Using Julia for Introductory Econometrics

Introduces the popular, powerful and free programming language and software package Julia. Julia an ideal candidate for starting to learn econometrics and data analysis. As we will show in this book, learning Julia and the basics of econometrics are two goals that can be achieved very well together. And Julia is completely free and available for all relevant operating systems. When using it in econometrics courses, students can easily download a copy to their own computers and use it at home (or their favorite cafés) to replicate examples and work on take-home assignments. This hands-on experience is essential for the understanding of the econometric models and methods. It also prepares students to conduct their own empirical analyses for their theses, research projects, and professional work. This book does not attempt to provide a self-contained discussion of econometric models and methods. Instead, it builds on the excellent and popular textbook “Introductory Econometrics” by Wooldridge. It is compatible in terms of topics, organization, terminology, and notation, and is designed for a seamless transition from theory to practice. The first chapter provides a gentle introduction to Julia, covers some of the topics of basic statistics and probability presented in the appendix of Wooldridge, and introduces Monte Carlo simulation as an additional tool. The other chapters have the same names and cover the same material as the respective chapters in Wooldridge. Assuming the reader has worked through the material discussed there, this book explains and demonstrates how to implement everything in Julia and replicates many textbook examples. We also open some black boxes of the built-in functions for estimation and inference by directly applying the formulas known from the textbook to reproduce the results. Some supplementary analyses provide additional intuition and insights. 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 Julia 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 Preface Introduction Getting Started Software Julia Scripts Packages File Names and the Working Directory Errors Other Resources Objects in Julia Variables Built-in Objects in Julia Matrix Algebra in LinearAlgebra.jl Objects in DataFrames.jl Using PyCall.jl External Data Data Sets in the Examples Import and Export of Data Files Data from other Sources Base Graphics with Plots.jl Basic Graphs Customizing Graphs with Options Overlaying Several Plots Exporting to a File Descriptive Statistics Discrete Distributions: Frequencies and Contingency Tables Continuous Distributions: Histogram and Density Empirical Cumulative Distribution Function (ECDF) Fundamental Statistics Probability Distributions Discrete Distributions Continuous Distributions Cumulative Distribution Function (CDF) Random Draws from Probability Distributions Confidence Intervals and Statistical Inference Confidence Intervals t Tests p Values Advanced Julia Conditional Execution Loops Functions Computational Speed Outlook Monte Carlo Simulation Finite Sample Properties of Estimators Asymptotic Properties of Estimators Simulation of Confidence Intervals and t Tests Regression Analysis with Cross-Sectional Data The Simple Regression Model Simple OLS Regression Coefficients, Fitted Values, and Residuals Goodness of Fit Nonlinearities Regression through the Origin and Regression on a Constant Expected Values, Variances, and Standard Errors Monte Carlo Simulations One Sample Many Samples Violation of SLR.4 Violation of SLR.5 Multiple Regression Analysis: Estimation Multiple Regression in Practice OLS in Matrix Form Ceteris Paribus Interpretation and Omitted Variable Bias Standard Errors, Multicollinearity, and VIF Multiple Regression Analysis: Inference The t Test General Setup Standard Case Other Hypotheses Confidence Intervals Linear Restrictions: F Tests Reporting Regression Results Multiple Regression Analysis: OLS Asymptotics Simulation Exercises Normally Distributed Error Terms Non-Normal Error Terms (Not) Conditioning on the Regressors LM Test Multiple Regression Analysis: Further Issues Model Formulae Data Scaling: Arithmetic Operations Within a Formula Standardization: Beta Coefficients Logarithms Quadratics and Polynomials Hypothesis Testing Interaction Terms Prediction Confidence and Prediction Intervals for Predictions Effect Plots for Nonlinear Specifications Multiple Regression Analysis with Qualitative Regressors Linear Regression with Dummy Variables as Regressors Boolean Variables Categorical Variables Breaking a Numeric Variable Into Categories Interactions and Differences in Regression Functions Across Groups Heteroscedasticity Heteroscedasticity-Robust Inference Heteroscedasticity Tests Weighted Least Squares More on Specification and Data Issues Functional Form Misspecification Measurement Error Missing Data and Nonrandom Samples Outlying Observations Least Absolute Deviations (LAD) Estimation Regression Analysis with Time Series Data Basic Regression Analysis with Time Series Data Static Time Series Models Time Series Data Types in Julia Equispaced Time Series in Julia Irregular Time Series in Julia Other Time Series Models Finite Distributed Lag Models Trends Seasonality Further Issues in Using OLS with Time Series Data Asymptotics with Time Series The Nature of Highly Persistent Time Series Differences of Highly Persistent Time Series Regression with First Differences Serial Correlation and Heteroscedasticity in Time Series Regressions Testing for Serial Correlation of the Error Term FGLS Estimation Serial Correlation-Robust Inference with OLS Autoregressive Conditional Heteroscedasticity Advanced Topics Pooling Cross Sections Across Time: Simple Panel Data Methods Pooled Cross Sections Difference-in-Differences Organizing Panel Data First Differenced Estimator Advanced Panel Data Methods Getting Started with Panel Data Fixed Effects Estimation Random Effects Models Dummy Variable Regression and Correlated Random Effects Instrumental Variables Estimation and Two Stage Least Squares Instrumental Variables in Simple Regression Models More Exogenous Regressors Two Stage Least Squares Testing for Exogeneity of the Regressors Testing Overidentifying Restrictions Instrumental Variables with Panel Data Simultaneous Equations Models Setup and Notation Estimation by 2SLS Outlook: Estimation by 3SLS Limited Dependent Variable Models and Sample Selection Corrections Binary Responses Linear Probability Models Logit and Probit Models: Estimation Inference Predictions Partial Effects Count Data: The Poisson Regression Model Corner Solution Responses: The Tobit Model Censored and Truncated Regression Models Sample Selection Corrections Advanced Time Series Topics Infinite Distributed Lag Models Testing for Unit Roots Spurious Regression Cointegration and Error Correction Models Forecasting Carrying Out an Empirical Project Working with Julia Scripts Logging Output in Text Files Formatted Documents with Jupyter Notebook Getting Started Cells Markdown Basics Appendices Julia Scripts Scripts Used in Chapter 01 Scripts Used in Chapter 02 Scripts Used in Chapter 03 Scripts Used in Chapter 04 Scripts Used in Chapter 05 Scripts Used in Chapter 06 Scripts Used in Chapter 07 Scripts Used in Chapter 08 Scripts Used in Chapter 09 Scripts Used in Chapter 10 Scripts Used in Chapter 11 Scripts Used in Chapter 12 Scripts Used in Chapter 13 Scripts Used in Chapter 14 Scripts Used in Chapter 15 Scripts Used in Chapter 16 Scripts Used in Chapter 17 Scripts Used in Chapter 18 Scripts Used in Chapter 19 Bibliography List of Wooldridge (2019) Examples Index