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Step1: Estimate the endogenous variable using the two binary instruments and other exogneous covariates.Įststo Probit_Gov1: probit CS4_govt CS23 CS22 i.TA10A Nchild_adult Income_person i.RO3 i.RO5 COPC i.HHEDUC I.ED6 CS10-CS12 i.CS8 CS5 i.ID11 ED7 i.ID13 i.STATE, vce(cluster IDHH) Q1: For a problem involving binary dependent, binary endogenous and two binary instruments, can I use the below-mentioned approach? Please advise. You should compute the average marginal effect from the biprobit and compare it with the 2SLS estimate.Ĭan I seek guidance on the following two questions please. This is a joint maximum likelihood procedure. Use the so-called "biprobit" model, where y1 and y2 are modeled as probits. This is what Angrist and Pischke propose in "Mostly Harmless Econometrics."Ģ. A standard linear model estimated by 2SLS. That's much different then measurement error, which is a population, not a sampling, issue.)īut with a binary y1 and binary y2, you should use two methods.ġ. It's estimation error, or sampling error, which goes away as N gets large. (Incidentally, there isn't "measurement error" in the instrument. In fact, it's a method I cover in Section 21.4 in my 2010 MIT Press book. If y1 were continuous, so that a linear model could reasonably represent a conditional mean, then the method would be fine.
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If you are going to acknowledge the discreteness of the endogenous explanatory variable it seems odd to then use a linear model for the main variable, y1. The second method doesn't make much logical sense.
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As I tell my students: A method that plugs in fitted values into nonlinear second stages should be assumed inconsistent unless you prove otherwise. It is an example of a "forbidden regression," where one tries to incorrectly extend 2SLS to a nonlinear model. The first proposed method does not estimate anything interesting - at least not that anyone has shown. Question: I wonder whether that is correct in my case? Or, can I just use ivreg2 command of stata to perform the IV estimation? And then, run ivregress 2sls of the dummy dependent variable on the fitted probabilities as excuded instrument adding control variables. And second, estimate a logit model of the dummy dependent variable on the fitted probabilities that replace the endogenous regressor.Ģ) I also use the two-step estimator, that is first estimate a logit or probit model of the binary endogenous regressor on the excluded instrument and control variables. I estimate a logit model where the dependent variable is a dummy and the predictor also is a binary variable that is likely endogenous (simultaneity problem).ġ) I attempt to perform IV estimation, that is first run logit model of my endogenous varaible (binary) on one excluded instrument (that takes values 1, 2, 3, 4 and 5) and control variables (age, age square, living location-rural or urban-, gender.).
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