How do I test for panel-level heteroskedasticity and autocorrelation?
Testing for panel-level heteroskedasticity and autocorrelation
Vince Wiggins, StataCorp
Brian Poi, StataCorp
June 2001; revised December 2003
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 ... , igls panels(heteroskedastic)
. estimates store hetero
to fit the model with panel-level heteroskedasticity and save the
We can fit the model without heteroskedasticity by typing
. xtgls ...
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')
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 user-written program, called xtserial, written by David
Drukker to perform this test in Stata. To install this user-written
. 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
. xtserial depvar indepvars
A significant test statistic indicates the presence of serial correlation.
- Drukker, D. M. 2003.
- Testing for serial correlation in linear
Wooldridge, J. M. 2002.
Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.