Chapter 1: introduction .................................................................................................................... 5
Chapter 2 & 3: review statistics ......................................................................................................... 5
An empirical problem ............................................................................................................... 5
Skewness and Kurtosis ............................................................................................................. 8
Correlation .............................................................................................................................. 8
Conditional distributions .......................................................................................................... 8
The sampling distribution of the sample average ....................................................................... 9
Least Squares Estimation ....................................................................................................... 11
P-value .................................................................................................................................. 11
The t-distribution.................................................................................................................... 13
Chapter 4: linear regression with one regressor .............................................................................. 14
The linear regression model .................................................................................................... 14
The ordinary least squares (OLS) estimator ............................................................................. 15
R² measure of fit ..................................................................................................................... 17
Stata output ........................................................................................................................... 17
The Least Squares Assumptions ............................................................................................. 18
The sampling distribution of the OLS estimator........................................................................ 18
Chapter 5: hypothesis test and confidence intervals ....................................................................... 19
The standard error of 𝛽1 ......................................................................................................... 20
Hypothesis test for 𝛽1 ............................................................................................................ 20
Confidence interval for 𝛽1 ...................................................................................................... 21
Regression when X is binary (dummy variable) ......................................................................... 21
Heteroskedasticity and homoskedasticity ............................................................................... 22
Comments............................................................................................................................. 23
Chapter 6: linear regression with multiple regressors....................................................................... 24
Omitted variable bias ............................................................................................................. 24
The multiple regression model ................................................................................................ 26
The OLS-estimator ................................................................................................................. 26
Measures of fit ....................................................................................................................... 28
The Least Squares Assumptions for multiple regression .......................................................... 28
(Sampling) distribution of the OLS estimator ........................................................................... 28
Multicollinearity ..................................................................................................................... 29
Categorical regressors ............................................................................................ 29
Imperfect multicollinearity .............................................................................................. 30
Chapter 7: Hypothesis tests and confidence intervals in multiple regression .................................... 30
1
, For one single coefficient........................................................................................................ 30
Test for joint hypothesis .......................................................................................................... 30
The F-statistic................................................................................................................. 31
***The overall F-statistic ................................................................................................. 32
Test for restrictions on multiple coefficient .............................................................................. 32
Model specification ................................................................................................................ 33
Example: analyzing test scores ............................................................................................... 34
Chapter 8: nonlinear regression function ........................................................................................ 36
General strategy ..................................................................................................................... 36
Non-linear functions of one variable ....................................................................................... 36
1.Polynomials in X .......................................................................................................... 36
Estimation of a Quadratic specification ................................................................... 37
Estimation of a Cubic specification ......................................................................... 38
2a.Linear-log model: ....................................................................................................... 38
2b.Log- linaer model ....................................................................................................... 39
2c.Log-Log model: .......................................................................................................... 39
Overzicht........................................................................................................................ 41
Interactions between regressors ............................................................................................. 41
Interactions between two binary variables ....................................................................... 41
Interactions between continuous and binary variables ..................................................... 42
interactions between two continuous variables ............................................................... 44
Examples ............................................................................................................................... 45
Case: the return to education and the gender gap .................................................... 45
Case: the demand for economics journals ............................................................... 47
Nonlinear effects on Test Scores of the STR ..................................................................... 48
Chapter 10: regression with Panel Data ........................................................................................... 50
Panel data.............................................................................................................................. 50
Example of a panel data set: .................................................................................... 51
Panel data with two time periods ............................................................................................ 52
Fixed effects regression .......................................................................................................... 53
Example ......................................................................................................................... 54
Assumptions and standard errors ........................................................................................... 56
Regression with Time Fixed Effects.......................................................................................... 57
Case: drunk driving laws and traffic deaths ............................................................................. 59
Chapter 11: regression with a binary dependent variable ................................................................. 62
2
, The linear probability model (LPM) .......................................................................................... 63
Probit and logit regression ...................................................................................................... 64
Estimation and inference for probit and logit regression ........................................................... 68
The likelihood function.................................................................................................... 68
Measures of fit................................................................................................................ 69
Case: the Boston HMDA data .................................................................................................. 71
Likelihood ratio test ................................................................................................................ 74
Extra MC-vragen rond hoofdstuk 11: ................................................................................ 77
Aanvullingen .................................................................................................................................. 79
Endogeniteit........................................................................................................................... 79
Voorspellen............................................................................................................................ 80
(niet perfecte) multicollineariteit ............................................................................................. 80
Herschalen van een variabele ................................................................................................. 81
