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From |
"Schaffer, Mark E" <[email protected]> |

To |
<[email protected]> |

Subject |
RE: st: Endogenous right hand side variable |

Date |
Fri, 18 Jan 2008 15:37:14 -0000 |

Maarten, > -----Original Message----- > From: [email protected] > [mailto:[email protected]] On Behalf Of > Maarten A Allers > Sent: Friday, January 18, 2008 9:21 AM > To: [email protected] > Subject: Re: st: Endogenous right hand side variable > > Dear All, > > The message I just sent (Endogenous right hand side variable) > was cut in two (the second part appearing under the heading > [no subject]). Please forgive me for trying again. > > Reading this thread puzzles me. Rodrigo's suggestion appears > to be different from Mark's, although it seems to be meant as > a clarification. > Rodrigo's solution is described in Wooldridge (2002, p. 574, > http://www.stata.com/bookstore/cspd.html). > I have a slightly different model: > > y1 = a*x1 + b*y3 +e1 > y2 = c*x2 + e2 > y3 = max(0 , y2) > where y2 is potentially endogenous, and only observed when > y2>0. y1, y3, > x1 and x2 are always observed. > > My model differs from Rodrigo's (and Wooldridge's) model > because y1 is always observed, whereas, in Rodrigo's model, > both y1 and y2 are unobserved when y2<0. My model seems more > in line with Kathleen's original question. > > I think I should: > 1) estimate y2 by -tobit- > 2) use fitted values of y2 to generate y3hat=max(0,y2hat) > 3) use y3hat to estimate y1. > > The problem is to obtain correct standard errors. Am I right > to assume Mark's suggestion will help me here? That is, use > y3hat as an instrument in step 3) as in > > ivreg y1 (y3 = y3hat) x1 > > I would very much appreciate your advise, and, if possible, a > reference. You need to argue that the procedure satisfies the requirements for consistency of IV, namely that y3hat is correlated with y3 (easy) y3hat is uncorrelated with e1 (needs a bit of thought) Your y3hat is defined as max(0,y2hat) where y2hat=chat*x2. The slightly tricky bit - but I think you're OK - is that you say y2 is potentially endogenous and observed only if it's strictly positive. Say for some i, e2_i is a big negative shock, so that even though c*x2_i>0, y2_i is < 0. You observe y3_i=0, and if y2 is endogenous because e1 and e2 are correlated (say positively), the fact that y3_i will be at its minimum will be associated with e1_i being also being a big negative shock. But you are using y2hat has your instrument, with an exogenous cut-off of 0. The fact that y3_i is a censored observation (because e2_i is << 0) doesn't make y3hat_i a "predicted censored" observation (because chat*x2_i>0). That is, your censoring for y3hat is driven by x2 and the (presumably consistently estimated) chat, and not by e2_i. Sooo... I think you're OK. Would be very interested to hear what others think about this? BTW [self-advertising warning] you might want to use -ivreg2- instead of -ivreg-. More diagnostics and options. HTH. Cheers, Mark Prof. Mark E. Schaffer Director Centre for Economic Reform and Transformation Department of Economics School of Management & Languages Heriot-Watt University Edinburgh EH14 4AS UK 44-131-451-3494 direct 44-131-451-3296 fax http://www.sml.hw.ac.uk/cert > > Regards - Maarten > > > > RE: st: Re: Endogenous right hand side variable From > "McCullough, Kathleen" <[email protected]> To > <[email protected]> Subject RE: st: Re: > Endogenous right hand side variable Date Tue, 6 Jun 2006 > 19:02:52 -0400 > > Thank you to all who have helped with this. I will try the > suggestion from Mark that relates to the Wooldridge text. > > The censored endogenous variable follows a distribution that > seems consistent with a tobit specification. If we were > merely modeling the determinates of the use of this factor, I > would use a Heckman model to control for selection bias, but > in this case we are interested in this variables relation to > another factor, so that approach will not with our research question. > > Thank you all! > Kathleen > > > From: [email protected] on behalf of Austin Nichols > Sent: Tue 6/6/2006 2:23 PM > To: [email protected] > Subject: Re: st: Re: Endogenous right hand side variable > > > > Rodrigo - > I assume Mark is referring to page 574 in > http://www.stata.com/bookstore/cspd.html > > if (y1, y2) observed when y3>0, > run a tobit of y3 on Z, > save the residuals vhat, and > then > . ivreg2 y1 (y2 = vhat Z) > > though it is not clear to me from the original post that any > tobit is required. (A variable with a lot of zeros could mean > a number of very different things.) > > On 6/6/06, Rodrigo A. Alfaro <[email protected]> wrote: > > > Mark, > > > > > > I don't understand this point "Finally, estimate using IV with the > predicted > > > values of the endogenous regressor as the single excluded > instrument." did > > > you mean IV regression using the predicted values as > instruments of > > > the original endogenous? > > > > > > Rodrigo. > > > > > > ----- Original Message ----- > > > From: "Schaffer, Mark E" <[email protected]> > > > To: <[email protected]> > > > Sent: Tuesday, June 06, 2006 12:54 PM > > > Subject: RE: st: Re: Endogenous right hand side variable > > > > > > > > > Kathleen, Rodrigo et al., > > > > > > An alternative to Rodrigo's proposal of full system > estimation is to > > > use a trick that Wooldridge describes in his 2002 book. > The method > > > takes advantage of the fact that simple IV gives > consistent estimates. > > > > > > In a first step, estimate the Tobit-type relationship between the > > > endogenous regressor and the full set of exogenous variables, > > > including the excluded instruments. > > > > > > Then, get the predicted values from this Tobit. > > > > > > Finally, estimate using IV with the predicted values of the > > > endogenous regressor as the single excluded instrument. > > > > > > No ex post adjustment of the var-cov matrix is necessary, > since the > > > last step is simple IV and therefore gets you consistent > estimates > > > of the var-cov matrix as well as the parameters. > > > > > > Very convenient, more efficient than IV on the original equation > > > (which is also consistent, btw), but not as efficient as a full > > > system estimation. > > > > > > Cheers, > > > Mark > > > > >> > > -----Original Message----- > >> > > From: [email protected] > >> > > [mailto:[email protected]] On Behalf Of > >> > > Rodrigo A. Alfaro > >> > > Sent: 06 June 2006 17:44 > >> > > To: [email protected] > >> > > Subject: Re: st: Re: Endogenous right hand side variable > >> > > > >> > > Deepankar, > >> > > > >> > > I think that Kathleen wants to use tobit because this > "endogenous > >> > > right-hand side variable that is zero for over half of the > >> > > observations" let's say censored, not because the variable is > >> > > discrete. Also, I think that -heckman- is not the solution (I > >> > > mean using the command)... in that procedure there is only one > >> > > endogenous variable, in the problem we have 2. A > two-stage here > >> > > involves do the tobit, makes the predictions, put into > the linear > >> > > equation and estimate that. > >> > > It seems easy to do it, the problem is to adjust the > standard errors. > >> > > > >> > > Rodrigo. > >> > > > >> > > > >> > > ----- Original Message ----- > >> > > From: "Deepankar Basu" <[email protected]> > >> > > To: <[email protected]> > >> > > Sent: Tuesday, June 06, 2006 12:08 PM > >> > > Subject: Re: st: Re: Endogenous right hand side variable > >> > > > >> > > > >> > > Kathleen, > >> > > > >> > > Some quick thoughts on your questions. > >> > > > >> > > 1. Why do you want the endogenous variable to be > estimated with a > >> > > tobit regression? The variable in question does not > seem to be a > >> > > discrete random variable. If it has a mixture > distribution, you > >> > > might want to do a joint likelihood estimation as Rodrigo > >> > > suggests. > >> > > > >> > > 2. If you want a two-stage procedure with a tobit in the first > >> > > stage and an OLS in the second, you could look at Heckman-type > >> > > selection > models. > >> > > > >> > > Deepankar > >> > > > >> > > On Tue, 2006-06-06 at 11:44 -0400, Rodrigo A. Alfaro wrote: > >>> > > > Dear Kathleen, > >>> > > > > >>> > > > I don't know if there is procedure in Stata for this model. > >> > > The model > >>> > > > sounds > >>> > > > interesting, maybe there is some code in Gauss, Matlab or R. > >>> > > > > >>> > > > An alternative solution if to estimate the entire > problem in a > joint > >>> > > > framework. You could write down the likelihood for this > >> > > problem and solve > >>> > > > it > >>> > > > using -ml- procedures in Stata. The book of Gould "MLE with > >> > > Stata" could > >>> > > > help you in this matter. > >>> > > > > >>> > > > Rodrigo. > >>> > > > > >>> > > > ----- Original Message ----- > >>> > > > From: "McCullough, Kathleen" <[email protected]> > >>> > > > To: <[email protected]> > >>> > > > Sent: Tuesday, June 06, 2006 9:20 AM > >>> > > > Subject: st: Endogenous right hand side variable > >>> > > > > >>> > > > > >>> > > > I seem to be having some trouble posting today, so I am > >> > > going to send this > >>> > > > message again. I am sorry if it is a duplicate. > >>> > > > > >>> > > > I am estimating a model with a endogenous right-hand side > >> > > variable that is > >>> > > > zero for over half of the observations. Otherwise it is a > >> > > continuous > >>> > > > variable. The dependent variable is continuous. Is there a > specific > >>> > > > procedure to help control for this situation? I was > >> > > concerned that using > >>> > > > IVREG2 might not be effective as you cannot specify that > >> > > the endogenous > >>> > > > variable should be estimated with a tobit model. It does > >> > > not appear that > >>> > > > there is a canned procedure with a first stage tobit and > >> > > second stage OLS > >>> > > > model. > >>> > > > > >>> > > > I appreciate any suggestions that you might have. > >>> > > > > >>> > > > Regards, > >>> > > > Kathleen > > * > * 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/ > * * 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**:**Re: st: Endogenous right hand side variable***From:*Maarten A Allers <[email protected]>

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