Whites standard errors and Arellano

[Prathvajeeth Rajmohan]

Hi there are whites standard errors the ones you get when you implement the -robust- after the regression in stata?

Do these deal with hetroskedascity only or auto-correlation aswell?

also what are Arellano standard errors and how are they different?

if you use the -robust- command in the fixed effects/xtreg regression are they whites or arellano?

+also with regards to clustering vs robust, what exactly does clustering account for the fact that observations over each i might be independant over time.

Thanks

[Philip Gigliotti]

robust is Huber white standard errors. They address only heteroskedasticity. To address autocorrelation you must add the cluster option as well.

[Marcos Almeida]

Several - if not all - of the questions in #1 may be clarified by taking the Stata Manual as the starting point.

Indeed, like a widespread mantra we all hear in this forum, the Stata Manual is truly a hit or miss.

For example, here you get insights on the "robust" vce:

Obtaining robust variance estimates Many Stata estimation commands provide robust and cluster-robust variance estimates. To obtain these estimates, you simply specify option vce(robust) to obtain robust standard errors or vce(cluster clustvar) to obtain cluster-robust standard errors. Below, we provide a general discussion of why you might specify one of these options, how to interpret standard errors with and without vce(robust) specified, and an overview of important concepts relating to cluster-robust standard errors. Estimates of variance refer to estimated standard errors or, more completely, the estimated variance– covariance matrix of the estimators of which the standard errors are a subset, being the square root of the diagonal elements. Call this matrix the variance. All estimation commands produce an estimate of variance and, using that, produce confidence intervals and significance tests. In addition to the conventional estimator of variance, there is another estimator that has been called by various names because it has been derived independently in different ways by different authors. Two popular names associated with the calculation are Huber and White, but it is also known as the sandwich estimator of variance (because of how the calculation formula physically appears) and the robust estimator of variance (because of claims made about it).

You may find information about "robust" vc in several other places, such as here and here.

xtreg, fe xtreg, fe produces estimates by running OLS on (yit − yi + y) = α + (xit − xi + x)β + (it − i + ν) + where yi = PTi t=1 yit/Ti , and similarly, y = P i P t yit/(nTi). The conventional covariance matrix of the estimators is adjusted for the extra n − 1 estimated means, so results are the same as using OLS on (1) to estimate νi directly. Specifying vce(robust) or vce(cluster clustvar) causes the Huber/White/sandwich VCE estimator to be calculated for the coefficients estimated in this regression

xtreg, re The key to the random-effects estimator is the GLS transform. Given estimates of the idiosyncratic component, σb 2 e , and the individual component, σb 2 u , the GLS transform of a variable z for the random-effects model is z ∗ it = zit − θbizi where zi = 1 Ti PTi t zit and θbi = 1 − s σb 2 e Tiσb 2 u + σb 2 e Given an estimate of θbi , one transforms the dependent and independent variables, and then the coefficient estimates and the conventional variance–covariance matrix come from an OLS regression of y ∗ it on x ∗ it and the transformed constant 1−θbi . Specifying vce(robust) or vce(cluster clustvar) causes the Huber/White/sandwich VCE estimator to be calculated for the coefficients estimated in this regression.

Hopefully that helps.

[Prathvajeeth Rajmohan]

robust is Huber white standard errors. They address only heteroskedasticity. To address autocorrelation you must add the cluster option as well.

Thanks is that autocorrelation across time, eg if you had firms in a panel, the obs across time are controlled for is it spatially. Thanks