Now in its fourth edition, this landmark text provides a fresh, accessible and well-written introduction to the subject. With a rigorous pedagogical framework, which sets it apart from comparable texts, the latest edition features an expanded website providing numerous real life data sets and examples.

Foreword xvii Preface to the Fourth Edition xix Part I Introduction and the Linear Regression Model 1 CHAPTER 1 What is Econometrics? 3 1.1 What is econometrics? 3 1.2 Economic and econometric models 4 1.3 The aims and methodology of econometrics 6 1.4 What constitutes a test of an economic theory? 8 CHAPTER 2 Statistical Background and Matrix Algebra 11 2.1 Introduction 11 2.2 Probability 12 2.3 Random variables and probability distributions 17 2.4 The normal probability distribution and related distributions 18 2.5 Classical statistical inference 21 2.6 Properties of estimators 22 2.7 Sampling distributions for samples from a normal population 26 2.8 Interval estimation 26 2.9 Testing of hypotheses 28 2.10 Relationship between confidence interval procedures and tests of hypotheses 31 2.11 Combining independent tests 32 CHAPTER 3 Simple Regression 59 3.1 Introduction 59 3.2 Specification of the relationships 61 3.3 The method of moments 65 3.4 The method of least squares 68 3.5 Statistical inference in the linear regression model 76 3.6 Analysis of variance for the simple regression model 83 3.7 Prediction with the simple regression model 85 3.8 Outliers 88 3.9 Alternative functional forms for regression equations 95 *3.10 Inverse prediction in the least squares regression model1 99 *3.11 Stochastic regressors 102 *3.12 The regression fallacy 102 CHAPTER 4 Multiple Regression 127 4.1 Introduction 127 4.2 A model with two explanatory variables 129 4.3 Statistical inference in the multiple regression model 134 4.4 Interpretation of the regression coefficients 143 4.5 Partial correlations and multiple correlation 146 4.6 Relationships among simple, partial, and multiple correlation coefficients 147 4.7 Prediction in the multiple regression model 153 4.8 Analysis of variance and tests of hypotheses 155 4.9 Omission of relevant variables and inclusion of irrelevant variables 160 4.10 Degrees of freedom and R2 165 4.11 Tests for stability 169 4.12 The LR, W, and LM tests 176 Part II Violation of the Assumptions of the Basic Regression Model 209 CHAPTER 5 Heteroskedasticity 211 5.1 Introduction 211 5.2 Detection of heteroskedasticity 214 5.3 Consequences of heteroskedasticity 219 5.4 Solutions to the heteroskedasticity problem 221 5.5 Heteroskedasticity and the use of deflators 224 5.6 Testing the linear versus log-linear functional form 228 CHAPTER 6 Autocorrelation 239 6.1 Introduction 239 6.2 The Durbin–Watson test 240 6.3 Estimation in levels versus first differences 242 6.4 Estimation procedures with autocorrelated errors 246 6.5 Effect of AR(1) errors on OLS estimates 250 6.6 Some further comments on the DW test 254 6.7 Tests for serial correlation in models with lagged dependent variables 257 6.8 A general test for higher-order serial correlation: The LM test 259 6.9 Strategies when the DW test statistic is significant 261 *6.10 Trends and random walks 266 *6.11 ARCH models and serial correlation 271 6.12 Some comments on the DW test and Durbin’s h-test and t-test 272 CHAPTER 7 Multicollinearity 279 7.1 Introduction 279 7.2 Some illustrative examples 280 7.3 Some measures of multicollinearity 283 7.4 Problems with measuring multicollinearity 286 7.5 Solutions to the multicollinearity problem: Ridge regression 290 7.6 Principal component regression 292 7.7 Dropping variables 297 7.8 Miscellaneous other solutions 300 CHAPTER 8 Dummy Variables and Truncated Variables 313 8.1 Introduction 313 8.2 Dummy variables for changes in the intercept term 314 8.3 Dummy variables for changes in slope coefficients 319 8.4 Dummy variables for cross-equation constraints 322 8.5 Dummy variables for testing stability of regression coefficients 324 8.6 Dummy variables under heteroskedasticity and autocorrelation 327 8.7 Dummy dependent variables 