On Estimating Long-Run Effects in Models with Lagged Dependent Variables

This note points out the hazards of estimating long-run effects from models with lagged dependent variables. We use Monte Carlo experiments to demonstrate that this practice often fails to produce reliable estimates. 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 alternative procedures such as jackknifing and indirect inference address the first issue, associated estimates of long-run effects remain unreliable.