Part I Introductory Econometrics
1 Introduction to Econometrics and Statistical Software
1.1 Introduction
1.2 Economic Model and Econometric Model
1.3 Population Regression Function and Sample Regression Function
1.4 Parametric and Nonparametric or Semiparametric Model
1.5 Steps in Formulating an Econometric Model
1.5.1 Specification
1.5.2 Estimation
1.5.3 Testing of Hypothesis
1.5.4 Forecasting
1.6 Data
1.6.1 Cross Section Data
1.6.2 Time Series Data
1.6.3 Pooled Cross Section
1.6.4 Panel Data
1.7 Use of Econometric Software:
Stata 15.1
1.7.1 Data Management
1.7.2 Generating Variables
1.7.3 Describing Data
1.7.4 Graphs
1.7.5 Logical Operators in Stata
1.7.6 Functions Used in Stata
1.8 Matrix Algebra
1.8.1 Matrix and Vector: Basic Operations
1.8.2 Partitioned Matrices
1.8.3 Rank of a Matrix
1.8.4 Inverse Matrix
1.8.5 Positive Definite Matrix
1.8.6 Trace of a Matrix
1.8.7 Orthogonal Vectors and Matrices
1.8.8 Eigenvalues and Eigenvectors
References
2 Linear Regression Model: Properties and Estimation
2.1 Introduction
2.2 The Simple Linear Regression Model
2.3 Multiple Linear Regression Model
2.4 Assumptions of Linear Regression Model
2.4.1 Non-stochastic Regressors
2.4.2 Linearity
2.4.3 Zero Unconditional Mean
2.4.4 Exogeneity
2.4.5 Homoscedasticity
2.4.6 Non-autocorrelation
2.4.7 Full Rank
2.4.8 Normal Distribution
2.5 Methods of Estimation
2.5.1 The Method of Moments (MM)
2.5.2 The Method of Ordinary Least Squares (OLS)
2.5.3 Maximum Likelihood Method
2.6 Properties of the OLS Estimation
2.6.1 Algebraic Properties
2.6.2 Statistical Properties
References
3 Linear Regression Model: Goodness of Fit and Testing of Hypothesis
3.1 Introduction
3.2 Goodness of Fit
3.2.1 The R2 as a Measure of Goodness of Fit
3.2.2 The Adjusted R2 as a Measure of Goodness of Fit
3.3 Testing of Hypothesis
3.3.1 Sampling Distributions of the OLS Estimators
3.3.2 Testing of Hypothesis for a Single Parameter
3.3.3 Use of P-Value
3.3.4 Interval Estimates
3.3.5 Testing of Hypotheses for More Than One Parameter: t Test
3.3.6 Testing Significance of the Regression: F Test
3.3.7 Testing for Linearity
3.3.8 Tests for Stability
3.3.9 Analysis of Variance
3.3.10 The Likelihood-Ratio, Wald and Lagrange Multiplier Test
3.4 Linear Regression Model by Using Stata 15.1
3.4.1 OLS Estimation in Stata
3.4.2 Maximum Likelihood Estimation (MLE) in Stata
References
4 Linear Regression Model: Relaxing the Classical Assumptions
4.1 Introduction
4.2 Heteroscedasticity
4.2.1 Problems with Heteroscedastic Data
4.2.2 Heteroscedasticity Robust Variance
4.2.3 Testing for Heteroscedasticity
4.2.4 Problem of Estimation
4.2.5 Illustration of Heteroscedastic Linear Regression by Using Stata
4.3 Autocorrelation
4.3.1 Linear Regression Model with Autocorrelated Error
4.3.2 Testing for Autocorrelation: Durbin—Watson Test
4.3.3 Consequences of Autocorrelation
4.3.4 Correcting for Autocorrelation
4.3.5 Illustration by Using Stata
References
5 Analysis of Collinear Data: Multicollinearity
5.1 Introduction
5.2 Multiple Correlation and Partial Correlation
5.3 Problems in the Presence of Multicollinearity
5.4 Detecting Multicollinearity
5.4.1 Determinant of (X'X)
5.4.2 Determinant of Correlation Matrix
5.4.3 Inspection of Correlation Matrix
5.4.4 Measure Based on Partial Regression
5.4.5 Theil's Measure
5.4.6 Variance Inflation Factor (VIF)
5.4.7 Eigenvalues and Condition Numbers
5.5 Dealing with Multicollinearity
5.6 Illustration by Using Stata
References
Part II Advanced Analysis of Cross Section Data
6 Linear Regression Model: Qualitative Variables as Predictors
6.1 Introduction
6.2 Regression Model with Intercept Dummy
6.2.1 Dichotomous Factor
6.2.2 Polytomous Factors
6.3 Regression Model with Interaction Dummy
6.4 Illustration by Using Stata
7 Limited Dependent Variable Model