329 8.8 The linear probability model and the linear discriminant function 329 8.9 The probit and logit models 333 8.10 Truncated variables: The tobit model 343 CHAPTER 9 Simultaneous Equation Models 355 9.1 Introduction 355 9.2 Endogenous and exogenous variables 357 9.3 The identification problem: Identification through reduced form 357 9.4 Necessary and sufficient conditions for identification 362 9.5 Methods of estimation: The instrumental variable method 365 9.6 Methods of estimation: The two-stage least squares method 371 9.7 The question of normalization 378 *9.8 The limited-information maximum likelihood method 379 *9.9 On the use of OLS in the estimation of simultaneous equation models 380 *9.10 Exogeneity and causality 386 9.11 Some problems with instrumental variable methods 392 CHAPTER 10 Diagnostic Checking, Model Selection, and Specification Testing 401 10.1 Introduction 401 10.2 Diagnostic tests based on least squares residuals 402 10.3 Problems with least squares residuals 404 10.4 Some other types of residual 405 10.5 DFFITS and bounded influence estimation 411 10.6 Model selection 414 10.7 Selection of regressors 419 10.8 Implied F-ratios for the various criteria 423 10.9 Cross-validation 427 10.10 Hausman’s specification error test 428 10.11 The Plosser–Schwert–White differencing test 435 10.12 Tests for nonnested hypotheses 436 10.13 Nonnormality of errors 440 10.14 Data transformations 441 CHAPTER 11 Errors in Variables 451 11.1 Introduction 451 11.2 The classical solution for a single-equation model with one explanatory variable 452 11.3 The single-equation model with two explanatory variables 455 11.4 Reverse regression 463 11.5 Instrumental variable methods 465 11.6 Proxy variables 468 11.7 Some other problems 471 Part III Special Topics 479 CHAPTER 12 Introduction to Time-Series Analysis 481 12.1 Introduction 481 12.2 Two methods of time-series analysis: Frequency domain and time domain 482 12.3 Stationary and nonstationary time series 482 12.4 Some useful models for time series 485 12.5 Estimation of AR, MA, and ARMA models 492 12.6 The Box–Jenkins approach 496 12.7 R2 measures in time-series models 503 CHAPTER 13 Models of Expectations and Distributed Lags 509 13.1 Models of expectations 509 13.2 Naive models of expectations 510 13.3 The adaptive expectations model 512 13.4 Estimation with the adaptive expectations model 514 13.5 Two illustrative examples 516 13.6 Expectational variables and adjustment lags 520 13.7 Partial adjustment with adaptive expectations 524 13.8 Alternative distributed lag models: Polynomial lags 526 13.9 Rational lags 533 13.10 Rational expectations 534 13.11 Tests for rationality 536 13.12 Estimation of a demand and supply model under rational expectations 538 13.13 The serial correlation problem in rational expectations models 544 CHAPTER 14 Vector Autoregressions, Unit Roots, and Cointegration 551 14.1 Introduction 551 14.2 Vector autoregressions 551 14.3 Problems with VAR models in practice 553 14.4 Unit roots 554 14.5 Unit root tests 555 14.6 Cointegration 563 14.7 The cointegrating regression 564 14.8 Vector autoregressions and cointegration 567 14.9 Cointegration and error correction models 571 14.10 Tests for cointegration 571 14.11 Cointegration and testing of the REH and MEH 572 14.12 A summary assessment of cointegration 574 CHAPTER 15 Panel Data Analysis 583 15.1 Introduction 583 15.2 The LSDV or fixed effects model 584 15.3 The random effects model 586 15.4 Fixed effects versus random effects 589 15.5 Dynamic panel data models 591 15.6 Panel data models with correlated effects and simultaneity 593 15.7 Errors in variables in panel data 595 15.8 The SUR model 597 15.9 The random coefficient model 597 CHAPTER 16 Small-Sample Inference: Resampling Methods 601 16.1 Introduction 601 16.2 Monte Carlo methods 602 16.3 Resampling methods: Jackknife and bootstrap 603 16.4 Bootstrap confidence intervals 605 16.5 Hypothesis testing with the bootstrap 606 16.6 Bootstrapping residuals versus bootstrapping the data 607 16.7 Non-IID errors and nonstationary models 607 Appendix 611 Index 621

