Undergraduate Econometrics, 2nd Edition

by R. Carter Hill (Louisiana State Univ.); William E. Griffiths (Univ. of New England); George G. Judge (Univ. of California at Berkeley )

• ISBN13: 9780471331841
• ISBN10: 0471331848
• Edition: 2nd
• Format: Hardcover
• Copyright: 2000-11-01
• Publisher: Wiley

Summary

This text on Econometrics is designed specifically for undergraduates- it is shorter and more focused on selective topics, important results are demonstrated in a simple manner, and algebra and proofs are presented so that instructors can choose to include or exclude them.

Author Biography

R. Carter Hill, Louisiana State University;
William Griffiths, University of New England; and
George Judge, University of California, Berkeley

Table of Contents

Preface	v
An Introduction to Econometrics	1	(10)
Why Study Econometrics?	1	(1)
What Is Econometrics?	2	(2)
Some Examples	3	(1)
The Econometric Model	4	(1)
How Do We Obtain Data?	5	(4)
Experimental Data	5	(3)
Nonexperimental Data	8	(1)
Statistical Inference	9	(1)
A Research Format	9	(2)
Some Basic Probability Concepts	11	(31)
Experiments, Outcomes and Random Variables	11	(3)
Controlled Experiments---Experimental Data	11	(1)
Uncontrolled Experiments---Nonexperimental Data	12	(1)
Discrete and Continuous Random Variables	13	(1)
The Probability Distribution of a Random Variable	14	(2)
Probability Distributions of Discrete Random Variables	14	(1)
The Probability Density Function of a Continuous Random Variable	15	(1)
Expected Values Involving a Single Random Variable	16	(5)
The Rules of Summation	17	(1)
The Mean of a Random Variable	18	(2)
Expectation of a Function of a Random Variable	20	(1)
The Variance of a Random Variable	21	(1)
Using Joint Probability Density Functions	21	(5)
Marginal Probability Density Functions	23	(1)
Conditional Probability Density Functions	24	(1)
Independent Random Variables	25	(1)
The Expected Value of a Function of Several Random Variables: Covariance and Correlation	26	(5)
The Mean of a Weighted Sum of Random Variables	30	(1)
The Variance of a Weighted Sum of Random Variables	31	(1)
The Normal Distribution	31	(4)
Learning Objectives	35	(1)
Exercises	36	(6)
The Simple Linear Regression Model: Specification and Estimation	42	(26)
An Economic Model	42	(3)
An Econometric Model	45	(5)
Introducing the Error Term	47	(3)
Estimating the Parameters for the Expenditure Relationship	50	(10)
The Least Squares Principle	51	(4)
Estimates for the Food Expenditure Function	55	(1)
Interpreting the Estimates	56	(1)
Elasticities	56	(1)
Prediction	57	(1)
Examining Computer Output	57	(1)
Other Economic Models	58	(2)
Learning Objectives	60	(1)
Exercises	61	(7)
Properties of the Least Squares Estimators	68	(22)
The Least Squares Estimators as Random Variables	68	(1)
The Sampling Properties of the Least Squares Estimators	69	(8)
The Expected Values of b1 and b2	70	(1)
The Repeated Sampling Context	71	(1)
Derivation of Equation 4.2.1	72	(1)
The Variances and Covariance of b1 and b2	73	(4)
Linear Estimators	77	(1)
The Gauss-Markov Theorem	77	(2)
The Probability Distributions of the Least Squares Estimators	79	(1)
Estimating the Variance of the Error Term	80	(4)
Estimating the Variances and Covariances of the Least Squares Estimators	81	(1)
The Estimated Variances and Covariances for the Food Expenditure Example	81	(1)
Sample Computer Output	82	(2)
Learning Objectives	84	(1)
Exercises	85	(5)
Inference in the Simple Regression Model: Interval Estimation, Hypothesis Testing, and Prediction	90	(31)
Interval Estimation	91	(7)
The Theory	91	(1)
