The Partially-Matched-Sample Correction in Pseudo Panel Minimum Distance Estimation

Certain repeated cross-sectional data sets, such as the Current Population Survey (CPS), use special sampling designs by which samples from different times periods are partially matched. This paper proposes a correction to the optimal weighting matrix in minimum distance (MD) estimation of pseudo panel models to account for such partially matched samples. This partially-matched-sample correction may be needed if the sample matching rate is nontrivial and, at the same time, there is a fixed effect, a serially correlated idiosyncratic error, or both in the underlying linear panel data model data generating process, all of which lead to a block diagonal structure of the optimal weighting matrix. Using the correction can result in considerable efficiency gains both in finite sample and asymptotically. As an illustration, the correction is applied to the classical question of estimating the monetary return to education using the yearly Merged Outgoing Rotation Group (MORG) files from CPS.