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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2$\begingroup$ 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 HardyCommented Aug 22, 2017 at 12:36
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$\begingroup$ Okey, but there will be any other disadvantages of using OLS? $\endgroup$– NeokokainaCommented Aug 23, 2017 at 5:25
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1$\begingroup$ 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 HardyCommented Aug 23, 2017 at 5:35
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$\begingroup$ 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. $\endgroup$– javlacalleCommented Aug 23, 2017 at 13:27
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