Estimation of the probability of labor force participation of the AFDC population-at-risk

Summary

In summary, the functional form makes quite a difference. An investigator should be quite wary of making generalizations based on any single specification or estimation technique. However, the above results have shown in striking fashion the superiority of MLE of the sigmoid specifications over the OLS estimation of the linear probability specification. Although the logistic or urban specification require iterative solution, this is no barrier on a modern digital computer, with appropriate special algorithms. A further advantage of the MLE is the asymptotic normality of the estimates of ϑ _i which permits large sample interval estimation, and the iteration method of scoring employed yields directly an estimate of the standard deviation of each normally distributed ϑ _i . Also standard tests of significance are now applicable.

Perhaps most importantly, the sigmoid specifications are consistent with a probability interpretation since the estimates lie inside the unit interval, and the sigmoid shape is consistent with the assumed unimodal distribution of the participation decision.

In conclusion, results reported in previous investigations of the probability of labor force participation or labor force participation rate which have relied on the least squares estimation of a linear probability specification are likely to be unreliable as to he magnitude of the response attributed to changes in explanatory variables.