G.S.Maddala was one of the leading figures in field of econometrics for more than 30 years until he passed away in 1999. At the time of his death, he held the University Eminent Scholar Professorship in the Department of Economics at Ohio State University. His previous affiliations include Stanford University, University of Rochester and University of Florida. Kajal Lahiri is Distinguished Professor of Economics, and Health Policy, and Management and Behaviour at the State University of New York, Albany where he is also Director of the Econometric Research Institute. Professor Lahiri is an Honorary Fellow of the International Institute of Forecasters.

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• Foreword xvii Preface to the Fourth Edition xixPart I Introduction and the Linear Regression Model 1CHAPTER 1 What is Econometrics? 31.1 What is econometrics? 31.2 Economic and econometric models 41.3 The aims and methodology of econometrics 61.4 What constitutes a test of an economic theory? 8CHAPTER 2 Statistical Background and Matrix Algebra 112.1 Introduction 112.2 Probability 122.3 Random variables and probability distributions 172.4 The normal probability distribution and related distributions 182.5 Classical statistical inference 212.6 Properties of estimators 222.7 Sampling distributions for samples from a normal population 262.8 Interval estimation 262.9 Testing of hypotheses 282.10 Relationship between confidence interval procedures and tests of hypotheses 312.11 Combining independent tests 32CHAPTER 3 Simple Regression 593.1 Introduction 593.2 Specification of the relationships 613.3 The method of moments 653.4 The method of least squares 683.5 Statistical inference in the linear regression model 763.6 Analysis of variance for the simple regression model 833.7 Prediction with the simple regression model 853.8 Outliers 883.9 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 102CHAPTER 4 Multiple Regression 1274.1 Introduction 1274.2 A model with two explanatory variables 1294.3 Statistical inference in the multiple regression model 1344.4 Interpretation of the regression coefficients 1434.5 Partial correlations and multiple correlation 1464.6 Relationships among simple, partial, and multiple correlation coefficients 1474.7 Prediction in the multiple regression model 1534.8 Analysis of variance and tests of hypotheses 1554.9 Omission of relevant variables and inclusion of irrelevant variables 1604.10 Degrees of freedom and R2 1654.11 Tests for stability 1694.12 The LR, W, and LM tests 176Part II Violation of the Assumptions of the Basic Regression Model 209CHAPTER 5 Heteroskedasticity 2115.1 Introduction 2115.2 Detection of heteroskedasticity 2145.3 Consequences of heteroskedasticity 2195.4 Solutions to the heteroskedasticity problem 2215.5 Heteroskedasticity and the use of deflators 2245.6 Testing the linear versus log-linear functional form 228CHAPTER 6 Autocorrelation 2396.1 Introduction 2396.2 The Durbin–Watson test 2406.3 Estimation in levels versus first differences 2426.4 Estimation procedures with autocorrelated errors 2466.5 Effect of AR(1) errors on OLS estimates 2506.6 Some further comments on the DW test 2546.7 Tests for serial correlation in models with lagged dependent variables 2576.8 A general test for higher-order serial correlation: The LM test 2596.9 Strategies when the DW test statistic is significant 261*6.10 Trends and random walks 266*6.11 ARCH models and serial correlation 2716.12 Some comments on the DW test and Durbin’s h-test and t-test 272CHAPTER 7 Multicollinearity 2797.1 Introduction 2797.2 Some illustrative examples 2807.3 Some measures of multicollinearity 2837.4 Problems with measuring multicollinearity 2867.5 Solutions to the multicollinearity problem: Ridge regression 2907.6 Principal component regression 2927.7 Dropping variables 2977.8 Miscellaneous other solutions 300CHAPTER 8 Dummy Variables and Truncated Variables 3138.1 Introduction 3138.2 Dummy variables for changes in the intercept term 3148.3 Dummy variables for changes in slope coefficients 3198.4 Dummy variables for cross-equation constraints 3228.5 Dummy variables for testing stability of regression coefficients 3248.6 Dummy variables under heteroskedasticity and autocorrelation 3278.7 Dummy dependent variables 3298.8 The linear probability model and the linear discriminant function 3298.9 The probit and logit models 3338.10 