The Chi-Square Distribution	92	(1)
The Probability Distribution of σ2	93	(1)
The t-Distribution	93	(1)
A Key Result	94	(1)
Obtaining Interval Estimates	95	(1)
The Repeated Sampling Context	96	(1)
An Illustration	97	(1)
Hypothesis Testing	98	(12)
The Null Hypothesis	99	(1)
The Alternative Hypothesis	99	(1)
The Test Statistic	100	(1)
The Rejection Region	101	(1)
The Food Expenditure Example	102	(1)
Type I and Type II Errors	103	(1)
The p-Value of a Hypothesis Test	104	(1)
Tests of Significance	105	(1)
A Significance Test in the Food Expenditure Model	105	(2)
Reading Computer Output	107	(1)
A Relationship Between Two-Tailed Hypothesis Tests and Interval Estimation	107	(1)
One-Tailed Tests	108	(1)
A Comment on Stating Null and Alternative Hypotheses	109	(1)
The Least Squares Predictor	110	(3)
Prediction in the Food Expenditure Model	113	(1)
Learning Objectives	113	(1)
Exercises	114	(7)
The Simple Linear Regression Model: Reporting the Results and Choosing the Functional Form	121	(24)
The Coefficient of Determination	121	(5)
Analysis of Variance Table and R2 for Food Expenditure Example	124	(1)
Correlation Analysis	125	(1)
Correlation Analysis and R2	126	(1)
Reporting Regression Results	126	(2)
The Effects of Scaling the Data	127	(1)
Choosing a Functional Form	128	(10)
Some Commonly Used Functional Forms	129	(3)
Examples Using Alternative Functional Forms	132	(1)
The Food Expenditure Model	132	(1)
Some Other Economic Models and Functional Forms	133	(2)
Choosing a Functional Form: Empirical Issues	135	(3)
Are the Residuals Normally Distributed?	138	(1)
Learning Objectives	139	(1)
Exercises	140	(5)
The Multiple Regression Model	145	(25)
Model Specification and the Data	145	(5)
The Economic Model	145	(2)
The Econometric Model	147	(1)
The General Model	148	(1)
The Assumptions of the Model	149	(1)
Estimating the Parameters of the Multiple Regression Model	150	(4)
Least Squares Estimation Procedure	151	(1)
Least Squares Estimates Using Hamburger Chain Data	151	(2)
Estimation of the Error Variance σ2	153	(1)
Sampling Properties of the Least Squares Estimator	154	(3)
The Variances and Covariances of the Least Squares Estimators	154	(2)
The Properties of the Least Squares Estimators Assuming Normally Distributed Errors	156	(1)
Interval Estimation	157	(2)
Hypothesis Testing for a Single Coefficient	159	(3)
Testing the Significance of a Single Coefficient	159	(1)
One-Tailed Hypothesis Testing for a Single Coefficient	160	(1)
Testing for Elastic Demand	161	(1)
Testing Advertizing Effectiveness	161	(1)
Measuring Goodness of Fit	162	(2)
Learning Objectives	164	(1)
Exercises	164	(6)
Further Inference in the Multiple Regression Model	170	(29)
The F-Test	170	(4)
The F-Distribution: Theory	173	(1)
Testing the Significance of a Model	174	(3)
The Relationship Between Joint and Individual Tests	176	(1)
An Extended Model	177	(1)
Testing Some Economic Hypotheses	178	(3)
The Significance of Advertising	178	(1)
The Optimal Level of Advertising	179	(2)
The Optimal Level of Advertising and Price	181	(1)
The Use of Nonsample Information	181	(3)
Model Specification	184	(5)
Omitted and Irrelevant Variables	185	(1)
Omitted Variable Bias: A Proof	186	(1)
Testing for Model Misspecification: The Reset Test	187	(2)
Collinear Economic Variables	189	(2)
The Consequences of Collinearity	189	(1)
Identifying and Mitigating Collinearity	190	(1)
Prediction	191	(1)
Learning Objectives	192	(1)
Exercises	193	(6)
Dummy (Binary) Variables	199	(19)
Introduction	199	(1)
The Use of Intercept Dummy Variables	200	(2)
Slope Dummy Variables	202	(1)
