Introduction to Econometrics, 3rd Edition

by G. S. Maddala (Formerly of Ohio State University, USA)

• ISBN13: 9780471497288
• ISBN10: 0471497282
• Edition: 3rd
• Format: Paperback
• Copyright: 2001-05-01
• Publisher: WILEY

Summary

'The second edition is well written and the chapters are focused and easy to follow from beginning to end. Maddala has an oustanding grasp of the issues, and the level of mathematics and statistics is appropriate as well.'

Author Biography

<B> G.S. MADDALA</B> passed away in June 1999 and had been a leading figure in the econometrics profession for more than three decades. At the time of his death, he held the University Eminent Scholar Professorship in the Department of Economics at Ohio State University. His previous university affiliations include Stanford University, University of Rochester and University of Florida.

Table of Contents

Foreword	xvii
Preface to the Second Edition	xix
Preface to the Third Edition	xxiii
Obituary	xxv
PART I INTRODUCTION AND THE LINEAR REGRESSION MODEL	1	(196)
What is Econometrics?	3	(8)
What is in this Chapter?	3	(6)
What is Econometrics?	3	(1)
Economic and Econometric Models	4	(2)
The Aims and Methodology of Econometrics	6	(3)
What Constitutes a Test of an Economic Theory?	9	(1)
Summary and an Outline of the Book	9	(2)
Statistical Background and Matrix Algebra	11	(48)
What is in this Chapter?	11	(22)
Introduction	12	(1)
Probability	12	(1)
Addition Rules of Probability	13	(1)
Conditional Probability and the Multiplication Rule	14	(1)
Bayes' Theorem	15	(1)
Summation and Product Operations	15	(2)
Random Variables and Probability Distributions	17	(1)
Joint, Marginal, and Conditional Distributions	18	(1)
Illustrative Example	18	(1)
The Normal Probability Distribution and Related Distributions	19	(1)
The Normal Distribution	19	(1)
Related Distributions	20	(1)
Classical Statistical Inference	21	(1)
Point Estimation	22	(1)
Properties of Estimators	23	(1)
Unbiasedness	23	(1)
Efficiency	24	(1)
Consistency	24	(1)
Other Asymptotic Properties	25	(1)
Sampling Distributions for Samples from a Normal Population	26	(1)
Interval Estimation	27	(1)
Testing of Hypotheses	28	(4)
Relationship Between Confidence Interval Procedures and Tests of Hypotheses	32	(1)
Combining Independent Tests	33	(1)
Summary	33	(1)
Exercises	34	(7)
Appendix to Chapter 2	41	(18)
Matrix Algebra	41	(15)
Exercises on Matrix Algebra	56	(3)
Simple Regression	59	(68)
What is in this Chapter?	59	(46)
Introduction	59	(2)
Specification of the Relationships	61	(4)
The Method of Moments	65	(1)
Illustrative Example	66	(2)
The Method of Least Squares	68	(3)
Reverse Regression	71	(1)
Illustrative Example	72	(3)
Statistical Inference in the Linear Regression Model	75	(2)
Illustrative Example	77	(1)
Confidence Intervals for α, β, and σ2	78	(1)
Testing of Hypotheses	79	(2)
Example of Comparing Test Scores from the GRE and GMAT Tests	81	(1)
Regression with No Constant Term	82	(1)
Analysis of Variance for the Simple Regression Model	83	(1)
Prediction with the Simple Regression Model	84	(2)
Prediction of Expected Values	86	(1)
Illustrative Example	87	(1)
Outliers	88	(1)
Some Illustrative Examples	89	(5)
Alternative Functional Forms for Regression Equations	94	(3)
Illustrative Example	97	(2)
Inverse Prediction in the Least Squares Regression Model	99	(2)
Stochastic Regressors	101	(1)
The Regression Fallacy	102	(1)
The Bivariate Normal Distribution	102	(2)
Galton's Result and the Regression Fallacy	104	(1)
