Search Results (3)

We discuss some conceptual and practical issues that arise from the presence of global energy balance effects on station level adjustment mechanisms in dynamic panel regressions with climate data. The paper provides asymptotic analyses, observational data computations, and Monte Carlo simulations to assess the use of various estimation methodologies, including standard dynamic panel regression and cointegration techniques that have been used in earlier research. The findings reveal massive bias in system GMM estimation of the dynamic panel regression parameters, which arise from fixed effect heterogeneity across individual station level observations. Difference GMM and Within Group (WG) estimation have little bias and WG estimation is recommended for practical implementation of dynamic panel regression with highly disaggregated climate data. Intriguingly, from an econometric perspective and importantly for global policy analysis, it is shown that in this model despite the substantial differences between the estimates of the regression model parameters, estimates of global transient climate sensitivity (of temperature to a doubling of atmospheric CO${}_2$) are robust to the estimation method employed and to the specific nature of the trending mechanism in global temperature, radiation, and CO${}_2.$ Full article

The usual t test, the t test based on heteroskedasticity and autocorrelation consistent (HAC) covariance matrix estimators, and the heteroskedasticity and autocorrelation robust (HAR) test are three statistics that are widely used in applied econometric work. The use of these significance tests in trend regression is of particular interest given the potential for spurious relationships in trend formulations. Following a longstanding tradition in the spurious regression literature, this paper investigates the asymptotic and finite sample properties of these test statistics in several spurious regression contexts, including regression of stochastic trends on time polynomials and regressions among independent random walks. Concordant with existing theory (Phillips 1986, 1998; Sun 2004, 2014b) the usual t test and HAC standardized test fail to control size as the sample size $n\to \infty$ in these spurious formulations, whereas HAR tests converge to well-defined limit distributions in each case and therefore have the capacity to be consistent and control size. However, it is shown that when the number of trend regressors $K\to \infty ,$ all three statistics, including the HAR test, diverge and fail to control size as $n\to \infty$ . These findings are relevant to high-dimensional nonstationary time series regressions where machine learning methods may be employed. Full article

This paper considers estimation and inference concerning the autoregressive coefficient ( $\rho$ ) in a panel autoregression for which the degree of persistence in the time dimension is unknown. Our main objective is to construct confidence intervals for $\rho$ that are asymptotically valid, having asymptotic coverage probability at least that of the nominal level uniformly over the parameter space. The starting point for our confidence procedure is the estimating equation of the Anderson–Hsiao (AH) IV procedure. It is well known that the AH IV estimation suffers from weak instrumentation when $\rho$ is near unity. But it is not so well known that AH IV estimation is still consistent when $\rho =1$ . In fact, the AH estimating equation is very well-centered and is an unbiased estimating equation in the sense of Durbin (1960), a feature that is especially useful in confidence interval construction. We show that a properly normalized statistic based on the AH estimating equation, which we call the $\mathbb{M}$ statistic, is uniformly convergent and can be inverted to obtain asymptotically valid interval estimates. To further improve the informativeness of our confidence procedure in the unit root and near unit root regions and to alleviate the problem that the AH procedure has greater variation in these regions, we use information from unit root pretesting to select among alternative confidence intervals. Two sequential tests are used to assess how close $\rho$ is to unity, and different intervals are applied depending on whether the test results indicate $\rho$ to be near or far away from unity. When $\rho$ is relatively close to unity, our procedure activates intervals whose width shrinks to zero at a faster rate than that of the confidence interval based on the $\mathbb{M}$ statistic. Only when both of our unit root tests reject the null hypothesis does our procedure turn to the $\mathbb{M}$ statistic interval, whose width has the optimal $N^{-1/2}{T}^{-1/2}$ rate of shrinkage when the underlying process is stable. Our asymptotic analysis shows this pretest-based confidence procedure to have coverage probability that is at least the nominal level in large samples uniformly over the parameter space. Simulations confirm that the proposed interval estimation methods perform well in finite samples and are easy to implement in practice. A supplement to the paper provides an extensive set of new results on the asymptotic behavior of panel IV estimators in weak instrument settings. Full article