AR(1) model

[Nouschka Snijders]

Dear all,

I am running a normal LS linear regression, with 1 dependent variable and 5 independent variables:
reg y x1 x2 x3 x4 x5

When I am estimating the residuals of this regression and testing them for autocorrelation, it seems to be a AR(1) model. That is, I have only autocorrelation for time lag 1 (derived from an autocorrelation plot).

I have read that I can "ignore" this autocorrelation (because only when I have no autocorrelation, the estimators are unbiased) as long as the independent variables are strictly exogenous. That is, the independent variables are uncorrelated with the error term.

Now, I would like to test if the coefficients remain unbiased. I thought I could do this by running the same regression with a time lag, because I thought the autocorrelation will disappear when I do so. So I have run:
reg y L.x1 L.x2 L.x3 L.x4 L.x5

But the autocorrelation remains for time lag 1 (when I plot an autocorrelation plot). So I am doing something wrong. Please can somebody help me?

Best regards

[Phil Bromiley]

I don't know about your specific question, but you can always use regar to estimate a model with serially correlated errors. I think you can also use robust errors - you'll need to check that they are robust to serial correlation in reg.