7.1 Introduction
7.2 Linear Probability Model
7.3 Binary Response Models: Logit and Probit
7.3.1 The Logit Model
7.3.2 The Probit Model
7.3.3 Difference Between Logit and Probit Models
7.4 Maximum Likelihood Estimation of Logit and Probit Models
7.4.1 Interpretation of the Estimated Coefficients
7.4.2 Goodness of Fit
7.4.3 Testing of Hypotheses
7.4.4 Illustration of Binary Response Model by Using Stata
7.5 Regression Model with Truncated Distributions
7.5.1 Illustration of Truncated Regression by Using Stata
7.6 Problem of Censoring: Tobit Model
7.6.1 Illustration of Tobit Model by Using Stata
7.7 Models with Sample Selection Bias
7.7.1 Illustration of Sample Selection Model by Using Stata
7.8 Multinomial Logit Regression
7.8.1 Illustration by Using Stata
References
8 Multivariate Analysisl
8.1 Introduction
8.2 Displaying Multivariate Data
8.2.1 Multivariate Observations
8.2.2 Sample Mean Vector
8.2.3 Population Mean Vector
8.2.4 Covariance Matrix
8.2.5 Correlation Matrix
8.2.6 Linear Combination of Variables
8.3 Multivariate Normal Distribution
8.4 Principal Component Anaylsis
8.4.1 Calculation of Principal Components
8.4.2 Properties of Principal Components
8.4.3 Illustration by Using Stata
8.5 Factor Analysis
8.5.1 Orthogonal Factor Model
8.5.2 Estimation of Loadings and Communalities
8.5.3 Factor Loadings Are not Unique
8.5.4 Factor Rotation
8.5.5 Illustration by Using Stata
8.6 Multivariate Regression
8.6.1 Structure of the Regression Model
8.6.2 Properties of Least Squares Estimators of B
8.6.3 Model Corrected for Means
8.6.4 Canonical Correlations
References
Part III Analysis of Time Series Data
9 Time Series: Data Generating Process
9.1 Introduction
9.2 Data Generating Process (DGP)
9.2.1 Stationary Process
9.2.2 Nonstationary Process
9.3 Methods of Time Series Analysis
9.4 Seasonality and Seasonal Adjustment
9.5 Creating a Time Variable by Using Stata
References
10 Stationary Time Series
10.1 Introduction
10.2 Univariate Time Series Model
10.3 Autoregressive Process (AR)
10.3.1 The First-Order Autoregressive Process
10.3.2 The Second-Order Autoregressive Process
10.3.3 The Autoregressive Process of Order p
10.3.4 General Linear Processes
10.4 The Moving Average (MA) Process
10.4.1 The First-Order Moving Average Process
10.4.2 The Second-Order Moving Average Process
10.4.3 The Moving Average Process of Order q
10.4.4 Invertibility in Moving Average Process
10.5 Autoregressive Moving Average (ARMA) Process
10.6 Autocorrelation Function
10.6.1 Autocorrelation Function for AR(1)
10.6.2 Autocorrelation Function for AR(2)
10.6.3 Autocorrelation Function for AR(p)
10.6.4 Autocorrelation Function for MA(1)
10.6.5 Autocorrelation Function for MA(2)
10.6.6 Autocorrelation Function for MA(p)
10.6.7 Autocorrelation Function for ARMA Process
10.7 Partial Autocorrelation Function (PACF)
10.7.1 Partial Autocorrelation for AR Series
10.7.2 Partial Autocorrelation for MA Series
10.8 Sample Autocorrelation Function
10.8.1 Illustration by Using Stata
References
11 Nonstationarity, Unit Root and Structural Break
11.1 Introduction
11.2 Analysis of Trend
11.2.1 Deterministic Function of Time
11.2.2 Stochastic Function of Time
11.2.3 Stochastic and Deterministic Function of Time
11.3 Concept of Unit Root
11.4 Unit Root Test
11.4.1 Dickey—Fuller Unit Root Test
11.4.2 Augmented Dickey—Fuller (ADF) Unit Root Test
11.4.3 Phillips—Perron Unit Root Test
11.4.4 Dickey—Fuller GLS Test
11.4.5 Stationarity Tests
11.4.6 Multiple Unit Roots
11.4.7 Some Problems with Unit Root Tests
11.4.8 Macroeconomic Implications of Unit Root
11.5 Testing for Structural Break
11.5.1 Tests with Known Break Points
11.5.2 Tests with Unknown Break Points
11.6 Unit Root Test with Break
11.6.1 When Break Point is Exogenous
11.6.2 When Break Point is Endogenous
