Partially time-invariant panel data regression

In panel data analysis, temporal variation in the variable of interest is commonly exploited to eliminate individual-specific effects. However, even when the outcome variable follows a continuous distribution, its temporal variation may equal zero with positive probability, resulting in a mixture distribution characterized by a mass at zero alongside a continuous component. To address this, we propose a mixture model and derive estimators for both the conditional probability of no variation and the expected value of the continuous component, focusing on the partial effects. We establish the asymptotic consistency and normality of these estimators and show that paired bootstrap provides consistent confidence intervals for the expected outcome. Monte Carlo simulations show good finite-sample performance of the estimators and reveal that the zero-inflated phenomenon under study can yield substantially different functional relationships depending on the underlying parameters, often making linear models unreliable.