Essentials of Econometrics

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Contents
1 The Nature and Scope of Econometrics
	1.1 WHAT IS ECONOMETRICS?
	1.2 WHY STUDY ECONOMETRICS?
	1.3 THE METHODOLOGY OF ECONOMETRICS
		Creating a Statement of Theory or Hypothesis
			Collecting Data
				Specifying the Mathematical Model of Labor Force Participation
					Specifying the Statistical, or Econometric, Model of Labor Force Participation
						Estimating the Parameters of the Chosen Econometric Model
						Checking for Model Adequacy: Model Specification Testing
						Testing the Hypothesis Derived from the Model
						Using the Model for Prediction or Forecasting
	1.4 THE ROAD AHEAD
		KEY TERMS AND CONCEPTS
			QUESTIONS
			PROBLEMS
			APPENDIX 1A: ECONOMIC DATA ON THE WORLD WIDE WEB
PART I THE LINEAR REGRESSION MODEL
	2 Basic Ideas of Linear Regression: The Two-Variable Model
		2.1 THE MEANING OF REGRESSION
		2.2 THE POPULATION REGRESSION FUNCTION (PRF): A HYPOTHETICAL EXAMPLE
		2.3 STATISTICAL OR STOCHASTIC SPECIFICATION OF THE POPULATION REGRESSION FUNCTION
		2.4 THE NATURE OF THE STOCHASTIC ERROR TERM
		2.5 THE SAMPLE REGRESSION FUNCTION (SRF)
		2.6 THE SPECIAL MEANING OF THE TERM “LINEAR” REGRESSION
			Linearity in the Variables
				Linearity in the Parameters
		2.7 TWO-VARIABLE VERSUS MULTIPLE LINEAR REGRESSION
		2.8 ESTIMATION OF PARAMETERS: THE METHOD OF ORDINARY LEAST SQUARES
			The Method of Ordinary Least Squares
		2.9 PUTTING IT ALL TOGETHER
			Interpretation of the Estimated Math S.A.T. Score Function
		2.10 SOME ILLUSTRATIVE EXAMPLES
		2.11 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
				OPTIONAL QUESTIONS
				APPENDIX 2A: DERIVATION OF LEAST-SQUARES ESTIMATES
	3 The Two-Variable Model: Hypothesis Testing
		3.1 THE CLASSICAL LINEAR REGRESSION MODEL
		3.2 VARIANCES AND STANDARD ERRORS OF ORDINARY LEAST SQUARES ESTIMATORS
		Variances and Standard Errors of the Math S.A.T. Score Example
			Summary of the Math S.A.T. Score Function
		3.3 WHY OLS? THE PROPERTIES OF OLS ESTIMATORS
			Monte Carlo Experiment
		3.4 THE SAMPLING, OR PROBABILITY, DISTRIBUTIONS OF OLS ESTIMATORS
		3.5 HYPOTHESIS TESTING
			Testing H0:B2 = 0 versus H1:B2 Z 0 : The Confidence Interval Approach
				The Test of Significance Approach to Hypothesis Testing
				Math S.A.T. Example Continued
		3.6 HOW GOOD IS THE FITTED REGRESSION LINE: THE COEFFICIENT OF DETERMINATION, r 2
			Formulas to Compute r 2
				r 2 for the Math S.A.T. Example
				The Coefficient of Correlation, r
		3.7 REPORTING THE RESULTS OF REGRESSION ANALYSIS
		3.8 COMPUTER OUTPUT OF THE MATH S.A.T. SCORE EXAMPLE
		3.9 NORMALITY TESTS
			Histograms of Residuals
				Normal Probability Plot
				Jarque-Bera Test
		3.10 A CONCLUDING EXAMPLE: RELATIONSHIP BETWEEN WAGES AND PRODUCTIVITY IN THE U.S. BUSINESS SECTOR, 1959–2006
		3.11 A WORD ABOUT FORECASTING
		3.12 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
	4 Multiple Regression: Estimation and Hypothesis Testing
		4.1 THE THREE-VARIABLE LINEAR REGRESSION MODEL
		The Meaning of Partial Regression Coefficient
		4.2 ASSUMPTIONS OF THE MULTIPLE LINEAR REGRESSION MODEL
		4.3 ESTIMATION OF THE PARAMETERS OF MULTIPLE REGRESSION
