Foreword xi
Preface xiii
Acknowledgements xvii
1 Introduction 1
1.1 Nature and Scope of Econometrics 2
1.1.1 What is Econometrics and Why Study Econometrics? 2
1.1.2 Econometrics and Scientific Credibility of Business and
Economic Decisions 4
1.2 Types of Economic Problems, Types of Data, and Types of
Models 5
1.2.1 Experimental Data from a Marketing Experiment 5
1.2.2 Cross-Section Data: National Sample Survey Data on
Consumer Expenditure 6
1.2.3 Non-Experimental Data Taken from Secondary Sources: The
Case of Pharmaceutical Industry in India 8
1.2.4 Loan Default Risk of a Customer and the Problem Facing
Decision on a Loan Application 9
1.2.5 Panel Data: Performance of Banks in India by the Type of
Ownership after Economic Reforms 10
1.2.6 Single Time Series Data: The Bombay Stock Exchange (BSE)
Index 12
1.2.7 Multiple Time Series Data: Stock Prices in BRIC Countries
12
1.3 Pattern Recognition and Exploratory Data Analysis 14
1.3.1 Some Basic Issues in Econometric Modeling 14
1.3.2 Exploratory Data Analysis Using Correlations and Scatter
Diagrams: The Relative Importance of Managerial Function and Labor
16
1.3.3 Cleaning and Reprocessing Data to Discover Patterns: BSE
Index Data 22
1.4 Econometric Modeling: The Roadmap of This Book 24
1.4.1 The Econometric Modeling Strategy 24
1.4.2 Plan of the Book 25
Electronic References for Chapter 1 27
References 27
2 Independent Variables in Linear Regression Models
29
2.1 Brief Review of Linear Regression 29
2.1.1 Brief Review of Univariate Linear Regression 29
2.1.2 Brief Review of Multivariate Linear Regression 38
2.2 Selection of Independent Variable and Stepwise Regression
49
2.2.1 Principles of Selection of Independent Variables 49
2.2.2 Stepwise Regression 52
2.3 Multivariate Data Transformation and Polynomial Regression
57
2.3.1 Linear Regression after Multivariate Data Transformation
57
2.3.2 Polynomial Regression on an Independent Variable 61
2.3.3 Multivariable Polynomial Regression 62
2.4 Column Multicollinearity in Design Matrix and Ridge
Regression 65
2.4.1 Effect of Column Multicollinearity of Design Matrix 65
2.4.2 Ridge Regression 68
2.4.3 Ridge Trace Analysis and Ridge Parameter Selection 70
2.4.4 Generalized Ridge Regression 71
2.5 Recombination of Independent Variable and Principal
Components Regression 72
2.5.1 Concept of Principal Components Regression 72
2.5.2 Determination of Principal Component 74
Electronic References for Chapter 2 79
References 80
3 Alternative Structures of Residual Error in Linear
Regression Models 83
3.1 Heteroscedasticity: Consequences and Tests for Its Existence
85
3.1.1 Consequences of Heteroscedasticity 85
3.1.2 Tests for Heteroscedasticity 87
3.2 Generalized Linear Model with Covariance Being a Diagonal
Matrix 90
3.2.1 Diagonal Covariance Matrix and Weighted Least Squares
90
3.2.2 Model with Two Unknown Variances 91
3.2.3 Multiplicative Heteroscedastic Model 92
3.3 Autocorrelation in a Linear Model 95
3.3.1 Linear Model with First-Order Residual Autoregression
96
3.3.2 Autoregressive Conditional Heteroscedasticity (ARCH) Model
101
3.4 Generalized Linear Model with Positive Definite Covariance
Matrix 106
3.4.1 Model Definition, Parameter Estimation and Hypothesis
Tests 106
3.4.2 Some Equivalent Conditions 108
3.5 Random Effects and Variance Component Model 109
3.5.1 Random Effect Regression Model 109
3.5.2 The Variance Component Model 112
3.5.3 Analysis of Variance Method to Solve Variance Component
Model 113
3.5.4 Minimum Norm Quadratic Unbiased Estimation (MINQUE) to
Solve Variance Component 121
3.5.5 Maximum Likelihood Method to Solve Variance Component
Model 124
Electronic References for Chapter 3 125
References 125
4 Discrete Variables and Nonlinear Regression Model
129
4.1 Regression Model When Independent Variables are Categorical
130
4.1.1 Problem About Wage and Gender Differences 131
4.1.2 Structural Changes in the Savings Function (Use of
Categorical Variables in Combination with Continuous Variables)
133
4.1.3 Cross Section Analysis 138
4.1.4 Seasonal Analysis Model 141
4.2 Models with Categorical or Discrete Dependent Variables
