Sharif University of Technology. Graduate School of Management and Economics. Econometrics I. Fall Seyed Mahdi Barakchian

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1 Sharif University of Technology Graduate School of Management and Economics Econometrics I Fall 2010 Seyed Mahdi Barakchian Textbook: Wooldridge, J., Introductory Econometrics: A Modern Approach, South Western College Pub (W., hereafter) Syllabus 1. Introduction 2. Probability Theory: A Review (W. Appendix B) 3. Statistical Theory: A Review (W. Appendix C) 4. The Simple Regression Model (W. Chapter 2) 4.1. Definition of The Simple Regression Model 4.2. Deriving The Ordinary Least Squares Estimates 4.3. Mechanics of OLS Fitted Values and Residuals Algebraic Properties of OLS Statistics Goodness of Fit 4.4. Units of Measurement and Functional Form The Effects of Changing Units of Measurement on OLS Statistics Incorporating Nonlinearities in Simple Regression The Meaning of Linear Regression 4.5. Expected Values and Variances of The OLS Estimators Unbiasedness of OLS Variances of the OLS Estimators Estimating the Error Variance 4.6. Regression Through The Origin

2 5. Multiple Regression Analysis: Estimation (W. Chapter 3) 5.1. Motivation for Multiple Regression The Model with Two Independent Variables The Model with k Independent Variables 5.2. Mechanics and Interpretation of Ordinary Least Squares Obtaining the OLS Estimates Interpreting the OLS Regression Equation On the Meaning of Holding Other Factors Fixed in Multiple Regression Changing More than One Independent Variable Simultaneously OLS Fitted Values and Residuals A Partialling Out Interpretation of Multiple Regression Comparison of Simple and Multiple Regression Estimates Goodness of Fit Regression Through the Origin 5.3. The Expected Value of the OLS Estimators Including Irrelevant Variables in a Regression Model Omitted Variable Bias: The Simple Case Omitted Variable Bias: More General Cases 5.4. The Variance of the OLS Estimators The Components of the OLS Variances: Multicollinearity Variances in Misspecified Models Estimating : Standard Errors of the OLS Estimators 5.5. Efficiency of OLS: The Gauss Markov Theorem 6. Mul ple Regression Analysis: Inference (W. Chapter 4) 6.1. Sampling Distributions of the OLS Estimators 6.2. Testing Hypotheses About A Single Population Parameter: The t Test Testing Against One Sided Alternatives Two Sided Alternatives Testing Other Hypotheses About j Computing p values for t tests Economic, or Practical, versus Statistical Significance 6.3. Confidence Intervals 6.4. Testing Hypotheses About A Single linear Combination of The Parameters 6.5. Testing Multiple Linear Restrictions: The F Test Testing Exclusion Restrictions Relationship Between F and t Statistics The R Squared Form of the F Statistic Computing p values for F Tests The F Statistic for Overall Significance of a Regression Testing General Linear Restrictions

3 6.6. Reporting Regression Results 7. Multiple Regression Analysis: OLS Asymptotics (W. Chapter 5) 7.1. Consistency Deriving the Inconsistency in OLS 7.2. Asymptotic Normality And Large Sample Inference Other Large Sample Tests: The Lagrange Multiplier Statistic 7.3. Asymptotic Efficiency of OLS 8. Multiple Regression Analysis: Further Issues (W. Chapter 6) 8.1. Effects of Data Scaling on OLS Statistics Beta Coefficients 8.2. More on Functional Form More on Using Logarithmic Functional Forms Models with Quadratics Models with Interaction Terms 8.3. More on Goodness of Fit and Selection of Regressors Adjusted R Squared Using Adjusted R Squared to Choose Between Nonnested Models Controlling for Too Many Factors in Regression Analysis Adding Regressors to Reduce the Error Variance 8.4. Prediction and Residual Analysis Confidence Intervals for Predictions Residual Analysis Predicting y When log(y) Is the Dependent Variable 9. Multiple Regression Analysis With Qualitative Information: Binary (or Dummy) Variables (W. Chapter 7) 9.1. Describing Qualitative Information 9.2. A Single Dummy Independent Variable Interpreting Coefficients on Dummy Explanatory Variables When the Dependent Variable Is log( y) 9.3. Using Dummy Variables for Multiple Categories Incorporating Ordinal Information by Using Dummy Variables 9.4. Interactions Involving Dummy Variables Interactions Among Dummy Variables Allowing for Different Slopes Testing for Differences in Regression Functions Across Groups 9.5. A Binary Dependent Variable: A Linear Probability Model 10. Heteroskedas city (W. Chapter 8) Consequences of Heteroskedasticity for OLS Heteroskedasticity Robust Inference After OLS Estimation Computing Heteroskedasticity Robust LM Tests

