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If the number to the right of “Prob > F is .05 or lower reject the null hypothesis of no first-order autocorrelation in favor of the alternative hypothesis the residuals show first-order autocorrelation.

If you do have first-order autocorrelation try:  

xtpcse top1 demcont repcont top1lag, corr(ar1)

xtpcse top1 demcont repcont top1lag, pairwise corr(ar1)

Pairwise includes all available observations with                           nonmissing pairs.  The alternative appears to be casewise (I’m assuming that’s what you get with “corr(ar1)”  Pairwise corr(ar1) seems to make little difference vs. corr(ar1)  If you can reasonably assume that all units (i.e., states in this case) have the same first order autocorrelation (i.e., constant autocorrelation across panels, i.e., states) then add a comma and correlation (ar1) after the last independent variable.  In something I read Beck and Katz argue in favor of this autocorrelation structure and against panel specific autocorrelation (i.e., where each unit, state in this case, could have a different value for rho).  For a panel specific (not the same for each unit – e.g., state) adjustment for first-order autocorrelation is:

xtpcse top1 demcont repcont top1lag, corr(psar1)

xtpcse top1 demcont repcont top1lag, correlation (ar1) rhotype (tscorr)

Note: may also incorporate state dummy variables

xtpcse top1 demcont repcont top1lag al-wi   (or do this by using the “i”

variable – thus, xtpcse top1 demcont repcont top1lag i.stnum  (where stnum is the state number)

. You can also estimate a heteroscedastic panel corrected standard errors model by putting “het” after the comma:

xtpcse top1 demcont repcont top1lag, het

You can estimate a heteroscedasitic first-order autocorrelation panel corrected standard errors model:

xtpcse top1 demcont repcont top1lag, het corr(ar1)

You may receive the following error message: no time periods are common to all panels, cannot estimate disturbance covariance matrix using casewise inclusion.  Sometimes adding an independent variable will overcome this problem.

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