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re:Re: Re: Re: RE: re:Re: st: Multiple endogenous regressors

 From Christopher Baum To "statalist@hsphsun2.harvard.edu" Subject re:Re: Re: Re: RE: re:Re: st: Multiple endogenous regressors Date Sat, 22 Oct 2011 13:28:55 -0400

```<>
Yuval said
> I would like to assure you that I would not write about this matter if
> I was not certain about my knowledge in this area.
>
> I believe you are confusing between 2SLS and IV estimators, which are
> not exactly the same:
>
> When you are talking about 2SLS you need literally to replace
> projected values from the solution equation - but here the second
> equation is simply an identity, so you cannot produce here projected
> values. I suppose what STATA did here is to use investment as
> instrumental variable to consumption in the right-hand-side of the
> consumption function. This is not 2SLS even if the command is 2SLS and
> even if the output tells otherwise!!!

The statement of the first paragraph is clearly contradicted by what follows. As clearly exposited in Baum, Schaffer, Stillman, Stata Journal (2003)--which I recommend to Yuval, as he might learn something if he read it-- 2SLS is an IV estimator where you construct one instrument for each variable in the X matrix, so that X and Z have the same number of columns. In the exact-ID case I illustrated via the Klein model, X and Z already have the same number of columns, and the 2SLS estimate is the same as one would compute via indirect least squares.

But estimation of that exactly ID model gives you exactly the same 2SLS point estimates (albeit with the wrong standard errors, as any textbook will warn you) as does running a first-stage regression and taking its predicted values and plugging them in to the second stage:

. ivregress 2sls consump (totinc = invest), first

First-stage regressions
-----------------------

Number of obs   =         22
F(   1,     20) =      12.04
Prob > F        =     0.0024
R-squared       =     0.3757
Adj R-squared   =     0.3445
Root MSE        =     8.7873

------------------------------------------------------------------------------
totinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
invest |   1.911859   .5510524     3.47   0.002     .7623838    3.061334
_cons |   56.82193   2.012079    28.24   0.000     52.62481    61.01906
------------------------------------------------------------------------------

Instrumental variables (2SLS) regression               Number of obs =      22
Wald chi2(1)  =   24.24
Prob > chi2   =  0.0000
R-squared     =  0.8430
Root MSE      =  2.8442

------------------------------------------------------------------------------
consump |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
totinc |   .4593425   .0932901     4.92   0.000     .2764971    .6421878
_cons |   26.07967   5.571562     4.68   0.000     15.15961    36.99973
------------------------------------------------------------------------------
Instrumented:  totinc
Instruments:   invest

. reg totinc invest

Source |       SS       df       MS              Number of obs =      22
-------------+------------------------------           F(  1,    20) =   12.04
Model |  929.473729     1  929.473729           Prob > F      =  0.0024
Residual |  1544.33406    20  77.2167032           R-squared     =  0.3757
-------------+------------------------------           Adj R-squared =  0.3445
Total |  2473.80779    21  117.800371           Root MSE      =  8.7873

------------------------------------------------------------------------------
totinc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
invest |   1.911859   .5510524     3.47   0.002     .7623838    3.061334
_cons |   56.82193   2.012079    28.24   0.000     52.62481    61.01906
------------------------------------------------------------------------------

. predict double inchat , xb

. reg consump inchat

Source |       SS       df       MS              Number of obs =      22
-------------+------------------------------           F(  1,    20) =    4.18
Model |  196.114769     1  196.114769           Prob > F      =  0.0542
Residual |  937.660109    20  46.8830054           R-squared     =  0.1730
-------------+------------------------------           Adj R-squared =  0.1316
Total |  1133.77488    21  53.9892799           Root MSE      =  6.8471

------------------------------------------------------------------------------
consump |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
inchat |   .4593425   .2245894     2.05   0.054    -.0091427    .9278276
_cons |   26.07967   13.41314     1.94   0.066     -1.89964    54.05899
------------------------------------------------------------------------------

Thus showing the fallacy of Yuval's statements above.

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming  |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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```