Developing Econometrics

Developing Econometrics......Page 5
Contents......Page 7
Foreword......Page 13
Preface......Page 15
Acknowledgements......Page 19
1 Introduction......Page 21
1.1.1 What is Econometrics and Why Study Econometrics?......Page 22
1.1.2 Econometrics and Scientific Credibility of Business and Economic Decisions......Page 24
1.2.1 Experimental Data from a Marketing Experiment......Page 25
1.2.2 Cross-Section Data: National Sample Survey Data on Consumer Expenditure......Page 26
1.2.3 Non-Experimental Data Taken from Secondary Sources: The Case of Pharmaceutical Industry in India......Page 28
1.2.4 Loan Default Risk of a Customer and the Problem Facing Decision on a Loan Application......Page 29
1.2.5 Panel Data: Performance of Banks in India by the Type of Ownership after Economic Reforms......Page 30
1.2.7 Multiple Time Series Data: Stock Prices in BRIC Countries......Page 32
1.3.1 Some Basic Issues in Econometric Modeling......Page 34
1.3.2 Exploratory Data Analysis Using Correlations and Scatter Diagrams: The Relative Importance of Managerial Function and Labor......Page 36
1.3.3 Cleaning and Reprocessing Data to Discover Patterns: BSE Index Data......Page 42
1.4.1 The Econometric Modeling Strategy......Page 44
1.4.2 Plan of the Book......Page 45
References......Page 47
2.1.1 Brief Review of Univariate Linear Regression......Page 49
2.1.2 Brief Review of Multivariate Linear Regression......Page 58
2.2.1 Principles of Selection of Independent Variables......Page 69
2.2.2 Stepwise Regression......Page 72
2.3.1 Linear Regression after Multivariate Data Transformation......Page 77
2.3.2 Polynomial Regression on an Independent Variable......Page 81
2.3.3 Multivariable Polynomial Regression......Page 82
2.4.1 Effect of Column Multicollinearity of Design Matrix......Page 85
2.4.2 Ridge Regression......Page 88
2.4.3 Ridge Trace Analysis and Ridge Parameter Selection......Page 90
2.4.4 Generalized Ridge Regression......Page 91
2.5.1 Concept of Principal Components Regression......Page 92
2.5.2 Determination of Principal Component......Page 94
Electronic References for Chapter 2......Page 99
References......Page 100
3 Alternative Structures of Residual Error in Linear Regression Models......Page 103
3.1.1 Consequences of Heteroscedasticity......Page 105
3.1.2 Tests for Heteroscedasticity......Page 107
3.2.1 Diagonal Covariance Matrix and Weighted Least Squares......Page 110
3.2.2 Model with Two Unknown Variances......Page 111
3.2.3 Multiplicative Heteroscedastic Model......Page 112
3.3 Autocorrelation in a Linear Model......Page 115
3.3.1 Linear Model with First-Order Residual Autoregression......Page 116
3.3.2 Autoregressive Conditional Heteroscedasticity (ARCH) Model......Page 121
3.4.1 Model Definition, Parameter Estimation and Hypothesis Tests......Page 126
3.4.2 Some Equivalent Conditions......Page 128
3.5.1 Random Effect Regression Model......Page 129
3.5.2 The Variance Component Model......Page 132
3.5.3 Analysis of Variance Method to Solve Variance Component Model......Page 133
3.5.4 Minimum Norm Quadratic Unbiased Estimation (MINQUE) to Solve Variance Component......Page 141
3.5.5 Maximum Likelihood Method to Solve Variance Component Model......Page 144
References......Page 145
4 Discrete Variables and Nonlinear Regression Model......Page 149
4.1 Regression Model When Independent Variables are Categorical......Page 150
4.1.1 Problem About Wage and Gender Differences......Page 151
4.1.2 Structural Changes in the Savings Function (Use of Categorical Variables in Combination with Continuous Variables)......Page 153
4.1.3 Cross Section Analysis......Page 158
4.1.4 Seasonal Analysis Model......Page 161
4.2.1 Linear Model with Binary Dependent Variable......Page 164
4.2.2 Logit Regression Model......Page 168
4.2.3 Probit Regression Model......Page 173
4.2.4 Tobit Regression Model......Page 174
4.3 Nonlinear Regression Model and Its Algorithm......Page 180