Truncated variables: The tobit model 343CHAPTER 9 Simultaneous Equation Models 3559.1 Introduction 3559.2 Endogenous and exogenous variables 3579.3 The identification problem: Identification through reduced form 3579.4 Necessary and sufficient conditions for identification 3629.5 Methods of estimation: The instrumental variable method 3659.6 Methods of estimation: The two-stage least squares method 3719.7 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 3869.11 Some problems with instrumental variable methods 392CHAPTER 10 Diagnostic Checking, Model Selection, and Specification Testing 40110.1 Introduction 40110.2 Diagnostic tests based on least squares residuals 40210.3 Problems with least squares residuals 40410.4 Some other types of residual 40510.5 DFFITS and bounded influence estimation 41110.6 Model selection 41410.7 Selection of regressors 41910.8 Implied F-ratios for the various criteria 42310.9 Cross-validation 42710.10 Hausman’s specification error test 42810.11 The Plosser–Schwert–White differencing test 43510.12 Tests for nonnested hypotheses 43610.13 Nonnormality of errors 44010.14 Data transformations 441CHAPTER 11 Errors in Variables 45111.1 Introduction 45111.2 The classical solution for a single-equation model with one explanatory variable 45211.3 The single-equation model with two explanatory variables 45511.4 Reverse regression 46311.5 Instrumental variable methods 46511.6 Proxy variables 46811.7 Some other problems 471Part III Special Topics 479CHAPTER 12 Introduction to Time-Series Analysis 48112.1 Introduction 48112.2 Two methods of time-series analysis: Frequency domain and time domain 48212.3 Stationary and nonstationary time series 48212.4 Some useful models for time series 48512.5 Estimation of AR, MA, and ARMA models 49212.6 The Box–Jenkins approach 49612.7 R2 measures in time-series models 503CHAPTER 13 Models of Expectations and Distributed Lags 50913.1 Models of expectations 50913.2 Naive models of expectations 51013.3 The adaptive expectations model 51213.4 Estimation with the adaptive expectations model 51413.5 Two illustrative examples 51613.6 Expectational variables and adjustment lags 52013.7 Partial adjustment with adaptive expectations 52413.8 Alternative distributed lag models: Polynomial lags 52613.9 Rational lags 53313.10 Rational expectations 53413.11 Tests for rationality 53613.12 Estimation of a demand and supply model under rational expectations 53813.13 The serial correlation problem in rational expectations models 544CHAPTER 14 Vector Autoregressions, Unit Roots, and Cointegration 55114.1 Introduction 55114.2 Vector autoregressions 55114.3 Problems with VAR models in practice 55314.4 Unit roots 55414.5 Unit root tests 55514.6 Cointegration 56314.7 The cointegrating regression 56414.8 Vector autoregressions and cointegration 56714.9 Cointegration and error correction models 57114.10 Tests for cointegration 57114.11 Cointegration and testing of the REH and MEH 57214.12 A summary assessment of cointegration 574CHAPTER 15 Panel Data Analysis 58315.1 Introduction 58315.2 The LSDV or fixed effects model 58415.3 The random effects model 58615.4 Fixed effects versus random effects 58915.5 Dynamic panel data models 59115.6 Panel data models with correlated effects and simultaneity 59315.7 Errors in variables in panel data 59515.8 The SUR model 59715.9 The random coefficient model 597CHAPTER 16 Small-Sample Inference: Resampling Methods 60116.1 Introduction 60116.2 Monte Carlo methods 60216.3 Resampling methods: Jackknife and bootstrap 60316.4 Bootstrap confidence intervals 60516.5 Hypothesis testing with the bootstrap 60616.6 Bootstrapping residuals versus bootstrapping the data 60716.7 Non-IID errors and nonstationary models 607Appendix 611Index 621

G.S.Maddala was one of the leading figures in field of econometrics for more than 30 years until he passed away in 1999. At the time of his death, he held the University Eminent Scholar Professorship in the Department of Economics at Ohio State University. His previous affiliations include Stanford University, University of Rochester and University of Florida. Kajal Lahiri is Distinguished Professor of Economics, and Health Policy, and Management and Behaviour at the State University of New York, Albany where he is also Director of the Econometric Research Institute. Professor Lahiri is an Honorary Fellow of the International Institute of Forecasters.

