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5.Alternative model to xtpcse with heteroscedastic, contemporaneously

correlated cross-sectionally correlated, and autocorrelated of type AR(1) (N -  number of units – states in this example, T – time - for feasibility – this model tends to produce optimistic estimates of standard errors – also, may not work with unbalanced panels – e.g., different years available for different states - xtpcse appears “safer”]

xtgls top1 demcont repcont top1lag, panels(heteroscedastic)  corr(ar1)

-you could also have put  , panels(hetero) corr(ar1) or corr(psar1)

6. If you have moving average autocorrelation:

newey top1 demcont repcont top1lag  q1cus, lag(1)  [might only work if

panels are balanced – e.g., same years available for all states]

7.If you have moving average autocorrelation and cross-sectional dependence:

xtscc top1 demcont repcont top1lag  q1cus, lag(1)

8. Bootstrap standard errors:

xtreg top1 demcont repcont top1lag, fe vce(boot)

The examples ahead use “long panels” (i.e., where the number of years is much greater than the number of states).

Fixed effects, autocorrelation but no heteroscedasticity:

xtgls top1  demcont repcont top1lag al-wi,   corr(ar1)

Fixed effects, autocorrelation and heteroscedasticity:

xtgls top1  demcont repcont top1lag al-wi,   panels(heteroskedastic)  corr(ar1)

If you want flexible autocorrelation across states and a distinct ar(1) process for the error in each state replace corr(ar1) with  corr(psar1) I believe the “p” is panel specific.  It the number of time periods is not much larger than the number of states use the more restrictive corr(ar1) option.

If you want random effects omit the dummy variables (al-wi) in the above command lines. Much of the above discussion was taken from Microeconometrics Using Stata, revised edition, by A. Colin Cameron and Pravin K. Trivedi, Stata Press, 2010 and “Panel Data Analysis Fixed and Random Effects (using Stata 10)” by Oscar Torres-Reyna (available at www.princeton.edu/~otorres).

Stationarity in Panel Models/Error Correction Models: You need the “xtfisher” command which can be downloaded (findit xtfisher).  This is a test to see if a

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