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Lecture 14

# Lecture 14 - LECTURE 14 INSTRUMENTAL VARIABLES(CONTINUED...

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12-1 LECTURE 14: INSTRUMENTAL VARIABLES (CONTINUED) Inference using TSLS In large samples, the sampling distribution of the TSLS estimator is normal Inference (hypothesis tests, confidence intervals) proceeds in the usual way Example: Cigarette demand ln( cigarettes i Q ) = 0 + 1 ln( cigarettes i P ) + ε i Panel data: Annual cigarette consumption and average prices paid (including tax) 48 continental US states, 1985-1995 Proposed instrumental variable: Z i = general sales tax per pack in the state = SalesTax i Is this a valid instrument? 1. Relevant? corr(SalesTax i , ln( cigarettes i P )) 0? 2. Exogenous? corr(SalesTax i , ε i ) = 0? STATA EXAMPLE: CIGARETTE DEMAND, STAGE 1 Instrument = Z = rtaxso = general sales tax (real \$/pack)

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12-2 X Z reg lravgprs rtaxso Regression Number of obs = 48 F( 1, 46) = 40.39 Prob > F = 0.0000 R-squared = 0.4710 Root MSE = .09394 ------------------------------------------------------------------------------ | Robust lravgprs | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- Rtaxso | .0307289 .0048354 6.35 0.000 .0209956 .0404621 _cons | 4.616546 .0289177 159.64 0.000 4.558338 4.674755 ------------------------------------------------------------------------------ X-hat predict lravphat Now we have the predicted values from the 1 st stage Second stage Y X-hat
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Lecture 14 - LECTURE 14 INSTRUMENTAL VARIABLES(CONTINUED...

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