Hands-On Intermediate Econometrics Using R : Templates for Extending Dozens of Practical Examples

by Vinod, Hrishikesh D.

• ISBN13: 9789812818850
• ISBN10: 9812818855
• Format: Hardcover
• Copyright: 2009-02-28
• Publisher: World Scientific Pub Co Inc

Table of Contents

Preface	p. vii
Foreword	p. xv
Production Function and Regression Methods Using R	p. 1
R and Microeconometric Preliminaries	p. 2
Data on Metals Production Available in R	p. 3
Descriptive Statistics Using R	p. 4
Writing Skewness and Kurtosis Functions in R	p. 5
Units of Measurement and Numerical Reliability of Regressions	p. 6
Basic Graphics in R	p. 7
The Isoquant	p. 8
Total Productivity of an Input	p. 9
The Marginal Productivity (MP) of an Input	p. 9
Slope of the Isoquant and MRTS	p. 9
Scale Elasticity as the Returns to Scale Parameter	p. 11
Elasticity of Substitution	p. 12
Typical Steps in Empirical Work	p. 13
Preliminary Regression Theory: Results Using R	p. 13
Regression as an Object `reg1' in R	p. 16
Accessing Objects Within an R Object by Using the Dollar Symbol	p. 17
Deeper Regression Theory: Diagonals of the Hat Matrix	p. 18
Discussion of Four Diagnostic Plots by R	p. 20
Testing Constant Returns and 3D Scatter Plots	p. 23
Homothetic Production and Cost Functions	p. 26
Euler Theorem and Duality Theorem	p. 29
Profit Maximizing Solutions	p. 30
Elasticity of Total Cost w.r.t. Output	p. 31
Miscellaneous Microeconomic Topics	p. 32
Analytic Input Demand Function for the Cobb-Douglas Form	p. 32
Separability in the Presence of Three or More Inputs	p. 32
Two or More Outputs as Joint Outputs	p. 33
Economies of Scope	p. 33
Nonhomogeneous Production Functions	p. 34
Three-Input Production Function for Widgets	p. 34
Isoquant Plotting for a Bell System Production Function	p. 42
Collinearity Problem, Singular Value Decomposition (SVD), and Ridge Regression	p. 45
What is Collinearity?	p. 45
Consequences of Near Collinearity	p. 48
Regression Theory Using the Singular Value Decomposition	p. 51
Near Collinearity Solutions by Coefficient Shrinkage	p. 55
Ridge Regression	p. 57
Principal Components Regression	p. 61
Bell System Production Function in Anti-Trust Trial	p. 62
Collinearity Diagnostics for Bell Data Trans-Log	p. 65
Shrinkage Solution and Ridge Regression for Bell Data	p. 65
Ridge Regression from Existing R Packages	p. 66
Comments on Wrong Signs, Collinearity, and Ridge Scaling	p. 69
Concluding Comments on the 1982 Bell System Breakup	p. 75
Data Appendix	p. 75
Univariate Time Series Analysis with R	p. 77
Econometric Univariate Time Series are Ubiquitous	p. 77
Stochastic Difference Equations	p. 81
Second-Order Stochastic Difference Equation and Business Cycles	p. 85
Complex Number Solution of the Stochastic AR(2) Difference Equation	p. 87
General Solution to ARMA (p,p - 1) Stochastic Difference Equations	p. 89
Properties of ARIMA Models	p. 91
Identification of the Lag Order	p. 93
ARIMA Estimation	p. 100
ARIMA Diagnostic Checking	p. 101
Stochastic Process and Stationarity	p. 108
Stochastic Process and Underlying Probability Space	p. 108
Autocovariance of a Stochastic Process and Ergodicity	p. 110
Stationary Process	p. 112
Detrending and Differencing to Achieve Stationarity	p. 117
Mean Reversion	p. 129
Autocovariance Generating Functions (AGF) and the Power Spectrum	p. 132
How to Get the Power Spectrum from the AGF?	p. 133
Explicit Modeling of Variance (ARCH, GARCH Models.)	p. 136
Tests of Independence, Neglected Nonlinearity, Turning Points	p. 139
Long Memory Models and Fractional Differencing	p. 143
Forecasting	p. 147
Concluding Remarks and Examples	p. 150
Bivariate Time Series Analysis Including Stochastic Diffusion and Cointegration	p. 153
Autoregressive Distributed Lag (ARDL) Models	p. 153
Economic Interpretations of ARDL(1,1) Model	p. 161
Description of M1 to M11 Model Specifications	p. 162
ARDL(0,q) as M12 Model, Impact and Long-Run Multipliers	p. 166
Adaptive Expectations Model to Test Rational Expectations Hypothesis	p. 167
Statistical Inference and Estimation with Lagged-Dependent Variables	p. 168
