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You are getting different estimates because your arima command specifies an ARMAX model, that is, a model with ARMA(1,0) errors and an additional 
regressor X. If you did not have the original regressor, then you could write the model either as an AR(1) model in y (with a lagged depvar) or 
as a regression of y on x with AR(1) errors. But the arima that will reproduce your regress results, perfectly, is

arima y x L.y

which will give you large-sample standard errors rather than the finite-sample VCE from OLS.


Kit Baum   |   Boston College Economics & DIW Berlin   |
                             An Introduction to Stata Programming  |
  An Introduction to Modern Econometrics Using Stata  |

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