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Measurement of diminishing or divergent cross section dispersion in a panel plays an important role in the assessment of convergence or divergence over time in key economic indicators. Econometric methods, known as weak σ-convergence tests, have recently been developed (Kong, Phillips, & Sul, 2019) to evaluate such trends in dispersion in panel data using simple linear trend regressions. To achieve generality in applications, these tests rely on heteroskedastic and autocorrelation consistent (HAC) variance estimates. The present chapter examines the behavior of these convergence tests when heteroskedastic and autocorrelation robust (HAR) variance estimates using fixed-b methods are employed instead of HAC estimates. Asymptotic theory for both HAC and HAR convergence tests is derived and numerical simulations are used to assess performance in null (no convergence) and alternative (convergence) cases. While the use of HAR statistics tends to reduce size distortion, as has been found in earlier analytic and numerical research, use of HAR estimates in nonparametric standardization leads to significant power differences asymptotically, which are reflected in finite sample performance in numerical exercises. The explanation is that weak σ-convergence tests rely on intentionally misspecified linear trend regression formulations of unknown trend decay functions that model convergence behavior rather than regressions with correctly specified trend decay functions. Some new results on the use of HAR inference with trending regressors are derived and an empirical application to assess diminishing variation in US State unemployment rates is included.

This paper is concerned with estimation and inference for difference-in-difference regressions with errors that exhibit high serial dependence, including near unit roots, unit roots, and linear trends. We propose a couple of solutions based on a parametric formulation of the error covariance. First stage estimates of autoregressive structures are obtained by using the Han, Phillips, and Sul (2011, 2013) X-differencing transformation. The X-differencing method is simple to implement and is unbiased in large N settings. Compared to similar parametric methods, the approach is computationally simple and requires fewer restrictions on the permissible parameter space of the error process. Simulations suggest that our methods perform well in the finite sample across a wide range of panel dimensions and dependence structures.

This paper proposes a new class of estimators for the autoregressive coefficient of a dynamic panel data model with random individual effects and nonstationary initial condition. The new estimators we introduce are weighted averages of the well-known first difference (FD) GMM/IV estimator and the pooled ordinary least squares (POLS) estimator. The proposed procedure seeks to exploit the differing strengths of the FD GMM/IV estimator relative to the pooled OLS estimator. In particular, the latter is inconsistent in the stationary case but is consistent and asymptotically normal with a faster rate of convergence than the former when the underlying panel autoregressive process has a unit root. By averaging the two estimators in an appropriate way, we are able to construct a class of estimators which are consistent and asymptotically standard normal, when suitably standardized, in both the stationary and the unit root case. The results of our simulation study also show that our proposed estimator has favorable finite sample properties when compared to a number of existing estimators.

This chapter develops robust panel estimation in the form of trimmed mean group estimation for potentially heterogenous panel regression models. It trims outlying individuals of which the sample variances of regressors are either extremely small or large. The limiting distribution of the trimmed estimator can be obtained in a similar way to the standard mean group (MG) estimator, provided the random coefficients are conditionally homoskedastic. The authors consider two trimming methods. The first one is based on the order statistic of the sample variance of each regressor. The second one is based on the Mahalanobis depth of the sample variances of regressors. The authors apply them to the MG estimation of the two-way fixed effects model with potentially heterogeneous slope parameters and to the common correlated effects regression, and the authors derive limiting distribution of each estimator. As an empirical illustration, the authors consider the effect of police on property crime rates using the US state-level panel data.

The authors develop a novel forecast combination approach based on the order statistics of individual predictability from panel data forecasts. To this end, the authors define the notion of forecast depth, which provides a ranking among different forecasts based on their normalized forecast errors during the training period. The forecast combination is in the form of a depth-weighted trimmed mean. The authors derive the limiting distribution of the depth-weighted forecast combination, based on which the authors can readily construct prediction intervals. Using this novel forecast combination, the authors predict the national level of new COVID-19 cases in the United States and compare it with other approaches including the ensemble forecast from the Centers for Disease Control and Prevention (CDC). The authors find that the depth-weighted forecast combination yields more accurate and robust predictions compared with other popular forecast combinations and reports much narrower prediction intervals.