Developing Econometrics

Hengqing Tong, Department of Mathematics, Wuhan University of Technology, P.R.China T. Krishna Kumar, Indian Institute of Management, Samkhya Analytica India Private Limited, Bangalore, IndiaYangxin Huang, Department of Epidemiology and Biostatistics, University of South Florida, USA

• Foreword xi Preface xiiiAcknowledgements xvii1 Introduction 11.1 Nature and Scope of Econometrics 21.1.1 What is Econometrics and Why Study Econometrics? 21.1.2 Econometrics and Scientific Credibility of Business and Economic Decisions 41.2 Types of Economic Problems, Types of Data, and Types of Models 51.2.1 Experimental Data from a Marketing Experiment 51.2.2 Cross-Section Data: National Sample Survey Data on Consumer Expenditure 61.2.3 Non-Experimental Data Taken from Secondary Sources: The Case of Pharmaceutical Industry in India 81.2.4 Loan Default Risk of a Customer and the Problem Facing Decision on a Loan Application 91.2.5 Panel Data: Performance of Banks in India by the Type of Ownership after Economic Reforms 101.2.6 Single Time Series Data: The Bombay Stock Exchange (BSE) Index 121.2.7 Multiple Time Series Data: Stock Prices in BRIC Countries 121.3 Pattern Recognition and Exploratory Data Analysis 141.3.1 Some Basic Issues in Econometric Modeling 141.3.2 Exploratory Data Analysis Using Correlations and Scatter Diagrams: The Relative Importance of Managerial Function and Labor 161.3.3 Cleaning and Reprocessing Data to Discover Patterns: BSE Index Data 221.4 Econometric Modeling: The Roadmap of This Book 241.4.1 The Econometric Modeling Strategy 241.4.2 Plan of the Book 25Electronic References for Chapter 1 27References 272 Independent Variables in Linear Regression Models 292.1 Brief Review of Linear Regression 292.1.1 Brief Review of Univariate Linear Regression 292.1.2 Brief Review of Multivariate Linear Regression 382.2 Selection of Independent Variable and Stepwise Regression 492.2.1 Principles of Selection of Independent Variables 492.2.2 Stepwise Regression 522.3 Multivariate Data Transformation and Polynomial Regression 572.3.1 Linear Regression after Multivariate Data Transformation 572.3.2 Polynomial Regression on an Independent Variable 612.3.3 Multivariable Polynomial Regression 622.4 Column Multicollinearity in Design Matrix and Ridge Regression 652.4.1 Effect of Column Multicollinearity of Design Matrix 652.4.2 Ridge Regression 682.4.3 Ridge Trace Analysis and Ridge Parameter Selection 702.4.4 Generalized Ridge Regression 712.5 Recombination of Independent Variable and Principal Components Regression 722.5.1 Concept of Principal Components Regression 722.5.2 Determination of Principal Component 74Electronic References for Chapter 2 79References 803 Alternative Structures of Residual Error in Linear Regression Models 833.1 Heteroscedasticity: Consequences and Tests for Its Existence 853.1.1 Consequences of Heteroscedasticity 853.1.2 Tests for Heteroscedasticity 873.2 Generalized Linear Model with Covariance Being a Diagonal Matrix 903.2.1 Diagonal Covariance Matrix and Weighted Least Squares 903.2.2 Model with Two Unknown Variances 913.2.3 Multiplicative Heteroscedastic Model 923.3 Autocorrelation in a Linear Model 953.3.1 Linear Model with First-Order Residual Autoregression 963.3.2 Autoregressive Conditional Heteroscedasticity (ARCH) Model 1013.4 Generalized Linear Model with Positive Definite Covariance Matrix 1063.4.1 Model Definition, Parameter Estimation and Hypothesis Tests 1063.4.2 Some Equivalent Conditions 1083.5 Random Effects and Variance Component Model 1093.5.1 Random Effect Regression Model 1093.5.2 The Variance Component Model 1123.5.3 Analysis of Variance Method to Solve Variance Component Model 1133.5.4 Minimum Norm Quadratic Unbiased Estimation (MINQUE) to Solve Variance Component 1213.5.5 Maximum Likelihood Method to Solve Variance Component Model 124Electronic References for Chapter 3 125References 1254 Discrete Variables and Nonlinear Regression Model 1294.1 Regression Model When Independent Variables are Categorical 1304.1.1 Problem About Wage and Gender Differences 1314.1.2 Structural Changes in the Savings