			Ordinary Least Squares Estimators
				Variance and Standard Errors of OLS Estimators
				Properties of OLS Estimators of Multiple Regression
		4.4 GOODNESS OF FIT OF ESTIMATED MULTIPLE REGRESSION: MULTIPLE COEFFICIENT OF DETERMINATION, R2
		4.5 ANTIQUE CLOCK AUCTION PRICES REVISITED
			Interpretation of the Regression Results
		4.6 HYPOTHESIS TESTING IN A MULTIPLE REGRESSION: GENERAL COMMENTS
		4.7 TESTING HYPOTHESES ABOUT INDIVIDUAL PARTIAL REGRESSION COEFFICIENTS
			The Test of Significance Approach
				The Confidence Interval Approach to Hypothesis Testing
		4.8 TESTING THE JOINT HYPOTHESIS THAT B2 = B3 = 0 OR R2 = 0
			An Important Relationship between F and R2
		4.9 TWO-VARIABLE REGRESSION IN THE CONTEXT OF MULTIPLE REGRESSION: INTRODUCTION TO SPECIFICATION BIAS
		4.10 COMPARING TWO R2 VALUES: THE ADJUSTED R2
		4.11 WHEN TO ADD AN ADDITIONAL EXPLANATORY VARIABLE TO A MODEL
		4.12 RESTRICTED LEAST SQUARES
		4.13 ILLUSTRATIVE EXAMPLES
			Discussion of Regression Results
		4.14 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
				APPENDIX 4A.1: DERIVATIONS OF OLS ESTIMATORS GIVEN IN EQUATIONS (4.20) TO (4.22)
				APPENDIX 4A.2: DERIVATION OF EQUATION (4.31)
				APPENDIX 4A.3: DERIVATION OF EQUATION (4.50)
				APPENDIX 4A.4: EVIEWS OUTPUT OF THE CLOCK AUCTION PRICE EXAMPLE
	5 Functional Forms of Regression Models
		5.1 HOW TO MEASURE ELASTICITY: THE LOG-LINEAR MODEL
		Hypothesis Testing in Log-Linear Models
		5.2 COMPARING LINEAR AND LOG-LINEAR REGRESSION MODELS
		5.3 MULTIPLE LOG-LINEAR REGRESSION MODELS
		5.4 HOW TO MEASURE THE GROWTH RATE: THE SEMILOG MODEL
			Instantaneous versus Compound Rate of Growth
				The Linear Trend Model
		5.5 THE LIN-LOG MODEL: WHEN THE EXPLANATORY VARIABLE IS LOGARITHMIC
		5.6 RECIPROCAL MODELS
		5.7 POLYNOMIAL REGRESSION MODELS
		5.8 REGRESSION THROUGH THE ORIGIN
		5.9 A NOTE ON SCALING AND UNITS OF MEASUREMENT
		5.10 REGRESSION ON STANDARDIZED VARIABLES
		5.11 SUMMARY OF FUNCTIONAL FORMS
		5.12 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
				APPENDIX 5A: LOGARITHMS
	6 Dummy Variable Regression Models
		6.1 THE NATURE OF DUMMY VARIABLES
		6.2 ANCOVA MODELS: REGRESSION ON ONE QUANTITATIVE VARIABLE AND ONE QUALITATIVE VARIABLE WITH TWO CATEGORIES: EXAMPLE 6.1 REVISITED
		6.3 REGRESSION ON ONE QUANTITATIVE VARIABLE AND ONE QUALITATIVE VARIABLE WITH MORE THAN TWO CLASSES OR CATEGORIES
		6.4 REGRESSION ON ONE QUANTIATIVE EXPLANATORY VARIABLE AND MORE THAN ONE QUALITATIVE VARIABLE
			Interaction Effects
				A Generalization
		6.5 COMPARING TWO REGESSIONS
		6.6 THE USE OF DUMMY VARIABLES IN SEASONAL ANALYSIS
		6.7 WHAT HAPPENS IF THE DEPENDENT VARIABLE IS ALSO A DUMMY VARIABLE? THE LINEAR PROBABILITY MODEL (LPM)
		6.8 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
PART II REGRESSION ANALYSIS IN PRACTICE
	7 Model Selection: Criteria and Tests
		7.1 THE ATTRIBUTES OF A GOOD MODEL
		7.2 TYPES OF SPECIFICATION ERRORS
		7.3 OMISSON OF RELEVANT VARIABLE BIAS: “UNDERFITTING” A MODEL
		7.4 INCLUSION OF IRRELEVANT VARIABLES: “OVERFITTING” A MODEL
		7.5 INCORRECT FUNCTIONAL FORM
		7.6 ERRORS OF MEASUREMENT
			Errors of Measurement in the Dependent Variable
				Errors of Measurement in the Explanatory Variable(s)
