Measuring the biases in self-reported disability status: evidence from aggregate data

Abstract

Self-reported health status measures are generally used to analyse Social Security Disability Insurance's (SSDI) application and award decisions as well as the relationship between its generosity and labour force participation. Due to endogeneity and measurement error, the use of self-reported health and disability indicators as explanatory variables in economic models is problematic. We employ county-level aggregate data, instrumental variables and spatial econometric techniques to analyse the determinants of variation in SSDI rates and explicitly account for the endogeneity and measurement error of the self-reported disability measure. Two surprising results are found. First, it is shown that measurement error is the dominating source of the bias and that the main source of measurement error is sampling error. Second, results suggest that there may be synergies for applying for SSDI when the disabled population is larger.

Acknowledgements

This article was supported in part by Grant number 5P50MH049173 from the National Institute of Mental Health. We thank Don Parsons for his helpful comments on an earlier draft of this article. Of course, we are responsible for any remaining errors.

Notes

¹See, for example, Parsons (1980), Bound (1989), Benítez-Silva et al. (1999), Kreider (1999), Gruber (2000), Kreider and Riphahn (2000) and Mitchell and Phillips (2002), among others.

²These issues have been noted by many studies such as Parsons (1980), Bound (1989, 1991), Stern (1989), Benítez-Silva et al. (1999, 2004), Kreider (1999), Bound and Waidmann (2002), Burkhauser et al. (2002) and Kreider and Pepper (2007).

³To identify employment disability, we use the variable P41013 (employment disability) from the 2000 Census. The relevant question asked people aged 16 years and older if a physical, mental or emotional condition caused them difficulty working at a job or business. When computing the relevant shares, we divide this variable by the county population between 18 and 64 years of age. Thus, we have assumed that the number of disabled individuals of ages 16 and 17 years is negligible.

Table 1. Sample moments of dependent and explanatory variables

⁴One might worry that bias does not aggregate from individuals to counties. In the Appendix, we show that aggregation does not change the qualitative nature of endogeneity bias.

⁵We use a standard normal density function truncated at ±4.

⁶To explore the validity of our instruments, we have estimated a model using all instruments and performed a Sargan over-identification test. At the 5% significance level, we cannot reject the null that the instruments are orthogonal to the residual.

⁷There is significant variation between the OLS and 2SLS estimates for the other coefficients as well. We choose not to focus on these given the evidence in favour of endogeneity.

⁸(0.078/0.272)² = 0.082.

⁹We assume that only the employment disability rate is measured with error. Thus, W = X + e where all elements of e not corresponding to employment disability are 0.

¹⁰At σ _e  = 0.1684, the smallest eigenvalue of is 0.0.

¹¹Bearse et al. (2004) found similar results with respect to the use of specialized transportation by disabled people. The share of disabled people using specialized transportation increases more than proportionally to an increase in the disability rate.

¹²Several studies have found that the number of disability applications rises during economic downturns. See, for example, Rupp and Stapleton (1995), Benítez-Silva et al. (1999) and Kreider (1999).

¹³On the contrary, other articles such as Benítez-Silva et al. (1999) and Kreider (1999) have modelled both the individual choice of applying for DI and the SSA award decision. Hence, they have been able to assess how changes in the economic environment affect both of these variables separately.