Hands-on intermediate econometrics using R: templates for extending dozens of practical examples

Preface

Foreword

1. Production Function and Regression Methods Using R

1.1. R and Microeconometric Preliminaries

1.1.1. Data on Metals Production Available in R

1.1.2. Descriptive Statistics Using R

1.1.3. Writing Skewness and Kurtosis Functions in R

1.1.4. Units of Measurement and Numerical Reliability of Regressions

1.1.5. Basic Graphics in R

1.1.6. The Isoquant

1.1.7. Total Productivity of an Input

1.1.8. The Marginal Productivity (MP) of an Input

1.1.9. Slope of the Isoquant and MRTS

1.1.10. Scale Elasticity as the Returns to Scale Parameter

1.1.11. Elasticity of Substitution

1.1.12. Typical Steps in Empirical Work

1.2. Preliminary Regression Theory: Results Using R

1.2.1. Regression as an Object `reg1' in R

1.2.2. Accessing Objects Within an R Object by Using the Dollar Symbol

1.3. Deeper Regression Theory: Diagonals of the Hat Matrix

1.4. Discussion of Four Diagnostic Plots by R

1.5. Testing Constant Returns and 3D Scatter Plots

1.6. Homothetic Production and Cost Functions

1.6.1. Euler Theorem and Duality Theorem

1.6.2. Profit Maximizing Solutions

1.6.3. Elasticity of Total Cost w.r.t. Output

1.7. Miscellaneous Microeconomic Topics

1.7.1. Analytic Input Demand Function for the Cobb-Douglas Form

1.7.2. Separability in the Presence of Three or More Inputs

1.7.3. Two or More Outputs as Joint Outputs

1.7.4. Economies of Scope

1.8. Nonhomogeneous Production Functions

1.8.1. Three-Input Production Function for Widgets

1.8.2. Isoquant Plotting for a Bell System Production Function

1.9. Collinearity Problem, Singular Value Decomposition (SVD), and Ridge Regression

1.9.1. What is Collinearity?

1.9.2. Consequences of Near Collinearity

1.9.3. Regression Theory Using the Singular Value Decomposition

1.10. Near Collinearity Solutions by Coefficient Shrinkage

1.10.1. Ridge Regression

1.10.2. Principal Components Regression

1.11. Bell System Production Function in Anti-Trust Trial

1.11.1. Collinearity Diagnostics for Bell Data Trans-Log

1.11.2. Shrinkage Solution and Ridge Regression for Bell Data

1.11.3. Ridge Regression from Existing R Packages

1.12. Comments on Wrong Signs, Collinearity, and Ridge Scaling

1.12.1. Concluding Comments on the 1982 Bell System Breakup

1.13. Data Appendix

2. Univariate Time Series Analysis with R

2.1. Econometric Univariate Time Series are Ubiquitous

2.2. Stochastic Difference Equations

2.3. Second-Order Stochastic Difference Equation and Business Cycles

2.3.1. Complex Number Solution of the Stochastic AR(2) Difference Equation

2.3.2. General Solution to ARMA (p,p - 1) Stochastic Difference Equations

2.4. Properties of ARIMA Models

2.4.1. Identification of the Lag Order

2.4.2. ARIMA Estimation

2.4.3. ARIMA Diagnostic Checking

2.5. Stochastic Process and Stationarity

2.5.1. Stochastic Process and Underlying Probability Space

2.5.2. Autocovariance of a Stochastic Process and Ergodicity

2.5.3. Stationary Process

2.5.4. Detrending and Differencing to Achieve Stationarity

2.6. Mean Reversion

2.7. Autocovariance Generating Functions (AGF) and the Power Spectrum

2.7.1. How to Get the Power Spectrum from the AGF?

2.8. Explicit Modeling of Variance (ARCH, GARCH Models.)

2.9. Tests of Independence, Neglected Nonlinearity, Turning Points

2.10. Long Memory Models and Fractional Differencing

2.11. Forecasting

2.12. Concluding Remarks and Examples

3. Bivariate Time Series Analysis Including Stochastic Diffusion and Cointegration

3.1. Autoregressive Distributed Lag (ARDL) Models

3.2. Economic Interpretations of ARDL(1,1) Model

3.2.1. Description of M1 to M11 Model Specifications

3.2.2. ARDL(0,q) as M12 Model, Impact and Long-Run Multipliers

3.2.3. Adaptive Expectations Model to Test Rational Expectations Hypothesis

3.2.4. Statistical Inference and Estimation with Lagged-Dependent Variables

3.2.5. Identification Problems Involving Expectational Variables (I. Fisher Example)

