# Practical. I conometrics. data collection, analysis, and application. Christiana E. Hilmer. Michael J. Hilmer San Diego State University

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1 Practical I conometrics data collection, analysis, and application Christiana E. Hilmer Michael J. Hilmer San Diego State University Mi

2 Table of Contents PART ONE THE BASICS 1 Chapter 1 An Introduction to Econometrics and Statistical Inference I Chapter Objectives 1 A Student's Perspective 1 Big Picture Overview Understand the Steps Involved in Conducting an Empirical Research Project Understand the Meaning of the Term Econometrics Understand the Relationship among Populations, Samples, and Statistical Inference 5 Populations and Samples 5 A Real-World Example of Statistical Inference: The Nielsen Ratings Understand the Important Role that Sampling Distributions Play in Statistical Inference 9 Toolkit 10 What We Have Learned in This Chapter 11 Looking Ahead to Chapter 2 11 Problems 11 Chapter 2 Collection and Management of Data 12 Chapter Objectives 12 A Student's Perspective 12 Big Picture Overview Consider Potential Sources of Data Work Through an Example of the First Three Steps in Conducting an Empirical Research Project Develop Data Management Skills Understand Some Useful Excel Commands 22 Installing the Data Analysis ToolPak 22 Importing Data from the Web 24 Creating New Worksheets 27 Sorting Data from Lowest to Highest and Highest to Lowest 28 Cut, Copy, and Paste Columns and Rows 29 Use the Function Tool in Excel 29 Copy Cell Entries Down a Column 30 Use the Paste Special Command to Copy Values 31 Use the Paste Special Command to Transpose Columns 32 Toolkit 33 Our New Empirical Tools in Practice: Using What We Have Learned in This Chapter 34 Looking Ahead to Chapter 3 34 Problems 34 Exercises 35 Chapter 3 Summary Statistics 36 Chapter Objectives 36 A Student's Perspective 36 Big Picture Overview Construct Relative Frequency Histograms for a Given Variable 38 Constructing a Relative Frequency Histogram Calculate Measures of Central Tendency for a Given Variable 42 The Sample Mean 43 The Sample Median Calculate Measures of Dispersion for a Given Variable 46 Variance and Standard Deviation 46 Percentiles 48 The Five-Number Summary Use Measures of Central Tendency and Dispersion for a Given Variable Detect Whether Outliers for a Given Variable Are Present in Our Sample 55 Detecting Outliers if the Data Set Is Symmetric 56 Detecting Outliers if the Data Set Is Skewed Construct Scatter Diagrams for the Relationship between Two Variables Calculate the Covariance and the Correlation Coefficient for the Linear Relationship between y and x for Two Variables of Interest 59 Toolkit 63 What We Have Learned in This Chapter 63 Looking Ahead to Chapter 4 65 Problems 65 Exercises 68 xiii

3 xiv Table of Contents PART TWO LINEAR REGRESSION ANALYSIS 70 Chapter 4 Simple Linear Regression 70 Chapter Objectives 70 A Student's Perspective 70 Big Picture Overview 71 Data to Be Analyzed: Our City Property Crime and CEO Compensation Samples 72 Data Analyzed in the Text 72 Data Analyzed in the Excel Boxes Understand the Goals of Simple Linear Regression Analysis Consider What the Random Error Component Contains Define the Population Regression Model and the Sample Regression Function Estimate the Sample Regression Function Interpret the Estimated Sample Regression Function Predict Outcomes Based on Our Estimated Sample Regression Function Assess the Goodness-of-Fit of the Estimated Sample Regression Function 85 Measure the Explained and Unexplained Variation in y 86 Two Potential Measures of the Relative Goodnessof-Fit of Our Estimated Sample Regression Function Understand How to Read Regression Output in Excel Understand the Difference between Correlation and Causation 96 Toolkit 98 What We Have Learned in This Chapter 98 Looking Ahead to Chapter 5 99 Problems 99 Exercises 101 References 102 Chapter 5 Hypothesis Testing for Linear Regression Analysis 103 Chapter Objectives 103 A Student's Perspective 103 Big Picture Overview Construct Sampling Distributions Understand Desirable Properties of Simple Linear Regression Estimators Understand the Simple Linear Regression Assumptions Required for OLS to be the Best Linear Unbiased Estimator Understand How to Conduct Hypothesis Tests in Linear Regression Analysis 115 Method 1: Construct Confidence Intervals around the Population Parameter 115 Method 2: Compare Calculated Test Statistics with Predetermined Critical Values 119 Method 3: Calculate and Compare p-values with Predetermined Levels of Significance Conduct Hypothesis Tests for the Overall Statistical Significance of the Sample Regression Function Conduct Hypothesis Tests for the Statistical Significance of the Slope Coefficient 125 Calculate the Standard Error of the Estimated Slope Coefficient 125 Test for the Individual Significance of the Slope Coefficient Understand How to Read Regression Output in Excel for the Purpose of Hypothesis Testing Construct Confidence Intervals around the Predicted Value of v 131 Toolkit 135 What We Have Learned in This Chapter 135 Looking Ahead to Chapter Problems 136 Exercises 139 Appendix 5A Common Theoretical Probability Distributions 141 Chapter 6 Multiple Linear Regression Analysis 147 Chapter Objectives 147 A Student's Perspective 147 Big Picture Overview 148 Data to Be Analyzed: Our MLB Position Player and International GDP Samples 149 Data Analyzed in the Text 149 Data Analyzed in the Excel Boxes Understand the Goals of Multiple Linear Regression Analysis Understand the "Holding All Other Independent Variables Constant" Condition in Multiple Linear Regression Analysis Understand the Multiple Linear Regression Assumptions Required for OLS to Be Blue Interpret Multiple Linear Regression Output in Excel Assess the Goodness-of-Fit of the Sample Multiple Linear Regression Function 160 7%e Coe#:c,'enf (R:) &() The Adjusted R 2 (R 2 ) 161 Sfaw&W Error off/,? Function 162

