Essentials of Econometrics

by Gujarati, Damodar N.

• ISBN13: 9780073032658
• ISBN10: 0073032654
• Edition: 2nd
• Format: Hardcover
• Copyright: 1999-06-01
• Publisher: McGraw-Hill

Table of Contents

Preface	xxiii
CHAPTER 1 THE NATURE AND SCOPE OF ECONOMETRICS	1	(20)
1.1 WHAT IS ECONOMETRICS?	1	(1)
1.2 WHY STUDY ECONOMETRICS?	2	(1)
1.3 THE METHODOLOGY OF ECONOMETRICS	3	(10)
Creating a Statement of Theory or Hypothesis	4	(1)
Collecting Data	4	(2)
Specifying the Mathematical Model of Labor Force Participation	6	(1)
Specifying the Statistical, or Econometric, Model of Labor Force Participation	7	(2)
Estimating the Parameters of the Chosen Econometric Model	9	(1)
Checking for Model Adequacy: Model Specification Testing	10	(1)
Testing the Hypothesis Derived from the Model	11	(1)
Using the Model for Prediction or Forecasting	12	(1)
1.4 THE ROAD AHEAD	13	(1)
Key Terms and Concepts	14	(1)
QUESTIONS	14	(1)
PROBLEMS	14	(2)
APPENDIX 1A ECONOMIC DATA ON THE WORLD WIDE WEB	16	(5)
PART I BASICS OF PROBABILITY AND STATISTICS	21	(102)
CHAPTER 2 A REVIEW OF BASIC STATISTICAL CONCEPTS	21	(44)
2.1 SOME NOTATION	21	(2)
The Summation Notation	21	(1)
Properties of the Summation Operator	22	(1)
2.2 EXPERIMENT, SAMPLE SPACE, SAMPLE POINT, AND EVENTS	23	(1)
Experiment	23	(1)
Sample Space or Population	23	(1)
Sample Point	24	(1)
Events	24	(1)
2.3 RANDOM VARIABLES	24	(1)
2.4 PROBABILITY	25	(5)
Probability of an Event: The Classical or A Priori Definition	25	(1)
Relative Frequency or Empirical Definition of Probability	26	(4)
Probability of Random Variables	30	(1)
2.5 RANDOM VARIABLES AND PROBABILITY DISTRIBUTION FUNCTION (PDF)	30	(4)
PDF of a Discrete Random Variable	31	(1)
PDF of a Continuous Random Variable	32	(1)
Cumulative Distribution Function (CDF)	33	(1)
2.6 MULTIVARIATE PROBABILITY DENSITY FUNCTIONS	34	(5)
Marginal Probability Density Function	36	(1)
Conditional Probability Density Function	37	(1)
Statistical Independence	38	(1)
2.7 CHARACTERISTICS OF PROBABILITY DISTRIBUTIONS	39	(13)
Expected Value: A Measure of Central Tendency	39	(3)
Variance: A Measure of Dispersion	42	(3)
Covariance	45	(1)
Correlation Coefficient	46	(3)
Conditional Expectation	49	(3)
2.8 FROM POPULATION TO THE SAMPLE	52	(5)
Sample Mean	53	(1)
Sample Variance	54	(1)
Sample Covariance	55	(1)
Sample Correlation Coefficient	56	(1)
Sample Skewness and Kurtosis	56	(1)
2.9 SUMMARY	57	(1)
Key Terms and Concepts	58	(1)
REFERENCES	58	(1)
QUESTIONS	59	(1)
PROBLEMS	60	(5)
CHAPTER 3 SOME IMPORTANT PROBABILITY DISTRIBUTIONS	65	(30)
