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Is a statistically correct to find the parameters of the model $$ Y_t = \beta_1 Y_{t-1} + \beta_2 X + \epsilon $$ by just using OLS? For example, there won't be any problems with bias of the coefficients?

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marked as duplicate by Tim Nov 10 '17 at 13:42

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    $\begingroup$ There will be bias, but that is hard to avoid in autoregressive models. Even if you manage to avoid the bias, you would be inflating the variance of the estimator because of that. $\endgroup$ – Richard Hardy Aug 22 '17 at 12:36
  • $\begingroup$ Okey, but there will be any other disadvantages of using OLS? $\endgroup$ – Neokokaina Aug 23 '17 at 5:25
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    $\begingroup$ Not that I would be aware of. If the error term happens to be highly nonnormal, then using maximum likelihood estimation would allow for a noticeable increase in estimation precision. Otherwise OLS is fine, and it is faster to compute. $\endgroup$ – Richard Hardy Aug 23 '17 at 5:35
  • $\begingroup$ In addition to Richard Hardy's comments, which may be the most relevant in practice, there are some issues regarding inference (the distribution of the t-statistics is unknown and inference is not valid in small samples). You may be interested in this post. $\endgroup$ – javlacalle Aug 23 '17 at 13:27