Hi all,

I have a (very) large N and small T panel. For convoluted reasons, I would like to quantify the extent of serial correlation you see in outcome variable Y, separately for two groups, call them treated and untreated. My panel is short: 7 time periods for each n.

First prize would be to actually estimate a serial correlation parameter for each n, based on its particular time series, and then look at the distribution of these parameters separately for the treated and untreated groups. Second prize would be a summary statistic of serial correlation by group.

I've tried simulating an AR(1) time series for each n, and then estimating the autoregressive parameter via OLS or Stata's ARIMA command separately for each n. These parameter estimates are typically much too low relative to the parameters I've simulated: perhaps it's an issue of OLS being biased in this setting, and consistency doesn't help much with such a short T?

While I have some background in panel econometrics, I have very limited background in time series methods. Any assistance would be gratefully received. Is my time series just too short for this exercise?

Thanks.

EDIT: to clarify, I'm not interested in *testing* for serial correlation. I want to look at the difference in magnitude of serial correlation between the two groups.