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• Foreword xvii Preface to the Fourth Edition xixPart I Introduction and the Linear Regression Model 1CHAPTER 1 What is Econometrics? 31.1 What is econometrics? 31.2 Economic and econometric models 41.3 The aims and methodology of econometrics 61.4 What constitutes a test of an economic theory? 8CHAPTER 2 Statistical Background and Matrix Algebra 112.1 Introduction 112.2 Probability 122.3 Random variables and probability distributions 172.4 The normal probability distribution and related distributions 182.5 Classical statistical inference 212.6 Properties of estimators 222.7 Sampling distributions for samples from a normal population 262.8 Interval estimation 262.9 Testing of hypotheses 282.10 Relationship between confidence interval procedures and tests of hypotheses 312.11 Combining independent tests 32CHAPTER 3 Simple Regression 593.1 Introduction 593.2 Specification of the relationships 613.3 The method of moments 653.4 The method of least squares 683.5 Statistical inference in the linear regression model 763.6 Analysis of variance for the simple regression model 833.7 Prediction with the simple regression model 853.8 Outliers 883.9 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 102CHAPTER 4 Multiple Regression 1274.1 Introduction 1274.2 A model with two explanatory variables 1294.3 Statistical inference in the multiple regression model 1344.4 Interpretation of the regression coefficients 1434.5 Partial correlations and multiple correlation 1464.6 Relationships among simple, partial, and multiple correlation coefficients 1474.7 Prediction in the multiple regression model 1534.8 Analysis of variance and tests of hypotheses 1554.9 Omission of relevant variables and inclusion of irrelevant variables 1604.10 Degrees of freedom and R2 1654.11 Tests for stability 1694.12 The LR, W, and LM tests 176Part II Violation of the Assumptions of the Basic Regression Model 209CHAPTER 5 Heteroskedasticity 2115.1 Introduction 2115.2 Detection of heteroskedasticity 2145.3 Consequences of heteroskedasticity 2195.4 Solutions to the heteroskedasticity problem 2215.5 Heteroskedasticity and the use of deflators 2245.6 Testing the linear versus log-linear functional form 228CHAPTER 6 Autocorrelation 2396.1 Introduction 2396.2 The Durbin–Watson test 2406.3 Estimation in levels versus first differences 2426.4 Estimation procedures with autocorrelated errors 2466.5 Effect of AR(1) errors on OLS estimates 2506.6 Some further comments on the DW test 2546.7 Tests for serial correlation in models with lagged dependent variables 2576.8 A general test for higher-order serial correlation: The LM test 2596.9 Strategies when the DW test statistic is significant 261*6.10 Trends and random walks 266*6.11 ARCH models and serial correlation 2716.12 Some comments on the DW test and Durbin’s h-test and t-test 272CHAPTER 7 Multicollinearity 2797.1 Introduction 2797.2 Some illustrative examples 2807.3 Some measures of multicollinearity 2837.4 Problems with measuring multicollinearity 2867.5 Solutions to the multicollinearity problem: Ridge regression 2907.6 Principal component regression 2927.7 Dropping variables 2977.8 Miscellaneous other solutions 300CHAPTER 8 Dummy Variables and Truncated Variables 3138.1 Introduction 3138.2 Dummy variables for changes in the intercept term 3148.3 Dummy variables for changes in slope coefficients 3198.4 Dummy variables for cross-equation constraints 3228.5 Dummy variables for testing stability of regression coefficients 3248.6 Dummy variables under heteroskedasticity and autocorrelation 3278.7 Dummy dependent variables 3298.8 The linear probability model and the linear discriminant function 3298.9 The probit and logit models 3338.10 Truncated variables: The tobit model 343CHAPTER 9 Simultaneous Equation Models 3559.1 Introduction 3559.2 Endogenous and exogenous variables 3579.3 The identification problem: Identification through reduced form 3579.4 Necessary and sufficient conditions for identification 3629.5 Methods of estimation: The instrumental variable