Maintaining G.S. Maddala’s brilliant expository style of cutting through the technical superstructure to reveal only essential details, while retaining the nerve centre of the subject matter, Professor Kajal Lahiri has brought forward this new edition of one of the most important textbooks in its field. The new edition continues to provide a large number of worked examples, and some shorter data sets.  Further data sets and additional supplementary material to assist both the student and lecturer are available on the companion website www.wileyeurope.com/college/maddala New features for the fourth edition: Chapters 5 and 6, on Heteroscedasticity and Autocorrelation, now reflect the latest professional practice in dealing with these common variations of the basic regression model.Chapter 10 includes extensive discussion on diagnostic checking in linear models, various nested and non-nested model selection procedures, specification testing, data transformations, and tests for non-normality.The first three chapters of Part III cover an introduction to time-series analysis, including the Box–Jenkins approach, forecasting and seasonality, models of expectations and distributed lag models, and vector auto-regressions, unit roots, and cointegration.Chapters 15 and 16 cover, respectively, the latest developments in panel data analysis and various re-sampling methods for use in small sample inference.

Part I: Introduction and the Linear Regression Model Chapter 1             What is Econometrics? 1.1          What is Econometrics? 1.2          Economic and Econometric Models 1.3          The Aims and Methodology of Econometrics 1.4          What Constitutes a Test of an Economic Theory? Summary and an Outline of the Book References Chapter 2              Statistical Background and Matrix Algebra 2.1          Introduction 2.2          Probability Addition Rules of Probability Conditional Probability and the Multiplication Rule Bayes? Theorem Summation and Product Operations 2.3          Random Variables and Probability Distributions Joint, Marginal, and Conditional Distributions Illustrative Example 2.4          The Normal Probability Distribution and Related Distributions The Normal Distribution Related Distributions 2.5          Classical Statistical Inference Point Estimation 2.6          Properties of Estimators Unbiasedness Efficiency Consistency Other Asymptotic Properties 2.7          Sampling Distributions for Samples from a Normal Population 2.8          Interval Estimation 2.9          Testing of Hypotheses 2.10        Relationship between Confidence Interval Procedures and Tests of Hypotheses 2.11        Combining Independent Tests Summary Exercises Appendix: Matrix Algebra Exercises on Matrix Algebra References Chapter 3             Simple Regression 3.1          Introduction Example 1: Simple Regression Example 2: Multiple Regression 3.2          Specification of the Relationships 3.3          The Method of Moments Illustrative Example 3.4          The Method of Least Squares Reverse Regression Illustrative Example 3.5          Statistical Inference in the Linear Regression Model Illustrative Example Confidence Intervals for a, b, and s2 Testing of Hypotheses Example of Comparing Test Scores from the GRE and GMAT Tests Regression with No Constant Term 3.6          Analysis of Variance for the Simple Regression Model 3.7          Prediction with the Simple Regression Model Prediction of Expected Values Illustrative Example 3.8          Outliers Some Illustrative Examples 3.9          Alternative Functional Forms for Regression Equations Illustrative Example 3.10        Inverse Prediction in the Least Squares Regression Model 3.11        Stochastic Regressors 3.12        The Regression Fallacy The Bivariate Normal Distribution Galton?s Result and the Regression Fallacy A Note on the Term ?Regression? Summary Exercises Appendix: Proofs References Chapter 4             Multiple Regression 4.1          Introduction 4.2          A Model with Two Explanatory Variables The Least Squares Method Illustrative