3.1 THE NORMAL DISTRIBUTION	66	(8)
Properties of the Normal Distribution	66	(2)
The Standard Normal Distribution	68	(4)
Random Sampling from a Normal Population	72	(1)
Bootstrap Sampling	72	(2)
3.2 THE SAMPLING, OR PROBABILITY, DISTRIBUTION OF THE SAMPLE MEAN X	74	(7)
The Central Limit Theorem (CLT)	78	(3)
3.3 THE CHI-SQUARE (X)(2) DISTRIBUTION	81	(2)
Properties of the Chi-square Distribution	82	(1)
3.4 THE t DISTRIBUTION	83	(4)
Properties of the t Distribution	84	(3)
3.5 THE F DISTRIBUTION	87	(3)
Properties of the F Distribution	88	(2)
3.6 RELATIONSHIPS AMONG THE t, F, AND X(2) AND THE NORMAL DISTRIBUTIONS	90	(1)
3.7 SUMMARY	91	(1)
Key Terms and Concepts	91	(1)
QUESTIONS	92	(1)
PROBLEMS	92	(3)
CHAPTER 4 STATISTICAL INFERENCE: ESTIMATION AND HYPOTHESIS TESTING	95	(28)
4.1 THE MEANING OF STATISTICAL INFERENCE	95	(1)
4.2 ESTIMATION AND HYPOTHESIS TESTING: TWIN BRANCHES OF STATISTICAL INFERENCE	96	(1)
4.3 ESTIMATION OF PARAMETERS	97	(4)
4.4 PROPERTIES OF POINT ESTIMATORS	101	(4)
Linearity	101	(1)
Unbiasedness	101	(1)
Efficiency	102	(1)
Best Linear Unbiased Estimator (BLUE)	103	(1)
Consistency	104	(1)
4.5 STATISTICAL INFERENCE: HYPOTHESIS TESTING	105	(12)
The Confidence Interval Approach to Hypothesis Testing	106	(1)
Type I and Type II Errors: A Digression	107	(2)
The Test of Significance Approach to Hypothesis Testing	109	(4)
A Word on Choosing the Level of Significance, Alpha, and the p Value	113	(1)
The X(2) and F Tests of Significance	114	(3)
4.6 SUMMARY	117	(1)
Key Terms and Concepts	117	(1)
QUESTIONS	117	(1)
PROBLEMS	118	(5)
PART II THE LINEAR REGRESSION MODEL	123	(190)
CHAPTER 5 BASIC IDEAS OF LINEAR REGRESSION: THE TWO-VARIABLE MODEL	123	(29)
5.1 THE MEANING OF REGRESSION	123	(1)
5.2 THE POPULATION REGRESSION FUNCTION (PRF): A HYPOTHETICAL EXAMPLE	124	(3)
5.3 STOCHASTIC SPECIFICATION OF THE POPULATION REGRESSION FUNCTION (PRF)	127	(2)
5.4 THE NATURE OF THE STOCHASTIC ERROR TERM	129	(1)
5.5 THE SAMPLE REGRESSION FUNCTION (SRF)	129	(3)
5.6 THE SPECIAL MEANING OF THE TERM "LINEAR" REGRESSION	132	(2)
Linearity in the Variables	133	(1)
Linearity in the Parameters	134	(1)
5.7 TWO-VARIABLE VERSUS MULTIPLE LINEAR REGRESSION	134	(1)
5.8 ESTIMATION OF PARAMETERS: THE METHOD OF ORDINARY LEAST SQUARES (OLS)	135	(5)
The Method of Ordinary Least Squares (OLS)	135	(1)
A Numerical Example: The Demand for Widgets	136	(3)
Interpretation of the Estimated Demand Function for Widgets	139	(1)
5.9 SOME ILLUSTRATIVE EXAMPLES	140	(3)