method 3659.6 Methods of estimation: The two-stage least squares method 3719.7 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 3869.11 Some problems with instrumental variable methods 392CHAPTER 10 Diagnostic Checking, Model Selection, and Specification Testing 40110.1 Introduction 40110.2 Diagnostic tests based on least squares residuals 40210.3 Problems with least squares residuals 40410.4 Some other types of residual 40510.5 DFFITS and bounded influence estimation 41110.6 Model selection 41410.7 Selection of regressors 41910.8 Implied F-ratios for the various criteria 42310.9 Cross-validation 42710.10 Hausman’s specification error test 42810.11 The Plosser–Schwert–White differencing test 43510.12 Tests for nonnested hypotheses 43610.13 Nonnormality of errors 44010.14 Data transformations 441CHAPTER 11 Errors in Variables 45111.1 Introduction 45111.2 The classical solution for a single-equation model with one explanatory variable 45211.3 The single-equation model with two explanatory variables 45511.4 Reverse regression 46311.5 Instrumental variable methods 46511.6 Proxy variables 46811.7 Some other problems 471Part III Special Topics 479CHAPTER 12 Introduction to Time-Series Analysis 48112.1 Introduction 48112.2 Two methods of time-series analysis: Frequency domain and time domain 48212.3 Stationary and nonstationary time series 48212.4 Some useful models for time series 48512.5 Estimation of AR, MA, and ARMA models 49212.6 The Box–Jenkins approach 49612.7 R2 measures in time-series models 503CHAPTER 13 Models of Expectations and Distributed Lags 50913.1 Models of expectations 50913.2 Naive models of expectations 51013.3 The adaptive expectations model 51213.4 Estimation with the adaptive expectations model 51413.5 Two illustrative examples 51613.6 Expectational variables and adjustment lags 52013.7 Partial adjustment with adaptive expectations 52413.8 Alternative distributed lag models: Polynomial lags 52613.9 Rational lags 53313.10 Rational expectations 53413.11 Tests for rationality 53613.12 Estimation of a demand and supply model under rational expectations 53813.13 The serial correlation problem in rational expectations models 544CHAPTER 14 Vector Autoregressions, Unit Roots, and Cointegration 55114.1 Introduction 55114.2 Vector autoregressions 55114.3 Problems with VAR models in practice 55314.4 Unit roots 55414.5 Unit root tests 55514.6 Cointegration 56314.7 The cointegrating regression 56414.8 Vector autoregressions and cointegration 56714.9 Cointegration and error correction models 57114.10 Tests for cointegration 57114.11 Cointegration and testing of the REH and MEH 57214.12 A summary assessment of cointegration 574CHAPTER 15 Panel Data Analysis 58315.1 Introduction 58315.2 The LSDV or fixed effects model 58415.3 The random effects model 58615.4 Fixed effects versus random effects 58915.5 Dynamic panel data models 59115.6 Panel data models with correlated effects and simultaneity 59315.7 Errors in variables in panel data 59515.8 The SUR model 59715.9 The random coefficient model 597CHAPTER 16 Small-Sample Inference: Resampling Methods 60116.1 Introduction 60116.2 Monte Carlo methods 60216.3 Resampling methods: Jackknife and bootstrap 60316.4 Bootstrap confidence intervals 60516.5 Hypothesis testing with the bootstrap 60616.6 Bootstrapping residuals versus bootstrapping the data 60716.7 Non-IID errors and nonstationary models 607Appendix 611Index 621

G.S.Maddala was one of the leading figures in field of econometrics for more than 30 years until he passed away in 1999. At the time of his death, he held the University Eminent Scholar Professorship in the Department of Economics at Ohio State University. His previous affiliations include Stanford University, University of Rochester and University of Florida. Kajal Lahiri is Distinguished Professor of Economics, and Health Policy, and Management and Behaviour at the State University of New York, Albany where he is also Director of the Econometric Research Institute. Professor Lahiri is an Honorary Fellow of the International Institute of Forecasters.