An Example: The University Effect on House Prices	203	(2)
Common Applications of Dummy Variables	205	(3)
Interactions Between Qualitative Factors	205	(1)
Qualitative Variables with Several Categories	206	(1)
Controlling for Time	207	(1)
Seasonal Dummies	207	(1)
Annual Dummies	207	(1)
Regime Effects	208	(1)
Testing the Existence of Qualitative Effects	208	(1)
Testing for a Single Qualitative Effect	208	(1)
Testing Jointly for the Presence of Several Qualitative Effects	209	(1)
Testing the Equivalence of Two Regressions Using Dummy Variables	209	(4)
The Chow Test	210	(1)
An Empirical Example of the Chow Test	211	(2)
Learning Objectives	213	(1)
Exercises	213	(5)
Nonlinear Models	218	(17)
Polynomial and Interaction Variables	218	(4)
Polynomial Terms in a Regression Model	219	(1)
Interactions Between Two Continuous Variables	220	(2)
A Simple Nonlinear-in-the-Parameters Model	222	(2)
A Logistic Growth Curve	224	(3)
Poisson Regression	227	(2)
Learning Objectives	229	(1)
Exercises	229	(6)
Heteroskedasticity	235	(23)
The Nature of Heteroskedasticity	235	(3)
The Consequences of Heteroskedasticity for the Least Squares Estimator	238	(3)
White's Approximate Estimator for the Variance of the Least Squares Estimator	240	(1)
Proportional Heteroskadesticity	241	(3)
Detecting Heteroskedasticity	244	(2)
Residual Plots	244	(1)
The Goldfeld-Quandt Test	245	(1)
A Sample with a Heteroskedastic Partition	246	(5)
Economic Model	246	(2)
Generalized Least Squares Through Model Transformation	248	(1)
Implementing Generalized Least Squares	249	(1)
Testing the Variance Assumption	250	(1)
Learning Objectives	251	(1)
Exercises	251	(7)
Autocorrelation	258	(25)
The Nature of the Problem	258	(3)
Area Response Model for Sugar Cane	259	(1)
Least Squares Estimation	260	(1)
First-Order Autoregressive Errors	261	(2)
Properties of an AR(1) Error	262	(1)
Consequences for the Least Squares Estimator	263	(2)
Generalized Least Square	265	(3)
A Transformation	265	(2)
Transforming the First Observation	267	(1)
Implementing Generalized Least Squares	268	(3)
The Sugar Cane Example Revisited	269	(2)
Testing for Autocorrelation	271	(4)
The Durbin-Waston Test	271	(2)
The Bounds Test	273	(1)
A Lagrange Multiplier Test	274	(1)
Prediction with AR(1) Errors	275	(2)
Learning Objectives	277	(1)
Exercises	277	(6)
Random Regressors and Moment Based Estimation	283	(21)
Introduction	283	(1)
Linear Regression with Random x's	284	(8)
The Finite (Small) Sample Properties of the Least Squares Estimator	285	(1)
The Asymptotic (Large) Sample Properties of the Least Squares Estimator When x Is Not Random	285	(1)
The Asymptotic (Large) Sample Properties of the Least Squares Estimator When x Is Random	286	(1)
The Inconsistency of the Least Squares Estimator When cov (x,e) ≠0	287	(1)
A Geometric Explanation of Why the Least Squares Estimator is Inconsistent When cov(x,e)≠0	287	(1)
Algebraic Proof That the Least Squares Estimator Is Inconsistent When Cov(x,e)≠0	288	(2)
Measurement Errors in Regression Equations	290	(1)
An Example of the Consequences of Measurement Errors	291	(1)
Estimators Based on the Method of Moments	292	(7)
Method of Moments Estimation of the Mean and Variance of a Random Variable	292	(1)
Method of Moments Estimation in the Simple Linear Regression Model	293	(1)
Instrumental Variables Estimation in the Simple Linear Regression Model	294	(1)
The Consistency of the Instrumental Variables Estimator	295	(1)
An Empirical Example of Instrumental Variables Estimation	296	(1)
Instrumental Variables Estimation When Surplus Instruments Are Available	297	(2)
