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From |
"Brian P. Poi (StataCorp)" <bpoi@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Doubt about Stata quantile regression code re: endogeneity |

Date |
Fri, 26 Sep 2003 20:55:37 -0500 (CDT) |

On Fri, 26 Sep 2003, Chih-Mao Hsieh wrote: > Dear Statalisters, > > Myself and a co-author are stuck on how to do the programming mentioned > by the Stata econometrician below... I thought this Statalist might > help. Can anybody provide some insight (or better yet, a few lines of > code as a potential guide!) on the dilemma outlined below between *****? > > > Chihmao. > > Dear Sergio, > > ***** The easiest way to get standard errors for the 2SLAD model is to > use the bootstrap. Note that you will want to bootstrap both > stages of estimation, not just the second stage. Therefore, when > you use -bootstrap- or -bstrap-, you will need to write a program > that estimates your entire model. > A seminal paper in this area is Amemiya (1982, Econometrica). There, > among other things he shows that even though you use quantile regress- > ion in the second stage, you should still use OLS in the first stage; > this is what he calls the 2SLAD model. He also derives the asymptotic > standard errors for this model, though my guess is that using the > bootstrap is easier. ***** > Chihmao and Sergio are referring to a method to estimate a quantile regression that contains an endogenous variable. For concreteness, suppose we wish to estimate the following model using least absolute deviations: (1) mpg = a + b*foreign + c*price + error We suspect that "price" may be correlated with the error term, and so we need to use an instrumental variables estimator. We have two variables, "weight" and "length", that are correlated with "price" but not the error term. A simple two-stage estimator proceeds as follows: 1. Regress "price" on "weight", "length", and "foreign" using OLS and calculate the fitted values; call them "phat" 2. Estimate equation (1) with "phat" in place of "price" using quantile regression (-qreg-) As is usually the case, the standard errors from the second-stage regression are incorrect because they ignore the fact that "phat" is itself estimated. Chihmao would like to know how to use the bootstrap to obtain standard errors. The following code does just that: sysuse auto, clear program bootit version 8.0 // Stage 1 regress price foreign weight length predict double phat, xb // Stage 2 qreg mpg foreign phat end bootstrap "bootit" _b, reps(1000) dots Whenever one bootstraps an estimator that uses iteration to find the optimal parameters (as -qreg- does), there is a chance that for some bootstrap samples the algorithm does not converge. If Chihmao runs into that problem with his model, I'll be happy to help him out if he sends his dataset and dofile to stata@stata.com or to me privately. -- Brian bpoi@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Doubt about Stata quantile regression code re: endogeneity***From:*"Chih-Mao Hsieh" <Hsieh@olin.wustl.edu>

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