On estimating long-run effects in models with lagged dependent variables

A common procedure in economics is to estimate long-run effects from models with lagged dependent variables. For example, macro panel studies frequently are concerned with estimating the long-run impacts of fiscal policy, international aid, or foreign investment. Our analysis points out the hazards of this practice. We use Monte Carlo experiments to demonstrate that estimating long-run impacts from dynamic, models produces unreliable results. Biases can be substantial, sample ranges very wide, and hypothesis tests can be rendered useless in realistic data environments. There are three reasons for this poor performance. First, OLS estimates of the coefficient of a lagged dependent variable are downwardly biased in finite samples. Second, small biases in the estimate of the lagged, dependent variable coefficient are magnified in the calculation of long-run effects. And third, and perhaps most importantly, the statistical distribution associated with estimates of the LRP is complicated, heavy-tailed, and difficult to use for hypothesis testing. While many of the underlying problems have been long known in the literature, the continued widespread use of the associated empirical procedures suggests that researchers are unaware of the extent and severity of the estimation problems. This study aims to illustrate their practical importance for applied research.