Using Python for Introductory Econometrics

Preface....11 Introduction....13 Getting Started....13 Software....13 Python Scripts....14 Modules ....18 File Names and the Working Directory....19 Errors and Warnings....19 Other Resources....20 Objects in Python....21 Variables....21 Objects in Python....21 Objects in numpy....25 Objects in pandas....29 External Data....33 Data Sets in the Examples....33 Import and Export of Data Files....34 Data from other Sources....36 Base Graphics with matplotlib....37 Basic Graphs....37 Customizing Graphs with Options....39 Overlaying Several Plots....40 Exporting to a File....41 Descriptive Statistics....43 Discrete Distributions: Frequencies and Contingency Tables....43 Continuous Distributions: Histogram and Density....48 Empirical Cumulative Distribution Function (ECDF)....50 Fundamental Statistics....52 Probability Distributions....54 Discrete Distributions....54 Continuous Distributions....57 Cumulative Distribution Function (CDF)....57 Random Draws from Probability Distributions....60 Confidence Intervals and Statistical Inference....62 Confidence Intervals....62 t Tests....65 p Values....67 Advanced Python....70 Conditional Execution....70 Loops....70 Functions....71 Object Orientation....72 Outlook....76 Monte Carlo Simulation....76 Finite Sample Properties of Estimators....76 Asymptotic Properties of Estimators....79 Simulation of Confidence Intervals and t Tests....80 Regression Analysis with Cross-Sectional Data....85 The Simple Regression Model....87 Simple OLS Regression....87 Coefficients, Fitted Values, and Residuals....92 Goodness of Fit....95 Nonlinearities....98 Regression through the Origin and Regression on a Constant....99 Expected Values, Variances, and Standard Errors....101 Monte Carlo Simulations....104 One Sample....104 Many Samples....106 Violation of SLR.4 ....108 Violation of SLR.5 ....109 Multiple Regression Analysis: Estimation....111 Multiple Regression in Practice....111 OLS in Matrix Form....117 Ceteris Paribus Interpretation and Omitted Variable Bias....120 Standard Errors, Multicollinearity, and VIF....122 Multiple Regression Analysis: Inference....125 The t Test....125 General Setup....125 Standard Case....126 Other Hypotheses....128 Confidence Intervals....131 Linear Restrictions: F-Tests....133 Multiple Regression Analysis: OLS Asymptotics....137 Simulation Exercises....137 Normally Distributed Error Terms....137 Non-Normal Error Terms....138 (Not) Conditioning on the Regressors....142 LM Test....145 Multiple Regression Analysis: Further Issues....147 Model Formulae....147 Data Scaling: Arithmetic Operations Within a Formula....147 Standardization: Beta Coefficients....148 Logarithms....150 Quadratics and Polynomials....150 Hypothesis Testing....152 Interaction Terms....153 Prediction....154 Confidence and Prediction Intervals for Predictions....154 Effect Plots for Nonlinear Specifications....157 Multiple Regression Analysis with Qualitative Regressors....161 Linear Regression with Dummy Variables as Regressors....161 Boolean Variables....164 Categorical Variables....165 ANOVA Tables....167 Breaking a Numeric Variable Into Categories....169 Interactions and Differences in Regression Functions Across Groups....171 Heteroscedasticity....175 Heteroscedasticity-Robust Inference....175 Heteroscedasticity Tests....178 Weighted Least Squares....181 More on Specification and Data Issues....187 Functional Form Misspecification....187 Measurement Error....190 Missing Data and Nonrandom Samples....194 Outlying Observations....198 Least Absolute Deviations (LAD) Estimation....200 Regression Analysis with Time Series Data....201 Basic Regression Analysis with Time Series Data....203 Static Time Series Models....203 Time Series Data Types in Python....204 Equispaced Time Series in Python....204 Irregular Time Series in Python....207 Other Time Series Models....209 Finite Distributed Lag Models....209 Trends....211 Seasonality....212 Further Issues in Using OLS with Time Series Data....215 Asymptotics with Time Series....215 The Nature of Highly Persistent Time Series....220 Differences of Highly Persistent Time Series....223 Regression with First Differences....223 Serial Correlation and Heteroscedasticity in Time Series Regressions....227 Testing for Serial Correlation of the Error Term....227 FGLS Estimation....232 Serial Correlation-Robust Inference with OLS....233 Autoregressive Conditional Heteroscedasticity....234 Advanced Topics....237 Pooling Cross-Sections Across Time: Simple Panel Data Methods....239 Pooled Cross-Sections....239 Difference-in-Differences....240 Organizing Panel Data....243 First Differenced Estimator....244 Advanced Panel Data Methods....249 Fixed Effects Estimation....249 Random Effects Models....250 Dummy Variable Regression and Correlated Random Effects....254 Robust (Clustered) Standard Errors....257 Instrumental Variables Estimation and Two Stage Least Squares....259 Instrumental Variables in Simple Regression Models....259 More Exogenous Regressors....261 Two Stage Least Squares....264 Testing for Exogeneity of the Regressors....266 Testing Overidentifying Restrictions....267 Instrumental Variables with Panel Data....269 Simultaneous Equations Models....271 Setup and Notation....271 Estimation by 2SLS....272 Outlook: Estimation by 3SLS....273 Limited Dependent Variable Models and Sample Selection Corrections....275 Binary Responses....275 Linear Probability Models....275 Logit and Probit Models: Estimation....277 Inference....280 Predictions....281 Partial Effects....283 Count Data: The Poisson Regression Model....286 Corner Solution Responses: The Tobit Model....289 Censored and Truncated Regression Models....291 Sample Selection Corrections....296 Advanced Time Series Topics....299 Infinite Distributed Lag Models....299 Testing for Unit Roots....301 Spurious Regression....302 Cointegration and Error Correction Models....305 Forecasting....305 Carrying Out an Empirical Project....309 Working with Python Scripts....309 Logging Output in Text Files....311 Formatted Documents with Jupyter Notebook....312 Getting Started....312 Cells....312 Markdown Basics....313 Appendices....319 Python Scripts....321 Scripts Used in Chapter 01....321 Scripts Used in Chapter 02....344 Scripts Used in Chapter 03....353 Scripts Used in Chapter 04....357 Scripts Used in Chapter 05....359 Scripts Used in Chapter 06....362 Scripts Used in Chapter 07....367 Scripts Used in Chapter 08....371 Scripts Used in Chapter 09....375 Scripts Used in Chapter 10....381 Scripts Used in Chapter 11....384 Scripts Used in Chapter 12....388 Scripts Used in Chapter 13....393 Scripts Used in Chapter 14....396 Scripts Used in Chapter 15....400 Scripts Used in Chapter 16....405 Scripts Used in Chapter 17....406 Scripts Used in Chapter 18....415 Scripts Used in Chapter 19....419 Bibliography....420 List of Wooldridge (2019) Examples....423 Index....425