Function (Use of Categorical Variables in Combination with Continuous Variables) 1334.1.3 Cross Section Analysis 1384.1.4 Seasonal Analysis Model 1414.2 Models with Categorical or Discrete Dependent Variables 1444.2.1 Linear Model with Binary Dependent Variable 1444.2.2 Logit Regression Model 1484.2.3 Probit Regression Model 1534.2.4 Tobit Regression Model 1544.3 Nonlinear Regression Model and Its Algorithm 1604.3.1 The Least Squares Estimate for Nonlinear Regression Model 1624.3.2 Maximum Likelihood Estimation of Nonlinear Regression Model 1644.3.3 Equivalence of Maximum Likelihood Estimation and Least Squares Estimation 1664.4 Nonlinear Regression Models in Practice 1694.4.1 Growth Curve Models 1694.4.2 Box–Cox Transformation Model 1764.4.3 Survival Data and Failure Rate Model 1774.4.4 Total Factor Productivity (TFP) 181Electronic References for Chapter 4 188References 1885 Nonparametric and Semiparametric Regression Models 1935.1 Nonparametric Regression and Weight Function Method 1945.1.1 The Concept of Nonparametric Regression 1945.1.2 Weight Function Method 1965.2 Semiparametric Regression Model 1995.2.1 Linear Semiparametric Regression Model 2025.2.2 Single-Index Semiparametric Regression Model 2055.3 Stochastic Frontier Regression Model 2085.3.1 Stochastic Frontier Linear Regression Model and Asymptotically Efficient Estimator of Its Parameters 2085.3.2 Semiparametric Stochastic Frontier Model 210Electronic References for Chapter 5 212References 2136 Simultaneous Equations Models and Distributed Lag Models 2156.1 Simultaneous Equations Models and Inconsistency of OLS Estimators 2166.1.1 Demand-and-Supply Model, Keynesian Model and Wage-Price Model (Phillips Curve) 2186.1.2 Macroeconomic IS Model, LM Model and Klein’s Econometric Model 2206.1.3 Inconsistency of OLS Estimation 2226.2 Statistical Inference for Simultaneous Equations Models 2236.2.1 Indirect Least Squares and Generalized Least Squares 2246.2.2 Two Stage Least Squares 2296.3 The Concepts of Lag Regression Models 2356.3.1 Consumption Lag 2366.3.2 Inflation Lag 2376.3.3 Deposit Re-Creation 2386.4 Finite Distributed Lag Models 2396.4.1 Estimation of Distributed Lag Models When the Lag Length is Known and Finite 2396.4.2 The Determination of Distributed Lag Length 2396.5 Infinite Distributed Lag Models 2426.5.1 Adaptive Expectations Model and Partial Adjustment Model 2436.5.2 Koyck Transformation and Estimation of Geometric Lag Models 245Electronic References for Chapter 6 249References 2507 Stationary Time Series Models 2537.1 Auto-Regression Model AR( p) 2557.1.1 AR( p) Model and Stationarity 2557.1.2 Auto-Covariance Function and Autocorrelation Function of AR( p) Model 2587.1.3 Spectral Density of AR( p) Model and Partial Correlation Coefficient 2637.1.4 Estimation of Parameters for AR( p) Model with Known Order p 2677.1.5 Order Identification for AR( p) Process 2747.2 Moving Average Model MA(q) 2767.2.1 MA(q) Model and Its Properties 2767.2.2 Parameter Estimation of MA(q) Model When the Order q is Known 2787.2.3 Spectral Density Estimation for MA(q) Process 2827.2.4 Order Identification for MA(q) Process 2847.3 Auto-Regressive Moving-Average Process ARMA( p, q) 2857.3.1 ARMA(p, q) Model and Its Properties 2857.3.2 Parameter Estimations for ARMA(p, q) Model 2887.3.3 Test for ARMA( p, q) Model 2917.3.4 Order Identification for ARMA( p, q) Model 2917.3.5 Univariate Time Series Modeling: The Basic Issues and Approaches 292Electronic References for Chapter 7 293References 2938 Multivariate and Nonstationary Time Series Models 2978.1 Multivariate Stationary Time Series Model 2998.1.1 General Description of Multivariable Stationary Time Series Model 2998.1.2 Estimation of Mean and Autocovariance Function of Multivariate Stationary Time Series 3008.1.3 Vector Autoregression Model of Order p: VAR( p) 3018.1.4 Wold Decomposition and Impulse-Response 3018.1.5 Variance Decomposition with VAR( p) 3068.1.6 Granger Causality with VAR(p) Specification 3098.2 Nonstationary Time Series 3118.2.1 Stochastic Trends and Unit Root Processes 3118.2.2 Test for Unit Root Hypothesis 3148.3 Cointegration and Error