3.2.6. Impulse Response, Mean Lag and Insights from a Polynomials in L

3.2.7. Choice Between M1 to M11 Models Using R

3.3. Stochastic Diffusion Models for Asset Prices

3.4. Spurious Regression (R2 > Durbin Watson) and Cointegration

3.4.1. Definition of a Process Integrated of Order d, I(d)

3.4.2. Cointegration Definition and Discussion

3.4.3. Error Correction Models of Cointegration

3.4.4. Economic Equilibria and Error Reductions through Learning

3.4.5. Signs and Significance of Coefficients on Past Errors while Agents Learn

3.5. Granger Causality Testing

4. Utility Theory and Empirical Implications

4.1. Utility Theory

4.1.1. Expected Utility Theory (EUT)

4.1.2. Arrow-Pratt Coefficient of Absolute Risk Aversion (CARA)

4.1.3. Risk Premium Needed to Encourage Risky Investments

4.1.4. Taylor Series Links EUT, Moments of f(x) and Derivatives of U(x)

4.2. Non-Expected Utility Theory

4.2.1. Lorenz Curve Scaling over the Unit Square

4.2.2. Mapping From EUT to Non-EUT within the Unit Square to Get Decision Weights

4.3. Incorporating Utility Theory into Risk Measurement and Stochastic Dominance

4.3.1. Class D1 of Utility Functions and Investors

4.3.2. Class D2 of Utility Functions and Investors

4.3.3. Explicit Utility Functions and Arrow-Pratt Measures of Risk Aversion

4.3.4. Class D3 of Utility Functions and Investors

4.3.5. Class D4 of Utility Functions and Investors

4.3.6. First-Order Stochastic Dominance (1SD)

4.3.7. Second-Order Stochastic Dominance (2SD)

4.3.8. Third-Order Stochastic Dominance (3SD)

4.3.9. Fourth-Order Stochastic Dominance (4SD)

4.3.10. Empirical Checking of Stochastic Dominance Using Matrix Multiplications and Incorporation of 4DPs of Non-EUT

5. Vector Models for Multivariate Problems

5.1. Introduction and VAR Models

5.1.1. Some R Packages for Vector Modeling

5.1.2. Vector Autoregression or VAR Models

5.1.3. Data Collection Tips Using R

5.1.4. VAR Estimation of Sims' Model

5.1.5. Granger-Causality Analysis in VAR Models

5.1.6. Forecasting Out-of-Sample in VAR Models

5.1.7. Impulse Response Analysis in VAR Models

5.2. Multivariate Regressions: Canonical Correlations

5.2.1. Why Canonical Correlation is Not Popular So Far

5.3. VAR Estimation and Cointegration Testing Using Canonical Correlations

5.4. Final Remarks: Multivariate Statisics Using R

6. Simultaneous Equation Models

6.1. Introduction

6.1.1. Simultaneous Equation Notation System with Stars and Subscripts

6.1.2. Simultaneous Equations Bias and the Reduced Form

6.1.3. Successively Weaker Assumptions Regarding the Nature of the Zj Matrix of Regressors

6.1.4. Reduced Form Estimation and Other Alternatives to OLS

6.1.5. Assumptions of Simultaneous Equations Models

6.2. Instrumental Variables and Generalized Least Squares

6.2.1. The Instrumental Variables (IV) and Generalized IV (GIV) Estimator

6.2.2. Choice Between OLS and IV by Using Wu-Hausman Specification Test

6.3. Limited Information and Two-Stage Least Squares

6.3.1. Two-Stage Least Squares

6.3.2. The k-class Estimator

6.3.3. Limited Information Maximum Likelihood (LIML) Estimator

6.4. Identification of Simultaneous Equation Models

6.4.1. Identification is Uniquely Going from the Reduced Form to the Structure

6.5. Full Information and Three-Stage Least Squares (3SLS)

6.5.1. Full Information Maximum Likelihood

6.6. Potential of Simultaneous Equations Beyond Econometrics

7. Limited Dependent Variable (GLM) Models

7.1. Problems with Dummy Dependent Variables

7.1.1. Proof of the Claim that Var(e [Page No. xxiv]i) = Pi(1 - Pi)

7.1.2. The General Linear Model from Biostatistics

7.1.3. Marginal Effects (Partial Derivatives) in Logit-Type GLM Models

7.1.4. Further Generalizations of Logit and Probit Models

7.1.5. Ordered Response

7.2. Quasi-Likelihood Function for Binary Choice Models

7.2.1. The ML Estimator in Binary Choice Models

7.2.2. Tobit Model for Censored Dependent Variables

7.3. Heckman Two-Step Estimator for Self-Selection Bias

7.4. Time Duration Length (Survival) Models