4 Table of Contents xv 6.6 Perform Hypothesis Tests for the Overall Significance of the Sample Regression Function Perform Hypothesis Tests for the Individual Significance of a Slope Coefficient Perform Hypothesis Tests for the Joint Significance of a Subset of Slope Coefficients Perform the Chow Test for Structural Differences Between Two Subsets of Data 173 Toolkit 175 What We Have Learned in This Chapter 176 Looking Ahead to Chapter Problems 177 Exercises 181 Chapter 7 Qualitative Variables and Nonlinearities in Multiple Linear Regression Analysis 183 Chapter Objectives 183 A Student's Perspective 183 Big Picture Overview Construct and Use Qualitative Independent Variables 184 Binary Dummy Variables 185 Categorical Variables 191 Categorical Variables as a Series of Dummy Variables Construct and Use Interaction Effects Control for Nonlinear Relationships 204 Quadratic Effects 204 Interaction Effects between Two Quantitative Variables Estimate Marginal Effects as Percent Changes and Elasticities 215 The Log-Linear Model 215 The Log-Log Model Estimate a More Fully Specified Model 219 Toolkit 222 What We Have Learned in This Chapter 222 Looking Ahead to Chapter Problems 224 Exercises 228 Chapter 8 Model Selection in Multiple Linear Regression Analysis 230 Chapter Objectives 230 A Student's Perspective 230 Big Picture Overview Understand the Problem Presented by Omitted Variable Bias Understand the Problem Presented by Including an Irrelevant Variable Understand the Problem Presented by Missing Data Understand the Problem Presented by Outliers Perform the Reset Test for the Inclusion of Higher-Order Polynomials Perform the Davidson-MacKinnon Test for Choosing among Non-Nested Alternatives Consider How to Implement the "Eye Test" to Judge the Sample Regression Function Consider What It Means for a /rvalue to be Just Above a Given Significance Level 248 Toolkit 249 What We Have Learned in This Chapter 249 Looking Ahead to Chapter Problems 251 Exercises 253 PART THREE VIOLATIONS OF ASSUMPTIONS 255 Chapter 9 Heteroskedasticity 255 Chapter Objectives 255 A Student's Perspective 255 Big Picture Overview 257 Our Empirical Example: The Relationship between Income and Expenditures 258 Data to Be Analyzed: Our California Home Mortgage Application Sample Understand Methods for Detecting Heteroskedasticity 262 The Informal Method for Detecting Heteroskedasticity 262 Formal Methods for Detecting Heteroskedasticity Correct for Heteroskedasticity 272 Weighted Least Squares 272 A Different Assumed Form of Heteroskedasticity 275 White's Heteroskedastic Consistent Standard Errors 275 Toolkit 278 What We Have Learned in This Chapter 278 Looking Ahead to Chapter Problems 280 Exercises 282