Testing for Correlation Between Explanatory Variables and the Error Term	299	(1)
An Empirical Example of the Hausman Test	300	(1)
Learning Objectives	300	(1)
Exercises	301	(3)
Simultaneous Equations Models	304	(15)
Introduction	304	(1)
A Supply and Demand Model	304	(2)
The Reduced Form Equations	306	(1)
The Failure of Least Squares Estimation in Simultaneous Equations Models	307	(2)
An Intuitive Explanation of the Failure of Least Squares	307	(1)
An Algebraic Explanation of the Failure of Least Squares	308	(1)
The Identification Problem	309	(2)
Two-Stage Least Squares Estimation	311	(2)
The General Two-Stage Least Squares Estimation Procedure	312	(1)
The Properties of the Two-Stage Least Squares Estimator	313	(1)
An Example of Two-Stage Least Squares Estimation	313	(3)
Identification	314	(1)
The Reduced Form Equations	314	(2)
Learning Objectives	316	(1)
Exercises	317	(2)
Distributed Lag Models	319	(16)
Introduction	319	(1)
Finite Distributed Lag Models	320	(7)
An Economic Model	320	(1)
The Econometric Model	321	(1)
An Empirical Illustration	321	(2)
Polynomial Distributed Lags	323	(2)
Selection of the Length of the Finite Lag	325	(2)
The Geometric Lag	327	(1)
The Koyck Transformation	328	(2)
Instrumental Variables Estimation of the Koyck Model	328	(1)
Testing for Autocorrelation in Models with Lagged Dependent Variables	329	(1)
Autoregressive Distributed Lags	330	(2)
The Autoregressive Distributed Lag Model	330	(1)
An Illustration of the ARDL Model	331	(1)
Learning Objectives	332	(1)
Exercises	332	(3)
Regression with Time Series Data	335	(16)
Stationary Time Series	335	(3)
Spurious Regressions	338	(3)
Checking Stationarity Using the Autocorrelation Function	341	(2)
Unit Root Tests for Stationarity	343	(3)
The Dickey-Fuller Tests	344	(1)
The Dickey-Fuller Tests: An Example	345	(1)
Cointegration	346	(1)
An Example of a Cointegration Test	347	(1)
Summarizing Estimation Strategies When Using Time Series Data	347	(1)
Learning Objectives	348	(1)
Exercises	349	(2)
Pooling Time-Series and Cross-Sectional Data	351	(17)
An Economic Model	351	(1)
Seemingly Unrelated Regressions	352	(5)
Estimating Separate Equations	353	(1)
Joint Estimation of the Equation	354	(1)
Separate or Joint Estimation	355	(2)
Testing Cross-Equation Restrictions	357	(1)
A Dummy Variable Specification	357	(2)
The Model	358	(1)
An Error Components Model	359	(1)
Learning Objectives	360	(1)
Exercises	361	(7)
Qualitative and Limited Dependent Variable Models	368	(15)
Introduction	368	(1)
Models with Binary Dependent Variables	368	(8)
The Linear Probability Model	369	(1)
The Probit Model	370	(2)
Maximum Likelihood Estimation of the Probit Model	372	(1)
Interpretation of the Probit Model	373	(1)
An Example	374	(2)
The Logit Model for Binary Choice	376	(1)
Other Models with Qualitative Dependent Variables	376	(2)
Multinomial Choice Models	377	(1)
Ordered Choice Models	377	(1)
Count Data Models and Poisson Regression	378	(1)
Limited Dependent Variable Models	378	(1)
The Tobit Model	378	(1)
Sample Selection	379	(1)
Learning Objectives	379	(1)
Exercises	380	(3)
Writing an Empirical Research Report, and Sources of Economic Data	383	(6)
Selecting a Topic for an Economics Project	383	(1)
Choosing a Topic	383	(1)
Writing an Abstract	384	(1)
A Format for Writing a Research Report	384	(2)
Sources of Economic Data	386	(2)
Links to Economic Data on the Internet	386	(1)
Economic Data on the Internet	387	(1)
Traditional Sources of Economic Data	387	(1)
Interpreting Economic Data	388	(1)
Exercises	388	(1)
Statistical Tables	389	(8)
Index	397