Hands-On Intermediate Econometrics Using R

The following sections are included:

• Preface

• Foreword

• Contents

The following sections are included:

• 𝑅 and Microeconometric Preliminaries
  • Data on Metals Production Available in 𝑅
  • Descriptive Statistics Using 𝑅
  • Writing Skewness and Kurtosis Functions in 𝑅
  • Units of Measurement and Numerical Reliability of Regressions
  • Basic Graphics in 𝑅
  • The Isoquant
  • Total Productivity of an Input
  • The Marginal Productivity (MP) of an Input
  • Slope of the Isoquant and MRTS
  • Scale Elasticity as the Returns to Scale Parameter
  • Elasticity of Substitution
  • Typical Steps in Empirical Work

• Preliminary Regression Theory: Results Using 𝑅
  • Regression as an Object ‘reg1’ in 𝑅
  • Accessing Objects Within an 𝑅 Object by Using the Dollar Symbol

• Deeper Regression Theory: Diagonals of the Hat Matrix

• Discussion of Four Diagnostic Plots by 𝑅

• Testing Constant Returns and 3D Scatter Plots

• Homothetic Production and Cost Functions
  • • The Constant Elasticity of Substitution (CES) Production Function
    • Hidden Restrictions of Homogeneous/Homethetic Functional Forms
    • Cost Function Lagrangian
    • Cost Minimizing Solution
  • Euler Theorem and Duality Theorem
    • Expansion Path
    • Duality Theorem
  • Profit Maximizing Solutions
  • Elasticity of Total Cost w.r.t. Output

• Miscellaneous Microeconomic Topics
  • Analytic Input Demand Function for the Cobb–Douglas Form
  • Separability in the Presence of Three or More Inputs
  • Two or More Outputs as Joint Outputs
  • Economies of Scope
    • Bell System Example on Economies of Scope

• Nonhomogeneous Production Functions
  • Three-Input Production Function for Widgets
    • Creating a Text File of Data on Your C Drive for Reading in 𝑅
    • Reading Data and MNH Estimation in 𝑅
  • Isoquant Plotting for a Bell System Production Function

• Collinearity Problem, Singular Value Decomposition (SVD), and Ridge Regression
  • What is Collinearity?
    • Rank Deficiency m
    • Near Collinearity
  • Consequences of Near Collinearity
    • Collinearity and Ill-Conditioned Matrices
    • Rule of Thumb for a Large Condition Number
    • Collinearity as a Nonproblem
  • Regression Theory Using the Singular Value Decomposition
    • MSE(b) and Extreme Unreliability of OLS Under Near Collinearity
    • REMARK 1 (Extreme Unreliability of OLS)
    • Forecasting and Collinearity

• Near Collinearity Solutions by Coefficient Shrinkage
  • Ridge Regression
    • Derivation of Shrinkage Factors Δ
    • Declining Deltas and Justification for Shrinking to Zero Prior
    • Choice of k in Ridge Regression
  • Principal Components Regression

• Bell System Production Function in Anti-Trust Trial
  • Collinearity Diagnostics for Bell Data Trans-Log
  • Shrinkage Solution and Ridge Regression for Bell Data
  • Ridge Regression from Existing 𝑅 Packages

• Comments on Wrong Signs, Collinearity, and Ridge Scaling
  • Concluding Comments on the 1982 Bell System Breakup

• Data Appendix

The following sections are included:

• Econometric Univariate Time Series are Ubiquitous

• Stochastic Difference Equations

• Second-Order Stochastic Difference Equation and Business Cycles
  • Complex Number Solution of the Stochastic A𝑅(2) Difference Equation
  • General Solution to ARMA (p, p − 1) Stochastic Difference Equations

• Properties of ARIMA Models
  • Identification of the Lag Order
  • ARIMA Estimation
  • ARIMA Diagnostic Checking

• Stochastic Process and Stationarity
  • Stochastic Process and Underlying Probability Space
  • Autocovariance of a Stochastic Process and Ergodicity
  • Stationary Process
  • Detrending and Differencing to Achieve Stationarity

• Mean Reversion

• Autocovariance Generating Functions (AGF) and the Power Spectrum
  • How to Get the Power Spectrum from the AGF?

