A Detailed Decomposition of Synthetic Cohort Analysis

Social scientists are often interested in assessing relative changes between two groups over time, for example, the convergence of black-white wages from 1940 to 1990. In such situations, we need a control group for both treatment groups to remove biases resulting from time trends and unobserved factors. Smith and Welch (1989) propose a decomposition technique that handles this situation using a difference-in-differences like method, attributing relative changes to four different effects. However, a method for specifying the contribution of every variable in the equation, referred to as the detailed decomposition, has not been developed. We present a detailed decomposition and provide a Stata estimator for practitioners to implement our method. Using the convergence of black-white wage between 1960 and 1970 as an example, our detailed decomposition result shows that education accounts for 73 percent of the value of change in characteristics while experience explains only 3 percent.