A Word about Computations	143	(1)
5.10 SUMMARY	143	(1)
Key Terms and Concepts	144	(1)
QUESTIONS	144	(1)
PROBLEMS	145	(5)
APPENDIX 5A DERIVATION OF LEAST-SQUARES ESTIMATES	150	(2)
CHAPTER 6 THE TWO-VARIABLE MODEL: HYPOTHESIS TESTING	152	(45)
6.1 THE CLASSICAL LINEAR REGRESSION MODEL (CLRM)	153	(3)
6.2 VARIANCES AND STANDARD ERRORS OF ORDINARY LEAST SQUARES (OLS) ESTIMATORS	156	(2)
Variances and Standard Errors of the Widget Example	157	(1)
Summary of Demand Function for Widgets	157	(1)
6.3 WHY ORDINARY LEAST SQUARES (OLS)? THE PROPERTIES OF OLS ESTIMATORS	158	(3)
Monte Carlo Experiment	159	(2)
6.4 THE SAMPLING, OR PROBABILITY, DISTRIBUTIONS OF OLS ESTIMATORS	161	(1)
6.5 HYPOTHESIS TESTING	162	(8)
Testing H(o): B(2) = O versus H(1): B(2) # O: The Confidence Interval Approach	164	(2)
The Test of Significance Approach to Hypothesis Testing	166	(1)
The Demand for Widgets Continued	167	(2)
The X(2) Test of Significance	169	(1)
6.6 HOW GOOD IS THE FITTED REGRESSION LINE: THE COEFFICIENT OF DETERMINATION, r(2)	170	(4)
Formulas to Compute r(2)	173	(1)
r(2) for the Widget Example	173	(1)
The Coefficient of Correlation, r	173	(1)
6.7 REPORTING THE RESULTS OF REGRESSION ANALYSIS	174	(1)
6.8 NORMALITY TESTS	175	(4)
Histograms of Residuals	176	(1)
Normal Probability Plot	176	(2)
Jarque-Bera Test	178	(1)
6.9 A WORD ON COMPUTATION: COMPUTER REGRESSION PACKAGES	179	(1)
6.10 AN ILLUSTRATIVE EXAMPLE: THE U.S. EXPENDITURE ON FOREIGN IMPORTS	179	(5)
Interpretation of Regression Results	183	(1)
Statistical Significance of Results	183	(1)
6.11 A WORD ABOUT FORECASTING	184	(3)
6.12 FURTHER NUMERICAL EXAMPLES	187	(2)
6.13 SUMMARY	189	(1)
Key Terms and Concepts	189	(1)
QUESTIONS	189	(2)
PROBLEMS	191	(6)
CHAPTER 7 MULTIPLE REGRESSION: ESTIMATION AND HYPOTHESIS TESTING	197	(42)
7.1 THE THREE-VARIABLE LINEAR REGRESSION MODEL	198	(3)
The Meaning of Partial Regression Coefficient	200	(1)
7.2 ASSUMPTIONS OF MULTIPLE LINEAR REGRESSION MODEL	201	(2)
7.3 ESTIMATION OF PARAMETERS OF MULTIPLE REGRESSION	203	(3)
Ordinary Least Squares (OLS) Estimators	203	(1)
Variances and Standard Errors of OLS Estimators	204	(1)
Properties of OLS Estimattors of Multiple Regression	205	(1)
7.4 MORTGAGE DEBT OUTSTANDING: UNITED STATES, 1980-1995-AN ILLUSTRATIVE EXAMPLE	206	(2)
Regression Results	207	(1)
Interpretation of Regression Results	207	(1)
7.5 GOODNESS OF FIT OF ESTIMATED MULTIPLE REGRESSION: MULTIPLE COEFFICIENT OF DETERMINATION, R(2)	208	(1)
7.6 HYPOTHESIS TESTING IN A MULTIPLE REGRESSION: GENERAL COMMENTS	209	(1)