5 xvi Table of Contents Chapter 10 Time-Series Analysis 284 Chapter Objectives 284 A Student's Perspective 284 Big Picture Overview 284 Data to Be Analyzed: Our U.S. Houses Sold Data, 1986Q2-2005Q Understand the Assumptions Required for OLS to Be the Best Linear Unbiased Estimator for Time- Series Data Understand Stationary and Weak Dependence 290 Stationarity in Time Series 290 Weakly Dependent Time Series Estimate Static Time-Series Models Estimate Distributed Lag Models Understand and Account for Time Trends and Seasonality 294 Time Trends 295 Seasonality Test for Structural Breaks in the Data Understand the Problem Presented by Spurious Regression Learn to Perform Forecasting 306 Toolkit 308 What We Have Learned in This Chapter 309 Looking Ahead to Chapter Problems 311 Exercises 311 Reference 312 Chapter 11 Autocorrelation 313 Chapter Objectives 313 A Student's Perspective 313 Big Picture Overview Understand the Autoregressive Structure of the Error Term 316 The AR( I) Process 316 The AR(2) Process 316 The AR( 1,4) Process Understand Methods for Detecting Autocorrelation 316 Informal Methods for Detecting Autocorrelation 317 forma/ Mef/W; /br Defecfmg /Wocorrekmon Understand How to Correct for Autocorrelation 325 The Cochrane-Orcutt Method for AR( 1) Processes 325 7%e Prms-Wmafen MefAod/or AKfJ) Pmc&Mej 332 KoWf Errors Understand Unit Roots and Cointegration 336 Unit Roots 336 CoMffgmfW 338 Toolkit 340 What We Have Learned in This Chapter 340 Looking Ahead to Chapter Problems 342 Exercises 343 PART 4 ADVANCED TOPICS IN ECONOMETRICS 345 Chapter 12 Limited Dependent Variable Analysis 345 Chapter Objectives 345 A Student's Perspective 345 Big Picture Overview 346 Data to Be Analyzed: Our 2010 House Election Data Estimate Models with Binary Dependent Variables 349 The Linear Probability Model 349 The Logit Model 35 l The Probit Model 354 Comparing the Three Estimators Estimate Models with Categorical Dependent Variables 358 A New Data Set: Analyzing Educational Attainment Using Our SIPP Education Data 359 The Multinomial Logit 36 I The Multinomial Probit 364 The Ordered Probit 365 Toolkit 367 What We Have Learned in This Chapter 368 Looking Ahead to Chapter Problems 369 Exercises 370 Chapter 13 Panel Data 371 Chapter Objectives 371 A Student's Perspective 371 Big Picture Overview Understand the Nature of Panel Data 373 Data to Be Analyzed: Our NFL Team Value Panel Employ Pooled Cross-Section Analysis 376 Pooled Cross-Section Analysis with Year Dummies Estimate Panel Data Models 380 First-Differenced Data in a Two-Period Model 380 FiW-EgWa PoW AWc/.s 382 Random-Effects Panel Data Models 385 Toolkit 387

6 Table of Contents xvii What We Have Learned in This Chapter 387 Looking Ahead to Chapter Problems 388 Exercises 389 Chapter 14 Instrumental Variables for Simultaneous Equations, Endogenous Independent Variables, and Measurement Error 390 Chapter Objectives 390 A Student's Perspective 390 Big Picture Overview Use Two-Stage Least Squares to Identify Simultaneous Demand and Supply Equations 392 Data to Be Analyzed: Our U.S. Gasoline Sales Data Use Two-Stage Least Squares to Correct for Endogeneity of an Independent Variable 399 Our Empirical Example: The Effect of a Doctor's Advice to Reduce Drinking 400 Data to Be Analyzed: Our Doctor Advice Data Use Two-Stage Least Squares to Correct for Measurement Error 405 Measurement Error in the Dependent Variable 406 Measurement Error in an Independent Variable 406 Our Empirical Example: Using a Spouse's Responses to Control for Measurement Error in an Individual's Self-Reported Drinking 407 Toolkit 410 What We Have Learned in This Chapter 410 Looking Ahead to Chapter Problems 411 Exercises 413 Chapter 15 Quantile Regression, Count Data, Sample Selection Bias, and Quasi-Experimental Methods 415 Chapter Objectives 415 A Student's Perspective 415 Big Picture Overview Estimate Quantile Regression Estimate Models with Non-Negative Count Data 420 Our Empirical Example: Early-Career Publications by Economics PhDs 420 Data to Be Analyzed: Our Newly Minted Economics PhD Publication Data 421 The Poisson Model 423 The Negative Binomial Model 425 Choosing between the Poisson and the Negative Binomial Models Control for Sample-Selection Bias 428 Data to Be Analyzed: Our CPS Salary Data Use Quasi-Experimental Methods 433 Our Empirical Example: Changes in State Speed Limits 434 Data to Be Analyzed: Our State Traffic Fatality Data 434 Toolkit 438 What We Have Learned in This Chapter 438 Looking Ahead to Chapter Problems 439 Exercises 439 Chapter 16 How to Conduct and Write Up an Empirical Research Project 441 Chapter Objectives 441 A Student's Perspective 441 Big Picture Overview General Approach to Conducting an Empirical Research Project 442 Collecting Data for the Dependent Variables 445 Collecting Data for the Independent Variables General Approach to Writing Up an Empirical Research Project An Example Write-Up of Our Movie Box-Office Project 461 Lights, Camera, Ticket Sales: An Analysis of the Determinants of Domestic Box-Office Gross Introduction Data Description Empirical Results Conclusion 465 References 466 Appendix A Data Collection 469 Appendix B Stata Commands 493 Appendix C Statistical Tables 515 Index 519

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