I am trying to estimate a multivariate linear regression model in the form of:

$Y(t) = c + b_1*X_1(t) + b_2*X_2(t) + b_3*X_3(t) + b_4*X_4(t)$

All my variables (both Xs and Y) are Year on Year changes of economic data measured Quarterly (Frequency = Quarterly).

When I run the regressions, my model suffers from Autocorrelation. This is logical if we think that between 2 consecutive quarters of yearly changes there is an overlap of 3 quarters.

Now, my question is. Would it be acceptable to introduce a lagged version of the dependent variable in my regression? i.e. estimate a model in the form of:

$Y(t) = c + k*Y(t-1) + b_1*X_1(t) + b_2*X_2(t) + b_3*X_3(t) + b_4*X_4(t)$

When I do that, there is not an Autocorrelation problem anymore. I would like though to make sure that this does not create any other problem that I can't imagine.

Thanks a lot in advance.


That is strange, but not impossible. Maybe tell us how you tested for serial correlation (SC)?

Anyway, I would worry less about SC and more about stationarity of the data. You can always use either FGLS, or robuts standard errors for inference - and these are easy to compute. But if you do not have stationairty, you get inconsistent estimates (unless you make the very strong Gauss Markov or the classical linear model assumptions). And this is by far, a much bigger problem.

  • $\begingroup$ I tested for autocorrelation using the Durbin-Watson test. I am more interested to understand conceptually if adding the lagged version of Y in my independent variables would create an issue for my model. $\endgroup$ – stratar Jul 10 '15 at 13:35
  • $\begingroup$ It will usually induce serial correlation... The problem with DW, is that it requires the classical linear model assumptions, including normality of the error term. This rarely applies to anything in economics, and therefore you cannot trust the test (unless you assume normality). Also it only test for first order serial correlation - what is to say that you do not have 2nd or 3rd order correlation, DW will not tell you this. Can you provide us with the estimate on $y_{t-1}$? $\endgroup$ – Repmat Jul 10 '15 at 13:48
  • $\begingroup$ Thank you very much for your reply Repmat. If my original model has an autocorrelation problem (first order) then, shouldn't adding the 1st order lag resolve it i.e. I will be now capturing first order effect and my errors shouldn't have this problem anymore.? What do you mean estimate of Y(t-1) , its coefficient? It is positive ~0.87. $\endgroup$ – stratar Jul 10 '15 at 14:06
  • $\begingroup$ Only if $E(u_t|y_{t-1}, X)=0$, which may or may not be true - it is only an assumption. You can get consistent estimates regardless of serial correlation, which is the important stuff. Again I would never trust the results from a DW test. $\endgroup$ – Repmat Jul 10 '15 at 14:15
  • $\begingroup$ Yes, that is true, my residuals have $E(u_t|y_{t-1}, X)=0$. I can get consistent estimates but when I also add the $y_{t-1}$ in my independent variables the fit improves massively as well. This is why I am asking if adding it can cause any other issues that I am missing. $\endgroup$ – stratar Jul 10 '15 at 14:19

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