4.3.1 The Least Squares Estimate for Nonlinear Regression Model......Page 182
4.3.2 Maximum Likelihood Estimation of Nonlinear Regression Model......Page 184
4.3.3 Equivalence of Maximum Likelihood Estimation and Least Squares Estimation......Page 186
4.4.1 Growth Curve Models......Page 189
4.4.2 Box–Cox Transformation Model......Page 196
4.4.3 Survival Data and Failure Rate Model......Page 197
4.4.4 Total Factor Productivity (TFP)......Page 201
References......Page 208
5 Nonparametric and Semiparametric Regression Models......Page 213
5.1.1 The Concept of Nonparametric Regression......Page 214
5.1.2 Weight Function Method......Page 216
5.2 Semiparametric Regression Model......Page 219
5.2.1 Linear Semiparametric Regression Model......Page 222
5.2.2 Single-Index Semiparametric Regression Model......Page 225
5.3.1 Stochastic Frontier Linear Regression Model and Asymptotically Efficient Estimator of Its Parameters......Page 228
5.3.2 Semiparametric Stochastic Frontier Model......Page 230
Electronic References for Chapter 5......Page 232
References......Page 233
6 Simultaneous Equations Models and Distributed Lag Models......Page 235
6.1 Simultaneous Equations Models and Inconsistency of OLS Estimators......Page 236
6.1.1 Demand-and-Supply Model, Keynesian Model and Wage-Price Model (Phillips Curve)......Page 238
6.1.2 Macroeconomic IS Model, LM Model and Klein’s Econometric Model......Page 240
6.1.3 Inconsistency of OLS Estimation......Page 242
6.2 Statistical Inference for Simultaneous Equations Models......Page 243
6.2.1 Indirect Least Squares and Generalized Least Squares......Page 244
6.2.2 Two Stage Least Squares......Page 249
6.3 The Concepts of Lag Regression Models......Page 255
6.3.1 Consumption Lag......Page 256
6.3.2 Inflation Lag......Page 257
6.3.3 Deposit Re-Creation......Page 258
6.4.2 The Determination of Distributed Lag Length......Page 259
6.5 Infinite Distributed Lag Models......Page 262
6.5.1 Adaptive Expectations Model and Partial Adjustment Model......Page 263
6.5.2 Koyck Transformation and Estimation of Geometric Lag Models......Page 265
Electronic References for Chapter 6......Page 269
References......Page 270
7 Stationary Time Series Models......Page 273
7.1.1 AR( p) Model and Stationarity......Page 275
7.1.2 Auto-Covariance Function and Autocorrelation Function of AR( p) Model......Page 278
7.1.3 Spectral Density of AR( p) Model and Partial Correlation Coefficient......Page 283
7.1.4 Estimation of Parameters for AR(p) Model with Known Order p......Page 287
7.1.5 Order Identification for AR( p) Process......Page 294
7.2.1 MA(q) Model and Its Properties......Page 296
7.2.2 Parameter Estimation of MA(q) Model When the Order q is Known......Page 298
7.2.3 Spectral Density Estimation for MA(q) Process......Page 302
7.2.4 Order Identification for MA(q) Process......Page 304
7.3.1 ARMA(p, q) Model and Its Properties......Page 305
7.3.2 Parameter Estimations for ARMA(p, q) Model......Page 308
7.3.4 Order Identification for ARMA( p, q) Model......Page 311
7.3.5 Univariate Time Series Modeling: The Basic Issues and Approaches......Page 312
References......Page 313
8 Multivariate and Nonstationary Time Series Models......Page 317
8.1.1 General Description of Multivariable Stationary Time Series Model......Page 319
8.1.2 Estimation of Mean and Autocovariance Function of Multivariate Stationary Time Series......Page 320
8.1.4 Wold Decomposition and Impulse-Response......Page 321
8.1.5 Variance Decomposition with VAR( p)......Page 326
8.1.6 Granger Causality with VAR(p) Specification......Page 329
8.2.1 Stochastic Trends and Unit Root Processes......Page 331
8.2.2 Test for Unit Root Hypothesis......Page 334
8.3 Cointegration and Error Correction......Page 341
8.3.1 The Concept and Representation of Cointegration......Page 342
8.3.2 Simultaneous (Structural) Equation System (SES) and Vector Auto Regression (VAR)......Page 344
8.3.3 Cointegration and Error Correction Representation......Page 345
