## Tuesday, September 17, 2013

### Another Regression Trick

Here's an exercise that I've set for one of my econometrics classes this week.

A researcher wishes to estimate the regression of y on X by OLS, but does not wish to include an intercept term in the model. Unfortunately, the only econometrics package available is one that "automatically" includes the intercept term. A colleague suggests that the following approach may be used to ‘trick’ the computer package into giving the desired result – namely a regression fitted through the origin:
Enter each data point twice, once with the desired signs for the data, and then with the opposite signs. That is, the sample would involve ‘2n’ observations – the first ‘n’ of them would be of the form (yi, xi') and the next ‘n’ of them would be of the form (-yi , -xi'). Then fit the model (with the intercept) using all ‘2n’ observations, and the estimated slope coefficients will be the same as if the model had been fitted with just the first ‘n’ observations but no intercept.”
Is your colleague's suggestion going to work?

I'll provide the answer after my students have completed their assignment.

© 2013, David E. Giles

#### 10 comments:

1. The applied folks would just add a billion points at the origin.

1. Hah!!!! Creative, but unacceptable. :-)

2. N goes to infinity faster down in the econometrics basement.

3. here's my take: solution will work for obtaining the no-intercept estimates but will over-estimate t-statistics because of artificial reduction in variation. a better solution would be to de-mean x and y. then there won't be an intercept in the answer.
interesting question. I'm curious to see the answer.

4. Hi Dave Giles,
nice post.

5. There are other comments that I'm "holding" until my students have finished their assignment. I'm not ignoring ya'll!

6. A smart person would start by noting that if the average value of the sample is 0 (by construction) then... A normal person like me instead would start with some algebra and then work out the intuition.

7. This comment has been removed by a blog administrator.

1. You don't need to do a partitioned regression. Just to use some properties of the OLS estimators.

8. The solution is now posted at:
http://davegiles.blogspot.ca/2013/09/solution-to-regression-trick.html