Example 4.3          Statistical Inference in the Multiple Regression Model Illustrative Example Formulas for the General Case of k Explanatory Variables Some Illustrative Examples 4.4          Interpretation of the Regression Coefficients Illustrative Example 4.5          Partial Correlations and Multiple Correlation 4.6          Relationships among Simple, Partial, and Multiple Correlation Coefficients Two Illustrative Examples 4.7          Prediction in the Multiple Regression Model Illustrative Example 4.8          Analysis of Variance and Tests of Hypotheses Nested and Nonnested Hypotheses Tests for Linear Functions of Parameters Illustrative Example 4.9          Omission of Relevant Variables and Inclusion of Irrelevant Variables Omission of Relevant Variables Example 1: Demand for Food in the United States Example 2: Production Functions and Management Bias Inclusion of Irrelevant Variables 4.10        Degrees of Freedom and 4.11        Tests for Stability The Analysis of Variance Test Example 1: Stability of the Demand for Food Function Example 2: Stability of Production Functions Predictive Tests for Stability Illustrative Example 4.12        The LR, W, and LM Tests Illustrative Example Summary Exercises Appendix 4.1: The Multiple Regression Model in Matrix Notation Appendix 4.2: Nonlinear Regressions Appendix 4.3: Large-Sample Theory Data Sets References Part II: Violation of the Assumptions of the Basic Model Chapter 5             Heteroskedasticity 5.1          Introduction Illustrative Example 5.2          Detection of Heteroskedasticity Illustrative Example Some Other Tests Illustrative Example An Intuitive Justification for the Breusch?Pagan Test 5.3          Consequences of Heteroskedasticity Estimation of the Variance of the OLS Estimator under Heteroskedasticity 5.4          Solutions to the Heteroskedasticity Problem Illustrative Example 5.5          Heteroskedasticity and the Use of Deflators Illustrative Example: The Density Gradient Model 5.6          Testing the Linear versus Log-Linear Functional Form The Box?Cox Test The BM Test The PE Test Summary Exercises Appendix: Generalized Least Squares References Chapter 6             Autocorrelation 6.1          Introduction 6.2          The Durbin?Watson Test Illustrative Example 6.3          Estimation in Levels versus First Differences Some Illustrative Examples 6.4          Estimation Procedures with Autocorrelated Errors Iterative Procedures Grid-Search Procedures 6.5          Effect of AR(1) Errors on OLS Estimates 6.6          Some Further Comments on the DW Test The von Neumann Ratio The Berenblut?Webb Test 6.7          Tests for Serial Correlation in Models with Lagged Dependent Variables Durbin?s h-Test Durbin?s Alternative Test Illustrative Example 6.8          A General Test for Higher-Order Serial Correlation: The LM Test 6.9          Strategies When the DW Test Statistic is Significant Errors Not AR(1) Autocorrelation Caused by Omitted Variables Serial Correlation Due to Misspecified Dynamics The Wald Test Illustrative Example 6.10        Trends and Random Walks Spurious Trends Differencing and Long-Run Effects: The Concept of Cointegration 6.11        ARCH Models and Serial Correlation 6.12        Some Comments on the DW Test and Durbin?s h-Test and t-Test Summary Exercises References Chapter 7             Multicollinearity 7.1          Introduction 7.2          Some Illustrative Examples 7.3          Some Measures of Multicollinearity 7.4          Problems with Measuring Multicollinearity 7.5          Solutions to the Multicollinearity Problem: Ridge Regression 7.6          Principal Component Regression 7.7          Dropping Variables 7.8          Miscellaneous Other Solutions Using Ratios or First Differences Using Extraneous Estimates Getting More Data Summary Exercises Appendix: Linearly Dependent Explanatory Variables References                 Chapter 8             Dummy Variables and Truncated Variables 8.1          Introduction 8.2          Dummy Variables for Changes in the Intercept Term Illustrative Example Two More Illustrative