Instrumental variable estimation for functional concurrent regression models

Abstract

In this work we propose a functional concurrent regression model to estimate labor supply elasticities over the years 1988 through 2014 using Current Population Survey data. Assuming, as is common, that individuals' wages are endogenous, we introduce instrumental variables in a two-stage least squares approach to estimate the desired labor supply elasticities. Furthermore, we tailor our estimation method to sparse functional data. Though recent work has incorporated instrumental variables into other functional regression models, to our knowledge this has not yet been done in the functional concurrent regression model, and most existing literature is not suited for sparse functional data. We show through simulations that this two-stage least squares approach greatly eliminates the bias introduced by a naive model (i.e. one that does not acknowledge endogeneity) and produces accurate coefficient estimates for moderate sample sizes.

Keywords: Functional concurrent regression; instrumental variable; labor supply elasticity; sparse functional data.

Figure 1.

Number of CPS respondents per year included in the data after all inclusion criteria were applied.

Figure 2.

Estimated coefficient functions from three example simulations following Scenario 2 and the CSD sample scheme. Each row represents a different sample size ( $N=100,200,400,\mathrm{or}800$) and each column represents one of the three example simulations (a, b, and c). Examples shown are simply the first three simulations for each scenario.

Figure 3.

Estimated coefficient functions from three example simulations following Scenario 3 and the CSD sample scheme. Each row represents a different sample size ( $N=100,200,400,\mathrm{or}800$) and each column represents one of the three example simulations (a, b, and c). Examples shown are simply the first three simulations for each scenario.

Figure 4.

Estimates of labor supply elasticities for married males (upper left), unmarried males (upper right), married females (lower left), and unmarried females (lower right). Dashed horizontal lines at an LSE of 0 are included for reference.