st: Testing for the Type of Error Correlation Structure in PA Model

[Ryan McCann <rmccann@keybridgeresearch.com>]

Dear Statalist Community Members,

I?m working with a small business firm survey (a 4 year panel of about 5000
small business start-ups which includes financial, geographic, and owner
data).  I am trying to assess the impact of credit card use on revenues. 
Where credit card use is defined as the average monthly balance of the
businesses? credit cards (i.e. we are trying to look at the impact of credit
cards as an alternative to traditional financing for small businesses). The
regression at present looks like this:

xtreg lnRevenue  lnCreditCard lnAssests AssetTurnover NetMargin
HumanCapitalVars StateLocationDummies [pweight=final longitudinal weight],
pa corr(exchangeable)

The random effects model would seem more appropriate than fixed effects
because most of the variation in the sample is between as opposed to within
 (the panel is not that wide to begin with (average time series for an
individual is only 2.5 periods).  STATA does not allow for the use of
weights with RE so we are using a Pooled Average regression.  At this point
I?m trying to determine the type of autocorrelation that is present.  The
?pa? regression in STATA allows for Independent, Exchangeable, Unstructured,
and AR error correlations over time.  I?ve run regressions by year and
predicted the error terms for each time period.  I then regressed these
errors on their lags and (t-2) lags and have come out with fairly consistent
coefficients on the lag term (around .57, a couple of the coeffecients came
out to be around .3) (I used this method in the absence of knowing any
Durbin-Watson type test that allows for weights).  The error correlations I
get by using the exchangeable option come out around .59.  It appears that
the independent option (i.e. no autocorrelation) is not appropriate, but I?m
wondering how I choose between Exchangeable and Unstructured (not sure if AR
process is present).

Any suggestions are greatly appreciated.

Best Regards,
Ryan


Ryan McCann
Senior Analyst
Keybridge Research LLC
Office: 202.965.9487 | Mobile: 774.521.8874





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