My objective is to perform a Chow Test with 2 coefficients estimated via IV regressions.
The procedure I am doing is estimating the first stages, and then running the second stage regression with the predicted values of the endogenous. Then I keep the difference of the two coefficients estimated separately (in two separate two stage regressions). I do this in 1000 replications resampling using bootstrap. Then I get the empirical standard error and I use it to perform the difference test.
In principle, I think its ok but I cannot find any reference of this done before. I know I can pool the equations and estimate a "SUR alike" equation via IV, and get directly the correct standard error. However, I want to avoid this procedure given the concern that if the equations are pooled, the instruments will not work as well compared to estimating the equations separately (I am worried about the first stages).
Hello,
Here the issue is more complicated than it seems, since when doing the boostrap you are already altering the usual way of calculating the SD.
So I suggest you check these links if you have not found them before.
http://faculty.washington.edu/ezivot/structuralchangeslides.pdf
If you have no idea where the break points are, you can use some method like in the example of.
http://forums.eviews.com/viewtopic.php?t=8038
I hope it helps you.
A greeting!
BREAK POINT. You need to identify the break point. The repeated measurement taken from the same data set will not work if those 1000 repetitions are re-sampling the same sample. However, if the repeated measures are to trace your data points in segments until you find break points or identifying the break points then the results would be more useful.
It is not known how long is your data string, suppose it has a length of n = 100. If you cut the data at 50 / 50 and work you way on both end -1 + 1, -2 + 2, ... - k, +k, sooner or later you will see the break point. A simple software like excel could do this task.
CHOW TEST. The purpose of the test is to see if the coefficient of two regressions model are significant different. it is used to test whether the introduction of a shock would cause a regime change. It does so by testing the sum squares residuals. It is easier to employ the test if the introduction of the shock is known. Trace that point and see whether there is a break point after that where the sum squares residuals starts to show significant difference. In your case, these are the first stage and stage stage.
LINKS:
Chow, Gregory C. (1960). "Tests of Equality Between Sets of Coefficients in Two Linear Regressions". Econometrica. 28 (3): 591–605. doi:10.2307/1910133. JSTOR 1910133.
https://www.jstor.org/stable/1910133?origin=crossref&seq=1#page_scan_tab_contents
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