3861 part 13 endogeneity wu test note 05544 54900

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Part 13: Endogeneity Wu Test Note: .05544 + . 54900 = .60444,  which is the 2SLS  coefficient on ED. ™  39/61
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Part 13: Endogeneity Alternative to Hausman’s Formula? p H test requires the difference between an efficient and an inefficient estimator. p Any way to compare any two competing estimators even if neither is efficient? p Bootstrap? (Maybe) ™  40/61
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Part 13: Endogeneity ™  41/61
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Part 13: Endogeneity Measurement Error y = x* + all of the usual assumptions x = x* + u the true x* is not observed (education vs. years of school) What happens when y is regressed on x? Least squares attenutation : ™  42/61 cov(x,y) cov(x * u, x * ) plim b =   var(x) var(x * u) var(x* )                           =    <   var(x* ) var(u) + β = + β β +
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Part 13: Endogeneity Why Is Least Squares Attenuated? y = x* + x = x* + u y = x + ( - u) y = x + v, cov(x,v) = -  var(u) Some of the variation in x is not associated with variation in y. The effect of variation in x on y is dampened by the measurement error. ™  43/61
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Part 13: Endogeneity Measurement Error in Multiple Regression ™  44/61 1 1 2 2 1 1 1 2 1 2 Multiple regression: y =  x * x *   x *  is measured with error; x x * u x  is measured with out error. The regression is estimated by least squares Popular myth # 1. b  is biased downward, b  consiste β + ε = + ij i j ij nt. Popular myth # 2. All coefficients are biased toward zero. Result for the simplest case.  Let cov(x * , x * ),i, j 1,2 (2x2 covariance matrix)  ijth element of the inverse of the covariance matrix σ = = σ = θ 2 2 12 1 1 2 2 1 2 11 2 11 var(u) For the least squares estimators: 1 plim b ,   plim b 1 1 The effect is called "smearing." = θ σ = β = β - β ÷ ÷ + θ σ + θ σ
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Part 13: Endogeneity Twins Application from the literature: Ashenfelter/Kreuger: A wage equation for twins that includes “schooling.” ™  45/61
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Part 13: Endogeneity Orthodoxy p A proxy is not an instrumental variable p Instrument is a noun, not a verb p Are you sure that the instrument really exogenous? The “ natural experiment .” ™  46/61
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Part 13: Endogeneity The First IV Study (Snow, J., On the Mode of Communication of Cholera, 1855) p London Cholera epidemic, ca 1853-4 p Cholera = f(Water Purity,u)+ε. n Effect of water purity on cholera? n Purity=f(cholera prone environment (poor, garbage in streets, rodents, etc.). Regression does not work. Two London water companies Lambeth Southwark p ======|||||====== Main sewage discharge Paul Grootendorst: A Review of Instrumental Variables Estimation of Treatment Effects… ™  47/61
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Part 13: Endogeneity IV Estimation p Cholera=f(Purity,u)+ε p Z = water company p Cov(Cholera,Z)=δCov(Purity,Z) p Z is randomly mixed in the population (two full sets of pipes) and uncorrelated with behavioral unobservables, u) p Cholera=α+δPurity+u+ε n Purity = Mean+random variation+λu n Cov(Cholera,Z)= δCov(Purity,Z) ™  48/61
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Part 13: Endogeneity Autism: Natural Experiment p Autism ----- Television watching p Which way does the causation go?
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