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Note: The vce(robust) option should be used with caution.  It is robust in the sense that, unlike default standard errors, no assumption is made about the functional form (A. Colin Cameron and Pravin K. Trivedi, Microeconometrics Using Stata, revised ed., p. 334).  From their discussion, this can lead to problems.  This is a reason for the cluster option discussed ahead.

2.The model with first-order autocorrelation:

xtregar top1 demcont repcont top1lag, fe

3.The model with both first-order autocorrelation and heteroscedasticity:

xtreg top1 demcont repcont top1lag, fe vce(cluster id)

If you have reason to below the disturbances are related to one of the variables use that variable after “cluster.”  For example, there may be correlation within states but not across states.  Thus, observations in different clusters (e.g., states) are independent but observations within the same cluster (e.g., states) are not independent.

xtreg top1 demcont repcont top1lag, fe vce(cluster stnum)

Note: if you replace “stnum” with “id” (cluster id) you get very different standard errors.  The “id” is suppose to represent an individual whereas  i.i.d. means(independent and identically distributed.  I would’ve thought it would be an individual state and, thus, would be the same as (cluster stnum) but this is not the case.  

4.The model with heteroscedastic, contemporaneously correlated cross-

sectionally correlated, and autocorrelated of type AR(1) [Beck & Katz’s panel corrected standard errors]. Assumptions: (1) if I assume no heteroscedasticity - panels(uncorrelated); (2)  if I assume the variances differ for each unit – panels(hetero); (3) if I assume that the error terms of panels are correlated – panels(correlated)]; (4) if I assume no autocorrelation – corr(independent); (5) if I assume each panel has first-order serial correlation and the correlation parameter is the same for all groups – corr(ar1); (6) if I assume first-order serial correlation where the correlation parameter is unique for each panel – corr(psar1).

xtpcse top1 demcont repcont top1lag

Note: You can run the xtserial test immediately after running the xtpcse model above to see if you should make an adjustment for first-order autocorrelation.  

xtserial top1 demcont repcont top1lag

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