Select Guide Rating

• Foreword xvii Preface to the Fourth Edition xixPart I Introduction and the Linear Regression Model 1CHAPTER 1 What is Econometrics? 31.1 What is econometrics? 31.2 Economic and econometric models 41.3 The aims and methodology of econometrics 61.4 What constitutes a test of an economic theory? 8CHAPTER 2 Statistical Background and Matrix Algebra 112.1 Introduction 112.2 Probability 122.3 Random variables and probability distributions 172.4 The normal probability distribution and related distributions 182.5 Classical statistical inference 212.6 Properties of estimators 222.7 Sampling distributions for samples from a normal population 262.8 Interval estimation 262.9 Testing of hypotheses 282.10 Relationship between confidence interval procedures and tests of hypotheses 312.11 Combining independent tests 32CHAPTER 3 Simple Regression 593.1 Introduction 593.2 Specification of the relationships 613.3 The method of moments 653.4 The method of least squares 683.5 Statistical inference in the linear regression model 763.6 Analysis of variance for the simple regression model 833.7 Prediction with the simple regression model 853.8 Outliers 883.9 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 102CHAPTER 4 Multiple Regression 1274.1 Introduction 1274.2 A model with two explanatory variables 1294.3 Statistical inference in the multiple regression model 1344.4 Interpretation of the regression coefficients 1434.5 Partial correlations and multiple correlation 1464.6 Relationships among simple, partial, and multiple correlation coefficients 1474.7 Prediction in the multiple regression model 1534.8 Analysis of variance and tests of hypotheses 1554.9 Omission of relevant variables and inclusion of irrelevant variables 1604.10 Degrees of freedom and R2 1654.11 Tests for stability 1694.12 The LR, W, and LM tests 176Part II Violation of the Assumptions of the Basic Regression Model 209CHAPTER 5 Heteroskedasticity 2115.1 Introduction 2115.2 Detection of heteroskedasticity 2145.3 Consequences of heteroskedasticity 2195.4 Solutions to the heteroskedasticity problem 2215.5 Heteroskedasticity and the use of deflators 2245.6 Testing the linear versus log-linear functional form 228CHAPTER 6 Autocorrelation 2396.1 Introduction 2396.2 The Durbin–Watson test 2406.3 Estimation in levels versus first differences 2426.4 Estimation procedures with autocorrelated errors 2466.5 Effect of AR(1) errors on OLS estimates 2506.6 Some further comments on the DW test 2546.7 Tests for serial correlation in models with lagged dependent variables 2576.8 A general test for higher-order serial correlation: The LM test 2596.9 Strategies when the DW test statistic is significant 261*6.10 Trends and random walks 266*6.11 ARCH models and serial correlation 2716.12 Some comments on the DW test and Durbin’s h-test and t-test 272CHAPTER 7 Multicollinearity 2797.1 Introduction 2797.2 Some illustrative examples 2807.3 Some measures of multicollinearity 2837.4 Problems with measuring multicollinearity 2867.5 Solutions to the multicollinearity problem: Ridge regression 2907.6 Principal component regression 2927.7 Dropping variables 2977.8 Miscellaneous other solutions 300CHAPTER 8 Dummy Variables and Truncated Variables 3138.1 Introduction 3138.2 Dummy variables for changes in the intercept term 3148.3 Dummy variables for changes in slope coefficients 3198.4 Dummy variables for cross-equation constraints 3228.5 Dummy variables for testing stability of regression coefficients 3248.6 Dummy variables under heteroskedasticity and autocorrelation 3278.7 Dummy dependent variables 3298.8 The linear probability model and the linear discriminant function 3298.9 The probit and logit models 3338.10 Truncated variables: The tobit model 343CHAPTER 9 Simultaneous Equation Models 3559.1 Introduction 3559.2 Endogenous and exogenous variables 3579.3 The identification problem: Identification through reduced form 3579.4 Necessary and sufficient conditions for identification 3629.5 Methods of estimation: The instrumental variable method 3659.6 Methods of estimation: The two-stage least squares method 3719.7 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 3869.11 Some problems with instrumental variable methods 392CHAPTER 10 Diagnostic Checking, Model Selection, and Specification Testing 40110.1 Introduction 40110.2 Diagnostic tests based on least squares residuals 40210.3 Problems with least squares residuals 40410.4 Some other types of residual 40510.5 DFFITS and bounded influence estimation 41110.6 Model selection 41410.7 Selection of regressors 41910.8 Implied F-ratios for the various criteria 42310.9 Cross-validation 42710.10 Hausman’s specification error test 42810.11 The Plosser–Schwert–White differencing test 43510.12 Tests for nonnested hypotheses 43610.13 Nonnormality of errors 44010.14 Data transformations 441CHAPTER 11 Errors in Variables 45111.1 Introduction 45111.2 The classical solution for a single-equation model with one explanatory variable 45211.3 The single-equation model with two explanatory variables 45511.4 Reverse regression 46311.5 Instrumental variable methods 46511.6 Proxy variables 46811.7 Some other problems 471Part III Special Topics 479CHAPTER 12 Introduction to Time-Series Analysis 48112.1 Introduction 48112.2 Two methods of time-series analysis: Frequency domain and time domain 48212.3 Stationary and nonstationary time series 48212.4 Some useful models for time series 48512.5 Estimation of AR, MA, and ARMA models 49212.6 The Box–Jenkins approach 49612.7 R2 measures in time-series models 503CHAPTER 13 Models of Expectations and Distributed Lags 50913.1 Models of expectations 50913.2 Naive models of expectations 51013.3 The adaptive expectations model 51213.4 Estimation with the adaptive expectations model 51413.5 Two illustrative examples 51613.6 Expectational variables and adjustment lags 52013.7 Partial adjustment with adaptive expectations 52413.8 Alternative distributed lag models: Polynomial lags 52613.9 Rational lags 53313.10 Rational expectations 53413.11 Tests for rationality 53613.12 Estimation of a demand and supply model under rational expectations 53813.13 The serial correlation problem in rational expectations models 544CHAPTER 14 Vector Autoregressions, Unit Roots, and Cointegration 55114.1 Introduction 55114.2 Vector autoregressions 55114.3 Problems with VAR models in practice 55314.4 Unit roots 55414.5 Unit root tests 55514.6 Cointegration 56314.7 The cointegrating regression 56414.8 Vector autoregressions and cointegration 56714.9 Cointegration and error correction models 57114.10 Tests for cointegration 57114.11 Cointegration and testing of the REH and MEH 57214.12 A summary assessment of cointegration 574CHAPTER 15 Panel Data Analysis 58315.1 Introduction 58315.2 The LSDV or fixed effects model 58415.3 The random effects model 58615.4 Fixed effects versus random effects 58915.5 Dynamic panel data models 59115.6 Panel data models with correlated effects and simultaneity 59315.7 Errors in variables in panel data 59515.8 The SUR model 59715.9 The random coefficient model 597CHAPTER 16 Small-Sample Inference: Resampling Methods 60116.1 Introduction 60116.2 Monte Carlo methods 60216.3 Resampling methods: Jackknife and bootstrap 60316.4 Bootstrap confidence intervals 60516.5 Hypothesis testing with the bootstrap 60616.6 Bootstrapping residuals versus bootstrapping the data 60716.7 Non-IID errors and nonstationary models 607Appendix 611Index 621