Econometrics

Cover
Title Page
Copyright Page
Dedication
Table of Contents
Foreword
Preface
Author\'s Note
Notations Used
Abbreviations
1: Definitions and Scope of Econometrics
	I. Why Do We Study Econometrics?
	II. Types of Econometrics
	III. Data Employed in Econometric Analysis
		Primary Data and Secondary Data
		Cross-Sectional Data and Time Series Data
		Univariate Data, Bivariate Data and Multivariate Data
		Micro Data and Macro Data
	IV. Terminology Used in Econometric Analysis
	V. Methodology of Econometrics
	Appendix
2: Correlation
	I. Pearson’s Correlation Coefficient ‘r’
	II. Scattergram
	III. Types of Correlation
		Positive Correlation, Negative Correlation and Zero Correlation
		Linear Correlation and Non – Linear Correlation
	IV. Methods or Formulae to Compute Correlation Coefficient
	V. Test of Significance of ‘r’
	VI. Methods of Studying the Significance of ‘r’ Value
	VII. Properties of Correlation Coefficient ‘r’
	VIII. Numerical Examples for Computation of Correlation Coefficient
	IX. Coefficient of Determination (r2)
		Relationship Between r and r2
		Limitation of r2
	X. Spearman’s Rank Correlation Coefficient ‘rs’
		Properties of rs
		Procedure to Work Out rs
		Test of Significance of ‘rs’
	XI. Partial Correlation Coefficient
	Appendix
3: Regression
	I. Methods of Estimating Regression Equations or Derivation of Regression Line
		Deriving Regression Equation Through Normal Equations
		Deriving Regression Equation Through Regression Coefficients
	II. Properties of Regression Coefficient and Relationship Between Correlation and Regression
		Differences Between Correlation and Regression
	III. Tests of Significance in Regression
		Classification of Regression Models
4: Basic Concepts in Simple (Two–Variable) Regression Analysis (SLRM)
	I. Concept of PRF
		PRF in Stochastic Form
	II. Concept of SRF
	III. OLS Estimation of SLRM
	IV. OLS Estimator
		Assumptions of OLS Estimator
		Features of OLS Method or Estimator
		Characteristics of the OLS Coefficient Estimates, â and b̂
	V. Interpretation of OLS Sample Estimates â and b̂
	VI. Measures of Variation
		Total Variation
		Explained Variation
		Unexplained Variation
	VII. SE Around the Estimated Regression Line (SEyx)
	VIII. Coefficient of Determination - Test of Goodness of Fit of Regression Line in SLRM
		Derivation of r2
		Interpretation of ‘r2’
		Properties of ‘r2’
	IX. Mean and Variances of the Sample Estimates in SRF â and b̂ in SRF
	X. Test of Significance of SLRM
	XI. Numerical Examples in Simple Linear Regression
	XII. How the Slope of Regression Equation Changes Due to Changes in the Units of Measurement of Variables
	XIII. Regression Through Origin (RTO) or Regression Model Without Intercept i.e., Estimation of a Regression Function, Whose Intercept Is Zero
	XIV. Elasticity vs Slope in an Estimated Regression Equation
	Appendix
5: Assumptions of the Classical Linear Regression Model (CLRM)
	I. Assumptions About Independent Variable (x)
	II. Assumptions Related to Error Term, ‘µ’
	III. Other Assumptions Related to Dependent Variable, Y
6: Establishing the Criteria for Judging the Goodness of the Parameter Estimates
