Much ado about nothing: conditional logit vs. random coefficient models for estimating labour supply elasticities

Abstract

This study compares several specifications of discrete choice labour supply estimations on basis of the German Socio Economic Panel. The results suggest that despite the restrictive assumptions of the error terms the conditional logit model provides an adequate model choice for the analysis of labour supply functions. Significance tests, which are based on bootstrapped confidence intervals, show that labour supply elasticities derived within the conditional logit model do not significantly differ from elasticities derived in flexible random coefficient models.

Notes

¹ Malachow-Moeller and Svarer (2003) provide a program code for multinomial logit models with random coefficients in SAS. Train has written a program for mixed models in GAUSS. GLLAMM, developed by Rabe-Hesketh et al. (2001) allows to estimate random coefficient models in Stata. All estimations in this application have been performed using GLLAMM. I would like to thank Sophia Rabe-Hesketh for her support using this program.

² In this application, the study employs numerical integration by Gauss-Hermite quadrature for the nonparametric model. The parametric model is estimated using adaptive Gauss-Hermite quadrature, which reduces the computational cost significantly (Rabe-Hesketh et al., 2001).

³ For a more detailed discussion see Haan (2004).

⁴ Because of the small number of men in part-time employment in the sample, only three categories could be specified for them, namely no work, full time, and overtime. For women, two additional part-time alternatives have been defined. Alternatives with too few observations are excluded. See Haan (2004) for more information about the definition of the alternatives.

⁵ Gerfin and Leu (2003) employ the same specification, van Soest (1995) allows the random effect to vary with leisure terms, whereas MacCrae (1999) employ a random specification that varies with income and both leisure terms.

⁶ Steiner (2001) is followed and the Akaike Information Criterion is used rather than the standard likelihood ratio test, as the latter violates standard regularity conditions and its parameter distribution is not known.