A Guide to Modern Econometrics

by Marno Verbeek (KU Leuven and Tilburg Univ.)

• ISBN13: 9780471899822
• ISBN10: 0471899828
• Format: Paperback
• Copyright: 2000-06-01
• Publisher: WILEY

Summary

Marno Verbeek2s intermediate level textbook explores a wide range of topics in modern econometrics and focuses on what is important for doing and understanding empirical work. A wide range of new topics are covered including time series analysis, limited dependent variables, cointegration and panel data analysis. FEATURES Concentrates on the intuition behind various techniques and their practical relevance rather than the formulae End of chapter exercises review key concepts in light of empircal examples discussed in the chapter Examples are drawn from a wide variety of fields including labour economics, environmental economics, finance, international economics and macroeconomics CONTENTS: Introduction; An Introduction to Linear Regression; Interpreting and Comparing Regression Models; Heteroskedasticity and Autocorrelation; Stochastic Regressors; Maximum Likelihood Estimation; Models with Limited Dependent Variables; Univariate Time Series Modelling; Multivariate Time Series Analysis; Models Based on Panel Data.

Author Biography

Marno Verbeek is Professor of Econometrics at the Center for Economic Studies, KU Leuven.

Table of Contents

Preface	xi
Introduction	1	(6)
About Econometrics	1	(2)
The Structure of this Book	3	(1)
Illustrations and Exercises	4	(3)
An Introduction to Linear Regression	7	(40)
Ordinary Least Squares as An Algebraic Tool	8	(5)
Ordinary Least Squares	8	(2)
Simple Linear Regression	10	(1)
Example: Individual Wages	11	(1)
Matrix Notation	12	(1)
The Linear Regression Model	13	(2)
Small Sample Properties of the OLS Estimator	15	(5)
The Gauss--Markov Assumptions	15	(1)
Properties of the OLS Estimator	16	(3)
Example: Individual Wages (Continued)	19	(1)
Goodness-of-fit	20	(2)
Hypothesis Testing	22	(9)
A Simple t-test	23	(1)
Example: Individual Wages (Continued)	24	(1)
Testing One Linear Restriction	24	(2)
A Joint Test of Significance of Regression Coefficients	26	(1)
Example: Individual Wages (Continued)	27	(2)
The General Case	29	(1)
Size, Power and p-values	30	(1)
Asymptotic Properties of the OLS Estimator	31	(3)
Consistency	31	(2)
Asymptotic Normality	33	(1)
Illustration: the Capital Asset Pricing Model	34	(4)
The CAPM as a Regression Model	35	(1)
Estimating and Testing the CAPM	36	(2)
Multicollinearity	38	(3)
Example: Individual Wages (Continued)	40	(1)
Prediction	41	(6)
Exercises	42	(5)
Interpreting and Comparing Regression Models	47	(26)
Interpreting the Linear Model	47	(3)
Selecting the Set of Regressors	50	(7)
Misspecifying the Set of Regressors	50	(2)
Selecting Regressors	52	(3)
Comparing Non-nested Models	55	(2)
Misspecifying the Functional Form	57	(2)
Nonlinear Models	57	(1)
Testing the Functional Form	58	(1)
Illustration: Explaining House Prices	59	(3)
Illustration: Explaining Individual Wages	62	(11)
Linear Models	63	(3)
Loglinear Models	66	(2)
The Effects of Gender	68	(2)
Some Words of warning	70	(1)
Exercises	71	(2)
Heteroskedasticity and Autocorrelation	73	(42)
Consequences for the OLS Estimator	74	(1)
Deriving an Alternative Estimator	75	(1)
Heteroskedasticity	76	(7)
Introduction	76	(2)
Estimator Properties and Hypothesis Testing	78	(1)
When the Variances are Unknown	79	(1)
Heteroskedasticity-consistent Standard Errors for OLS	80	(1)
A Model with Two Unknown Variances	81	(1)
Multiplicative Heteroskedasticity	82	(1)
Testing for Heteroskedasticity	83	(3)
Testing Equality of Two Unknown Variances	84	(1)
Testing for Multiplicative Heteroskedasticity	84	(1)
The Breusch--Pagan Test	84	(1)
The White Test	85	(1)
