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From |
Christopher Baum <kit.baum@bc.edu> |

To |
"statalist@hsphsun2.harvard.edu" <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 * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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