	I. Specification of the Model:
		Variables that are to be Included in the Model
		Size (Magnitude) and Signs of the Estimates
		Formulation of the Econometric Model
	II. Estimation of the Model by Employing an Appropriate Econometric Method
	III. Evaluation of the Estimates
		Economic ‘a Priori’ Criteria or Theoretical Criteria
		Statistical Criteria or First Order Tests
		Econometric Criteria or Second Order Tests
	IV. Forecasting the Findings of Econometric Model
7: Tests of Significance of the Parameter Estimates and Gauss-Markov Theorem
	I. Means and Variances of OLS Estimates
	II. Tests of Significance
	III. Steps in Testing of Hypothesis
		General Procedure for Statistical Testing of Hypothesis
	III. Errors in Drawing Conclusions in Research
		Type I Error, Type II Error
	IV. Size of Test vs Power of a Test
		Benefits of Hypothesis Testing
	V. Gauss-Markov Theorem
		Small or Finite Sample Properties
		Unbiasedness
		Minimum Variance
		Efficiency
		Linearity
		Minimum Mean-Square-Error (MSE)
		Sufficiency
		Large Sample or Asymptotic Properties: Consistency
		Importance of Blue Properties of OLS Estimates
	Appendix
8: Functional Form Specifications of (Linear) Regression Model
	I. Linear Regression Model
	II. Different Functional Forms of Linear Regression Model
		Semi Log Functional Form
		Double Log Functional Form or Log-Log (Double-Log) Model
		Polynomial Functional Form
		Inverse Functional Form
		Regression Through Origin (RTO) Model
		Choice of Functional Form
		Box-Cox Test for Comparing Different Forms of Linear Regression Models
		Other Tests for Functional Form
		Adjusted R2 Test
		Ramsey’s Regression Specification Error Test (RESET) Test
9: Multiple Linear Regression Model (MLRM)
	I. Differences Between SLRM and MLRM
	II. Formulation of MLRM
		The MLRM Building - Input to a Regression Problem
		MLRM with Two Independent Variables
		MLRM with ‘k’ Independent Variables
	III. Assumptions of MLRM
	IV. Deriving Normal Equations for MLRM
		Considering Actual Values of Observations
		Considering Deviations of Observations of Variables Taken from their Respective Means
	V. General Procedure to Derive Normal Equations of MLRM for ‘k’ Variables
	VI. Normal Equations in SLRM and MLRM
	VII. Interpretation of MLRM Equation
		Interpretation of the Intercept
		Interpretation of Partial Regression Coefficients
		Error Term
	VIII. Properties of OLS Estimates in MLRM
	IX. Expressions for the OLS Coefficient Estimates of (Three Variable) MLRM
	X. Goodness of Fit of MLRM (R2)
		Derivation of Formula of R2
		Generalization of Formula of R2
		Properties of R2
	XI. Adjusted Coefficient of Multiple Determination ( R̄2 )
		Differences Between R2 and R̄2
	XII. Tests of Significance of MLRM
		Test of Significance of Individual Sample Estimate or Individual Partial Regression Coefficient
		Test for the Overall Significance of MLRM
		Regression Statistics Table
		ANOVA Table
		Regression Coefficients Table
		Test Hypothesis of Estimated Slope Coefficients (Test of Statistical Significance of Slope Coefficient Estimates)