A Note on the Term: ``Regression''	104	(1)
Summary	105	(1)
Exercises	106	(6)
Appendix to Chapter 3	112	(15)
Multiple Regression	127	(70)
What is in this Chapter?	127	(50)
Introduction	127	(2)
A Model with Two Explanatory Variables	129	(1)
The Least Squares Method	130	(2)
Illustrative Example	132	(2)
Statistical Inference in the Multiple Regression Model	134	(1)
Illustrative Example	135	(4)
Formulas for the General Case of k Explanatory Variables	139	(1)
Some Illustrative Examples	140	(3)
Interpretation of the Regression Coefficients	143	(2)
Illustrative Example	145	(1)
Partial Correlations and Multiple Correlation	146	(1)
Relationships Among Simple, Partial, and Multiple Correlation Coefficients	147	(1)
Two Illustrative Examples	148	(5)
Prediction in the Multiple Regression Model	153	(1)
Illustrative Example	153	(1)
Analysis of Variance and Tests of Hypotheses	154	(2)
Nested and Nonnested Hypotheses	156	(1)
Tests for Linear Functions of Parameters	157	(1)
Illustrative Example	158	(1)
Omission of Relevant Variables and Inclusion of Irrelevant Variables	159	(1)
Omission of Relevant Variables	160	(1)
Demand for Food in the United States	161	(1)
Production Functions and Management Bias	162	(1)
Inclusion of Irrelevant Variables	163	(1)
Degrees of Freedom and R2	164	(4)
Tests for Stability	168	(1)
The Analysis of Variance Test	168	(1)
Stability of the Demand for Food Function	169	(1)
Stability of Production Functions	170	(3)
Predictive Tests for Stability	173	(1)
Illustrative Example	173	(3)
The LR, W, and LM Tests	176	(1)
Illustrative Example	176	(1)
Summary	177	(2)
Exercises	179	(6)
Appendix to Chapter 4	185	(7)
The Multiple Regression Model in Matrix Notation	185	(7)
Data Sets	192	(5)
PART II VIOLATION OF THE ASSUMPTIONS OF THE BASIC MODEL	197	(266)
Heteroskedasticity	199	(28)
What is in this Chapter?	199	(21)
Introduction	199	(1)
Illustrative Example	200	(2)
Detection of Heteroskedasticity	202	(1)
Illustrative Example	202	(1)
Some Other Tests	203	(2)
Illustrative Example	205	(1)
An Intuitive Justification for the Breusch-Pagan Test	206	(1)
Consequences of Heteroskedasticity	207	(2)
Estimation of the Variance of the OLS Estimator Under Heteroskedasticity	209	(1)
Solutions to the Heteroskedasticity Problem	209	(2)
Illustrative Example	211	(1)
Heteroskedasticity and the Use of Deflators	212	(3)
Illustrative Example: The Density Gradient Model	215	(2)
Testing the Linear Versus Log-Linear Functional Form	217	(1)
The Box-Cox Test	217	(2)
The BM Test	219	(1)
The PE Test	219	(1)
Summary	220	(1)
Exercises	221	(3)
Appendix to Chapter 5	224	(3)
Generalized Least Squares	224	(3)
Autocorrelation	227	(40)
What is in this Chapter?	227	(35)
Introduction	227	(1)
Durbin-Watson Test	228	(1)
Illustrative Example	229	(1)
Estimation in Levels Versus First Differences	230	(2)
Some Illustrative Examples	232	(2)
Estimation Procedures with Autocorrelated Errors	234	(2)
Iterative Procedures	236	(1)
Grid-Search Procedures	237	(1)
Illustrative Example	238	(1)
Effect of AR(1) Errors on OLS Estimates	238	(4)
Some Further Comments on the DW Test	242	(1)
The von Neumann Ratio	243	(1)
The Berenblut-Webb Test	243	(2)
Tests for Serial Correlation in Models with Lagged Dependent Variables	245	(1)
Durbin's h-Test	246	(1)
Durbin's Alternative Test	246	(1)
Illustrative Example	247	(1)
A General Test for Higher-Order Serial Correlation: The LM Test	248	(1)
Strategies When the DW Test Statistic is Significant	249	(1)
Errors Not AR(1)	249	(1)
Autocorrelation Caused by Omitted Variables	250	(2)
