Instrumental Variables ISQS 5349

1. Anh Dang Sam Karimi Instrumental VariablesISQS 5349

2. Endogenous variable and inconsistency in OLS estimation • Instrumental variable (IV) • Two stage least square (2SLS) • Identification • Weak instruments • R implementation. Outline

3. Demand = β0 + β1Price +  • Wages = β0 + β1Education +  • Medical Expenses = β0 + β1Health Insurance +  Source: Instrumental Variables by Collin Cameron http://espin086.wordpress.com/2010/08/02/hausman-test-for-endogeneity-parents-education-as-iv-for-offspring-education-transmission-of-inate-ability/ QUESTIONABLE CAUSAL CLAIMS

4. Conditional distribution model: Y = β0 + β1X +  plimn-> σ̂xy/ σ̂2x = β1 (Theorem 3) • Causal model: Y = 0 + 1X +  where X = X1and  = 2X2 + 3X3 + …. + kXk + ’ plimn-> σ̂xy/ σ̂2x = 1 + σx/ σ2x (Theorem 5) Source: http://courses.ttu.edu/isqs5349-westfall/images/5349/inst_var.pdf Inconsistency in OLS Estimator

5. Def: Regressor correlated with the error term . x y •  Y = 0 + 1X +  where X = X1and  = 2X2 + 3X3 + …. + kXk + ’ Cov(X, )  0 Endogenous Regressor

6. Omitted variable bias. • Simultaneous causality bias. • Measurement error. CAUSES OF ENDOGENEITY

7. z x y  Z is a valid instrumental variable if: • Z is correlated with X (Relevance) ( Cov(Z, X)  0 ) • Z is uncorrelated with  (Exogeneity) ( Cov(Z, ) = 0 ) Source: Instrumental Variables by Collin Cameron Instrumental Variable

8. Source: http://eml.berkeley.edu/users/cle/e250a_f13/mroz-paper.pdf http://espin086.wordpress.com/2010/08/02/hausman-test-for-endogeneity-parents-education-as-iv-for-offspring-education-transmission-of-inate-ability/ Instrumental Variable - example Fathers’ Education Education Wages Mothers’ Education 

9. Regress X on Z using OLS Xi = 0 + 1 i + i Compute X̂i,where X̂i= ̂0 + ̂1 i . Replace Xi by X̂iin the regression of interest Y = β0 + β1X̂i + i Source: http://www2.dse.unibo.it/golinelli/teaching/corsi/corsi_ea/ea_aq/SWc12.pdf Two Stage Least Squares (2SLS)

10. First regression: education = 0 + 1experience + 2experience2 + 3fathers’ education + 4mothers’ education +  Second regression: lwages = β0 + β1 + β2experience + β3experience2 +  Source: http://espin086.wordpress.com/2010/08/02/hausman-test-for-endogeneity-parents-education-as-iv-for-offspring-education-transmission-of-inate-ability/ EXAMPLE- One endogenous variable and one iv

11. Yi = β0 + β1X1i +…+ βkXki + βk+1W1i +…+ βk+rWri + i Yi : dependent variable X1i ,X2i,...,Xki: endogenous variables W1i ,W2i,...,Wri: included exogenous variables β0 ,β1,...,βk+r: unknown regression coefficients 1i ,2i,...,mi: IVs Source:http://www2.dse.unibo.it/golinelli/teaching/corsi/corsi_ea/ea_aq/SWc12.pdf The general IV regression model

12. The coefficients β0 ,β1,...,βk are: Exactly identified if m = k Overidentified if m > k Underidentified if m < k Identification

13. Weak Cov (,X) • Bias towards OLS estimate. • Use the most relevant IVs. • Find additional IVs. Weak instruments

14. Estimating the causal effect of Health insurance on Medical expenses

17. http://courses.ttu.edu/isqs5349-westfall/images/5349/inst_var.pdfhttp://courses.ttu.edu/isqs5349-westfall/images/5349/inst_var.pdf • http://cameron.econ.ucdavis.edu/e240a/ch04iv.pdf • http://homepage.univie.ac.at/Christine.Zulehner/iv.pdf • http://www2.warwick.ac.uk/fac/soc/economics/staff/academic/waldinger/teaching/ec9a8/slides/lecture_2_-_iv.pdf • http://www2.dse.unibo.it/golinelli/teaching/corsi/corsi_ea/ea_aq/SWc12.pdf • http://eml.berkeley.edu/users/cle/e250a_f13/mroz-paper.pdf references