		7.7 DETECTING SPECIFICATION ERRORS: TESTS OF SPECIFICATION ERRORS
			Detecting the Presence of Unnecessary Variables
				Tests for Omitted Variables and Incorrect Functional Forms
				Choosing between Linear and Log-linear Regression Models: The MWD Test
				Regression Error Specification Test: RESET
		7.8 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
	8 Multicollinearity: What Happens If Explanatory Variables are Correlated?
		8.1 THE NATURE OF MULTICOLLINEARITY: THE CASE OF PERFECT MULTICOLLINEARITY
		8.2 THE CASE OF NEAR, OR IMPERFECT, MULTICOLLINEARITY
		8.3 THEORETICAL CONSEQUENCES OF MULTICOLLINEARITY
		8.4 PRACTICAL CONSEQUENCES OF MULTICOLLINEARITY
		8.5 DETECTION OF MULTICOLLINEARITY
		8.6 IS MULTICOLLINEARITY NECESSARILY BAD?
		8.7 AN EXTENDED EXAMPLE: THE DEMAND FOR CHICKENS IN THE UNITED STATES, 1960 TO 1982
			Collinearity Diagnostics for the Demand Function for Chickens (Equation [8.15])
		8.8 WHAT TO DO WITH MULTICOLLINEARITY: REMEDIAL MEASURES
			Dropping a Variable(s) from the Model
				Acquiring Additional Data or a New Sample
				Rethinking the Model
				Prior Information about Some Parameters
				Transformation of Variables
				Other Remedies
		8.9 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
	9 Heteroscedasticity: What Happens If the Error Variance Is Nonconstant?
		9.1 THE NATURE OF HETEROSCEDASTICITY
		9.2 CONSEQUENCES OF HETEROSCEDASTICITY
		9.3 DETECTION OF HETEROSCEDASTICITY: HOW DO WE KNOW WHEN THERE IS A HETEROSCEDASTICITY PROBLEM?
			Nature of the Problem
				Graphical Examination of Residuals
				Park Test
				Glejser Test
				White’s General Heteroscedasticity Test
				Other Tests of Heteroscedasticity
		9.4 WHAT TO DO IF HETEROSCEDASTICITY IS OBSERVED: REMEDIAL MEASURES
		9.5 WHITE’S HETEROSCEDASTICITY-CORRECTED STANDARD ERRORS AND t STATISTICS
		9.6 SOME CONCRETE EXAMPLES OF HETEROSCEDASTICITY
		9.7 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
	10 Autocorrelation: What Happens If Error Terms Are Correlated?
		10.1 THE NATURE OF AUTOCORRELATION
		Inertia
		Model Specification Error(s)
			The Cobweb Phenomenon
				Data Manipulation
		10.2 CONSEQUENCES OF AUTOCORRELATION
		10.3 DETECTING AUTOCORRELATION
			The Graphical Method
				The Durbin-Watson d Test
		10.4 REMEDIAL MEASURES
		10.5 HOW TO ESTIMATE �
			� � 1: The First Difference Method
				� Estimated from Durbin-Watson d Statistic
				� Estimated from OLS Residuals, et
				Other Methods of Estimating �
		10.6 A LARGE SAMPLE METHOD OF CORRECTING OLS STANDARD ERRORS: THE NEWEY-WEST (NW) METHOD
		10.7 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
				APPENDIX 10A: THE RUNS TEST
				Swed-Eisenhart Critical Runs Test
				Decision Rule
				APPENDIX 10B: A GENERAL TEST OF AUTOCORRELATION: THE BREUSCH-GODFREY (BG) TEST
PART III ADVANCED TOPICS IN ECONOMETRICS
	11 Simultaneous Equation Models
		11.1 THE NATURE OF SIMULTANEOUS EQUATION MODELS
		11.2 THE SIMULTANEOUS EQUATION BIAS: INCONSISTENCY OF OLS ESTIMATORS
		11.3 THE METHOD OF INDIRECT LEAST SQUARES (ILS)
		11.4 INDIRECT LEAST SQUARES: AN ILLUSTRATIVE EXAMPLE
		11.5 THE IDENTIFICATION PROBLEM: A ROSE BY ANY OTHER NAME MAY NOT BE A ROSE
			Underidentification
				Just or Exact Identification
				Overidentification
		11.6 RULES FOR IDENTIFICATION: THE ORDER CONDITION OF IDENTIFICATION
		11.7 ESTIMATION OF AN OVERIDENTIFIED EQUATION: THE METHOD OF TWO-STAGE LEAST SQUARES
		11.8 2SLS: A NUMERICAL EXAMPLE
		11.9 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
				APPENDIX 11A: INCONSISTENCY OF OLS ESTIMATORS
	12 Selected Topics in Single Equation Regression Models
		12.1 DYNAMIC ECONOMIC MODELS: AUTOREGRESSIVE AND DISTRIBUTED LAG MODELS
		Reasons for Lag
		Estimation of Distributed Lag Models
