Disability insurance benefits and labor supply decisions: evidence from a discontinuity in benefit awards

Abstract

The effect of disability insurance (DI) benefits on the labor supply of individuals is a disputed topic in both academia and policy. We identify the impact of DI benefits on working full-time, working part-time or being out of the labor force by exploiting a discontinuity in the DI benefit award rate in Switzerland above the age of 56. Using rich survey data and a discrete endogenous switching model, we find that DI benefit receipt increases the probability of working part-time by approximately 32% points, decreases the probability of working full-time by approximately 35% points and has little effect on the probability of being out of the labor force for the average beneficiary. Looking at the treatment effect distribution, we find that male, middle- to high-income and relatively healthy DI beneficiaries are more likely to adjust their labor supply from full-time to part-time, whereas women, low-income and ill beneficiaries tend to drop out of the labor market. Our results shed new light on the mechanisms explaining low DI outflow rates and may help better target interventions.

Appendix

1.1 A.1 Variable construction

The indicator for DI benefits is constructed from a question about DI benefit receipt in the past year and equals one for individuals who report to receive DI benefits and equals zero for those who report that they do not receive benefits. There is also information about the amount of DI pensions in the Swiss Household Panel, but we decided against using this variable because of many missing values and the likely presence of reporting error, which would bias the results. Moreover, our instrument likely has a stronger effect on the extensive margin of DI benefits than the intensive margin. The discrete labor supply variable takes three values for individuals who work part-time (1), full-time (2) or are unemployed or not in the labor force (3).

Regarding the control variables, we create a binary variable from the life satisfaction variable (originally scaled from “not satisfied” (0) to “completely satisfied” (10)), which is coded such that it is one for individuals with a satisfaction score of at least seven (the median value) and zero else. General health status ranges from “very well” (1) to “not well at all” (5) and is recoded as a dummy variable good health that takes the value one for individuals with a “very well” or “well” health status, and zero else. Physical activity is a binary variable indicating whether a person exercises for at least half an hour a week (1) or if that person remains inactive (0). Health impediments in everyday activities and medication needed in everyday functioning are measured on an 11-point scale from “not at all” (0) to “a great deal” (10). For both of these variables, we generated an indicator equal to one for individuals with a value of at least 5 in terms of severity of health impediments and medication needed for everyday functioning, and zero for all others. Depression, anxiety and blues are measured on a scale of “never” (0) to “always” (10). We constructed an indicator depression from this information that equals zero for all observations below 3, and one for the rest. The cutoff value of 3 is chosen here as the 75% quantile in the distribution of the original depression variable. Finally, indicators for back problems, weakness and weariness, sleeping problems and headaches are dummy variables, which were created in the way that they are one for observations that report that they are suffering “very much,” and zero for those who are suffering “not at all” or “somewhat” on the original three-point scale.

1.2 A.2 Simulated log-likelihood

The vector of model parameters $\theta _j \equiv \left\{ \beta _j, \gamma _j \right\}$ and $\Omega$ are estimated by maximizing a simulated log-likelihood function of the form,

$$\begin{aligned} {\hbox {SLL}}(\theta , \Omega ; x,y) =&\sum _{j = 1}^3 \sum _{n=1}^N d_{ij} D_i \log (\tilde{P}(y_i = j | D_i = 1)) \nonumber \\&+ \sum _{j = 1}^3 \sum _{n=1}^N d_{ij} (1-D_i) \log (\tilde{P}(y_i = j | D_i = 0)) \end{aligned}$$

(6)

where $d_{ij}$ is an indicator for the choice taken by individual i, $D_i$ is the indicator for the DI benefits and $\tilde{P}(\cdot )$ is the simulated (conditional) choice probability.

Table 8 shows the discrete ES estimates for 1, 10, 100 and 1000 draws per observation, the number of iterations that were needed to reach convergence, the value of the pseudo-log-likelihood at the coefficient vector and the computation time in seconds. All simulations were ran on an Intel(R) Core(TM) i7-4790 CPU @ 3.60 GHz with 16GB RAM on Windows 10 using Stata/MP 14.0. Recall that the main results are based on 1000 draws per observation so that Table 8, column 4 is identical to the results presented in Sect. 6. For small numbers of draws, we know from asymptotic theory that the MSL estimator is not equivalent to the ML estimator and inconsistent (Gouriéroux and Monfort 1991). This is likely the case for the estimates corresponding to $S = 1$ and $S=10$ draws per observation. For such small S, the reduced computation time comes at the cost of inconsistent parameter estimates. However, as the number of draws is increased, the MSL estimates stabilize and remain basically unchanged. Table 8 suggests that estimates with as few as 100 random draws per observation produce reliable coefficient estimates that are close to those with $S = 1000$. This is also relevant to know from a practical point of view since the differences in computation time are considerable: For the full specification, the computation time is roughly 7 minutes for $S = 100$, but already 18 minutes for $S = 1000$. If the number of draws is further increased,¹⁵ the coefficient estimates hardly change but again come at the cost of a significantly higher computational time.

Table 8 Sensitivity checks on the number of simulation draws