Xtspj: Split-Panel Jackknife Estimation for Nonlinear Fixed-Effect Models

Abstract

We introduce a new Stata program xtspj as a bias correction tool for nonlinear models with fixed effects. The correction removes the first-order bias term using the split-panel jackknife estimation technique introduced by Dhaene and Jochmans (2015). Both the jackknife of the parameter and the jackknife of the log-likelihood function are implemented, and both balanced and unbalanced panel are allowed. In simulations, we study how the unbalancedness of the panel may affect the estimates and the performance of the jackknife under various designs and for various models. We bundled three preprogrammed models, the probit, the logit, and the linear model. Other user-written models may also be accommodated provided that the log-likelihood function is specified. The user-written models may take a very general form in the sense that we do not limit the number of linear indices and that the users do not need to provide the score or the Hessian function. In addition, the model may be dynamic and may contain predetermined covariates. The program is fast and less memory-aggressive in the sense that a maximization routine is implemented taking into account the sparsity of the Hessian.