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1 G604, BLP Lectures Spring 2006, 2 March 2006 Eric Rasmusen, erasmuse@Indiana.eduerasmuse@Indiana.edu

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2 GMM in canned programs Just like instrumental variables. You say, in SAS or STATA or whatever, that you are estimating REGRESS: Y X1 X2 X3 and then you say INSTRUMENT: X2 X3 Z1 Z2 Z3 This uses Z2, Z2, Z3 to instrument for X1 and correct for heteroskedasticity. The package calculates the variance-covariance weighting matrix for you.

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3 From Wooldridge. Log(wage) is the dependent variable (hourly wage). The instrument, neare4, is a mans distance from a 4-year college when he was 16. An extra year of education is worth 3.7% more for a black man than a white man. The difference between 2SLS and GMM is the weighting matrix.

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4 GMM Benefit 1. You can add all kinds of crazy instruments to improve your estimates 2. But the weighting matrix means that the additional effect of bad instruments is slight 3. And also that if they are correlated with the other instruments the effect is slight (you get heteroskedasticity correction too, but you can get that in other ways)

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5 Dangers of GMM The crazy instruments can hurt you in small samples (e.g., real samples), because of accidental correlations You can do data-mining searches for crazy instruments

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6 Estimating causes of lawyer income Taxes-paid = Experience, Talent, GDP/lawyer, Lawsuits/lawyer The first three variables are for a given lawyer, the last two are for the prefecture in which he lives. What is wrong with this regression?

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7 Estimating causes of lawyer income Taxes-paid = Experience, Talent, GDP/capita, Lawsuits/capita GDP/capita comes in *negative*. Lawyers in rich prefectures have lower incomes! Why? (IV with variables such as hospitals/capita and cars/capita as instrument)

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8 Estimating causes of lawyer income Taxes-paid = Experience, Talent, Lawyers in the prefecture, Lawsuits/capita (demand) Taxes-paid = Number of movie theaters/capita (IV with variables such as hospitals/capita and cars/capita as instrument)

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