Serial Correlation Due to Misspecified Dynamics	252	(1)
The Wald Test	253	(1)
Illustrative Example	254	(1)
Trends and Random Walks	255	(2)
Spurious Trends	257	(1)
Differencing and Long-Run Effects: The Concept of Cointegration	258	(2)
ARCH Models and Serial Correlation	260	(2)
Some Comments on the DW Test and Durbin's h-Test and t-Test	262	(1)
Summary	262	(2)
Exercises	264	(3)
Multicollinearity	267	(34)
What is in this Chapter?	267	(24)
Introduction	268	(1)
Some Illustrative Examples	268	(4)
Some Measures of Multicollinearity	272	(2)
Problems with Measuring Multicollinearity	274	(4)
Solutions to the Multicollinearity Problem: Ridge Regression	278	(3)
Principal Component Regression	281	(5)
Dropping Variables	286	(3)
Miscellaneous Other Solutions	289	(1)
Using Ratios or First Differences	289	(1)
Using Extraneous Estimates	289	(2)
Getting More Data	291	(1)
Summary	291	(1)
Exercises	291	(2)
Appendix to Chapter 7	293	(8)
Linearly Dependent Explanatory Variables	293	(8)
Dummy Variables and Truncated Variables	301	(42)
What is in this Chapter?	301	(37)
Introduction	301	(1)
Dummy Variables for Changes in the Intercept Term	302	(3)
Illustrative Example	305	(1)
Two More Illustrative Examples	306	(1)
Dummy Variables For Changes in Slope Coefficients	307	(3)
Dummy Variables for Cross-Equation Constratints	310	(3)
Dummy Variables for Testing Stability of Regression Coefficients	313	(3)
Dummy Variables Under Heteroskedasticity and Autocorrelation	316	(1)
Dummy Dependent Variables	317	(1)
The Linear Probability Model and the Linear Discriminant Function	318	(1)
The Linear Probability Model	318	(2)
The Linear Discriminant Function	320	(2)
The Probit and Logit Models	322	(2)
Illustrative Example	324	(1)
The Problem of Disproportionate Sampling	325	(2)
Prediction of Effects of Changes in the Explanatory Variables	327	(1)
Measuring Goodness of Fit	327	(2)
Illustrative Example	329	(4)
Truncated Variables: The Tobit Model	333	(1)
Some Examples	333	(1)
Method of Estimation	334	(1)
Limitations of the Tobit Model	335	(1)
The Truncated Regression Model	336	(2)
Summary	338	(1)
Exercises	339	(4)
Simultaneous Equations Models	343	(48)
What is in this Chapter?	343	(39)
Introduction	343	(2)
Endogenous and Exogenous Variables	345	(1)
The Identification Problem: Identification Through Reduced Form	346	(2)
Illustrative Example	348	(3)
Necessary and Sufficient Conditions for Identification	351	(2)
Illustrative Example	353	(1)
Methods of Estimation: The Instrumental Variable Method	354	(2)
Measuring R2	356	(1)
Illustrative Example 3	357	(3)
Methods of Estimation: The Two-Stage Least Squares Method	360	(1)
Computing Standard Errors	361	(2)
Illustrative Example	363	(3)
The Question of Normalization	366	(1)
The Limited-Information Maximum Likelihood Method	367	(1)
Illustrative Example	368	(1)
On the Use of OLS in the Estimation of Simultaneous Equations Models	369	(2)
Working's Concept of Identification	371	(2)
Recursive Systems	373	(1)
Estimation of Cobb-Douglas Production Functions	373	(2)
Exogeneity and Causality	375	(3)
Weak Exogeneity	378	(1)
Superexogeneity	378	(1)
Strong Exogeneity	378	(1)
Granger Causality	379	(1)
Granger Causality and Exogeneity	380	(1)
Tests for Exogeneity	380	(1)
Some Problems with Instrumental Variable Methods	381	(1)
Summary	382	(1)
Exercises	383	(3)
Appendix to Chapter 9	386	(5)
Nonlinear Regressions, Models of Expectations, and Nonnormality	391	(46)
What is in this Chapter?	391	(42)
Introduction	392	(1)
The Newton-Raphson Method	392	(1)
