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From |
Misha Spisok <misha.spisok@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: How to implement Wald estimator (for IV that is a ratio of coefficients)? |

Date |
Fri, 9 Oct 2009 18:21:39 -0700 |

Hello, Statalist! In short, does -ivregress- (or -reg3-) include what I think is called the Wald estimator? If so, how can I implement it for a problem like the one below? I've searched for a command for the Wald estimator, but can only find references to Wald _tests_. I am considering a model similar to Ashenfelter and Greenstone (2004) with two reduced-form equations, the estimates of which are used to find an instrumental variable estimator in a third equation, the one of primary interest. My question is, how can I do this in Stata in one fell swoop? The two equations are F = lambda_F*VMT + PI_F*1(65mph limit in force) + epsilon H = lambda_H*VMT + PI_H*1(65mph limit in force) + epsilon' where 1(.) is an indicator variable which I'll call "65mph" below. The equation of interest is H = beta*VMT + theta*F + nu The parameter of interest is theta. From the estimate of the reduced form equations the IV for theta, theta_IV, is theta_IV = (PI_H)/(PI_F) Given estimates of PI_H and PI_F (as presented in the paper), one can form the corresponding theta_IV. It seems that the authors use a formula for the standard error of theta_IV like the following: se_theta = theta_IV*sqrt((se_PI_H/PI_H)^2 + (se_PI_F/PI_F)^2) I tried doing this in the following ways, but the results are not the same. I wouldn't expect them to be, but I can't find a reference for Wald estimator in Stata, so I thought I'd try it. Method 1: . reg F VMT 65mph . reg H VMT 65mph Calculate theta_IV from coefficients on 65mph in the above equations. Method 2: . ivregress 2sls H VMT (F 65mph) Hope that theta_IV would be the coefficient on F. Method 3: . reg3 (F VMT 65mph) (H VMT F) Hope that theta_IV would be the coefficient on F in the equation for H. What is the correct way to get this ratio of coefficients (theta_IV = (PI_H)/(PI_F)) and its standard error all at once in Stata? Thanks, Misha * * 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/

**Follow-Ups**:**Re: st: How to implement Wald estimator (for IV that is a ratio of coefficients)?***From:*Stas Kolenikov <skolenik@gmail.com>

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