			Confidence Intervals for Partial Slope Coefficients
			Predicted Value of Y from Sample Estimates
	XIII. The Regression Equation: Standardized Coefficients
	XIV. Incremental or Marginal Contribution of an Independent Variable
	XV. Testing the Equality of Two Regression Coefficients
	XVI. Regression Analysis Under Linear Restrictions and Preliminary Test Estimation
	XVII. Relationship Between SLRM and MLRM
	XVIII.Different Methods of Entering Independent Variables in the MLRM
		Forced Entry Method
		Hierarchical Method
		Step-Wise Method
			Forward Selection
			Backward Elimination or Deletion
	XIX. Extension of MLRM to Non-Linear Relationships
	XX. Regression and Analysis of Variance (ANOVA)
		ANOVA as a Statistical Method to Study Variation
		Regression Analysis
		Comparison of ANOVA and Regression Analysis
	XXI. Multiple Regression - Specification Bias
		Omission of Right Independent Variable from the Model
		Inclusion of Irrelevant Independent Variable into the Model
	XXII. MLRM with Interaction Among Independent Variables
	Appendix
10: Relaxing the Assumptions of CLRM
11: Multicollinearity
	I. Why Is Multicollinearity a Problem?
	II. Types of Multicollinearity:
		Exact or Perfect Multicollinearity
		Near or Less Than Perfect or Imperfect Multicollinearity
	III. Sources of Multicollinearity
	IV. Examples for Multicollinearity
	V. Consequences of Multicollinearity
		Theoretical Consequences
		Practical Consequences
	VI. Detecting Multicollinearity
		Tests for Detecting Multicollinearity Problem in MLRM
		Frisch’s Confluence Analysis or Bunch Map Analysis
		The Farrar - Glauber Test for Multicollinearity
		Solutions for the Incidence of Multicollinearity
12: Hetroscedasticity
	I. Forms of Heteroscedasticity
		Pure Heteroscedasticity
		Impure Heteroscedasticity
	II. Reasons for the Presence of Heteroscedasticity
	III. Interpretation and Graphical Representation of Homoscedasticity and Heteroscedasticity
	IV. Consequences of the Violation of the Assumption of Homoscedasticity
	V. Differences Between OLS and GLS Methods
		Case 1 -Transforming the Variables and Applying OLS
		Case 2 - Application of GLS Method
		Deriving the GLS Estimates for a General Linear Regression Model with Heteroscedasticity
		WLS Estimator
		Problems with Using the GLS Estimator
		Feasible Generalized Least Squares (FGLS) Estimator
	VI. Tests for Detection of Heteroscedasticity Problem
		Informal Methods
			Nature of the Problem
			Graphical Method (Residual Plot Method)
		Formal Methods
			Park Test
			Glejser Test
			Spearman Rank Correlation Test
			Goldfeld and Quandt Test
			Koenker–Bassett (KB) Test
			Breusch-pagan-godfrey (BPG) Test
			White Test
	VII. Solutions for Heteroscedasticity Problem
		Transforming the Heteroscedastic Model
			When σ2iμ is Specified or Known
			Use of Robust SEs - Robust Inference After OLS
			Change the Functional Form of Regression Model
			Drop Outliers
	VII. Testing for Heteroscedasticity in Time Series Data
13: Autocorrelation
	I. FOARS or First Order Markov Process
	II. Second Order Autoregressive Scheme (SOARS)
	III. Calculation of ‘ρ’ in Case of FOARS for Population Data
	IV. Calculation of ‘ρ’ in Case of FOARS for Sample Data
	V. Autocorrelation vis-à-vis Serial Correlation
		Spatial Autocorrelation
		True or Pure Autocorrelation
		False or Impure Autocorrelation
	VI. Sources of Autocorrelation
	VII. Estimation of Error Term (μt) in the Presence of Autocorrelation (FOARS)
	VIII. Mean, Variance and Covariance of Autocorrelated Error Terms
	IX. Consequences of Autocorrelation or Consequences of Using OLS in the Presence of Autocorrelation
	X. Detection of Autocorrelation or Tests for Autocorrelation
		Graphical Method
		Qualitative Approach
		Plot Residuals and Lagged Values in a 4-Quadrant Diagram
		Plot Residuals Across Time
		Plot Standardized Residuals Across Time
		Quantitative Approach or Formal Tests
			The Runs Test
			Durbin-Watson ‘d’ Test
			The Durbin’s ‘h’ Test
			Berenblut-Webb’s ‘g’ Test
			Theil Nagar’s Modified ‘d’ Statistic
			An Alternative Test for Autocorrelation
			An Asymptotic or Large Sample Test
			Breusch-Godfrey (BG) Test of High-Order Autocorrelation
			Ljung-box ‘Q’ Test
	XI. Model Mis-Specification Versus Pure Autocorrelation
	XII. Remedial Measures of Autocorrelation
		Generalized Least Squares (GLS) Procedure
		Rationalization of the Transformation Procedure
		A Priori Information About ‘ρ’
		Estimation of ‘ρ’ from Durbin-Watson’s ‘d’ Statistic
		Iterative Procedures
			The Cochrane-Orcutt Iterative Procedure
			Durbin’s Two-Step Method of ‘ρ’ Estimation
			Hildreth-Lu (HILU) Search Procedure
			Newey-West SEs
	XIII. Autoregressive Conditional Heteroscedasticity (ARCH) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) Models
	Appendix
14: Regression on Dummy Variables
	I. ANOVA Model
		Regression by Employing a Single Dummy Variable
		Regression by Employing Two Dummy Variables
	II. ANOVA Model
		Regression by Employing One Quantitative Independent Variable and One Dummy Variable (with Two Classes)
		Regression by Employing One Quantitative Independent Variable and Two Dummy Variables (with Two Classes Each)
	III. Interaction Effects Using Dummy Variables
		Interaction Between Quantitative Independent Variable and Qualitative Independent (Dummy) Variable
		Interaction Between Two Qualitative Independent (Dummy) Variables
	IV. Caution in the Use of Dummy Variables
	V. Testing for Structural Stability of Regression Models - Chow Test
	VI. Testing for Structural Stability of Regression Models by Employing Dummy Variables – Use of Dummy Variable Technique Alternative to Chow Test
	VII. Use of Dummy Variables in Seasonal Analysis
References