• Explicit Modeling of Variance (ARCH, GARCH Models)

• Tests of Independence, Neglected Nonlinearity, Turning Points

• Long Memory Models and Fractional Differencing

• Forecasting

• Concluding Remarks and Examples

The following sections are included:

• Autoregressive Distributed Lag (ARDL) Models

• Economic Interpretations of ARDL(1,1) Model
  • Description of M1 to M11 Model Specifications
  • ARDL(0,q) as M12 Model, Impact and Long-Run Multipliers
  • Adaptive Expectations Model to Test Rational Expectations Hypothesis
  • Statistical Inference and Estimation with Lagged-Dependent Variables
  • Identification Problems Involving Expectational Variables (I. Fisher Example)
  • Impulse Response, Mean Lag and Insights from a Polynomials in L
  • Choice Between M1 to M11 Models Using 𝑅

• Stochastic Diffusion Models for Asset Prices

• Spurious Regression (R² > Durbin Watson) and Cointegration
  • Definition of a Process Integrated of Order d, I(d)
  • Cointegration Definition and Discussion
  • Error Correction Models of Cointegration
  • Economic Equilibria and Error Reductions through Learning
  • Signs and Significance of Coefficients on Past Errors while Agents Learn

• Granger Causality Testing

The following sections are included:

• Utility Theory
  • Expected Utility Theory (EUT)
  • Arrrow–Pratt Coefficient of Absolute Risk Aversion (CARA)
  • Risk Premium Needed to Encourage Risky Investments
  • Taylor Series Links EUT, Moments of f(x) and Derivatives of U(x)

• Non-Expected Utility Theory
  • Lorenz Curve Scaling over the Unit Square
  • Mapping From EUT to Non-EUT within the Unit Square to Get Decision Weights

• Incorporating Utility Theory into Risk Measurement and Stochastic Dominance
  • Class D1 of Utility Functions and Investors
  • Class D2 of Utility Functions and Investors
  • Explicit Utility Functions and Arrow–Pratt Measures of Risk Aversion
  • Class D3 of Utility Functions and Investors
  • Class D4 of Utility Functions and Investors
  • First-Order Stochastic Dominance (1SD)
  • Second-Order Stochastic Dominance (2SD)
  • Third-Order Stochastic Dominance (3SD)
  • Fourth-Order Stochastic Dominance (4SD)
  • Empirical Checking of Stochastic Dominance Using Matrix Multiplications and Incorporation of 4DPs of Non-EUT

The following sections are included:

• Introduction and VAR Models
  • Some 𝑅 Packages for Vector Modeling
  • Vector Autoregression or VAR Models
  • Data Collection Tips Using 𝑅
  • VAR Estimation of Sims' Model
  • Granger-Causality Analysis in VAR Models
  • Forecasting Out-of-Sample in VAR Models
  • Impulse Response Analysis in VAR Models

• Multivariate Regressions: Canonical Correlations
  • Why Canonical Correlation is Not Popular So Far

• VAR Estimation and Cointegration Testing Using Canonical Correlations

• Final Remarks: Multivariate Statisics Using 𝑅

The following sections are included:

• Introduction
  • Simultaneous Equation Notation System with Stars and Subscripts
  • Simultaneous Equations Bias and the Reduced Form
  • Successively Weaker Assumptions Regarding the Nature of the Z_j Matrix of Regressors
  • Reduced Form Estimation and Other Alternatives to OLS
  • Assumptions of Simultaneous Equations Models

• Instrumental Variables and Generalized Least Squares
  • The Instrumental Variables (IV) and Generalized IV (GIV) Estimator
  • Choice Between OLS and IV by Using Wu–Hausman Specification Test

• Limited Information and Two-Stage Least Squares
  • Two-Stage Least Squares
  • The k-class Estimator
  • Limited Information Maximum Likelihood (LIML) Estimator

• Identification of Simultaneous Equation Models
  • Identification is Uniquely Going from the Reduced Form to the Structure

• Full Information and Three-Stage Least Squares (3SLS)
  • Full Information Maximum Likelihood

• Potential of Simultaneous Equations Beyond Econometrics

The following sections are included:

• Problems with Dummy Dependent Variables
  • Proof of the Claim that Var(ε_i) = P_i(1 − P_i)
  • The General Linear Model from Biostatistics
  • Marginal Effects (Partial Derivatives) in Logit-Type GLM Models
  • Further Generalizations of Logit and Probit Models
  • Ordered Response