Examples 8.3          Dummy Variables for Changes in Slope Coefficients 8.4          Dummy Variables for Cross-Equation Constraints 8.5          Dummy Variables for Testing Stability of Regression Coefficients 8.6          Dummy Variables under Heteroskedasticity and Autocorrelation 8.7          Dummy Dependent Variables 8.8          The Linear Probability Model and the Linear Discriminant Function The Linear Probability Model The Linear Discriminant Function 8.9          The Probit and Logit Models Illustrative Example The Problem of Disproportionate Sampling Prediction of Effects of Changes in the Explanatory Variables Measuring Goodness of Fit 8.10        Illustrative Example 8.11        Truncated Variables: The Tobit Model Some Examples Method of Estimation Limitations of the Tobit Model The Truncated Regression Model Summary Exercises References Chapter 9             Simultaneous Equations Models 9.1          Introduction 9.2          Endogenous and Exogenous Variables 9.3          The Identification Problem: Identification through Reduced Form Illustrative Example 9.4          Necessary and Sufficient Conditions for Identification Illustrative Example 9.5          Methods of Estimation: The Instrumental Variable Method Measuring R2 Illustrative Example 9.6          Methods of Estimation: The Two-Stage Least Squares Method Computing Standard Errors Illustrative Example 9.7          The Question of Normalization 9.8          The Limited-Information Maximum Likelihood Method Illustrative Example 9.9          On the Use of OLS in the Estimation of Simultaneous Equations Models Working?s Concept of Identification Recursive Systems Estimation of Cobb?Douglas Production Functions 9.10        Exogeneity and Causality Weak Exogeneity Superexogeneity Strong Exogeneity Granger Causality Granger Causality and Exogeneity Tests for Exogeneity 9.11        Some Problems with Instrumental Variable Methods Summary Exercises Appendix References Chapter 10           Diagnostic Checking, Model Selection, and Specification Testing 10.1        Introduction 10.2        Diagnostic Tests Based on Least Squares Residuals Tests for Omitted Variables Tests for ARCH Effects 10.3        Problems with Least Squares Residuals 10.4        Some Other Types of Residuals Predicted Residuals and Studentized Residuals Dummy Variable Method for Studentized Residuals BLUS Residuals Recursive Residuals Illustrative Example 10.5        DFFITS and Bounded Influence Estimation Illustrative Example 10.6        Model Selection Hypothesis-Testing Search Interpretive Search Simplification Search Proxy Variable Search Data Selection Search Post-Data Model Construction Hendry?s Approach to Model Selection 10.7        Selection of Regressors Theil?s   Criterion Criteria Based on Minimizing the Mean-Squared Error of Prediction Akaike?s Information Criterion 10.8        Implied F-Ratios for the Various Criteria Bayes? Theorem and Posterior Odds for Model Selection 10.9        Cross-Validation 10.10      Hausman?s Specification Error Test An Application: Testing for Errors in Variables or Exogeneity Some Illustrative Examples An Omitted Variable Interpretation of the Hausman Test 10.11      The Plosser?Schwert?White Differencing Test 10.12      Tests for Nonnested Hypotheses The Davidson and MacKinnon Test The Encompassing Test A Basic Problem in Testing Nonnested Hypotheses Hypothesis Testing versus Model Selection as a Research Strategy 10.13      Nonnormality of Errors Tests for Normality 10.14      Data Transformations Summary Exercises Appendix References Chapter 11           Errors in Variables 11.1        Introduction 11.2        The Classical Solution for a Single-Equation Model with One Explanatory Variable 11.3        The Single-Equation Model with Two Explanatory Variables Two Explanatory Variables: One Measured with Error Illustrative Example Two Explanatory Variables: Both Measured with Error 11.4        Reverse Regression 11.5        Instrumental Variable Methods 11.6        Proxy Variables Coefficient of the Proxy Variable 11.7        Some Other Problems