144
4.2.1 Linear Model with Binary Dependent Variable 144
4.2.2 Logit Regression Model 148
4.2.3 Probit Regression Model 153
4.2.4 Tobit Regression Model 154
4.3 Nonlinear Regression Model and Its Algorithm 160
4.3.1 The Least Squares Estimate for Nonlinear Regression Model
162
4.3.2 Maximum Likelihood Estimation of Nonlinear Regression
Model 164
4.3.3 Equivalence of Maximum Likelihood Estimation and Least
Squares Estimation 166
4.4 Nonlinear Regression Models in Practice 169
4.4.1 Growth Curve Models 169
4.4.2 Box?Cox Transformation Model 176
4.4.3 Survival Data and Failure Rate Model 177
4.4.4 Total Factor Productivity (TFP) 181
Electronic References for Chapter 4 188
References 188
5 Nonparametric and Semiparametric Regression Models
193
5.1 Nonparametric Regression and Weight Function Method 194
5.1.1 The Concept of Nonparametric Regression 194
5.1.2 Weight Function Method 196
5.2 Semiparametric Regression Model 199
5.2.1 Linear Semiparametric Regression Model 202
5.2.2 Single-Index Semiparametric Regression Model 205
5.3 Stochastic Frontier Regression Model 208
5.3.1 Stochastic Frontier Linear Regression Model and
Asymptotically Efficient Estimator of Its Parameters 208
5.3.2 Semiparametric Stochastic Frontier Model 210
Electronic References for Chapter 5 212
References 213
6 Simultaneous Equations Models and Distributed Lag Models
215
6.1 Simultaneous Equations Models and Inconsistency of OLS
Estimators 216
6.1.1 Demand-and-Supply Model, Keynesian Model and Wage-Price
Model (Phillips Curve) 218
6.1.2 Macroeconomic IS Model, LM Model and Klein?s
Econometric Model 220
6.1.3 Inconsistency of OLS Estimation 222
6.2 Statistical Inference for Simultaneous Equations Models
223
6.2.1 Indirect Least Squares and Generalized Least Squares
224
6.2.2 Two Stage Least Squares 229
6.3 The Concepts of Lag Regression Models 235
6.3.1 Consumption Lag 236
6.3.2 Inflation Lag 237
6.3.3 Deposit Re-Creation 238
6.4 Finite Distributed Lag Models 239
6.4.1 Estimation of Distributed Lag Models When the Lag Length
is Known and Finite 239
6.4.2 The Determination of Distributed Lag Length 239
6.5 Infinite Distributed Lag Models 242
6.5.1 Adaptive Expectations Model and Partial Adjustment Model
243
6.5.2 Koyck Transformation and Estimation of Geometric Lag
Models 245
Electronic References for Chapter 6 249
References 250
7 Stationary Time Series Models 253
7.1 Auto-Regression Model AR( p) 255
7.1.1 AR( p) Model and Stationarity 255
7.1.2 Auto-Covariance Function and Autocorrelation Function of
AR( p) Model 258
7.1.3 Spectral Density of AR( p) Model and Partial
Correlation Coefficient 263
7.1.4 Estimation of Parameters for AR( p) Model with
Known Order p 267
7.1.5 Order Identification for AR( p) Process 274
7.2 Moving Average Model MA(q) 276
7.2.1 MA(q) Model and Its Properties 276
7.2.2 Parameter Estimation of MA(q) Model When the Order
q is Known 278
7.2.3 Spectral Density Estimation for MA(q) Process
282
7.2.4 Order Identification for MA(q) Process 284
7.3 Auto-Regressive Moving-Average Process ARMA( p, q)
285
7.3.1 ARMA(p, q) Model and Its Properties 285
7.3.2 Parameter Estimations for ARMA(p, q) Model 288
7.3.3 Test for ARMA( p, q) Model 291
7.3.4 Order Identification for ARMA( p, q) Model 291
7.3.5 Univariate Time Series Modeling: The Basic Issues and
Approaches 292
Electronic References for Chapter 7 293
References 293
8 Multivariate and Nonstationary Time Series Models
297
8.1 Multivariate Stationary Time Series Model 299
8.1.1 General Description of Multivariable Stationary Time
Series Model 299
8.1.2 Estimation of Mean and Autocovariance Function of
Multivariate Stationary Time Series 300
8.1.3 Vector Autoregression Model of Order p: VAR(
p) 301
8.1.4 Wold Decomposition and Impulse-Response 301
8.1.5 Variance Decomposition with VAR( p) 306
8.1.6 Granger Causality with VAR(p) Specification 309
8.2 Nonstationary Time Series 311
8.2.1 Stochastic Trends and Unit Root Processes 311
8.2.2 Test for Unit Root Hypothesis 314
8.3 Cointegration and Error Correction 321
8.3.1 The Concept and Representation of Cointegration 322