Identification Problems Involving Expectational Variables (I. Fisher Example)	p. 168
Impulse Response, Mean Lag and Insights from a Polynomials in L	p. 169
Choice Between M1 to M11 Models Using R	p. 170
Stochastic Diffusion Models for Asset Prices	p. 176
Spurious Regression (R2 > Durbin Watson) and Cointegration	p. 183
Definition of a Process Integrated of Order d, I(d)	p. 183
Cointegration Definition and Discussion	p. 184
Error Correction Models of Cointegration	p. 185
Economic Equilibria and Error Reductions through Learning	p. 186
Signs and Significance of Coefficients on Past Errors while Agents Learn	p. 187
Granger Causality Testing	p. 189
Utility Theory and Empirical Implications	p. 191
Utility Theory	p. 191
Expected Utility Theory (EUT)	p. 192
Arrow-Pratt Coefficient of Absolute Risk Aversion (CARA)	p. 197
Risk Premium Needed to Encourage Risky Investments	p. 199
Taylor Series Links EUT, Moments of f(x) and Derivatives of U(x)	p. 200
Non-Expected Utility Theory	p. 202
Lorenz Curve Scaling over the Unit Square	p. 203
Mapping From EUT to Non-EUT within the Unit Square to Get Decision Weights	p. 206
Incorporating Utility Theory into Risk Measurement and Stochastic Dominance	p. 210
Class D1 of Utility Functions and Investors	p. 210
Class D2 of Utility Functions and Investors	p. 210
Explicit Utility Functions and Arrow-Pratt Measures of Risk Aversion	p. 211
Class D3 of Utility Functions and Investors	p. 212
Class D4 of Utility Functions and Investors	p. 212
First-Order Stochastic Dominance (1SD)	p. 214
Second-Order Stochastic Dominance (2SD)	p. 216
Third-Order Stochastic Dominance (3SD)	p. 217
Fourth-Order Stochastic Dominance (4SD)	p. 218
Empirical Checking of Stochastic Dominance Using Matrix Multiplications and Incorporation of 4DPs of Non-EUT	p. 218
Vector Models for Multivariate Problems	p. 227
Introduction and VAR Models	p. 227
Some R Packages for Vector Modeling	p. 228
Vector Autoregression or VAR Models	p. 228
Data Collection Tips Using R	p. 229
VAR Estimation of Sims' Model	p. 237
Granger-Causality Analysis in VAR Models	p. 240
Forecasting Out-of-Sample in VAR Models	p. 242
Impulse Response Analysis in VAR Models	p. 243
Multivariate Regressions: Canonical Correlations	p. 248
Why Canonical Correlation is Not Popular So Far	p. 251
VAR Estimation and Cointegration Testing Using Canonical Correlations	p. 257
Final Remarks: Multivariate Statisics Using R	p. 259
Simultaneous Equation Models	p. 261
Introduction	p. 261
Simultaneous Equation Notation System with Stars and Subscripts	p. 263
Simultaneous Equations Bias and the Reduced Form	p. 266
Successively Weaker Assumptions Regarding the Nature of the Zj Matrix of Regressors	p. 269
Reduced Form Estimation and Other Alternatives to OLS	p. 269
Assumptions of Simultaneous Equations Models	p. 271
Instrumental Variables and Generalized Least Squares	p. 272
The Instrumental Variables (IV) and Generalized IV (GIV) Estimator	p. 273
Choice Between OLS and IV by Using Wu-Hausman Specification Test	p. 275
Limited Information and Two-Stage Least Squares	p. 277
Two-Stage Least Squares	p. 277
The k-class Estimator	p. 278
Limited Information Maximum Likelihood (LIML) Estimator	p. 280
Identification of Simultaneous Equation Models	p. 282
Identification is Uniquely Going from the Reduced Form to the Structure	p. 285
Full Information and Three-Stage Least Squares (3SLS)	p. 288
Full Information Maximum Likelihood	p. 293
Potential of Simultaneous Equations Beyond Econometrics	p. 294
Limited Dependent Variable (GLM) Models	p. 295
Problems with Dummy Dependent Variables	p. 295
Proof of the Claim that Var(e<$$$>[Page No. xxiv]i) = Pi(1 - Pi)	p. 300
The General Linear Model from Biostatistics	p. 304
Marginal Effects (Partial Derivatives) in Logit-Type GLM Models	p. 308
Further Generalizations of Logit and Probit Models	p. 309
Ordered Response	p. 312
Quasi-Likelihood Function for Binary Choice Models	p. 314
The ML Estimator in Binary Choice Models	p. 315
Tobit Model for Censored Dependent Variables	p. 317
Heckman Two-Step Estimator for Self-Selection Bias	p. 322
Time Duration Length (Survival) Models	p. 326