7.7 TESTING HYPOTHESES ABOUT INDIVIDUAL PARTIAL REGRESSION COEFFICIENTS	210	(3)
The Test of Significance Approach	211	(1)
The Confidence Interval Approach to Hypothesis Testing	212	(1)
7.8 TESTING THE JOINT HYPOTHESIS THAT B(2) = B(3) = O OR R(2) = O	213	(5)
An Important Relationship between F and R(2)	217	(1)
7.9 TWO-VARIABLE REGRESSION IN CONTEXT OF MULTIPLE REGRESSION: INTRODUCTION TO SPECIFICATION BIAS	218	(1)
7.10 COMPARING TWO R(2) VALUES: THE ADJUSTED R(2)	219	(1)
7.11 WHEN TO ADD AN ADDITIONAL EXPLANATORY VARIABLE TO THE MODEL	220	(1)
7.12 TESTING FOR STRUCTURAL STABILITY OF REGRESSION MODELS: THE CHOW TEST	221	(3)
7.13 ILLUSTRATIVE EXAMPLES	224	(5)
Discussion of Regression Results	225	(4)
7.14 SUMMARY	229	(1)
Key Terms and Concepts	230	(1)
QUESTIONS	230	(1)
PROBLEMS	231	(5)
APPENDIX 7A.1 DERIVATIONS OF OLS ESTIMATORS GIVEN IN EQUATION (7.20) TO (7.22)	236	(1)
APPENDIX 7A.2 DERIVATION OF EQUATION (7.31)	236	(1)
APPENDIX 7A.3 DERIVATION OF EQUATION (7.53)	237	(1)
APPENDIX 7A.4 EVIEWS' COMPUTER OUTPUT OF THE MORTGAGE DEBT OUTSTANDING EXAMPLE	238	(1)
CHAPTER 8 FUNCTIONAL FORMS OF REGRESSION MODELS	239	(36)
8.1 HOW TO MEASURE ELASTICITY: THE LOG-LINEAR MODEL	240	(4)
Hypothesis Testing in Log-Linear Models	244	(1)
8.2 COMPARING LINEAR AND LOG-LINEAR REGRESSION MODELS	244	(3)
8.3 MULTIPLE LOG-LINEAR REGRESSION MODLES	247	(3)
8.4 HOW TO MEASURE THE GROWTH RATE: THE SEMILOG MODEL	250	(5)
Instantaneous versus Compound Rate of Growth	253	(1)
The Linear Trend Model	254	(1)
8.5 THE LIN-LOG MODEL: WHEN THE EXPLANATORY VARIABLE IS LOGARITHMIC	255	(1)
8.6 RECIPROCAL MODELS	256	(5)
8.7 POLYNOMIAL REGRESSION MODELS	261	(1)
8.8 SUMMARY OF FUNCTIONAL FORMS	262	(1)
8.9 SUMMARY	263	(1)
Key Terms and Concepts	264	(1)
QUESTIONS	264	(2)
PROBLEMS	266	(6)
APPENDIX 8A LOGARITHMS	272	(3)
CHAPTER 9 REGRESSION ON DUMMY EXPLANATORY VARIABLES	275	(38)
9.1 THE NATURE OF DUMMY VARIABLES	275	(4)
9.2 REGRESSION WITH ONE QUANTITATIVE VARIABLE AND ONE QUALITATIVE VARIABLE WITH TWO CATEGORIES	279	(5)
9.3 REGRESSION ON A QUANTITATIVE VARIABLE AND A QUALITATIVE VARIABLE WITH MORE THAN TWO CLASSES OR CATEGORIES	284	(3)
9.4 REGRESSION ON ONE QUANTITATIVE VARIABLE AND TWO QUALITATIVE VARIABLES	287	(1)
9.5 A GENERALIZATION	288	(2)
9.6 STRUCTURAL STABILITY OF REGRESSION MODELS: THE DUMMY VARIABLE APPROACH	290	(6)
9.7 THE USE OF DUMMY VARIABLES IN SEASONAL ANALYSIS	296	(4)
9.8 SUMMARY	300	(1)
Key Terms and Concepts	301	(1)
QUESTIONS	301	(2)
PROBLEMS	303	(10)