Centreren van een variabele ................................................................................................... 81
3
, 4
Chapter 2 & 3: review statistics ......................................................................................................... 5
An empirical problem ............................................................................................................... 5
Skewness and Kurtosis ............................................................................................................. 8
Correlation .............................................................................................................................. 8
Conditional distributions .......................................................................................................... 8
The sampling distribution of the sample average ....................................................................... 9
Least Squares Estimation ....................................................................................................... 11
P-value .................................................................................................................................. 11
The t-distribution.................................................................................................................... 13
Chapter 4: linear regression with one regressor .............................................................................. 14
The linear regression model .................................................................................................... 14
The ordinary least squares (OLS) estimator ............................................................................. 15
R² measure of fit ..................................................................................................................... 17
Stata output ........................................................................................................................... 17
The Least Squares Assumptions ............................................................................................. 18
The sampling distribution of the OLS estimator........................................................................ 18
Chapter 5: hypothesis test and confidence intervals ....................................................................... 19
The standard error of 𝛽1 ......................................................................................................... 20
Hypothesis test for 𝛽1 ............................................................................................................ 20
Confidence interval for 𝛽1 ...................................................................................................... 21
Regression when X is binary (dummy variable) ......................................................................... 21
Heteroskedasticity and homoskedasticity ............................................................................... 22
Comments............................................................................................................................. 23
Chapter 6: linear regression with multiple regressors....................................................................... 24
Omitted variable bias ............................................................................................................. 24
The multiple regression model ................................................................................................ 26
The OLS-estimator ................................................................................................................. 26
Measures of fit ....................................................................................................................... 28
The Least Squares Assumptions for multiple regression .......................................................... 28
(Sampling) distribution of the OLS estimator ........................................................................... 28
Multicollinearity ..................................................................................................................... 29
Categorical regressors ............................................................................................ 29
Imperfect multicollinearity .............................................................................................. 30
Chapter 7: Hypothesis tests and confidence intervals in multiple regression .................................... 30
1
, For one single coefficient........................................................................................................ 30
Test for joint hypothesis .......................................................................................................... 30
The F-statistic................................................................................................................. 31
***The overall F-statistic ................................................................................................. 32
Test for restrictions on multiple coefficient .............................................................................. 32
Model specification ................................................................................................................ 33
Example: analyzing test scores ............................................................................................... 34
Chapter 8: nonlinear regression function ........................................................................................ 36
General strategy ..................................................................................................................... 36
Non-linear functions of one variable ....................................................................................... 36
1.Polynomials in X .......................................................................................................... 36
Estimation of a Quadratic specification ................................................................... 37
Estimation of a Cubic specification ......................................................................... 38
2a.Linear-log model: ....................................................................................................... 38
2b.Log- linaer model ....................................................................................................... 39
2c.Log-Log model: .......................................................................................................... 39
Overzicht........................................................................................................................ 41
Interactions between regressors ............................................................................................. 41
Interactions between two binary variables ....................................................................... 41
Interactions between continuous and binary variables ..................................................... 42
interactions between two continuous variables ............................................................... 44
Examples ............................................................................................................................... 45
Case: the return to education and the gender gap .................................................... 45
Case: the demand for economics journals ............................................................... 47
Nonlinear effects on Test Scores of the STR ..................................................................... 48
Chapter 10: regression with Panel Data ........................................................................................... 50
Panel data.............................................................................................................................. 50
Example of a panel data set: .................................................................................... 51
Panel data with two time periods ............................................................................................ 52
Fixed effects regression .......................................................................................................... 53
Example ......................................................................................................................... 54
Assumptions and standard errors ........................................................................................... 56
Regression with Time Fixed Effects.......................................................................................... 57
Case: drunk driving laws and traffic deaths ............................................................................. 59
Chapter 11: regression with a binary dependent variable ................................................................. 62
2
, The linear probability model (LPM) .......................................................................................... 63
Probit and logit regression ...................................................................................................... 64
Estimation and inference for probit and logit regression ........................................................... 68
The likelihood function.................................................................................................... 68
Measures of fit................................................................................................................ 69
Case: the Boston HMDA data .................................................................................................. 71
Likelihood ratio test ................................................................................................................ 74
Extra MC-vragen rond hoofdstuk 11: ................................................................................ 77
Aanvullingen .................................................................................................................................. 79
Endogeniteit........................................................................................................................... 79
Voorspellen............................................................................................................................ 80
(niet perfecte) multicollineariteit ............................................................................................. 80
Herschalen van een variabele ................................................................................................. 81
Centreren van een variabele ................................................................................................... 81
3
, 4