Correction 3218.3.1 The Concept and Representation of Cointegration 3228.3.2 Simultaneous (Structural) Equation System (SES) and Vector Auto Regression (VAR) 3248.3.3 Cointegration and Error Correction Representation 3258.3.4 Estimation of Parameters of Cointegration Process 3298.3.5 Test of Hypotheses on the Number of Cointegrating Equations 3308.4 Autoregression Conditional Heteroscedasticity in Time Series 3338.4.1 ARCH Model 3348.4.2 Generalized ARCH Model—GARCH Model 3388.4.3 Other Generalized Forms of ARCH Model 3428.5 Mixed Models of Multivariate Regression with Time Series 3468.5.1 Mixed Model of Multivariate Regression with Time Series 3468.5.2 Mixed Model of Multivariate Regression and Cointegration with Time Series 349Electronic References for Chapter 8 353References 3539 Multivariate Statistical Analysis and Data Analysis 3579.1 Model of Analysis of Variance 3589.1.1 Single Factor Analysis of Variance Model 3589.1.2 Two Factor Analysis of Variance with Non-Repeated Experiment 3619.1.3 Two Factor Analysis of Variance with Repeated Experiment 3649.2 Other Multivariate Statistical Analysis Models 3709.2.1 Discriminate Analysis Model 3709.2.2 Factor Analysis Model 3769.2.3 Principal Component Analysis and Multidimensional Scaling Method 3809.2.4 Canonical Correlation Analysis 3849.3 Customer Satisfaction Model and Path Analysis 3879.3.1 Customer Satisfaction Model and Structural Equations Model 3879.3.2 Partial Least Square and the Best Iterative Initial Value 3919.3.3 Definite Linear Algorithm for SEM 3999.3.4 Multi-Layers Path Analysis Model 4029.4 Data Analysis and Process 4049.4.1 Panel Data Analysis 4049.4.2 Truncated Data Analysis 4059.4.3 Censored Data Analysis 4069.4.4 Duration Data Analysis 4079.4.5 High Dimensional Data Visualization 409Electronic References for Chapter 9 412References 41310 Summary and Further Discussion 41510.1 About Probability Distributions: Parametric and Non-Parametric 41610.1.1 Distributions of Functions of Random Variables 41610.1.2 Parametric, Non-Parametric, and Semi-Parametric Specification of Distributions 41710.1.3 Non-Parametric Specification of Density Functions 41810.2 Regression 42110.2.1 Regression as Conditional Mean of the Dependent Variable 42110.2.2 Regressions with Homoscedastic and Heteroscedastic Variance 42110.2.3 General Regression Functions: Quantiles and Quantile Regression 42310.2.4 Design of Experiments, Regression, and Analysis of Variance 42410.3 Model Specification and Prior Information 42510.3.1 Data Generation Process (DGP) and Economic Structure 42610.3.2 Deterministic but Unknown Parameters and Model Specification as a Maintained Hypothesis 42810.3.3 Stochastic Prior Information on Unknown Parameters 42910.4 Classical Theory of Statistical Inference 43010.4.1 The Likelihood Function, Sufficient Statistics, Complete Statistics, and Ancillary Statistics 43010.4.2 Different Methods of Estimation of Unknown Parameters 43410.4.3 Biased and Unbiased Estimators, Consistency of Estimators 43710.4.4 Information Limit to Variance of an Estimator, Cramer-Rao Bound, and Rao-Blackwell Theorem 43810.4.5 Approximate Sufficiency and Robust Estimation 44010.5 Computation of Maximum Likelihood Estimates 44110.5.1 Newton-Raphson Method and Rao’s Method of Scoring 44210.5.2 Davidon-Fletcher-Powell-Reeves Conjugate Gradient Procedure 44310.5.3 Estimates of the Variance Covariance Matrix of Maximum Likelihood Estimators 44410.6 Specification Searches 44510.6.1 Choice Between Alternate Specifications: Akaike and Schwarz Information Criteria 44510.6.2 Generalized Information and Complexity-Based Model Choice Criterion 44710.6.3 An Illustration of Model Choice: Engel Curve for Food Consumption in India 44810.7 Resampling and Sampling Distributions – The Bootstraps Method 45010.7.1 The Concept of Resampling and the Bootstraps Method 45010.7.2 Bootstraps in Regression Models 45210.8 Bayesian Inference 45410.8.1 The Bayes Rule 45410.8.2 Choice of Prior Probability Distribution for the Parameter 45510.8.3 Bayesian Concepts for Statistical Inference 456Electronic References for Chapter 10 457References 458Index 461