0
$\begingroup$

I'm working on a project on time series regression. The independent variable was non stationary so I took first differences to stationarize it. Now when I regress it against the dependent variable the coefficient is significant. How does one interpret a series regressed against another which has been differenced? So for instance I have

$$ Income_t= c + 0.10 \Delta GDP_t+\varepsilon_t. $$

Improve this question
$\endgroup$
2
  • $\begingroup$ I edited your equation to include the time subscript for $\Delta GDP$ and the error term. I hope it is correct, or should the time subscript be $_{t-1}$? $\endgroup$
    – Richard Hardy
    Commented Feb 5, 2016 at 19:48
  • $\begingroup$ Yes , this is correct. Thank you very much for your assistance. $\endgroup$
    – Aboubacar Coulibaly
    Commented Feb 5, 2016 at 19:51

1 Answer 1

Reset to default
1
$\begingroup$

If you assume that the independent variable is exogenous (i.e. the dependent variable is not affecting the independent variable), then

$$ y_t=\beta_0+\beta_1 \Delta x_t+\varepsilon_t $$

implies that when $\Delta x_t$ increases (decreases) by one unit (that is, $x_t$ accelerates by one unit), $y_t$ tends to increase (decrease) by $\beta_1$ units on average.

In your case that would mean that for every unit increase (decrease) in $\Delta GDP_t$, $Income_t$ increases (decreases) by $0.10$ on average. In other words, a one unit acceleration of GDP brings an increase in the level of income of $0.10$ units on average.

For the model to work you should ensure at least a couple of things. First, the dependent variable should be stationary (or should be made stationary by a transformation); otherwise you will get an unbalanced regression. Second, if $GDP_t$ is endogenous to $Income_t$, this violates the exogeneity assumption and makes the OLS estimator of the regression coefficient inconsistent. If this is the case, you should look for alternative model specifications.

Improve this answer
$\endgroup$
3
  • $\begingroup$ Thank you very much for your help. The dependent variable was stationary, the exogeneity issue is an important point issue that I didn't consider before. Thanks again. $\endgroup$
    – Aboubacar Coulibaly
    Commented Feb 5, 2016 at 20:17
  • $\begingroup$ Your answer was extremely helpful. This is my first time on the forum, forgive my lack of familiarity with the process. I think I got it now. Thank you once again. I had been googling this for hours with no luck. $\endgroup$
    – Aboubacar Coulibaly
    Commented Feb 5, 2016 at 20:54
  • $\begingroup$ No problem, I am glad I could help. $\endgroup$
    – Richard Hardy
    Commented Feb 5, 2016 at 21:06

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.