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## How do I test for panel-level heteroskedasticity and autocorrelation?

 Title Testing for panel-level heteroskedasticity and autocorrelation Author Vince Wiggins, StataCorp Brian Poi, StataCorp

### Question:

I see how one can correct for potential heteroskedasticity across panels using xtgls, but I am unsure of a simple way to test for it.

Since iterated GLS with only heteroskedasticity produces maximum-likelihood parameter estimates, we can easily do an LR test.

We can type

. xtgls depvar indepvars, igls panels(heteroskedastic) . estimates store hetero

to fit the model with panel-level heteroskedasticity and save the likelihood.

We can fit the model without heteroskedasticity by typing

. xtgls depvar indepvars, igls

Now there is one trick. Normally, lrtest infers the number of constraints when we fit nested models by looking at the number of parameters estimated. For xtgls, however, the panel-level variances are estimated as nuisance parameters, and their count is NOT included in the parameters estimated. So, we will need to tell lrtest how many constraints we have implied.

The number of panels/groups is stored in e(N_g) and, in the second model, we are constraining all of these to be single value, so our number of constraints can be computed and stored in a local macro by typing

. local df = e(N_g) - 1

The test is then obtained by typing

. lrtest hetero . , df(`df')

### Autocorrelation

Iterated GLS with autocorrelation does not produce the maximum likehood estimates, so we cannot use the likelihood-ratio test procedure, as with heteroskedasticity. However, Wooldridge (2002, 282–283) derives a simple test for autocorrelation in panel-data models. Drukker (2003) provides simulation results showing that the test has good size and power properties in reasonably sized samples.

There is a community-contributed program, called xtserial, written by David Drukker to perform this test in Stata. To install this community-contributed program, type

. findit xtserial . net sj 3-2 st0039 (or click on st0039) . net install st0039 (or click on click here to install)

To use xtserial, you simply specify the dependent and independent variables:

. xtserial depvar indepvars

A significant test statistic indicates the presence of serial correlation.

### References

Drukker, D. M. 2003.
Testing for serial correlation in linear panel-data models. Stata Journal  3: 168–177.
Wooldridge, J. M. 2010.
Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.