st: Wald test of the stability of coefficients across different periods in 3SLS

 From "GROSLAMBERT Bertrand" To Subject st: Wald test of the stability of coefficients across different periods in 3SLS Date Wed, 21 Mar 2007 14:43:07 +0100

```Dear Stata members,

I already posted a question last week about using the commands "suest"
and "test" after "reg3" 3SLS estimation. Right now it has remained
unanswered. The question I ask here is a bit different but also aims at
testing the stability of coefficients across different periods in 3SLS.

I estimate a system of simultaneous equations in 3SLS over three periods

reg3 (y x w) (z x v)

and I want to test if the coefficients are the same across the three
periods. I consider to use two dummy variables for the second and third
periods, interactive with all independant variables.

First of all, when I run in OLS:

reg y x w xD2 xD3 wD2 wD3 D2 D3      and       reg z x v xD2 xD3 vD2 vD3
D2 D3

I can find back the same coefficients as when I run:

reg y x w     and      reg z x v      if D1==1
reg y x w     and      reg z x v      if D2==1
reg y x w     and      reg z x v      if D3==1

Exactly as explained for instance in
http://www.stata.com/support/faqs/stat/chow3.html

In OLS, I can then do some Wald tests to check if the coefficients of
the dummy and interactive dummy variables equal zero and consequently if
the coefficients are stable across the three periods.

However when I run the 3SLS command reg 3:

reg3 (y x xD2 xD3 w wD2 wD3 D2 D3) (z x xD2 xD3 v vD2 vD3 D2 D3)

I cannot find the same coefficients as in:

reg3 (y x w) (z x v) if D1==1
reg3 (y x w) (z x v) if D2==1
reg3 (y x w) (z x v) if D3==1

Coefficients from the pooled regression with dummy slightly differ from
the single-period regressions by 5 to 20% (even much more for the
constant term). Therefore, I wonder if in 3SLS I can test the
coefficient of dummy and interactive dummy variables and conclude about
the stability of the coefficients across the three periods.

Would somebody know why I cannot find back the same coefficients in 3SLS
using reg3? Does it mean that I cannot apply this procedure to test the
stability of coefficients? And is there any alternative method to test
it in 3SLS?

Prof. Bertrand Groslambert
CERAM Sophia Antipolis
www.globalfinance.org
www.ceram.edu
Tel. 33 (0)4 93 95 45 54
Fax. 33 (0)4 93 95 44 29

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```