The Case of Multiple Equations Correlated Errors Summary Exercises References Part III: Special Topics Chapter 12           Introduction to Time-Series Analysis 12.1        Introduction 12.2        Two Methods of Time-Series Analysis: Frequency Domain and Time Domain 12.3        Stationary and Nonstationary Time Series Strict Stationarity Weak Stationarity Properties of Autocorrelation Function Nonstationarity 12.4        Some Useful Models for Time Series Purely Random Process Random Walk Moving Average Process Autoregressive Process Autoregressive Moving Average Process Autoregressive Integrated Moving Average Process 12.5        Estimation of AR, MA, and ARMA Models Estimation of MA Models Estimation of ARMA Models Residuals from the ARMA Models Testing Goodness of Fit 12.6        The Box?Jenkins Approach Forecasting from Box?Jenkins Models Illustrative Example Trend Elimination: The Traditional Method A Summary Assessment Seasonality in the Box?Jenkins Modeling 12.7        R 2 Measures in Time-Series Models Summary Exercises Data Sets References Chapter 13           Models of Expectations and Distributed Lags 13.1        Models of Expectations 13.2        Naive Models of Expectations 13.3        The Adaptive Expectations Model 13.4        Estimation with the Adaptive Expectations Model Estimation in the Autoregressive Form Estimation in the Distributed Lag Form 13.5        Two Illustrative Examples 13.6        Expectational Variables and Adjustment Lags 13.7        Partial Adjustment with Adaptive Expectations 13.8        Alternative Distributed Lag Models: Polynomial Lags Finite Lags: The Polynomial Lag Illustrative Example Choosing the Degree of the Polynomial 13.9        Rational Lags 13.10      Rational Expectations 13.11      Tests for Rationality 13.12      Estimation of a Demand and Supply Model Under Rational Expectations Case 1 Case 2 Illustrative Example 13.13      The Serial Correlation Problem in Rational Expectations Models Summary Exercises References Chapter 14           Vector Autoregressions, Unit Roots, and Cointegration 14.1        Introduction 14.2        Vector Autoregressions 14.3        Problems with VAR Models in Practice 14.4        Unit Roots 14.5        Unit Root Tests The Dickey?Fuller Tests The Serial Correlation Problem The Low Power of Unit Root Tests The DF-GLS Test What are the Null and Alternative Hypotheses in Unit Root Tests? Tests with Stationarity as Null Confirmatory Analysis Panel Data Unit Root Tests Structural Change and Unit Roots 14.6        Cointegration 14.7        The Cointegrating Regression 14.8        Vector Autoregressions and Cointegration 14.9        Cointegration and Error Correction Models 14.10      Tests for Cointegration 14.11      Cointegration and Testing of the REH and MEH 14.12      A Summary Assessment of Cointegration Summary Exercises References Chapter 15           Panel Data Analysis 15.1        Introduction 15.2        The LSDV or Fixed Effects Model Illustrative Example: Fixed Effect Estimation 15.3        The Random Effects Model 15.4        Fixed Effects versus Random Effects Hausman Test Breusch and Pagan Test Tests for Serial Correlation 15.5        Dynamic Panel Data Models 15.6        Panel Data Models with Correlated Effects and Simultaneity 15.7        Errors in Variables in Panel Data 15.8        The SUR Model 15.9        The Random Coefficient Model Summary References Chapter 16           Small-Sample Inference: Resampling Methods 16.1        Introduction 16.2        Monte Carlo Methods More Efficient Monte Carlo Methods Response Surfaces 16.3        Resampling Methods: Jackknife and Bootstrap Some Illustrative Examples Other Issues Relating to the Bootstrap 16.4        Bootstrap Confidence Intervals 16.5        Hypothesis Testing with the Bootstrap 16.6        Bootstrapping Residuals versus Bootstrapping the Data 16.7        Non-IID Errors and Nonstationary Models Heteroskedasticity and Autocorrelation Unit Root Tests Based on the Bootstrap Cointegration Tests 16.8        Miscellaneous Other Applications Summary References Appendix Index