J}, wage rates for each type of workers {w Lj, w Hj } j {1,...,J}, tax rate on labor income τ, and a distribution of individuals over the states Φ (s), such that 1. Given prices and government policies, V (s) solves (2) and {c (s), l (s), a (s)} are associated policy functions. 4 Social Security pays disability benefits if the worker does not engage in the Substantial Gainful Activity (SGA), which in 2015 is a monthly earning of $1,090 for non-blind individuals and $1,820 for blind individuals. If the worker earns more than the SGA, his benefit terminates. 13

15 2. Wage rates satisfy, for each j {1,..., J}, ( ) 1 w Lj = Y = θ L (θ L L ρ + θ H H ρ ) 1 η 1 ρ 1 L ρ 1 α Lj α Lj L η j L η 1 j L j j ( ) 1 w Hj = Y = θ H (θ H L ρ + θ H H ρ ) 1 η 1 ρ 1 H ρ 1 α Hj α Hj H η j H η 1 j. H j 3. Government satisfies its budget constraint: ˆ τ ˆ y (s) dφ(s) = I {h<h DI,l(s)=0}d(y (s))φ(s)ds, j where y (s) = w ij hl (s), for i {L, H} and j {1,..., J}. The revenues are labor income taxes and the expenditures are disability insurance payments to qualified individuals. 4. Labor market clears for all age groups j {1,..., J}: ˆ L j = hl (s) Φ(s)ds ˆ H j = hl(s)φ(s)ds. 5. The distribution of individuals Φ (s) is stationary. An important channel in general equilibrium is the process through which a lower relative supply of old workers changes the wages of young workers (and thus, their incentives). In a competitive equilibrium, the relative wages across age groups within high school graduates satisfy w Lj w L j = α Lj α L j ( Lj L j ) η 1, (3) where L j is the total effective high school labor supplied by age group j (an analogous condition holds for the college graduates). We clearly see that η the degree to substitutability of labor across age groups j is important in analyzing the macro effects of DI. In particular, when η < 1, an increase supply of age group j decreases the relative wages of age group j. We can also derive an analogous expression for wages across skill groups: w H w L = θ H θ L 14 ( ) ρ 1 H. (4) L

16 In the next section we use (3) and (4) to identify the key parameters for the macro effects: η and ρ. 4 Quantitative Analysis The Elasticity of Substitution. The most important parameter of interest for our analysis is the elasticity of substitution across generations (ε A ). Following Card and Lemieux (2001), we obtain the elasticity of substitution across heterogeneous workers using the equilibrium conditions of the model, under the assumption of a CES technology. Under the production function presented in the previous section, we derive the relationship between relative supply of workers and relative wages, which vary with the elasticity of substitution across labor: log log ( wlj w L j ( whj w Lj ) ) = log = log ( αlj α L j ( θh θ L ) + (η 1) log ) + (ρ η) log ( Lj L j ( H L ) ) + log ( αhj α Lj ) + (η 1) log ( Hj Equation (5) represents the relationship between the relative supply of different generations within education and their wages, while equation (6) represents the relationship between the relative supply of workers across education and their relative wages within generation. While Card and Lemieux (2001) uses time-series variation in relative supplies and wages to identify the CES across generations and education, we use cross-state variation in demographics and wages for our identification. A similar approach was taken in Karabarbounis and Neiman (2014), where they use cross-country variation to identify the CES parameter between capital and labor. Other Parameters. Given the production function parameters, we focus on understanding the labor supply decisions of households which are heterogeneous in age, skill, and health status. This would be the first step in correctly identifying how DI influences decisions at the household level, which will be aggregated to quantify the macro effects. Therefore, we plan to use micro-level data that provides rich information on the health and labor market outcomes of households of young and old workers. For young workers, we use the Survey of Income and Program Participation (SIPP), which includes detailed information on health-related variables and labor market outcomes. As we emphasize, DI distorts incentives for the old more than it does for the young. Thus, for the old workers, we use the Health and Retirement Survey (HRS), which surveys a representative L j ) (5) (6) 15

17 sample of workers over the age of 50. We make use of the information on health, disability, income, and work for calibrating relevant parameters. We will calibrate the model so that the equilibrium outcomes of the economy matches those of the behavior of workers in the data. [to be completed] 5 Conclusion [to be completed] 16

18 References Autor, David H., and Mark G. Duggan The Rise in the Disability Rolls and The Decline in Unemployment. Quarterly Journal of Economics, 118(1): Autor, David H., and M. G. Duggan The Growth in the Social Security Disability Rolls: A Fiscal Crisis Unfolding. Journal of Economic Perspectives, 20(3): Bound, John The Health and Earnings of Rejected Disability Insurance Applicants. American Economic Review, 79: Card, David, and Thomas Lemieux Can Falling Supply Explain the Rising Return to College for Younger Men? A Cohort-Based Analysis. Quarterly Journal of Economics, 116(2): French, Eric, and Jae Song The Effect of Disability Insurance Receipt on Labor Supply. American Economic Journal: Policy, forthcoming. Gruber, Jonathan, and Kevin Milligan Social Security Programs and Retirement around the World: The Relationship to Youth Employment., ed. Jonathan Gruber and David A. Wise, Chapter Do Elderly Workers Substitute for Younger Workers in the United States?, University of Chicago Press. Karabarbounis, Loukas, and Brent Neiman The Global Decline of the Labor Share. Quarterly Journal of Economics, 129(1): Kitao, Sagiri A Life-Cycle Model of Unemployment and Disability Insurance. Journal of Monetary Economics, 68: Krusell, Per, Lee E. Ohanian, Jose-Victor Rios-Rull, and G. L. Violante Capital-Skill Complementarity and Inequality: A Macroeconomic Analysis. Econometrica, 68: Low, Hamish, and Luigi Pistaferri Disability Insurance and the Dynamics of the Incentive-Insurance Tradeoff. Working Paper. Maestas, Nicole, Kathleen J. Mullen, and Alexander Strand Does Disability Insurance Receipt Discourage Work? Using Examiner Assignment to Estimate Causal Effects of SSDI Receipt. American Economic Review, 103(5):

19 Munnell, Alicia H., and April Yanyuan Wu Will Delayed Retirement by the Baby Boomers Lead to Higher Unemployment Among Younger Workers? Working Paper, Center for Retirement Research at Boston College. Shimer, Robert The impact of young workers on the aggregate labor market. Quarterly Journal of Economics, 116(3): von Wachter, Till, Jae Song, and Joyce Manchester Trends in Employment and Earnings of Allowed and Rejected Applicants to the Social Disability Insurance Program. American Economic Review, 101(7):