8.3.4 Estimation of Parameters of Cointegration Process......Page 349
8.3.5 Test of Hypotheses on the Number of Cointegrating Equations......Page 350
8.4 Autoregression Conditional Heteroscedasticity in Time Series......Page 353
8.4.1 ARCH Model......Page 354
8.4.2 Generalized ARCH Model—GARCH Model......Page 358
8.4.3 Other Generalized Forms of ARCH Model......Page 362
8.5.1 Mixed Model of Multivariate Regression with Time Series......Page 366
8.5.2 Mixed Model of Multivariate Regression and Cointegration with Time Series......Page 369
References......Page 373
9 Multivariate Statistical Analysis and Data Analysis......Page 377
9.1.1 Single Factor Analysis of Variance Model......Page 378
9.1.2 Two Factor Analysis of Variance with Non-Repeated Experiment......Page 381
9.1.3 Two Factor Analysis of Variance with Repeated Experiment......Page 384
9.2.1 Discriminate Analysis Model......Page 390
9.2.2 Factor Analysis Model......Page 396
9.2.3 Principal Component Analysis and Multidimensional Scaling Method......Page 400
9.2.4 Canonical Correlation Analysis......Page 404
9.3.1 Customer Satisfaction Model and Structural Equations Model......Page 407
9.3.2 Partial Least Square and the Best Iterative Initial Value......Page 411
9.3.3 Definite Linear Algorithm for SEM......Page 419
9.3.4 Multi-Layers Path Analysis Model......Page 422
9.4.1 Panel Data Analysis......Page 424
9.4.2 Truncated Data Analysis......Page 425
9.4.3 Censored Data Analysis......Page 426
9.4.4 Duration Data Analysis......Page 427
9.4.5 High Dimensional Data Visualization......Page 429
Electronic References for Chapter 9......Page 432
References......Page 433
10 Summary and Further Discussion......Page 435
10.1.1 Distributions of Functions of Random Variables......Page 436
10.1.2 Parametric, Non-Parametric, and Semi-Parametric Specification of Distributions......Page 437
10.1.3 Non-Parametric Specification of Density Functions......Page 438
10.2.2 Regressions with Homoscedastic and Heteroscedastic Variance......Page 441
10.2.3 General Regression Functions: Quantiles and Quantile Regression......Page 443
10.2.4 Design of Experiments, Regression, and Analysis of Variance......Page 444
10.3 Model Specification and Prior Information......Page 445
10.3.1 Data Generation Process (DGP) and Economic Structure......Page 446
10.3.2 Deterministic but Unknown Parameters and Model Specification as a Maintained Hypothesis......Page 448
10.3.3 Stochastic Prior Information on Unknown Parameters......Page 449
10.4.1 The Likelihood Function, Sufficient Statistics, Complete Statistics, and Ancillary Statistics......Page 450
10.4.2 Different Methods of Estimation of Unknown Parameters......Page 454
10.4.3 Biased and Unbiased Estimators, Consistency of Estimators......Page 457
10.4.4 Information Limit to Variance of an Estimator, Cramer-Rao Bound, and Rao-Blackwell Theorem......Page 458
10.4.5 Approximate Sufficiency and Robust Estimation......Page 460
10.5 Computation of Maximum Likelihood Estimates......Page 461
10.5.1 Newton-Raphson Method and Rao’s Method of Scoring......Page 462
10.5.2 Davidon-Fletcher-Powell-Reeves Conjugate Gradient Procedure......Page 463
10.5.3 Estimates of the Variance Covariance Matrix of Maximum Likelihood Estimators......Page 464
10.6.1 Choice Between Alternate Specifications: Akaike and Schwarz Information Criteria......Page 465
10.6.2 Generalized Information and Complexity-Based Model Choice Criterion......Page 467
10.6.3 An Illustration of Model Choice: Engel Curve for Food Consumption in India......Page 468
10.7.1 The Concept of Resampling and the Bootstraps Method......Page 470
10.7.2 Bootstraps in Regression Models......Page 472
10.8.1 The Bayes Rule......Page 474
10.8.2 Choice of Prior Probability Distribution for the Parameter......Page 475
10.8.3 Bayesian Concepts for Statistical Inference......Page 476
Electronic References for Chapter 10......Page 477
References......Page 478
Index......Page 481