Optimally Combining Censored and Uncensored Datasets

Economists and other social scientists often face situations where they have access to two datasets that they can use but one set of data suffers from censoring or truncation. If the censored sample is much bigger than the uncensored sample, it is common for researchers to use the censored sample alone and attempt to deal with the problem of partial observation in some manner. Alternatively, they simply use only the uncensored sample and ignore the censored one so as to avoid biases. It is rarely the case that researchers use both datasets together, mainly because they lack guidance about how to combine them. In this paper, we develop a tractable semiparametric framework for combining the censored and uncensored datasets so that the resulting estimators are consistent, asymptotically normal, and use all information optimally. When the censored sample, which we refer to as the master sample, is much bigger than the uncensored sample (which we call the refreshment sample), the latter can be thought of as providing identification where it is otherwise absent. In contrast, when the refreshment sample is large and could typically be used alone, our methodology can be interpreted as using information from the censored sample to increase effciency. To illustrate our results in an empirical setting, we show how to estimate the effect of changes in compulsory schooling laws on age at first marriage, a variable that is censored for younger individuals. We also demonstrate how refreshment samples for this application can be created by matching cohort information across census datasets.

Last Hired, First Fired? Black-White Unemployment and the Business Cycle

Past studies have tested the claim that blacks are the last hired during periods of economic growth and the first fired in recessions by examining the movement of relative unemployment rates over the business cycle. Any conclusion drawn from this type of analysis must be viewed as tentative because the cyclical movements in the underlying transitions into and out of unemployment are not examined. Using Current Population Survey data matched across adjacent months from 1989 to 2004, this paper examines labor market transitions for prime age males to test this hypothesis. Considerable evidence is presented that blacks are the first fired as the business cycle weakens. However, no evidence is found that blacks are the last hired. Instead, blacks are initially hired from the ranks of the unemployed early in the business cycle and later are drawn from non-participation. Narrowing of the racial unemployment gap near the peak of the business cycle is driven by a reduction in the rate of job loss for blacks rather than increases in hiring. There is also evidence that residual differences in the racial unemployment gap vary systematically over the business cycle in a manner consistent with discrimination being more evident in the economy at times when its cost is lower.