8.3.2 Simultaneous (Structural) Equation System (SES) and Vector
Auto Regression (VAR) 324
8.3.3 Cointegration and Error Correction Representation 325
8.3.4 Estimation of Parameters of Cointegration Process 329
8.3.5 Test of Hypotheses on the Number of Cointegrating
Equations 330
8.4 Autoregression Conditional Heteroscedasticity in Time Series
333
8.4.1 ARCH Model 334
8.4.2 Generalized ARCH Model?GARCH Model 338
8.4.3 Other Generalized Forms of ARCH Model 342
8.5 Mixed Models of Multivariate Regression with Time Series
346
8.5.1 Mixed Model of Multivariate Regression with Time Series
346
8.5.2 Mixed Model of Multivariate Regression and Cointegration
with Time Series 349
Electronic References for Chapter 8 353
References 353
9 Multivariate Statistical Analysis and Data Analysis
357
9.1 Model of Analysis of Variance 358
9.1.1 Single Factor Analysis of Variance Model 358
9.1.2 Two Factor Analysis of Variance with Non-Repeated
Experiment 361
9.1.3 Two Factor Analysis of Variance with Repeated Experiment
364
9.2 Other Multivariate Statistical Analysis Models 370
9.2.1 Discriminate Analysis Model 370
9.2.2 Factor Analysis Model 376
9.2.3 Principal Component Analysis and Multidimensional Scaling
Method 380
9.2.4 Canonical Correlation Analysis 384
9.3 Customer Satisfaction Model and Path Analysis 387
9.3.1 Customer Satisfaction Model and Structural Equations Model
387
9.3.2 Partial Least Square and the Best Iterative Initial Value
391
9.3.3 Definite Linear Algorithm for SEM 399
9.3.4 Multi-Layers Path Analysis Model 402
9.4 Data Analysis and Process 404
9.4.1 Panel Data Analysis 404
9.4.2 Truncated Data Analysis 405
9.4.3 Censored Data Analysis 406
9.4.4 Duration Data Analysis 407
9.4.5 High Dimensional Data Visualization 409
Electronic References for Chapter 9 412
References 413
10 Summary and Further Discussion 415
10.1 About Probability Distributions: Parametric and
Non-Parametric 416
10.1.1 Distributions of Functions of Random Variables 416
10.1.2 Parametric, Non-Parametric, and Semi-Parametric
Specification of Distributions 417
10.1.3 Non-Parametric Specification of Density Functions 418
10.2 Regression 421
10.2.1 Regression as Conditional Mean of the Dependent Variable
421
10.2.2 Regressions with Homoscedastic and Heteroscedastic
Variance 421
10.2.3 General Regression Functions: Quantiles and Quantile
Regression 423
10.2.4 Design of Experiments, Regression, and Analysis of
Variance 424
10.3 Model Specification and Prior Information 425
10.3.1 Data Generation Process (DGP) and Economic Structure
426
10.3.2 Deterministic but Unknown Parameters and Model
Specification as a Maintained Hypothesis 428
10.3.3 Stochastic Prior Information on Unknown Parameters
429
10.4 Classical Theory of Statistical Inference 430
10.4.1 The Likelihood Function, Sufficient Statistics, Complete
Statistics, and Ancillary Statistics 430
10.4.2 Different Methods of Estimation of Unknown Parameters
434
10.4.3 Biased and Unbiased Estimators, Consistency of Estimators
437
10.4.4 Information Limit to Variance of an Estimator, Cramer-Rao
Bound, and Rao-Blackwell Theorem 438
10.4.5 Approximate Sufficiency and Robust Estimation 440
10.5 Computation of Maximum Likelihood Estimates 441
10.5.1 Newton-Raphson Method and Rao?s Method of Scoring
442
10.5.2 Davidon-Fletcher-Powell-Reeves Conjugate Gradient
Procedure 443
10.5.3 Estimates of the Variance Covariance Matrix of Maximum
Likelihood Estimators 444
10.6 Specification Searches 445
10.6.1 Choice Between Alternate Specifications: Akaike and
Schwarz Information Criteria 445
10.6.2 Generalized Information and Complexity-Based Model Choice
Criterion 447
10.6.3 An Illustration of Model Choice: Engel Curve for Food
Consumption in India 448
10.7 Resampling and Sampling Distributions ? The
Bootstraps Method 450
10.7.1 The Concept of Resampling and the Bootstraps Method
450
10.7.2 Bootstraps in Regression Models 452
10.8 Bayesian Inference 454
10.8.1 The Bayes Rule 454
10.8.2 Choice of Prior Probability Distribution for the
Parameter 455
10.8.3 Bayesian Concepts for Statistical Inference 456
Electronic References for Chapter 10 457
References 458
Index 461