Which Test?	85	(1)
Illustration: Explaining Labour Demand	86	(4)
Autocorrelation	90	(4)
First Order Autocorrelation	91	(2)
Unknown ρ	93	(1)
Testing for First Order Autocorrelation	94	(3)
Asymptotic Tests	94	(1)
The Durbin--Watson Test	95	(2)
Illustration: The Demand for Ice Cream	97	(3)
Alternative Autocorrelation Patterns	100	(1)
Higher Order Autocorrelation	100	(1)
Moving Average Errors	100	(1)
What to do When you Find Autocorrelation?	101	(4)
Misspecification	102	(1)
Heteroskedasticity-and-autocorrelation-consistent Standard Errors for OLS	103	(2)
Illustration: Risk Premia in Foreign Exchange Markets	105	(10)
Notation	105	(2)
Tests for Risk Premia in the One-month Market	107	(3)
Tests for Risk Premia using Overlapping Samples	110	(2)
Exercises	112	(3)
Endogeneity, Instrumental Variables and GMM	115	(36)
A Review of the Properties of the OLS Estimator	116	(3)
Cases Where the OLS Estimator Cannot be Saved	119	(5)
Autocorrelation with a Lagged Dependent Variable	119	(1)
An Example with Measurement Error	120	(2)
Simultaneity: the Keynesian Model	122	(2)
The Instrumental Variables Estimator	124	(6)
Estimation with a Single Endogenous Regressor and a Single Instrument	125	(3)
Back to the Keynesian Model	128	(1)
Back to the Measurement Error Problem	129	(1)
Multiple Endogenous Regressors	129	(1)
Illustration: Estimating the Returns to Schooling	130	(4)
The Generalized Instrumental Variables Estimator	134	(5)
Multiple Endogenous Regressors with an Arbitrary Number of Instruments	134	(4)
Two-stage Least Squares and the Keynesian Model Again	138	(1)
The Generalized Method of Moments	139	(5)
Example	140	(1)
The Generalized Method of Moments	141	(2)
Some Simple Examples	143	(1)
Illustration: Estimating Intertemporal Asset Pricing Models	144	(4)
Concluding Remarks	148	(3)
Exercises	148	(3)
Maximum Likelihood Estimation and Specification Tests	151	(26)
An Introduction to Maximum Likelihood	152	(8)
Some Examples	152	(4)
General Properties	156	(2)
An Example (Continued)	158	(1)
The Normal Linear Regression Model	159	(1)
Specification Tests	160	(7)
Three Test Principles	160	(2)
Lagrange Multiplier Tests	162	(4)
An Example (Continued)	166	(1)
Tests in the Normal Linear Regression Model	167	(3)
Testing for Omitted Variables	167	(1)
Testing for Heteroskedasticity	168	(1)
Testing for Autocorrelation	169	(1)
Quasi-maximum Likelihood and Moment Conditions Tests	170	(7)
Quasi-maximum Likelihood	171	(1)
Conditional Moment Tests	172	(1)
Testing for Normality	173	(1)
Exercises	174	(3)
Models with Limited Dependent Variables	177	(48)
Binary Choice Models	178	(11)
Using Linear Regession?	178	(1)
Introducing Binary Choice Models	178	(2)
An Underlying Latent Model	180	(1)
Estimation	180	(2)
Goodness-of-fit	182	(2)
Illustration: the Impact of Unemployment Benefits on Recipiency	184	(2)
Specification Tests in Binary Choice Models	186	(2)
Relaxing Some Assumptions in Binary Choice Models	188	(1)
Multi-response Models	189	(8)
Ordered Response Models	190	(1)
About Normalization	191	(1)
Illustration: Willingness to Pay for Natural Areas	192	(2)
Multinomial Models	194	(3)
Tobit Models	197	(10)
The Standard Tobit Model	197	(3)
Estimation	200	(1)
Illustration: Expenditures on Alcohol and Tobacco (Part 1)	201	(3)
Specification Tests in the Tobit Model	204	(3)
Extensions of Tobit Models	207	(9)
The Tobit II Model	207	(3)
Estimation	210	(2)
Further Extensions	212	(1)
Illustration: Expenditures on Alcohol and Tobacco (Part 2)	212	(4)
Sample Selection Bias	216	(9)
The Nature of the Selection Problem	217	(2)
Semi-parametric Estimation of the Sample Selection Model	219	(1)
Exercises	220	(5)
Univariate Time Series Models	225	(52)
Introduction	226	(5)
