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  • Fei Wang
    replied
    Originally posted by Devon Smith View Post
    Hi Jeff and Joao:

    In the above example, which first stage F-stat should be reported? D = A0 + A1Z + A2X + V or D= AZ+ D-hat?
    Devon, if you only use Z as the instrument, then the first-stage regression is as below and the F stat is only related to Z.
    Code:
    regress D Z X
    If you use both Z and Dhat as instruments, then the first-stage regression would be as below and the F stat is related to the joint significance of Z and Dhat.

    Code:
    regress D Z Dhat X
    ADD: But you should't "manually" run the first stage. Use -ivregress- and correctly specify the set of instruments there. After -ivregress-, run -estat firststage- (for homoskedasticity) or -weakivtest- (for heteroskedasticity, from SSC) to obtain the correct F stat.
    Last edited by Fei Wang; 02 Jul 2022, 20:45.

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  • Devon Smith
    replied
    Hi Jeff and Joao:

    In the above example, which first stage F-stat should be reported? D = A0 + A1Z + A2X + V or D= AZ+ D-hat?

    Leave a comment:


  • Jeff Wooldridge
    replied
    Mat: Yes, the standard errors are valid provided the error satisfies the zero conditional mean restriction in my earlier post (which is essentially needed for consistency, anyway). I show this in Chapter 6 of my MIT Press book. You should make them robust to heteroskedasticity, as usual.

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  • Mat Log
    replied
    Dear all,

    Do we get the proper standard errors when running the following command that you suggested:
    ivregress 2sls Y (D = Z Dhat) X
    Thanks a lot,

    Mat

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  • Jeff Wooldridge
    replied
    Provided E(U|X,Z) = 0, using either Z, Dhat, or both produces consistent estimators. Joao's proposal has the advantage of being asymptotically no worse than either of the other two approaches if Var(U|X,Z) is constant. It also produces an overidentifying restriction, although I'm not sure how valuable that is as a specification test in this context.

    A potential downside is that using (Z,Dhat) is more likely to lead to a weak instruments problem. If the probit model for D is correct then Z is redundant as an IV. Therefore, the rule for having a strong enough instrument -- roughly, the first-stage F statistic is above 10 -- would be harder to achieve.

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  • Joao Santos Silva
    replied
    Dear Eric de Souza,

    A LPM in the first stage is not wrong and that is actually what should be done.

    The question is what instrument to use in the first stage. We can just use Z, but that is unlikely to be a good instrument if Z is continuous and D binary. An alternative is to replace Z with E(D|Z,X), which is likely a better instrument; this can be approximated using a logit or probit. What we did in the 1997 paper was actually to use both Z and an estimate of E(D|Z,X) obtained with a logit.

    So, the command I would suggest is something like (which has a LPM in the first stage):

    ivregress 2sls Y (D = Z Dhat) X

    Does is make sense?

    Best wishes,

    Joao

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  • Eric de Souza
    replied
    @João: Why would using an LPM in the first stage be wrong? And since the Dhat from a probit model is non-linear in X and Z, is there not a risk that it still be linearly correlated with U as defined in the equation in #1 above?

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  • Joao Santos Silva
    replied
    Dear Maria,

    Just to add to the variety of (late) advice you are getting, I would suggest using both Z and Dhat as instruments. That is what we did in (see the top of page 291):

    Windmeijer, F. and Santos Silva, J.M.C. (1997), Estimation of Count Data Models with Endogenous Regressors; An Application to Demand for Health Care, Journal of Applied Econometrics, 12(3), pp. 281-294.

    Best wishes,

    Joao

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  • Eric de Souza
    replied
    What you need is that Dhat not be correlated with the residual is the original model: Y = B0 + B1D + B2X + U,
    A probit model in the first stage will not give you that because it is nonlinear.
    Just run a 2SLS regression using Z as an instrument for D: ivregress 2sls Y (D = Z) X

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  • Peter Perera
    replied
    Hi Maria,
    See pages 142-144 of Mostly Harmless Econometrics by Angrist and Pischke. I believe you need to only include only Dhat and X.

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  • Marcos Almeida
    replied
    I gather the biprobit model would fit your needs.

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