# Estimation and Finite Sample Bias and MSE of FGLS Estimator of Paired Data Model

• Weiqiang Qian
• Aman Ullah
Chapter

There is a growing interest in treating the cross sectional dependence in panel data models. The need to control the intracluster dependence was demonstrated in Kloek (1981) and Moulton (1990). When the cross sectional dependence is ignored, the estimated standard errors computed without considering clustering can be understated for OLS estimator, as shown in Cameron and Golotvina (2005). Recent work on treating cross-sectional dependence can be found in Pesaran (2006).

In this paper, we consider a paired data model where the dependent variable is measured according to different pairs of cross sectional units. The cross sectional dependence is introduced by each unit’s influence on the paired data. Examples of such paired data can be exchange rates and trade data on countries. Cameron and Golotvina (2005) considered feasible generalized least square estimator (FGLS) for a paired data model. We consider a similar model to theirs and give a tractable FGLS estimator and investigate its finite sample bias and mean square error (MSE). Our estimator uses OLS and fixed effect (FE) residuals to estimate the covariance matrix of composite errors. Under the assumption of normal disturbances, we derive the finite sample bias and MSE of the slope estimator up to orders O(n−2) and O(n−4), respectively. We conducted simulation studies to investigate the influence of number of cross section units on bias and MSE of our FGLS estimator and the influence of changing variances of clustering effects and individual effects. We found that the change in variance of individual effects has a much bigger effect on MSE than that of variance of clustering effect. The finite sample MSE becomes close to asymptotic MSE when n is relatively large and exhibit downward correction from asymptotic MSE for large n and upward correction for small n.

The paper is organized as follows: Section 2 introduces the model; Section 3 develops a FGLS estimator and states the main results of its finite sample bias and MSE under normality; Section 4 provides the derivations of main results; Section 5 reports the simulation results and Section 6 concludes.

## Keywords

Mean Square Error Finite Sample Cross Sectional Dependence Fixed Effect Estimator Feasible Generalize Little Square
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## References

1. Kloek T (1981) OLS Estimation in a Model where a Microvariable is Explained by Aggregates and Contemporaneous Disturbances are Equicorrelated. Econometrica 49:205-207
2. Cameron A, Golotvina N (2005) Estimation of Models for Country-Pair Data controlling for Clustered Errors: with Applications. UC Davis, ManuscriptGoogle Scholar
3. Moulton BR (1986) Random Group Effects and the Precision of Re-gression Estimates. Journal of Econometrics 32:385-97
4. Pesaran H (2006) Estimation And Inference In Large Heterogeneous Panels With A Multifactor Error Structure. Econometrica 74(4):967-1012
5. Ullah A (2004) Finite Sample Econometrics. Oxford University PressGoogle Scholar