Some Examples	226	(2)
Stationarity and the Autocorrelation Function	228	(3)
General ARMA Processes	231	(4)
Formulating ARMA Processes	231	(3)
Invertibility of Lag Polynomials	234	(1)
Common Roots	235	(1)
Stationarity and Unit Roots	235	(3)
Testing for Unit Roots	238	(7)
Testing for Unit Roots in a First Order Autoregressive Model	238	(3)
Testing for Unit Roots in Higher Order Autoregressive Models	241	(2)
Illustration: Quarterly Disposable Income	243	(2)
Illustration: Long-run Purchasing Power Parity (Part 1)	245	(3)
Estimation of ARMA Models	248	(2)
Least Squares	248	(1)
Maximum Likelihood	249	(1)
Choosing a Model	250	(6)
The Autocorrelation Function	250	(2)
The Partial Autocorrelation Function	252	(1)
Diagnostic Checking	253	(1)
Criteria for Model Selection	254	(1)
Illustration: Modelling Quarterly Disposable Income	254	(2)
Predicting with ARMA Models	256	(5)
The Optimal Predictor	257	(2)
Prediction Accuracy	259	(2)
Illustration: The Expectations Theory of the Term Structure	261	(4)
Autoregressive Conditional Heteroskedasticity	265	(8)
ARCH and GARCH Models	265	(4)
Estimation and Prediction	269	(1)
Illustration: Volatility in Daily Exchange Rates	270	(3)
What about Multivariate Models?	273	(4)
Exercises	273	(4)
Multivariate Time Series Models	277	(32)
Dynamic Models with Stationary Variables	278	(3)
Models with Nonstationary Variables	281	(5)
Spurious Regressions	281	(1)
Cointegration	282	(3)
Cointegration and Error-correction Mechanisms	285	(1)
Illustration: Long-run Purchasing Power Parity (Part 2)	286	(3)
Vector Autoregressive Models	289	(3)
Cointegration: The Multivariate Case	292	(7)
Cointegration in a VAR	292	(2)
Example: Cointegration in a Bivariate VAR	294	(1)
Testing for Cointegration	295	(2)
Illustration: Long-run Purchasing Power Parity (Part 3)	297	(2)
Illustration: Money Demand and Inflation	299	(6)
Concluding Remarks	305	(4)
Exercises	305	(4)
Models Based on Panel Data	309	(42)
Advantages of Panel Data	310	(3)
Efficiency of Parameter Estimators	311	(1)
Identification of Parameters	311	(2)
The Static Linear Model	313	(12)
The Fixed Effects Model	313	(2)
The Random Effects Model	315	(3)
Fixed Effects or Random Effects?	318	(2)
Goodness-of-fit	320	(1)
Alternative Instrumental Variables Estimators	321	(1)
Alternative Error Structures	322	(2)
Testing for Heteroskedasticity and Autocorrelation	324	(1)
Illustration: Explaining Individual Wages	325	(2)
Dynamic Linear Models	327	(7)
An Autoregressive Panel Data Model	327	(5)
Dynamic Models with Exogenous Variables	332	(1)
Unit Roots and Cointegration	333	(1)
Illustration: Wage Elasticities of Labour Demand	334	(2)
Models with Limited Dependent Variables	336	(6)
Binary Choice Models	336	(1)
The Fixed Effects Logit Model	337	(1)
The Random Effects Probit Model	338	(2)
Tobit Models	340	(1)
Dynamics and the Problem of Initial Conditions	341	(1)
Incomplete Panels and Selection Bias	342	(9)
Estimation with Randomly Missing Data	343	(2)
Selection Bias and Some Simple Tests	345	(2)
Estimation with Nonrandomly Missing Data	347	(1)
Exercises	347	(4)
A Vectors and Matrices	351	(8)
A.1 Terminology	351	(1)
A.2 Matrix Manipulations	352	(1)
A.3 Properties of Matrices and Vectors	353	(1)
A.4 Inverse Matrices	354	(1)
A.5 Idempotent Matrices	355	(1)
A.6 Eigenvalues and Eigenvectors	355	(1)
A.7 Differentiation	356	(1)
A.8 Some Least Squares Manipulations	357	(2)
B Statistical and Distribution Theory	359	(10)
B.1 Discrete Random Variables	359	(1)
B.2 Continuous Random Variables	360	(1)
B.3 Expectations and Moments	361	(1)
B.4 Multivariate Distributions	362	(1)
B.5 Conditional Distributions	363	(1)
B.6 The Normal Distribution	364	(3)
B.7 Related Distributions	367	(2)
Bibliography	369	(10)
Index	379