Alternatives to polynomial trend-corrected differences-in-differences models

A common problem with differences-in-differences (DD) estimates is the failure of the parallel-trend assumption. To cope with this, most authors include polynomial (linear, quadratic…) trends among the regressors, and estimate the treatment effect as a once-in-a-time trend shift. In practice, that strategy does not work very well, because inter alia the estimation of the trend uses post-treatment data. An extreme case is when sample covers only one period before treatment and many after. Then the trend’s estimate relies almost completely on post-treatment developments, and absorbs most of the treatment effect. What is needed is a method that i) uses pretreatment observations to capture linear or nonlinear trend differences, and ii) extrapolates these to compute the treatment effect. This article shows how this can be achieved using a fully flexible version of the canonical DD equation. It also contains an illustration using data on a 1994–2000 EU programme that was implemented in the Belgian province of Hainaut