P we need an instrument rainfall n rainfall effects

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p We need an instrument: Rainfall n Rainfall effects staying indoors which influences TV watching n Rainfall is definitely absolutely truly exogenous, so it is a perfect instrument. p The correlation survives, so TV“causes” autism. ™  49/61
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Part 13: Endogeneity Two Problems with 2SLS p Z’X /n may not be sufficiently large. The covariance matrix for the IV estimator is Asy.Cov(b ) = σ2[( Z’X )( Z’Z )-1( X’Z )]-1 n If Z’X /n -> 0, the variance explodes. n Additional problems: p 2SLS biased toward plim OLS p Asymptotic results for inference fall apart. p When there are many instruments, is too close to X ; 2SLS becomes OLS. ™  50/61 ˆ X
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Part 13: Endogeneity Weak Instruments p Symptom: The relevance condition , plim Z’X /n not zero, is close to being violated. p Detection: n Standard F test in the regression of xk on Z. F < 10 suggests a problem. n F statistic based on 2SLS – see text p. 351. p Remedy: n Not much – most of the discussion is about the condition, not what to do about it. n Use LIML? Requires a normality assumption. Probably not too restrictive. ™  51/61
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Part 13: Endogeneity Endogenous Dummy Variable p Y = + δT + ε ( unobservable factors ) p T = a dummy variable (treatment) p T = 0/1 depending on: n x and z n The same unobservable factors p T is endogenous – same as ED ™  52/61
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Part 13: Endogeneity Application: Health Care Panel Data German Health Care Usage Data , 7,293 Individuals, Varying Numbers of Periods Variables in the file are Data downloaded from Journal of Applied Econometrics Archive. This is an unbalanced panel with  7,293 individuals. They can be used for regression, count models, binary choice, ordered choice, and  bivariate binary choice.   This is a large data set.  There are altogether 27,326 observations.  The  number of observations ranges from 1 to 7.  (Frequencies are: 1=1525, 2=2158, 3=825, 4=926,  5=1051, 6=1000, 7=987).   Note, the variable NUMOBS below tells how many observations there are for  each person.  This variable is repeated in each row of the data for the person.  (Downloaded from the  JAE Archive)                     DOCTOR   =  1(Number of doctor visits > 0)                    HOSPITAL =  1(Number of hospital visits > 0)                    HSAT        =  health satisfaction, coded 0 (low) - 10 (high)                       DOCVIS     =  number of doctor visits in last three months                    HOSPVIS   =  number of hospital visits in last calendar year                     PUBLIC     =  insured in public health insurance = 1; otherwise = 0                    ADDON  =  insured by add-on insurance = 1; otherswise = 0                     HHNINC  =  household nominal monthly net income in German marks / 10000 .
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