		The Koyck, Adaptive Expectations, and Stock Adjustment Models Approach to Estimating Distributed Lag Models
		12.2 THE PHENOMENON OF SPURIOUS REGRESSION: NONSTATIONARY TIME SERIES
		12.3 TESTS OF STATIONARITY
		12.4 COINTEGRATED TIME SERIES
		12.5 THE RANDOM WALK MODEL
		12.6 THE LOGIT MODEL
			Estimation of the Logit Model
		12.7 SUMMARY
			KEY TERMS AND CONCEPTS
				QUESTIONS
				PROBLEMS
INTRODUCTION TO APPENDIXES A, B, C, AND D: BASICS OF PROBABILITY AND STATISTICS
Appendix A: Review of Statistics: Probability and Probability Distributions
	A.1 SOME NOTATION
		The Summation Notation
			Properties of the Summation Operator
		A.2 EXPERIMENT, SAMPLE SPACE, SAMPLE POINT, AND EVENTS
			Experiment
				Sample Space or Population
				Sample Point
				Events
				Venn Diagrams
		A.3 RANDOM VARIABLES
		A.4 PROBABILITY
			Probability of an Event: The Classical or A Priori Definition
				Relative Frequency or Empirical Definition of Probability
				Probability of Random Variables
		A.5 RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS
			Probability Distribution of a Discrete Random Variable
				Probability Distribution of a Continuous Random Variable
				Cumulative Distribution Function (CDF)
		A.6 MULTIVARIATE PROBABILITY DENSITY FUNCTIONS
			Marginal Probability Functions
				Conditional Probability Functions
				Statistical Independence
		A.7 SUMMARY AND CONCLUSIONS
			KEY TERMS AND CONCEPTS
				REFERENCES
				QUESTIONS
				PROBLEMS
		Appendix B: Characteristics of Probability Distributions
			B.1 EXPECTED VALUE: A MEASURE OF CENTRAL TENDENCY
				Properties of Expected Value
					Expected Value of Multivariate Probability Distributions
			B.2 VARIANCE: A MEASURE OF DISPERSION
				Properties of Variance
					Chebyshev’s Inequality
					Coefficient of Variation
			B.3 COVARIANCE
				Properties of Covariance
			B.4 CORRELATION COEFFICIENT
				Properties of Correlation Coefficient
					Variances of Correlated Variables
			B.5 CONDITIONAL EXPECTATION
				Conditional Variance
			B.6 SKEWNESS AND KURTOSIS
			B.7 FROM THE POPULATION TO THE SAMPLE
				Sample Mean
				Sample Variance
				Sample Covariance
				Sample Correlation Coefficient
				Sample Skewness and Kurtosis
			B.8 SUMMARY
				KEY TERMS AND CONCEPTS
					QUESTIONS
					PROBLEMS
					OPTIONAL EXERCISES
Appendix C: Some Important Probability Distributions
	C.1 THE NORMAL DISTRIBUTION
		Properties of the Normal Distribution
			The Standard Normal Distribution
			Random Sampling from a Normal Population
			– The Sampling or Probability Distribution of the Sample Mean X
			The Central Limit Theorem (CLT)
	C.2 THE t DISTRIBUTION
		Properties of the t Distribution
	C.3 THE CHI-SQUARE ( x 2) PROBABILITY DISTRIBUTION
		Properties of the Chi-square Distribution
	C.4 THE F DISTRIBUTION
		Properties of the F Distribution
	C.5 SUMMARY
		KEY TERMS AND CONCEPTS
			QUESTIONS
			PROBLEMS
Appendix D: Statistical Inference: Estimation and Hypothesis Testing
	D.1 THE MEANING OF STATISTICAL INFERENCE
	D.2 ESTIMATION AND HYPOTHESIS TESTING: TWIN BRANCHES OF STATISTICAL INFERENCE
	D.3 ESTIMATION OF PARAMETERS
	D.4 PROPERTIES OF POINT ESTIMATORS
		Linearity
			Unbiasedness
			Minimum Variance
			Efficiency
			Best Linear Unbiased Estimator (BLUE)
			Consistency
	D.5 STATISTICAL INFERENCE: HYPOTHESIS TESTING
	The Confidence Interval Approach to Hypothesis Testing
		Type I and Type II Errors: A Digression
		The Test of Significance Approach to Hypothesis Testing
			A Word on Choosing the Level of Significance, �, and the p Value
			The x 2 and F Tests of Significance
	D.6 SUMMARY
		KEY TERMS AND CONCEPTS
			QUESTIONS
			PROBLEMS
Appendix E: Statistical Tables
Appendix F: Computer Output of EViews, MINITAB, Excel, and STATA
SELECTED BIBLIOGRAPHY
INDEXES
Name Index
Subject Index