What is it about?
The Common Correlated Effects methodology is a highly popular estimation approach to estimate panel data models with unobserved common factors. Essentially, by adding cross-section averages (CA) of the observables to the regression model, the method controls for a wide variety of possible unobserved heterogeneity in the dataset. The method is simple and effective, but it was not originally intended for use in dynamic panel data models. Dynamic models include lags of the dependent variable as regressors to account for the slow adaptation of economic variables to changes in their determinants, and are hence very common in empirical economics. In this paper we show how the Common Correlated Effects (CCE) estimator should be specified in dynamic models. That is, we illustrate which cross-section averages should be added to the specification to capture the unobserved heterogeneity. Next, we show that although adding the appropriate CA to the specification will control for the unobserved heterogeneity, which is essential for consistency, an important by-product of this augmentation is that it leads to substantial bias in dynamic models estimated using datasets with a finite time series dimension. In response, we introduce a simple bias correction which, as shown in both theory and simulations, effectively removes all bias even in finite samples. The resulting bias-adjusted CCE estimator is a highly effective, unbiased estimator and provides a reliable tool for inference in the dynamic model.
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Why is it important?
Given that economic variables tend to be highly persistent and react slowly to changes in their determinants, dynamic panel (longitudinal) data models are very common in empirical economics. The CCE methodology is becoming a workhorse in empirical work, yet when applied to estimate dynamic specifications we show that the methodology is unreliable for inference even when both the time series and cross-section dimension of the panel dataset tend to infinity. This implies that inference based on the estimated coefficients will always lead to misleading conclusions. In response, we develop a corrected CCE estimator and show, through both theory and simulations, that it will allow reliable estimation and inference even in small datasets.
Perspectives
The CCE methodology is commonly applied to estimate panel data models with unobserved common factors. However, given the widespread use of dynamic specifications in empirical economics it was key that the methodology, initially developed for static specifications, is also appropriately extended to the dynamic setting, and its strengths and weaknesses are exposed. In so doing, we found that the original methodology, while very simple and powerful for approximating the unobserved common factors, has the important downside of being unreliable for inference due to bias, even as both dimensions of the panel dataset grow large. The key contribution of this article is that we managed to resolve this problem with a simple correction, and that the resulting corrected estimator displays the same favourable finite sample properties as the CCE estimators display in the original static model.
Dr. Ignace De Vos
Lunds Universitet
Read the Original
This page is a summary of: Bias-Corrected Common Correlated Effects Pooled Estimation in Dynamic Panels, Journal of Business and Economic Statistics, September 2019, Taylor & Francis, DOI: 10.1080/07350015.2019.1654879.
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Resources
Common Correlated Effects Estimation of Dynamic Panels with Cross-Sectional Dependence
We derive inconsistency expressions for dynamic panel data estimators under error cross-sectional dependence generated by an unobserved common factor in both the fixed effect and the incidental trends case. We show that for a temporally dependent factor, the standard within groups (WG) estimator is inconsistent even as both N and T tend to infinity. Next we investigate the properties of the common correlated effects pooled (CCEP) estimator of Pesaran (2006) which eliminates the error cross-sectional dependence using cross-sectional averages of the data. In contrast to the static case, the CCEP estimator is only consistent when next to N also T tends to infinity. It is shown that for the most relevant parameter settings, the inconsistency of the CCEP estimator is larger than that of the infeasible WG estimator, which includes the common factors as regressors. Restricting the CCEP estimator results in a somewhat smaller inconsistency. The small sample properties of the various estimators are analysed using Monte Carlo experiments. The simulation results suggest that the CCEP estimator can be used to estimate dynamic panel data models provided T is not too small. The size of N is of less importance.
Bias-Corrected Estimation in Dynamic Panel Data Models
This study develops a new bias-corrected estimator for the fixed-effects dynamic panel data model and derives its limiting distribution for finite number of time periods, T, and large number of cross-section units, N. The bias-corrected estimator is derived as a bias correction of the least squares dummy variable (within) estimator. It does not share some of the drawbacks of recently developed instrumental variables and generalized method-of-moments estimators and is relatively easy to compute. Monte Carlo experiments provide evidence that the bias-corrected estimator performs well even in small samples. The proposed technique is applied in an empirical analysis of unemployment dynamics at the U.S. state level for the 1991–2000 period.
Estimation and inference in large heterogeneous panels with a multifactor error structure
Pesaran (2006), the article where the CCE methodology was originally proposed
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