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From |
"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
RE: st: RE: overidentification test after treatreg |

Date |
Fri, 22 Oct 2010 18:37:15 +0100 |

Xiang, > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Xiang Ao > Sent: 22 October 2010 18:06 > To: statalist@hsphsun2.harvard.edu > Subject: Re: st: RE: overidentification test after treatreg > > Thank you, Mark, for the prompt reply. I guess my question > is still why this would tell you the robustness of > instruments? It tells you only what any overidentification test tells you, namely, are the identifying restrictions supported by the data? > The reason we can do a LR test is because of > the nonlinearity of the selection process (probit). True. The probit selection equation means there's only one way to specify a just-identified model. > Think of > a 2sls setting, we cannot do something like that since there > has to be excluded instrument(s), otherwise it's > unidentified. Not so. The standard Hansen-Sargan overid test is the same thing as a GMM distance test between an overidentified model and a just-identified model. We're doing the same thing, transplanted to treatreg/probit/LR-land. > In treatreg, you can have no excluded > instruments simply because it's nonlinear. The only > identification is through the normality assumption. If your > rationale holds, we should be able to do this LR test for any > nonlinear model with endogenous regressors, as an > overidentification test. True! But I'd be interested to know if others agree. > Also, do you have any idea what went wrong with my gmm codes? Sorry, I had only a quick look but couldn't work it out. --Mark > > Thanks, > > Xiang > > On 10/22/2010 11:19 AM, Schaffer, Mark E wrote: > > > Xiang, > > > > > >> -----Original Message----- > >> From: owner-statalist@hsphsun2.harvard.edu > >> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Xiang Ao > >> Sent: 22 October 2010 15:10 > >> To: statalist@hsphsun2.harvard.edu > >> Subject: st: overidentification test after treatreg > >> > >> Dear Statalisters, > >> > >> I have a question on how to do a Sargan's test after treatreg. I > >> found Mark Schaffer's comments on this question from 2006: > >> http://www.stata.com/statalist/archive/2006-08/msg00804.html > >> > >> In the reply, Mark suggested using a LR test between a full model > >> with all instruments in the second stage and a regular treatreg. > >> My question > >> is: this only tests the hypothesis that all excluded instruments > >> jointly being zero, how would that tell us the robustness of > >> instruments, as Sargan's test would do in an ivreg setting? > >> > >> Mark kindly replied to my email to him and suggested posting to > >> statalist to get more inputs. > >> > >> I am thinking of using gmm to frame the treatreg problem, then > >> Jansen's J would be a byproduct. However, my code with > gmm does not > >> generate consistent estimates with treatreg, which I am > sure is due > >> to my lack of knowledge on this. I post my code here; any > suggestion > >> is greatly appreciated. > >> > >> > >> sysuse auto, clear > >> global xb "{b1}*gear_ratio + {b2}*length + {b3}*headroom + {b0}" > >> global phi "normalden($xb)" > >> global Phi "normal($xb)" > >> global lambda "foreign*$phi/$Phi - (1-foreign)*$phi/(1-$Phi)" > >> global xb2 "{c1}*gear_ratio + {c2}*length + {c3}*headroom + {c0} + > >> {c5}*foreign" > >> gmm (eq1: $lambda) (eq2: turn-$xb2), instruments(eq1: > >> gear_ratio length > >> headroom mpg) instruments(eq2: gear_ratio length headroom > foreign ) > >> winitial(unadjusted, independent) wmatrix(unadjusted) > >> > >> This is to try to estimate the same model as: > >> > >> treatreg turn gear_ratio length headroom, treat(foreign=gear_ratio > >> length headroom mpg) > >> > > Here was my rationale for how to do an overid test using an LR > > statistic. As I wrote it in that Statalist post from 2006 that you > > cite, I think I got it wrong. Here's my next attempt: > > > > Consider a slightly simplified version of your treatreg model: > > > > treatreg turn, treat(foreign=mpg) > > > > There are two overidentifying restrictions. First, mpg > appears in the > > treatment equation (foreign) but not in the outcome equation (turn). > > Second, normality is also an identifying restriction, much > in the same > > way as normality can be used in a Heckman selection model as an > > identifying restriction. > > > > Now consider your treatreg model, but with mpg as a > regressor in the > > outcome equation: > > > > treatreg turn mpg, treat(foreign=mpg) > > > > This second version is just-identified, with normality as the sole > > identifying restriction. > > > > So, the following should be an LR test of the overidentifying > > restrctions in your original model: > > > > treatreg turn, treat(foreign=mpg) > > est store troverid > > treatreg turn mpg, treat(foreign=mpg) > > est store trjustid > > lrtest troverid trjustid, df(1) > > > > I should also note that this is a system test. The overidentified > > system is (pardon the terrible shorthand notation): > > > > turn = a + b*foreign + c*mpg > > foreign = d + e*mpg > > > > The just-identified system is > > > > turn = a + b*foreign > > foreign = d + e*mpg > > > > And your overid test is an LR test of c=0. > > > > I *think* this is right, but perhaps you or others on the > list could > > comment. > > > > Cheers, > > Mark > > > > > >> But they don't match. > >> > >> Thank you for your time, > >> > >> Xiang > >> > >> > >> * > >> * 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/ > >> > >> > > > > > > * > * 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/ > -- Heriot-Watt University is a Scottish charity registered under charity number SC000278. * * 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: RE: overidentification test after treatreg***From:*Xiang Ao <xao@hbs.edu>

**References**:**st: overidentification test after treatreg***From:*Xiang Ao <xao@hbs.edu>

**st: RE: overidentification test after treatreg***From:*"Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>

**Re: st: RE: overidentification test after treatreg***From:*Xiang Ao <xao@hbs.edu>

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