Married Women’s Labor Supply and Spousal Health Insurance Coverage in the United States: Results from Panel Data

Abstract

This paper investigates the effect of spousal insurance coverage on married women’s labor supply. This effect was hypothesized to be negative, since married women have an incentive to seek employment in jobs that will provide insurance when their husbands do not provide coverage. Panel data from the 1996–2004 Medical Expenditure Panel Surveys was used to control for the potential correlation between unobserved characteristics and spousal insurance. The findings suggest that spousal coverage does have a negative effect on married women’s labor supply, and that most of the reduction in labor supply seems to derive from shifts out of the labor force rather than between part-time and full-time work.

Appendix

This appendix presents the two-step procedure for estimating the censor-correction terms and parameters for Eq. 5 in the paper. For the original derivation of the model, see Kalwij (2004) or Kalwij and Gregory (2005).

Step 1: For two time periods, estimate a bivariate probit model of the form:

$$ W_{i1} = X_{i1} \beta + c_i + \varepsilon _{i1} $$

(1a)

$$ W_{i2} = X_{i2} \beta + c_i + \varepsilon _{i2} $$

(2a)

where W _it is an indicator variable for positive work hours for individual i in time t, c _i are unobserved couple-specific effects, and ε _it is an error term. To model the correlation between c _i and the explanatory variables, a conditional mean independence assumption is used (Rochina-Barrachina 1999; Wooldridge 1995):

$$ c_i = h(X_i )\gamma + \mu _i $$

(3a)

where μ _i is a random individual-specific error term. The function h(·) is commonly treated as the average over time, so that $h(X_i ) = \bar X_i .$ Substituting into (1a) and (2a), the model yields:

$$ W_{i1} = X_{i1} \beta + \bar X_i \gamma + \varepsilon _{i1} $$

(4a)

$$ W_{i2} = X_{i2} \beta + \bar X_i \gamma + \varepsilon _{i2} $$

(5a)

Step 2: The bivariate model given by (4a) and (5a) is estimated to yield the predicted values $\hat M_{i1} = X_{i1} \hat \beta + \bar X_i \hat \gamma$ and $\hat M_{i2} = X_{i2} \hat \beta + \bar X_i \hat \gamma .$ These are used to derive the correction terms given by:

$$ \Uplambda _1 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho ) = \frac{{\phi (\hat M_{i1} )\Upphi \left( {{{(\hat M_{i2} - \hat \rho \hat M_{i1} )} \mathord{\left/ {\vphantom {{(\hat M_{i2} - \hat \rho \hat M_{i1} )} {\sqrt {1 - \hat \rho ^2 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - \hat \rho ^2 } }}} \right)}}{{\Upphi _2 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho )}} $$

(6a)

$$ \Uplambda _2 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho ) = \frac{{\phi (\hat M_{i2} )\Upphi \left( {{{(\hat M_{i1} - \hat \rho \hat M_{i2} )} \mathord{\left/ {\vphantom {{(\hat M_{i1} - \hat \rho \hat M_{i2} )} {\sqrt {1 - \hat \rho ^2 } }}} \right. \kern-\nulldelimiterspace} {\sqrt {1 - \hat \rho ^2 } }}} \right)}}{{\Upphi _2 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho )}} $$

(7a)

where $\hat \rho$ is the estimated correlation between the error terms in (4a) and (5a), $\phi ( \cdot )$ is the standard normal density function, $\Upphi ( \cdot )$ is the standard normal distribution function, and $\Upphi _2 ( \cdot )$ is the bivariate standard normal distribution function. Given $\Uplambda _1 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho )$ and $\Uplambda _2 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho ),$ Eq. 5 in the paper is estimated by least squares on a subset of individuals with positive working hours in both time periods:

$$ \Updelta Y_{it} = \Updelta X_{it} \beta + \Updelta I_{it} \gamma - \pi _2 \Uplambda _2 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho ) + \pi _1 \Uplambda _1 (\hat M_{i1} ,\hat M_{i2} ,\hat \rho ) + \xi _{it} $$

(8a)