Econometrics

This textbook offers a simple survey over the most basic concepts that are studied within introductory courses in econometrics. The theory is clarified with numerous examples.

Subjects as basic probability and statistics, statistical inference with the simple and multiple regression model, dummy variables and auto correlation are explained.

1. Basics of probability and statistics
1.1 Random variables and probability distributions
1.1.1 Properties of probabilities
1.1.2 The probability function – the discrete case
1.1.3 The cumulative probability function – the discrete case
1.1.4 The probability function – the continuous case
1.1.5 The cumulative probability function – the continuous case
1.2 The multivariate probability distribution function
1.3 Characteristics of probability distributions
1.3.1 Measures of central tendency
1.3.2 Measures of dispersion
1.3.3 Measures of linear relationship
1.3.4 Skewness and kurtosis

2. Basic probability distributions in econometrics
2.1 The normal distribution
2.2 The t-distribution
2.3 The Chi-square distribution
2.4 The F-distribution

3. The simple regression model
3.1 The population regression model
3.1.1 The economic model
3.1.2 The econometric model
3.1.3 The assumptions of the simple regression model
3.2 Estimation of population parameters
3.2.1 The method of ordinary least squares
3.2.2 Properties of the least squares estimator

4. Statistical inference
4.1 Hypothesis testing
4.2 Confidence interval
4.2.1 P-value in hypothesis testing
4.3 Type I and type II errors
4.4 The best linear predictor

5. Model measures
5.1 The coefficient of determination (R2)
5.2 The adjusted coefficient of determination (Adjusted R2)
5.3 The analysis of variance table (ANOVA)

6. The multiple regression model
6.1 Partial marginal effects
6.2 Estimation of partial regression coefficients
6.3 The joint hypothesis test
6.3.1 Testing a subset of coefficients
6.3.2 Testing the regression equation

7. Specification
7.1 Choosing the functional form
7.1.1 The linear specification
7.1.2 The log-linear specification
7.1.3 The linear-log specification
7.1.4 The log-log specification
7.2 Omission of a relevant variable
7.3 Inclusion of an irrelevant variable
7.4 Measurement errors

8. Dummy variables
8.1 Intercept dummy variables
8.2 Slope dummy variables
8.3 Qualitative variables with several categories
8.4 Piecewise linear regression
8.5 Test for structural differences

9. Heteroskedasticity and diagnostics
9.1 Consequences of using OLS
9.2 Detecting heteroskedasticity
9.2.1 Graphical methods
9.2.2 Statistical tests
9.3 Remedial measures
9.3.1 Heteroskedasticity-robust standard errors

10. Autocorrelation and diagnostics
10.1 Definition and the nature of autocorrelation
10.2 Consequences
10.3 Detection of autocorrelation
10.3.1 The Durbin Watson test
10.3.2 The Durbins h test statistic
10.3.3 The LM-test
10.4 Remedial measures
10.4.1 GLS with AR(1)
10.4.2 GLS with AR(2)

11. Multicollinearity and diagnostics
11.1 Consequences
11.2 Measuring the degree of multicollinearity
11.3 Remedial measures

12. Simultaneous equation models
12.1 Introduction
12.2 The structural and reduced form equation
12.3 Identification
12.3.1 The order condition of identification
12.3.2 The rank condition of identification
12.4 Estimation methods
12.4.1 Indirect Least Squares (ILS)
12.4.2 Two Stage Least Squares (2SLS)

A. Statistical tables
A1 Area below the standard normal distribution
A2 Right tail critical values for the t-distribution
A3 Right tail critical value of the Chi-Square distribution
A4 Right tail critical for the F-distribution: 5 percent level