Nonlinear Least Squares	393	(1)
The Gauss-Newton Method	393	(1)
Models of Expectations	394	(1)
Naive Models of Expectations	395	(2)
The Adaptive Expectations Model	397	(2)
Estimation with the Adaptive Expectations Model	399	(1)
Estimation in the Autoregressive Form	399	(1)
Estimation in the Distributed Lag Form	400	(1)
Two Illustrative Examples	401	(4)
Expectational Variables and Adjustment Lags	405	(4)
Partial Adjustment with Adaptive Expectations	409	(2)
Alternative Distributed Lag Models: Polynomial Lags	411	(1)
Finite Lags: The Polynomial Lag	412	(3)
Illustrative Example	415	(1)
Choosing the Degree of the Polynomial	416	(1)
Rational Lags	417	(2)
Rational Expectations	419	(3)
Tests for Rationality	422	(2)
Estimation of a Demand and Supply Model Under Rational Expectations	424	(1)
Case 1	424	(1)
Case 2	425	(3)
Illustrative Example	428	(3)
The Serial Correlation Problem in Rational Expectations Models	431	(1)
Nonnormality of Errors	431	(1)
Tests for Normality	432	(1)
Data Transformations	433	(1)
Summary	433	(2)
Exercises	435	(2)
Errors in Variables	437	(26)
What is in this Chapter?	437	(22)
Introduction	437	(1)
The Classical Solution for a Single-Equation Model with One Explanatory Variable	438	(3)
The Single-Equation Model with Two Explanatory Variables	441	(1)
Two Explanatory Variables: One Measured with Error	441	(3)
Illustrative Example	444	(2)
Two Explanatory Variables: Both Measured with Error	446	(3)
Reverse Regression	449	(2)
Instrumental Variable Methods	451	(3)
Proxy Variables	454	(2)
Coefficient of the Proxy Variable	456	(1)
Some Other Problems	457	(1)
The Case of Multiple Equations	458	(1)
Correlated Errors	459	(1)
Summary	459	(2)
Exercises	461	(2)
PART III SPECIAL TOPICS	463	(142)
Diagnostic Checking, Model Selection, and Specification Testing	465	(48)
What is in this Chapter?	465	(41)
Introduction	465	(1)
Diagnostic Tests Based on Least Squares Residuals	466	(1)
Tests for Omitted Variables	467	(1)
Tests for ARCH Effects	468	(1)
Problems with Least Squares Residuals	469	(1)
Some Other Types of Residuals	470	(1)
Predicted Residuals and Studentized Residuals	470	(1)
Dummy Variable Method for Studentized Residuals	471	(1)
BLUS Residuals	472	(1)
Recursive Residuals	472	(2)
Illustrative Example	474	(2)
DFFITS and Bounded Influence Estimation	476	(2)
Illustrative Example	478	(1)
Model Selection	479	(1)
Hypothesis-Testing Search	480	(1)
Interpretive Search	481	(1)
Simplification Search	481	(1)
Proxy Variable Search	481	(1)
Data Selection Search	482	(1)
Post-Data Model Construction	482	(1)
Hendry's Approach to Model Selection	483	(1)
Selection of Regressors	484	(2)
Theil's R2 Criterion	486	(1)
Criteria Based on Minimizing the Mean-Squared Error of Prediction	486	(2)
Akaike's Information Criterion	488	(1)
Implied F-Ratios for the Various Criteria	488	(3)
Bayes' Theorem and Posterior Odds for Model Selection	491	(1)
Cross-Validation	492	(2)
Hausman's Specification Error Test	494	(2)
An Application: Testing for Errors in Variables or Exogeneity	496	(1)
Some Illustrative Examples	497	(1)
An Omited Variable Interpretation of the Hausman Test	498	(3)
The Plosser-Schwert-White Differencing Test	501	(1)
Tests for Nonnested Hypotheses	502	(1)
The Davidson and MacKinnon Test	502	(3)
The Encompassing Test	505	(1)
A Basic Problem in Testing Nonnested Hypotheses	506	(1)
Hypothesis Testing Versus Model Selection as a Research Strategy	506	(1)
Summary	506	(2)
Exercises	508	(2)
Appendix to Chapter 12	510	(3)
