Bootstrapping trending timevarying coefficient panel models with missing observations

We study a class of trending panel regression models with time-varying coefficients that incorporate cross-sectional and serial dependence, as well as heteroskedasticity. Our models also allow for missing observations in the dependent variable. We introduce a local linear dummy variable estimator capable of handling missing observations and derive its asymptotic properties. A key ingredient in our theoretical framework is a generic uniform convergence result for near-epoch processes in kernel estimation for large panels (N, T → ∞). The resulting limiting distribution reflects the pattern of missing values and depends on various nuisance parameters. An autoregressive wild bootstrap (AWB) is proposed to construct confidence intervals and bands. The AWB accommodates missing observations and automatically replicates all the nuisance parameters, demonstrating good finite sample performance. We apply our methods to investigate (i) the relationship between PM2.5 and mortality and (ii) common trends in atmospheric ethane emissions in the Northern Hemisphere. Both examples yield statistical evidence for time variation.