Introduction to Microeconometrics SS 2008 1 Alexander Spermann

Introduction to Microeconometrics SS 2008 1 Alexander Spermann, University of Freiburg

Introduction 2 1. Endogeneity 2. Simultaneity 3. Missing Variables Börsch-Supan, Axel und Jens Köke (2002), An Applied Econometricians‘ View of Empirical Corporate Governance Studies, German Economic Review, 3 (3), S. 295 -326 Alexander Spermann, University of Freiburg

Introduction (1) True Model (2) whereas , , OLS estimation of (1): z from (1) 3 Alexander Spermann, University of Freiburg

Introduction Example: Rule II Rule I (3) 4 Alexander Spermann, University of Freiburg

Introduction x from (2) z from (1) Rule II Rule I (4) 5 Alexander Spermann, University of Freiburg

Introduction Solving for Cov(x, ε): 6 Alexander Spermann, University of Freiburg

Introduction Case 1 7 Case 2 OLS estimators are biased and inconsistent Alexander Spermann, University of Freiburg

Introduction 1. Covariance 2. Expected Value 3. Conditional Expected Value 8 Alexander Spermann, University of Freiburg

Introduction 9 Alexander Spermann, University of Freiburg

Introduction In case x and y are independent, then: conditional expected value unconditional expected value , if ε and x are independent 10 (assumption of exogeneity). Alexander Spermann, University of Freiburg

Introduction Emphasis of this lesson is the assumption of exogeneity: • Independence of residual and explaining variables • All missing variables are captured by a disturbance term 11 Alexander Spermann, University of Freiburg

Introduction If the assumption of exogeneity is violated then OLS is • biased • inconsistent 12 Alexander Spermann, University of Freiburg

Introduction Problem of Endogeneity Cov(x, ε) ≠ 0 respectively E(ε|x) ≠ 0 True Model: z = βx + ε x = γz + η γ≠ 0 structural reverse causality = simultaneity y = βx + ε x = x* + η σεη ≠ 0 omitted variables = unobserved heterogeneity = spurious correlation = unobserved common factors time variant 13 measurement error time invariant sample selectivity Alexander Spermann, University of Freiburg

Introduction Problem of Endogeneity Cov(x, ε) ≠ 0 respectively E(ε|x) ≠ 0 True Model: z = βx + ε x = γz + η γ≠ 0 structural reverse causality = simultaneity 14 Alexander Spermann, University of Freiburg

Introduction 15 Basic Problem: Direction of causal effects between variables is ambiguous. Example: y x No. of Rate of policemen criminality Consumption GDP Application of Unemployment (1) y = βx + ε active (2) x = γy + η labour market Estimation of (1) with OLS Estimated policy coefficients biased, if γ≠ 0, as Cov(x, ε) ≠ 0. Alexander Spermann, University of Freiburg

Introduction Problem of Endogeneity Cov(x, ε) ≠ 0 respectively E(ε|x) ≠ 0 True Model: z = βx + ε x = γz + η γ≠ 0 structural reverse causality =simultaneity 16 σεη ≠ 0 omitted variables = unobserved heterogeneity = spurious correlation 1 = unobserved common factors 1 The denomination is deceptive; a better denomination would be „spurious causality“ Alexander Spermann, University of Freiburg

Introduction • Classification: Omission of variables leads to an endogeneity bias and thus to misleading regression results • In case the incorrect specification is assumed instead of , then the effect of the omitted variable is captured in the residual • If either Cov(x 1, x 2)=0 or β 2=0 is violated then the disturbance term is correlated with x 1 endogeneity bias 17 Alexander Spermann, University of Freiburg

Introduction 1) Unobserved Heterogeneity = unobservable individual effect Examples: • Motivation • Intelligence • Management Skills 18 Alexander Spermann, University of Freiburg

Introduction 19 2) Spurious Correlation / Spurious Causality Due to an omitted variable, a pseudocorrelation between regressor x and regressand y emerges Example: Estimation of the effect of education on wages: Individuals A and B differ in regard to their intelligence Due to higher intelligence, A has more years of education Due to higher intelligence, A receives higher wages Alexander Spermann, University of Freiburg

Introduction 3) Unobserved Common Factors Unobserved Variable (Intelligence) Dependent Variable y (Wage) 20 Independent Variable x (Education) In case intelligence is not specified within the model: Regression overestimates the real effect of education on wages because of a positive correlation between intelligence and education. Alexander Spermann, University of Freiburg

Introduction Problem of Endogeneity Cov(x, ε) ≠ 0 respectively E(ε|x) ≠ 0 True Model: z = βx + ε x = γz + η γ≠ 0 structural reverse causality =simultaneity σεη ≠ 0 omitted variables = unobserved heterogeneity = spurious correlation 1 = unobserved common factors time variant 21 time invariant sample selectivity Alexander Spermann, University of Freiburg

Introduction Selection Bias 22 Panel-specific selection bias Incomplete observability Individual/company has diverged from the sample in the meantime. E. g. : Insolvency/ acquisition of a company („survival bias“) Individual/Company is not included in sample „censored data“ e. g. employees and unemployed in sample; working hours (y) only for employees observable (censored at 0) Evaluation. Problem Separation into participants and non participants (both groups not observable at the same time) e. g. evaluation of measures of active labour market policy „truncated data“ e. g. sample only contains data of employees Alexander Spermann, University of Freiburg

Introduction Selection Bias „positive sample selection“ „negative sample selection“ e. g. particular motivation in case of placement vouchers e. g. small companies do not appear in DAX investigations 23 Alexander Spermann, University of Freiburg

Introduction Selection Bias Self Selection Individuals select themselves into a sample. z. B. Individual applies for a career advancement External Selection Individuals are selected into a sample. e. g. Individual is registered for a career advancement by a referee‘s decision 24 Alexander Spermann, University of Freiburg

Approaches: Introduction „selection on observables“ „Propensity -Score. Matching“ Regression Methods 25 „selection on unobservables “ Differencein. Difference. Estimators (Di. D) Instrumental Variable Approaches (IV) Selection Models Alexander Spermann, University of Freiburg