The Stata Journal ( Robust Standard Errors for Panel ...

1 The Stata Journal (yyyy)vv,Numberii, pp. 1 31 Robust Standard Errors for Panel Regressionswith cross - sectional DependenceDaniel HoechleUniversity of this paper I present a new Stata program,xtscc, which estimatespooled OLS/WLS and fixed effects (within) regression models with Driscoll andKraay (Review of Economics and Statistics80: 549-560) Standard Errors . By run-ning Monte Carlo simulations, I compare the finite sample properties of the cross - sectional dependence consistent Driscoll-Kraay estimator with the properties ofother, more commonly employed covariance matrix estimators that do not accountfor cross - sectional dependence .

2 The results indicate that Driscoll-Kraay standarderrors are well calibrated when cross - sectional dependence is present. However,erroneously ignoring cross - sectional correlation in the estimation of Panel modelscan lead to severely biased statistical results. I illustrate the use of thextsccprogram by considering an application from empirical finance. Thereby, I alsopropose a Hausman-type test for fixed-effects that is Robust to very general formsof cross - sectional and temporal :First Draft, Robust Standard Errors , nonparametric covariance estima-tion1 IntroductionIn social sciences and particularly in economics it has become common to analyze large-scale microeconometric Panel datasets.

3 Compared to purely cross - sectional data, panelsare attractive since they often contain far more information than single cross -sectionsand thus allow for an increased precision in estimation. Unfortunately, however, actualinformation of microeconometric panels is often overstated since microeconometric datais likely to exhibit all sorts of cross - sectional and temporal dependencies. In the wordsof Cameron and Trivedi (2005, p. 702) NT correlated observations have less infor-mation than NT independent observations.

4 Therefore, erroneously ignoring possiblecorrelation of regression disturbances overtime and between subjects can lead to biasedstatistical inference. To ensure validity of the statistical results, most recent studieswhich include a regression on Panel data therefore adjust the Standard Errors of thecoefficient estimates for possible dependence in the residuals. However, according toPetersen (2007) a substantial fraction of recently published articles in leading financejournals still fails to adjust the Standard Errors appropriately.

5 Furthermore, while mostempirical studies now provide Standard error estimates that are heteroscedasticity andautocorrelation consistent, cross - sectional or spatial dependence is still largely , assuming that the disturbances of a Panel model are cross -sectionally in-dependent is often inappropriate. While it might be difficult to convincingly argue whyc yyyyStataCorp LPFirst Draft2xtscccountry or state level data should be spatially uncorrelated, numerous studies on sociallearning, herd behavior, and neighborhood effects clearly indicatethat microeconomet-ric Panel datasets are likely to exhibit complex patterns of mutual dependence betweenthe cross - sectional units ( individuals or firms).

6 1 Furthermore, because social normsand psychological behavior patterns typically enter Panel regressions as unobservablecommon factors, complex forms of spatialand temporal dependence may even arisewhen the cross - sectional units have been randomly and independently that the unobservable common factors are uncorrelated with the explana-tory variables, the coefficient estimates from Standard Panel estimators2are still con-sistent (but inefficient). However, Standard error estimates of commonly applied co-variance matrix estimation techniques3are biased and hence statistical inference thatis based on such Standard Errors is invalid.

7 Fortunately, Driscoll and Kraay (1998) pro-pose a nonparametric covariance matrix estimator which produces heteroscedasticityconsistent Standard Errors that are Robust to very general forms of spatial and has a long tradition of providing the option to estimate Standard Errors thatare Robust to certain violations of the underlying econometric model. It is the aim ofthis paper to contribute to this tradition by providing a Stata implementation of Driscolland Kraay s (1998) covariance matrix estimator for use with pooled OLS estimation andfixed effects regression .

8 In contrast to Driscoll and Kraay s original contribution whichonly considers balanced panels, I adjust their estimator for use with unbalanced panelsand use Monte Carlo simulations to investigate the adjusted estimator s finite sampleperformance in case of medium- and large-scale (microeconometric) panels. Consistentwith Driscoll and Kraay s original finding for small balanced panels, the Monte Carloexperiments reveal that erroneously ignoring spatial correlation in Panel regressions typ-ically leads to overly optimistic (anti-conservative) Standard error estimates irrespectiveof whether a Panel is balanced or not.

9 Although Driscoll and Kraay Standard errorstend also to be slightly optimistic, their small sample properties are significantly betterthan those of the alternative covariance estimators when cross - sectional dependence rest of the paper is organized as follows. In the next section, I motivate whyDriscoll and Kraay s covariance matrix estimator serves as a valuable supplement toStata s existing capabilities. Section 3 describes thextsccprogram which producesDriscoll and Kraay Standard Errors for coefficients estimated by pooled OLS/WLS andfixed effects (within) regression .

10 Section 4 provides the formulas as they are implementedin thextsccprogram. In Section 5, I present the set-up and the results of Monte Carloexperiments which compare the finite sample properties of the Driscoll-Kraay estimatorwith those of other, more commonly employed covariance matrix estimation techniqueswhen the cross - sectional units are spatially dependent. Section 6 considers an empiricalexample from financial economics and demonstrates how thextsccprogram can be used1. see Trueman (1994), Welch (2000), Feng and Seasholes (2004), and the survey article byHirshleifer and Teoh (2003).