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 *R*^{2} as a Measure of Goodness of Fit

3.2.2 The Adjusted *R*^{2} 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