Probability Distributions and Implied Hazard Functions	p. 330
Parametric Survival (Hazard) Models	p. 331
Semiparametric Including Cox Proportional Hazard Models	p. 333
Dynamic Optimization and Empirical Analysis of Consumer Behavior	p. 343
Introduction	p. 343
Dynamic Optimization	p. 344
Hall's Random Walk Model	p. 346
Data from the Internet and an Implementation	p. 349
OLS Estimation of the Random Walk Model	p. 350
Direct Estimation of Hall's NLHS Specification	p. 352
Strong Assumptions and Granger-Causality Tests	p. 356
Nonparametric Kernel Estimation	p. 358
Kernel Estimation of Amorphous Partials	p. 360
Wiener-Hopf-Whittle Model if Consumption Precedes Income	p. 364
Determination of Target Consumption	p. 365
Implications for Various Puzzles of Consumer Theory	p. 368
Final Remarks on Consumer Theory	p. 369
Appendix: Additional R Code	p. 370
Single, Double and Maximum Entropy Bootstrap and Inference	p. 377
The Motivation and Background Behind Bootstrapping	p. 377
Pivotal Quantity and p-Value	p. 378
Uncertainty Regarding Proper Density for Regression Errors Illustrated	p. 380
The Delta Method for Standard Error of Functions	p. 382
Description of Parametric iid Bootstrap	p. 383
Simulated Sampling Distribution for Statistical Inference Using OLS Residuals	p. 383
Steps in a Parametric Approximation	p. 386
Percentile Confidence Intervals	p. 387
Reflected Percentile Confidence Interval for Bias Correction	p. 388
Significance Tests as Duals to Confidence Intervals	p. 388
Description of Nonparametric iid Bootstrap	p. 391
Map Data from Time-Domain to (Numerical Magnitudes) Values-Domain	p. 391
Double Bootstrap Illustrated with a Nonlinear Model	p. 398
A Digression on the Size of Resamples	p. 399
Double Bootstrap Theory Involving Roots and Uniform Density	p. 399
GNR Implementation of Nonlinear Regression for Metals Data	p. 401
Maximum Entropy Density Bootstrap for Time-Series Data	p. 407
Wiener, Kolmogorov, Khintchine (WKK) Ensemble of Time Series	p. 408
Avoiding Unrealistic Properties of iid Bootstrap	p. 409
Maximum Entropy Density is Uniform When Limits are Known	p. 410
Quantiles of the Patchwork of the ME Density	p. 412
Numerical Illustration of "Meboot" Package in R	p. 413
Simple and Size-Corrected Confidence Bounds	p. 418
Generalized Least Squares, VARMA, and Estimating Functions	p. 419
Feasible Generalized Least Squares (GLS) to Adjust for Autocorrelated Errors and/or Heteroscedasticity	p. 419
Consequences of Ignoring Nonspherical Errors O ≠<$$$>[Page No. xxvi] IT	p. 419
Derivation of the GLS and Efficiency Comparison	p. 420
Computation of the GLS and Feasible GLS	p. 422
Improved OLS Inference for Nonspherical Errors	p. 424
Efficient Estimation of b<$$$>[Page No. xxvi] Coefficients	p. 425
An Illustration Using Fisher's Model for Interest Rates	p. 426
Vector ARMA Estimation for Rational Expectations Models	p. 429
Greater Realism of VARMA(p,q) Models	p. 431
Expectational Variables from Conditional Forecasts in a General Model	p. 432
A Rational Expectation Model Using VARMA	p. 433
Further Forecasts, Transfer Function Gains, and Response Analysis	p. 438
Optimal Estimating Function (OptEF) and Generalized Method of Moments (GMM)	p. 443
Derivation of Optimal Estimating Functions for Regressions	p. 443
Finite Sample Optimality of OptEF	p. 445
Introduction to the GMM	p. 445
Cases Where OptEF Viewpoint Dominates GMM	p. 447
Advantages and Disadvantages of GMM and OptEF	p. 449
Godambe Pivot Functions (GPFs) and Statistical Inference	p. 450
Application of the Frisch-Waugh Theorem to Constructing CI95	p. 452
Steps in Application of GPF to Feasible GLS Estimation	p. 453
Box-Cox, Loess and Projection Pursuit Regression	p. 459
Further R Tools for Studying Nonlinear Relations	p. 459
Box-Cox Transformation	p. 459
Logarithmic and Square Root Transformations	p. 459
Scatterplot Smoothing and Loess Regressions	p. 463
Improved Fit (Forecasts) by Loess Smoothing	p. 465
Projection Pursuit Methods	p. 466
Remarks on Nonlinear Econometrics	p. 477
Appendix	p. 479
References	p. 485
Index	p. 505
Table of Contents provided by Ingram. All Rights Reserved.