11.7 Seasonal Adjustment
11.7.1 Unit Roots at Various Frequencies: Seasonal Unit Root
11.7.2 Generating Time Variables and Seasonal Dummies in Stata
11.8 Decomposition of a Time Series into Trend and Cycle
References
12 Cointegration, Error Correction and Vector Autoregression
12.1 Introduction
12.2 Regression with Trending Variables
12.3 Concept of Cointegration
12.4 Granger's Representation Theorem
12.5 Testing for Cointegration: Engle—Granger's Two-Step Method
12.5.1 Illustrations by Using Stata
12.6 Vector Autoregression (VAR)
12.6.1 Stationarity Restriction of a Var Process
12.6.2 Autocovariance Matrix of a VAR Process
12.6.3 Estimation of a VAR Process
12.6.4 Selection of Lag Length of a VAR Model
12.6.5 Illustration by Using Stata
12.7 Vector Moving Average Processes
12.8 Impulse Response Function
12.8.1 Illustration by Using Stata
12.9 Variance Decomposition
12.10 Granger Causality
12.10.1 Illustration by Using Stata
12.11 Vector Error Correction Model
12.11.1 Illustration by Using Stata
12.12 Estimation and Testing of Hypotheses of Cointegrated Systems
12.12.1 Illustration by Using Stata
References
13 Modelling Volatility Clustering
13.1 Introduction
13.2 Modelling Non-constant Conditional Variance
13.3 The ARCH Model
13.4 The GARCH Model
13.5 Asymmetric ARCH Models
13.6 ARCH-in-Mean Model
13.7 Testing and Estimation of a GARCH Model
13.7.1 Testing for ARCH Effect
13.7.2 Maximum Likelihood Estimation for GARCH (1, 1)
13.8 The ARCH Regression Model in Stata
13.8.1 Illustration with Market Capitalisation Data
References
14 Time Series Forecasting
14.1 Introduction
14.2 Simple Exponential Smoothing
14.3 Forecasting—Univariate Model
14.4 Forecasting with General Linear Processes
14.5 Multivariate Forecasting
14.6 Forecasting of a VAR Model
14.7 Forecasting GARCH Processes
14.8 Time Series Forecasting by Using Stata
References
Part IV Analysis of Panel Data
15 Panel Data Analysis: Static Models
15.1 Introduction
15.2 Structure and Types of Panel Data
15.2.1 Data Description by Using Stata 15.1
15.3 Benefits of Panel Data
15.4 Sources of Variation in Panel Data
15.5 Unrestricted Model with Panel Data
15.6 Fully Restricted Model: Pooled Regression
15.6.1 Illustration by Using Stata
15.7 Error Component Model
15.8 First-Differenced (FD) Estimator
15.8.1 Illustration by Using Stata
15.9 One-Way Error Component Fixed Effects Model
15.9.1 The "Within" Estimation
15.9.2 Least Squares Dummy Variable (LSDV)
15.10 One-Way Error Component Random Effects Model
15.10.1 The GLS Estimation
15.10.2 Maximum Likelihood Estimation
15.10.3 Illustration by Using Stata
References
16 Panel Data Static Model: Testing of Hypotheses
16.1 Introduction
16.2 Measures of Goodness of Fit
16.3 Testing for Pooled Regression
16.4 Testing for Fixed Effects
16.4.1 Illustration by Using Stata
16.5 Testing for Random Effects
16.5.1 Illustration by Using Stata
16.6 Fixed or Random Effect: Hausman Test
16.6.1 Illustration by Using Stata
References
17 Panel Unit Root Test
17.1 Introduction
17.2 First-Generation Panel Unit Root Tests
17.2.1 Wu (1996) Unit Root Test
17.2.2 Levin, Lin and Chu Unit Root Test
17.2.3 Im, Pesaran and Shin (IPS) Unit Root Test
17.2.4 Fisher-Type Unit Root Tests
17.3 Stationarity Tests
17.3.1 Illustration by Using Stata
17.4 Second-Generation Panel Unit Root Tests
17.4.1 The Covariance Restrictions Approach
17.4.2 The Factor Structure Approach
References
18 Dynamic Panel Model
18.1 Introduction
18.2 Linear Dynamic Model
18.3 Fixed and Random Effects Estimation
18.3.1 Illustration by Using Stata
18.4 Instrumental Variable Estimation
18.4.1 Illustration by Using Stata
18.5 Arellano—Bond GMM Estimator
18.5.1 Illustration by Using Stata
18.6 System GMM Estimator
18.6.1 Illustration by Using Stata
Appendix: Generalised Method of Moments
References
