Split-panel jackknife estimation of fixed-effect models

We propose a jackknife for reducing the order of the bias of maximum likelihood estimates of nonlinear dynamic fixed-effect panel models. In its simplest form, the half-panel jackknife, the estimator is just $2\hat{\theta} - \bar{\theta}_{1/2}$, where $\hat{\theta}$ is the MLE from the full panel and $\bar{\theta}_{1/2}$ is the average of the two half-panel MLEs, each using T/2 time periods and all N cross-sectional units. This estimator eliminates the first-order bias of $\hat{theta}. The order of the bias is further reduced if two partitions of the panel are used, for example, two half-panels and three 1/3-panels, and the corresponding MLEs. On further partitioning the panel, any order of bias reduction can be achieved. The split-panel jackknife estimators are asymptotically normal, centered at the true value, with variance equal to that of the MLE under asymptotics where T is allowed to grow slowly with N. In analogous fashion, the split-panel jackknife reduces the bias of the profile likelihood and the bias of marginal-effect estimates. Simulations in fixed-effect dynamic discrete-choice models with small T show that the split-panel jackknife effectively reduces the bias and mean squared error of the MLE, and yields confidence intervals with much better coverage.