How Taxes Affect Economic Behavior

By Henry J. Aaron; Joseph A. Pechman | Go to book overview

hours are zero. Here vij = ηj + βyij, so that vij is distributed normally as

and qij = - αwij - zjγ. The joint probability density of this term is bivariate normal. The last term in equation 9 corresponds to desired hours falling at one of the m - 1 kink points but actual hours are zero due to ηj. For those observed to be working, the probability of actual hours of work is similar but simpler because the first term is absent and only univariate probability densities are required since truncation of hours worked does not take place. Thus the probability that individual j works hj hours is

(10)

.

The first term corresponds to the budget segments and the second term to kink points, so that

corresponds to kink hours Hij. Then over the n sample observations the log likelihood function takes the form

,

where Dj is an indicator variable with Dj = 0 if person j does not work and Dj = 1 otherwise. The parameters are estimated by maximum likelihood techniques.61. Thus the estimated parameters are chosen by the criterion of maximizing the likelihood of the model of equations 9 and 10 explaining the observed hours of work in the sample hj over the n individuals. Since my sample sizes are typically about 1,000 individuals, the optimal large-sample properties of maximum likelihood estimation should apply in this case.


Appendix B: Econometric Issues and Techniques

Female Labor Supply

I briefly consider two econometric issues that arise in female labor supply. First, I consider the possibility that the market wage rate may depend

____________________
61.
I used the algorithm by E. K. Berndt, B. H. Hall, R. E. Hall, and J. A. Haus man , "Estimation and Inference in Nonlinear Structural Models," Annals of Economic and Social Measurement, vol. 3 ( October 1974), pp. 653-65. Starting values were obtained by instrumental variable estimates.

-67-

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