4 10.3. Testing for Heteroskedasticity The Breusch Pagan Test For Heteroskedasticity The White Test for Heteroskedasticity Weighted Least Squares The Heteroskedasticity Is Known up to a Multiplicative Constant The Heteroskedasticity Function Must Be Estimated: Feasible GLS The Linear Probability Model Revisited 11. More On Specification and Data Problems (W. Chapter 9) Functional Form Misspecification RESET as a General Test for Functional Form Misspecification Tests Against Nonnested Alternatives Using Proxy Variables for Unobserved Explanatory Variables Using Lagged Dependent Variables as Proxy Variables Properties of OLS under Measurement Error Measurement Error in the Dependent Variable Measurement Error in an Explanatory Variable Missing Data, Non Random Samples, and Outlying Observations Missing Data Nonrandom Samples Outlying Observations 12. Instrumental Variables Estimation and Two Stage Least Squares (W. Chapter 15) Omitted Variables in a Simple Regression Model Statistical Inference with the IV Estimator Properties of IV with a Poor Instrumental Variable Computing R Squared After IV Estimation IV Estimation of the Multiple Regression Model Two Stage Least Squares A Single Endogenous Explanatory Variable Mul collinearity and 2SLS Multiple Endogenous Explanatory Variables Tes ng Mul ple Hypotheses A er 2SLS Es ma on IV Solutions to Errors in Variables Problems Testing for Endogeneity and Testing for Over identifying Restrictions Testing for Endogeneity Testing Overidentification Restrictions SLS with Heteroskedas city Applying 2SLS to Time Series Equations 13. Basic Regression Analysis with Time Series Data (W. Chapters 10) The Nature of Time Series Data Examples of Time Series Regression Models

5 Static Models Finite Distributed Lag Models Finite Sample Properties of OLS under Classical Assumptions Unbiasedness of OLS The Variances of the OLS Estimators and the Gauss Markov Theorem Inference Under the Classical Linear Model Assumptions Functional Forms, Dummy Variables, and Index Numbers Trends and Seasonality Characterizing Trending Time Series Using Trending Variables in Regression Analysis A Detrending Interpretation of Regressions with a Time Trend Computing R squared when the Dependent Variable is Trending Seasonality 14. Serial Correlation and Heteroskedasticity in Time Series Regressions (W. Chapters 12) Properties of OLS with Serially Correlated Errors Unbiasedness and Consistency Efficiency and Inference Serial Correlation in the Presence of Lagged Dependent Variables Testing for Serial Correlation A t test for AR(1) Serial Correla on with Strictly Exogenous Regressors The Durbin Watson Test Under Classical Assumptions Tes ng for AR(1) Serial Correlation without Strictly Exogenous Regressors Testing for Higher Order Serial Correlation Correcting for Serial Correlation with Strictly Exogenous Regressors Obtaining the Best Linear Unbiased Es mator in the AR(1) Model Feasible GLS Estimation with AR(1) Errors Comparing OLS and FGLS Correcting for Higher Order Serial Correlation Differencing and Serial Correlation Serial Correlation Robust Inference after OLS Heteroskedasticity in Time Series Regressions Heteroskedasticity Robust Statistics Testing for Heteroskedasticity Autoregressive Conditional Heteroskedasticity Heteroskedasticity and Serial Correlation in Regression Models