XTLHAZARD: Stata module for Adjusted First-Differences Estimation of the Linear Discrete-Time Hazard Model

xtlhazard implements the adjusted first-differences estimator for the linear discrete-time hazard model proposed by Tauchmann (2019). This procedure addresses the issue that, conventional linear fixed-effects panel estimators (within-transformation, first-differences), fail to eliminate unobserved time-invariant heterogeneity and are biased and inconsistent if the dependent variable is a binary dummy indicating an absorbing state. This even applies if the unobserved time-invariant heterogeneity is uncorrelated with the regressors in the population. Besides conventional survivor bias - from which also pooled OLS suffers even if the unobserved heterogeneity is uncorrelated with the regressors - these estimators suffer from a second source of bias. This second bias, which is severe in many settings, originates from the transformation of the data itself und is present even in the absence of any unobserved heterogeneity. The adjusted first-differences estimator eliminates this second source of bias and confines the asymptotic bias to survivor bias under the assumption that the unobserved heterogeneity is uncorrelated with changes in the regressors in the population, while allowing for correlations with their levels. Technically, xtlhazard rescales the coefficients from unadjusted first-differences estimation (with constant terms) by the matrix inv(I+inv(d.X'd.X)*d.X'l.X), which ('s transpose) is stored in the macro e(Adjust). By specifying the option difference(#), one makes the estimation procedure use higher-order rather than first-differences. This allows confining the asymptotic bias to survivor bias under the alternative assumption of unobserved heterogeneity being uncorrelated with higher-order differences of the explanatory variables.