Improved Coefficient and Variance Estimation in Stable First-Order Dynamic Regression Models

In dynamic regression models the least-squares coefficient estimators are biased in finite samples, and so are the usual estimators for the disturbance variance and for the variance of the coefficient estimators. By deriving the expectation of the initial terms in an expansion of the usual expression for the asymptotic coefficient variance estimator and by comparing these with an approximation to the true variance we find an approximation to the bias in variance estimation from which a bias corrected estimator for the variance readily follows. This is also achieved for a bias corrected coefficient estimator and allows to compare analytically the second-order approximation to the mean squared error of the least-squares estimator and its counterpart for the first-order bias corrected coefficient estimator. Two rather strong results on efficiency gains through bias correction for AR(1) models follow. Illustrative simulation results on the magnitude of bias in coefficient and variance estimation and on the scope for effective bias correction and efficiency improvement are presented for some relevant particular cases of the ARX(1) class of models.

Efficiency profiles of MM estimators in dynamic panel data models

In dynamic panel data models with unobserved individual effects least-squares estimators are inconsistent when the number of cross-section units N gets large while the number of time-series observations T remains finite. For that situation an abundance of method of moments (MM) estimators is available, which differ in the way unobserved heterogeneity is dealt with and regarding the number and nature of instruments that is being exploited. For some stylized models we derive and compare characteristics concerning instrument weakness (or fitness) and the resulting effectiveness with respect to estimator efficiency for T small and N infinite. We make extensive use of graphical methods to show the characteristic qualities of and differences between estimation methods over relevant areas of the parameter space

Microeconometric Dynamic Panel Data Methods: Model Specification and Selection Issues

A motivated strategy is presented to find step by step an adequate model specification and a matching set of instrumental variables by applying the programming tools provided by the Stata package Xtabond2. The aim is to implement generalized method of moment techniques such that useful and reasonably accurate inferences are extracted from an observational panel data set on a single microeconometric structural presumably dynamic behavioral relationship. In the suggested specification search three comprehensive heavily interconnected goals are pursued, namely: (i) to include all the relevant appropriately transformed possibly lagged regressors, as well as any interactions between these if it is required to relax the otherwise very strict homogeneity restrictions on the dynamic impacts of the explanatories in standard linear panel data models; (ii) to correctly classify all regressors as either endogenous, predetermined or exogenous, as well as being either effect-stationary or effect-nonstationary, implying which internal variables could represent valid and relatively strong instruments; (iii) to enhance the accuracy of inference in finite samples by omitting irrelevant regressors and by profitably reducing the space spanned by the full set of available internal instruments. For the various tests which trigger the decisions to be made in the sequential selection process the relevant considerations are spelled out to interpret the magnitude of p-values. Also the complexities to establish and interpret the ultimately established dynamic impacts are explained. Finally the developed strategy is applied to a classic data set and is shown to yield new insights