PART III REGRESSION ANALYSIS IN PRACTICE	313	(160)
CHAPTER 10 MULTICOLLINEARITY: WHAT HAPPENS IF EXPLANATORY VARIABLES ARE CORRELATED	313	(28)
10.1 THE NATURE OF MULTICOLLINEARITY: THE CASE OF PERFECT MULTICOLLINEARITY	314	(2)
10.2 THE CASE OF NEAR, OR IMPERFECT, MULTICOLLINEARITY	316	(2)
10.3 THEORETICAL CONSEQUENCES OF MULTICOLLINEARITY	318	(2)
10.4 PRACTICAL CONSEQUENCES OF MULTICOLLINEARITY	320	(2)
10.5 DETECTION OF MULTICOLLINEARITY	322	(4)
10.6 IS MULTICOLLINEARITY NECESSARILY BAD?	326	(1)
10.7 AN EXTENDED EXAMPLE: THE DEMAND FOR CHICKENS IN THE UNITED STATES, 1960 TO 1982	327	(4)
Collinearity Diagnostics for the Demand Function for Chickens	329	(2)
10.8 WHAT TO DO WITH MULTICOLLINEARITY: REMEDIAL MEASURES	331	(4)
10.9 SUMMARY	335	(1)
Key Terms and Concepts	336	(1)
QUESTIONS	336	(2)
PROBLEMS	338	(3)
CHAPTER 11 HETEROSCEDASTICITY: WHAT HAPPENS IF THE ERROR VARIANCE IS NONCONSTANT	341	(36)
11.1 THE NATURE OF HETEROSCEDASTICITY	341	(7)
11.2 CONSEQUENCES OF HETEROSCEDASTICITY	348	(2)
11.3 DETECTION OF HETEROSCEDASTICITY: HOW DO WE KNOW WHEN THERE IS A HETEROSCEDASTICITY PROBLEM?	350	(9)
Nature of the Problem	351	(1)
Graphical Examination of Residuals	351	(2)
Park Test	353	(2)
Glejser Test	355	(1)
White's General Heteroscedasticity Test	356	(2)
Other Tests of Heteroscedasticity	358	(1)
11.4 WHAT TO DO IF HETEROSCEDASTICITY IS OBSERVED: REMEDIAL MEASURES	359	(6)
When Sigma(2)(i) Is Known: The Method of Weighted Least Squares (WLS)	359	(1)
When True Sigma(2)(I) Is Unknown	360	(4)
Respecification of the Model	364	(1)
11.5 WHITE'S HETEROSCEDASTICITY-CORRECTED STANDARD ERRORS AND t STATISTICS	365	(1)
11.6 SOME CONCRETE EXAMPLES OF HETEROSCEDASTICITY	366	(2)
11.7 SUMMARY	368	(1)
Key Terms and Concepts	369	(1)
QUESTIONS	369	(1)
PROBLEMS	370	(7)
CHAPTER 12 AUTOCORRELATION: WHAT HAPPENS IF ERROR TERMS ARE CORRELATED	377	(28)
12.1 THE NATURE OF AUTOCORRELATION	378	(3)
Inertia	379	(1)
Model Specification Error(s)	380	(1)
The Cobweb Phenomenon	380	(1)
Data Manipulation	380	(1)
12.2 CONSEQUENCES OF AUTOCORRELATION	381	(1)
12.3 DETECTING AUTOCORRELATION	382	(9)
The Graphical Method	383	(2)
The Runs Test	385	(1)
The Durbin-Watson d Test	386	(5)
12.4 REMEDIAL MEASURES	391	(2)
12.5 HOW TO ESTIMATE p	393	(5)
p = 1: The First Difference Method	393	(1)
p Estimated from Durbin-Watson d Statistic	394	(1)
p Estimated from OLS Residuals, e(t)	395	(1)
Other Methods of Estimating p	395	(3)
12.6 SUMMARY	398	(1)
Key Terms and Concepts	398	(1)
QUESTIONS	399	(1)
PROBLEMS	400	(5)