• Quasi-Likelihood Function for Binary Choice Models
  • The ML Estimator in Binary Choice Models
  • Tobit Model for Censored Dependent Variables

• Heckman Two-Step Estimator for Self-Selection Bias

• Time Duration Length (Survival) Models
  • Probability Distributions and Implied Hazard Functions
  • Parametric Survival (Hazard) Models
  • Semiparametric Including Cox Proportional Hazard Models

The following sections are included:

• Introduction

• Dynamic Optimization

• Hall's Random Walk Model
  • Data from the Internet and an Implementation
  • OLS Estimation of the Random Walk Model
  • Direct Estimation of Hall's NLHS Specification
    • Monthly to Quarterly Data Conversion
  • Strong Assumptions and Granger-Causality Tests

• Nonparametric Kernel Estimation
  • Kernel Estimation of Amorphous Partials

• Wiener–Hopf–Whittle Model if Consumption Precedes Income
  • Determination of Target Consumption
  • Implications for Various Puzzles of Consumer Theory

• Final Remarks on Consumer Theory

• Appendix: Additional 𝑅 Code

The following sections are included:

• The Motivation and Background Behind Bootstrapping
  • Pivotal Quantity and p-Value
  • Uncertainty Regarding Proper Density for Regression Errors Illustrated
  • The Delta Method for Standard Error of Functions

• Description of Parametric iid Bootstrap
  • Simulated Sampling Distribution for Statistical Inference Using OLS Residuals
  • Steps in a Parametric Approximation
  • Percentile Confidence Intervals
  • Reflected Percentile Confidence Interval for Bias Correction
  • Significance Tests as Duals to Confidence Intervals

• Description of Nonparametric iid Bootstrap
  • Map Data from Time-Domain to (Numerical Magnitudes) Values-Domain

• Double Bootstrap Illustrated with a Nonlinear Model
  • A Digression on the Size of Resamples
  • Double Bootstrap Theory Involving Roots and Uniform Density
  • GNR Implementation of Nonlinear Regression for Metals Data

• Maximum Entropy Density Bootstrap for Time-Series Data
  • Wiener, Kolmogorov, Khintchine (WKK) Ensemble of Time Series
  • Avoiding Unrealistic Properties of iid Bootstrap
  • Maximum Entropy Density is Uniform When Limits are Known
  • Quantiles of the Patchwork of the ME Density
  • Numerical Illustration of “Meboot” Package in 𝑅
  • Simple and Size-Corrected Confidence Bounds

The following sections are included:

• Feasible Generalized Least Squares (GLS) to Adjust for Autocorrelated Errors and/or Heteroscedasticity
  • Consequences of Ignoring Nonspherical Errors Ω ≠ I_T
  • Derivation of the GLS and Efficiency Comparison
  • Computation of the GLS and Feasible GLS
  • Improved OLS Inference for Nonspherical Errors
  • Efficient Estimation of β Coefficients
  • An Illustration Using Fisher's Model for Interest Rates

• Vector ARMA Estimation for Rational Expectations Models
  • Greater Realism of VARMA(p, q) Models
  • Expectational Variables from Conditional Forecasts in a General Model
  • A Rational Expectation Model Using VARMA
  • Further Forecasts, Transfer Function Gains, and Response Analysis

• Optimal Estimating Function (OptEF) and Generalized Method of Moments (GMM)
  • Derivation of Optimal Estimating Functions for Regressions
  • Finite Sample Optimality of OptEF
  • Introduction to the GMM
  • Cases Where OptEF Viewpoint Dominates GMM
  • Advantages and Disadvantages of GMM and OptEF

• Godambe Pivot Functions (GPFs) and Statistical Inference
  • Application of the Frisch–Waugh Theorem to Constructing CI95
  • Steps in Application of GPF to Feasible GLS Estimation

The following sections are included:

• Further 𝑅 Tools for Studying Nonlinear Relations

• Box–Cox Transformation
  • Logarithmic and Square Root Transformations

• Scatterplot Smoothing and Loess Regressions
  • Improved Fit (Forecasts) by Loess Smoothing

• Projection Pursuit Methods

• Remarks on Nonlinear Econometrics

The following sections are included:

• Appendix

• List of References

• Index