Treatment-effect identification without parallel paths

Imagine a region suffering from a widening income gap that becomes eligible for a generous transfer programme (the treatment). Imagine difference-in-differences analysis (DD) - a before-and-after comparison of the income-level difference - shows that the handicap has risen. Most observers would conclude to the policy's inefficiency. But second thoughts are needed, because DD rests heavily on the validity of a key assumption: parallel paths in the absence of treatment; an assumption that is often violated. To cope with this problem, economists traditionally 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. What is needed is a method that i) uses pre-treatment observations to capture linear or non-linear trend differences, and ii) extrapolates these to compute the treatment effect. This paper 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 1994-2006 EU programme that was implemented in the Belgian province of Hainaut.