Small sample bias in synthetic cohort models of labor supply

In synthetic cohort models (cross-sectional data grouped at the cohort and year level), researchers often ignore potential biases induced by sampling error because they have 100 or 200 observations per group. I investigate small sample biases in the context of two synthetic cohort labor supply applications - a model of intertemporal labor supply of men (similar to that of Browning, Deaton, and Irish, 1985) and a female labor supply model (similar to that of Blundell, Duncan, and Meghir, 1998). My approach is to use the Current Population Survey to compare the estimates when group sizes are extremely large to those that arise from randomly drawing subsamples of observations from the large groups. This provides a natural framework for examining the extent of small sample biases and the group sizes required so that small sample biases are negligible. I augment this approach with Monte Carlo analysis so as to precisely quantify biases and coverage rates. I find that, in these two applications, thousands of observations per group are required before small sample issues can be ignored in estimation. In these applications, sampling error leads one to underestimate intertemporal labor supply elasticities for men, and conclude that the income response of female labor supply is zero or tiny when in fact it is quite large.