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

• Introduces the popular, powerful and free programming language and software package Python
• Focus: implementation of standard tools and methods used in econometrics
• Compatible with "Introductory Econometrics" by Jeffrey M. Wooldridge in terms of topics, organization, terminology and notation
• Companion website with full text, all code for download and other goodies

Topics:

• A gentle introduction to Python
• Simple and multiple regression in matrix form and using black box routines
• Inference in small samples and asymptotics
• Monte Carlo simulations
• Heteroscedasticity
• Time series regression
• Pooled cross-sections and panel data
• Instrumental variables and two-stage least squares
• Simultaneous equation models
• Limited dependent variables: binary, count data, censoring, truncation, and sample selection
• Formatted reports using Jupyter Notebooks