7.4.1. Probability Distributions and Implied Hazard Functions

7.4.2. Parametric Survival (Hazard) Models

7.4.3. Semiparametric Including Cox Proportional Hazard Models

8. Dynamic Optimization and Empirical Analysis of Consumer Behavior

8.1. Introduction

8.2. Dynamic Optimization

8.3. Hall's Random Walk Model

8.3.1. Data from the Internet and an Implementation

8.3.2. OLS Estimation of the Random Walk Model

8.3.3. Direct Estimation of Hall's NLHS Specification

8.3.4. Strong Assumptions and Granger-Causality Tests

8.4. Nonparametric Kernel Estimation

8.4.1. Kernel Estimation of Amorphous Partials

8.5. Wiener-Hopf-Whittle Model if Consumption Precedes Income

8.5.1. Determination of Target Consumption

8.5.2. Implications for Various Puzzles of Consumer Theory

8.6. Final Remarks on Consumer Theory

8.7. Appendix: Additional R Code

9. Single, Double and Maximum Entropy Bootstrap and Inference

9.1. The Motivation and Background Behind Bootstrapping

9.1.1. Pivotal Quantity and p-Value

9.1.2. Uncertainty Regarding Proper Density for Regression Errors Illustrated

9.1.3. The Delta Method for Standard Error of Functions

9.2. Description of Parametric iid Bootstrap

9.2.1. Simulated Sampling Distribution for Statistical Inference Using OLS Residuals

9.2.2. Steps in a Parametric Approximation

9.2.3. Percentile Confidence Intervals

9.2.4. Reflected Percentile Confidence Interval for Bias Correction

9.2.5. Significance Tests as Duals to Confidence Intervals

9.3. Description of Nonparametric iid Bootstrap

9.3.1. Map Data from Time-Domain to (Numerical Magnitudes) Values-Domain

9.4. Double Bootstrap Illustrated with a Nonlinear Model

9.4.1. A Digression on the Size of Resamples

9.4.2. Double Bootstrap Theory Involving Roots and Uniform Density

9.4.3. GNR Implementation of Nonlinear Regression for Metals Data

9.5. Maximum Entropy Density Bootstrap for Time-Series Data

9.5.1. Wiener, Kolmogorov, Khintchine (WKK) Ensemble of Time Series

9.5.2. Avoiding Unrealistic Properties of iid Bootstrap

9.5.3. Maximum Entropy Density is Uniform When Limits are Known

9.5.4. Quantiles of the Patchwork of the ME Density

9.5.5. Numerical Illustration of "Meboot" Package in R

9.5.6. Simple and Size-Corrected Confidence Bounds

10. Generalized Least Squares, VARMA, and Estimating Functions

10.1. Feasible Generalized Least Squares (GLS) to Adjust for Autocorrelated Errors and/or Heteroscedasticity

10.1.1. Consequences of Ignoring Nonspherical Errors O ≠ [Page No. xxvi] IT

10.1.2. Derivation of the GLS and Efficiency Comparison

10.1.3. Computation of the GLS and Feasible GLS

10.1.4. Improved OLS Inference for Nonspherical Errors

10.1.5. Efficient Estimation of b [Page No. xxvi] Coefficients

10.1.6. An Illustration Using Fisher's Model for Interest Rates

10.2. Vector ARMA Estimation for Rational Expectations Models

10.2.1. Greater Realism of VARMA(p,q) Models

10.2.2. Expectational Variables from Conditional Forecasts in a General Model

10.2.3. A Rational Expectation Model Using VARMA

10.2.4. Further Forecasts, Transfer Function Gains, and Response Analysis

10.3. Optimal Estimating Function (OptEF) and Generalized Method of Moments (GMM)

10.3.1. Derivation of Optimal Estimating Functions for Regressions

10.3.2. Finite Sample Optimality of OptEF

10.3.3. Introduction to the GMM

10.3.4. Cases Where OptEF Viewpoint Dominates GMM

10.3.5. Advantages and Disadvantages of GMM and OptEF

10.4. Godambe Pivot Functions (GPFs) and Statistical Inference

10.4.1. Application of the Frisch-Waugh Theorem to Constructing CI95

10.4.2. Steps in Application of GPF to Feasible GLS Estimation

11. Box-Cox, Loess and Projection Pursuit Regression

11.1. Further R Tools for Studying Nonlinear Relations

11.2. Box-Cox Transformation

11.2.1. Logarithmic and Square Root Transformations

11.3. Scatterplot Smoothing and Loess Regressions

11.3.1. Improved Fit (Forecasts) by Loess Smoothing

11.4. Projection Pursuit Methods

11.5. Remarks on Nonlinear Econometrics

Appendix

References

Index