CHAPTER 13 MODEL SELECTION: CRITERIA AND TESTS	405	(26)
13.1 THE ATTRIBUTES OF A GOOD MODEL	406	(1)
13.2 TYPES OF SPECIFICATION ERRORS	407	(9)
Omitting a Relevant Variable: "Underfitting" a Model	407	(4)
Inclusion of Irrelevant Variable: "Overfitting" a Model	411	(3)
Incorrect Functional Form	414	(2)
13.3 DETECTING SPECIFICATION ERRORS: TESTS OF SPECIFICATION ERRORS	416	(7)
Detecting the Presence of Unnecessary Variables	416	(2)
Tests for Omitted Variables and Incorrect Functional Forms	418	(5)
13.4 MODEL SELECTION CRITERIA FOR FORECASTING PURPOSES	423	(1)
13.5 SUMMARY	424	(2)
Key Terms and Concepts	425	(1)
QUESTIONS	426	(1)
PROBLEMS	426	(5)
CHAPTER 14 SELECTED TOPICS IN SINGLE EQUATION REGRESSION MODELS	431	(42)
14.1 RESTRICTED LEAST SQUARES (RLS)	431	(5)
14.2 DYNAMIC ECONOMIC MODELS: AUTOREGRESSIVE AND DISTRIBUTED LAG MODELS	436	(5)
Estimation of Distributed Lag Models	439	(2)
14.3 THE KOYCK, ADAPTIVE EXPECTATIONS, AND STOCK ADJUSTMENT MODELS APPROACHES TO ESTIMATING DISTRIBUTED LAG MODELS	441	(4)
14.4 WHAT HAPPENS WHEN THE DEPENDENT VARIABLE IS DUMMY?	445	(4)
14.5 THE LOGIT MODEL	449	(6)
Estimation of the Logit Model: Individual Data	449	(2)
Logit Estimation of Grouped Data	451	(4)
14.6 THE PHENOMENON OF SPURIOUS REGRESSION	455	(9)
Test of Nonstationarity: The Unit Root Test	459	(1)
Cointegrated Time Series	460	(1)
The Random Walk Model	461	(3)
14.7 SUMMARY	464	(2)
Key Terms and Concepts	465	(1)
QUESTIONS	466	(1)
PROBLEMS	467	(6)
PART IV INTRODUCTION TO SIMULTANEOUS EQUATION MODELS	473	(26)
CHAPTER 15 SIMULTANEOUS EQUATION MODELS	473	(26)
15.1 THE NATURE OF SIMULTANEOUS EQUATION MODELS	474	(2)
15.2 THE SIMULTANEOUS EQUATION BIAS: INCONSISTENCY OF OLS ESTIMATORS	476	(2)
15.3 THE METHOD OF INDIRECT LEAST SQUARES	478	(1)
15.4 INDIRECT LEAST SQUARES: AN ILLUSTRATIVE EXAMPLE	479	(2)
15.5 THE IDENTIFICATION PROBLEM: A ROSE BY ANY OTHER NAME MAY NOT BE A ROSE	481	(7)
Underidentification	483	(1)
Just or Exact Identification	484	(2)
Overidentification	486	(2)
15.6 RULES FOR IDENTIFICATION: THE ORDER CONDITION OF IDENTIFICATION	488	(1)
15.7 ESTIMATION OF AN OVERIDENTIFIED EQUATION: THE METHOD OF TWO-STAGE LEAST SQUARES	488	(2)
15.8 2SLS: A NUMERICAL EXAMPLE	490	(2)
15.9 SUMMARY	492	(2)
Key Terms and Concepts	494	(1)
QUESTIONS	494	(1)
PROBLEMS	494	(2)
APPENDIX 15A INCONSISTENCY OF OLS ESTIMATORS	496	(3)
APPENDIX A: STATISTICAL TABLES	499	(18)
ANSWERS TO SELECTED PROBLEMS	517	(6)
SELECTED BIBLIOGRAPHY	523	(4)
INDICES
Name Index	527	(2)
Subject Index	529