Introduction to Time-Series Analysis	513	(30)
What is in this Chapter?	513	(27)
Introduction	513	(1)
Two Methods of Time-Series Analysis: Frequency Domain and Time Domain	514	(1)
Stationary and Nonstationary Time Series	514	(1)
Strict Stationarity	515	(1)
Weak Stationarity	516	(1)
Properties of Autocorrelation Function	517	(1)
Nonstationarity	517	(1)
Some Useful Models for Time Series	517	(1)
Purely Random Process	517	(1)
Random Walk	518	(1)
Moving Average Process	519	(1)
Autoregressive Process	520	(2)
Autoregressive Moving Average Process	522	(2)
Autoregressive Integrated Moving Average Process	524	(1)
Estimation of AR, MA, and ARMA Models	524	(1)
Estimation of MA Models	524	(1)
Estimation of ARMA Models	525	(1)
Residuals from the ARMA Models	526	(1)
Testing Goodness of Fit	527	(2)
The Box-Jenkins Approach	529	(2)
Forecasting from Box-Jenkins Models	531	(1)
Illustrative Example	532	(2)
Trend Elimination: The Traditional Method	534	(1)
A Summary Assessment	535	(1)
Seasonality in the Box-Jenkins Modeling	535	(1)
R2 Measures in Time-Series Models	536	(4)
Summary	540	(1)
Exercises	540	(1)
Data Sets	541	(2)
Vector Autoregressions, Unit Roots, and Cointegration	543	(30)
What is in this Chapter?	543	(26)
Introduction	543	(1)
Vector Autoregressions	544	(2)
Problems with VAR Models in Practice	546	(1)
Unit Roots	547	(1)
Unit Root Tests	548	(1)
Dickey-Fuller Test	548	(1)
The Serial Correlation Problem	549	(1)
The Low Power of Unit Root Tests	550	(1)
The DF-GLS Tests	550	(1)
What are the Null and Alternative Hypotheses in Unit Root Tests?	550	(2)
Tests with Stationarity as Null	552	(1)
Confirmatory Analysis	553	(1)
Panel Data Unit Root Tests	554	(1)
Structural Change and Unit Roots	555	(1)
Cointegration	556	(1)
The Cointegrating Regression	557	(3)
Vector Autoregressions and Cointegration	560	(4)
Cointegration and Error Correction Models	564	(1)
Tests for Cointegration	565	(1)
Cointegration and Testing of the REH and MEH	566	(2)
A Summary Assessment of Cointegration	568	(1)
Summary	569	(1)
Exercises	570	(3)
Panel Data Analysis	573	(12)
What is in this Chapter?	573	(10)
Introduction	573	(1)
The LSDV or Fixed Effects Model	574	(1)
The Random Effects Model	575	(3)
Fixed Effects Versus Random Effects	578	(1)
Hausman Test	578	(1)
Breusch and Pagan Test	579	(1)
The SUR Model	579	(1)
Dynamic Panel Data Models	580	(1)
The Random Coefficient Model	581	(2)
Summary	583	(2)
Large-Sample Theory	585	(8)
What is in this Chapter?	585	(6)
The Maximum Likelihood Method	585	(1)
Methods of Solving the Likelihood Equations	586	(2)
The Cramer-Rao Lower Bound	588	(1)
Large-Sample Tests Based on ML	588	(1)
GIVE and GMM	589	(2)
Summary	591	(2)
Small-Sample Inference: Resampling Methods	593	(12)
What is in this Chapter?	593	(9)
Introduction	593	(1)
Monte Carlo Methods	594	(1)
More Efficient Monte Carlo Methods	595	(1)
Response Surfaces	595	(1)
Resampling Methods: Jackknife and Bootstrap	595	(2)
Some Illustrative Examples	597	(1)
Other Issues Relating to Bootstrap	598	(1)
Bootstrap Confidence Intervals	599	(1)
Hypothesis Testing with the Bootstrap	599	(1)
Bootstrapping Residuals Versus Bootstrapping the Data	600	(1)
NonIID Errors and Nonstationary Models	601	(1)
Heteroskedasticity and Autocorrelation	601	(1)
Unit Root Tests Based on the Bootstrap	601	(1)
Cointegration Tests	601	(1)
Miscellaneous Other Applications	602	(1)
Summary	602	(3)
Appendices	605	(12)
Appendix A: Data Sets	605	(8)
Appendix B: Data Sets on the Web	613	(2)
Appendix C: Computer Programs	615	(2)
Index	617