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
, Econometrie voor bedrijfseconomen
Chapter 1: introduction
Economics suggests important relations, often with policy implications, but virtually never suggests
quantitative magnitudes of causal effects → het causal effect isoleren
- What is the quantitative effect of reducing class size on student achievement?
o Doen leerlingen het beter door een kleine klas of omdat ze uit landelijk gebied komen,
want landelijke gebieden hebben kleinere klassen
- How does another year of education (X) change earnings (Y)
o Hoeveel stijgt het loon met elk jaar extra studie? Andere oorzaak kan ook zijn dat je
gewoon al slimmer was vanaf de start. Of dat je minder verdiend door minder ervaring.
- What is the price (X) elasticity of cigarettes? (Y= sales of sigarettes)
→ proberen te kwantificeren. Als prijs stijgt met €1, wat gebeurd met de verkoop?
Causaal effect: als de prijs stijgt, daalt de vraag, maar dat kan bv ook door dat consumenten ouder zijn
geworden. Wij willen weten wat het effect van prijs is, alle andere factoren dus constant gehouden
(ceteris paribus: c.p.)
Using data to measure causal effects
Ideally, we would like an experiment → experiment is de beste methode maar heel moeilijk op te
zetten. Het is praktisch niet haalbaar, zeker niet voor macro effecten (bv: effect van inflatie via
experiment gaat niet, niemand wilt express hoge inflatie hebben voor een experiment)
We hebben bijna altijd enkel observationele data (non-experimentel), zeker in economie → In this
course we try to measure causal effects from observational data.
- Bv: nagaan of latijn studeren helpt bij hogere punten op de unief, wat idd zo blijkt te zijn. De
vraag is dan: is het de kennis van latijn die helpt, of is de kennis van bij start (slimheid). → het is
niet omdat er correlatie is dat er een oorzakelijk verband is
! Correlation does not imply causation!
Chapter 2 & 3: review statistics
An empirical problem
Policy question: what is the effect on test scores of reducing class size by one student per class? By 8
students per class? (effect van klasgrootte op testscores)
Hoe operationaliseer (meet) je klasgrootte? Kijk naar het niveau van de data. Wij hebben geen data op
microniveau (per lln), bij ons zijn de observaties per district: 1 obs = 1 district, en we hebben 420
districten dus n=420.
5
, Hoe goed een leerling het doet = testscore, Y = gemiddelde testscore van alle leerlingen in het district
Klasgrootte X = totaal # lln in district / totaal # lkr in district → Student-teacher-ratio STR
Y = testscore (max 700), X = STR
De gemiddelde klas-grootte is
dus 19.6
Mediaan STR = 19.7, de helft is
groter en de helft is kleiner dan
40% percentiel heeft de eigenschap dat 40% van de klasgroottes kleiner zijn dan dat percentiel, en dus
60% groter.
- 10% percentiel = 1ste deciel | 25% percentiel = 1ste kwartiel | 75% percentiel = 3de kwartiel
- Percentiel = kwantiel, kwantielen worden gewoon in cijfers uitgedrukt tussen 0-1, dus het 75%
percentiel is 0,75 kwantiel
→this table doesn’t tell us anything about the relationship between test scores and the STR. Het is een
beschrijvende statistiek = univariaten (It focuses on describing the distribution, mean, median, and
standard deviation of a single dataset, rather than examining relation-ships between variables)
deze grafiek toont de relatie tussen X en Y (het is dus
niet meer univariaat). De beide variabelen hun relatie
wordt berekend dus bivariaat.
We zien een negatief verband, als X stijgt daalt Y Grotere
klassen hebben lagere test scores
Hoe kunnen we dit kwantificeren? De correlatie
berekenen
Initial analysis: compare districts with small (STR < 20)
and large (STR > 20) class sizes:
Standard deviatie hebben we nodig om de standard
error SE te berekenen. (SE(∆̂)= de typische fout die je
maakt)
Estimation of ∆ ? = ∆̂ = 7.4 (657.4 – 650.0)
∆̂: omdat het een schatting is van het verschil, want we werken met steekproeven dus het zijn
schatting dat we doen. En bij schatting is er altijd schattingsfout. Het echte verschil (∆) kennen we niet
en gaan we nooit kennen
6
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
, Econometrie voor bedrijfseconomen
Chapter 1: introduction
Economics suggests important relations, often with policy implications, but virtually never suggests
quantitative magnitudes of causal effects → het causal effect isoleren
- What is the quantitative effect of reducing class size on student achievement?
o Doen leerlingen het beter door een kleine klas of omdat ze uit landelijk gebied komen,
want landelijke gebieden hebben kleinere klassen
- How does another year of education (X) change earnings (Y)
o Hoeveel stijgt het loon met elk jaar extra studie? Andere oorzaak kan ook zijn dat je
gewoon al slimmer was vanaf de start. Of dat je minder verdiend door minder ervaring.
- What is the price (X) elasticity of cigarettes? (Y= sales of sigarettes)
→ proberen te kwantificeren. Als prijs stijgt met €1, wat gebeurd met de verkoop?
Causaal effect: als de prijs stijgt, daalt de vraag, maar dat kan bv ook door dat consumenten ouder zijn
geworden. Wij willen weten wat het effect van prijs is, alle andere factoren dus constant gehouden
(ceteris paribus: c.p.)
Using data to measure causal effects
Ideally, we would like an experiment → experiment is de beste methode maar heel moeilijk op te
zetten. Het is praktisch niet haalbaar, zeker niet voor macro effecten (bv: effect van inflatie via
experiment gaat niet, niemand wilt express hoge inflatie hebben voor een experiment)
We hebben bijna altijd enkel observationele data (non-experimentel), zeker in economie → In this
course we try to measure causal effects from observational data.
- Bv: nagaan of latijn studeren helpt bij hogere punten op de unief, wat idd zo blijkt te zijn. De
vraag is dan: is het de kennis van latijn die helpt, of is de kennis van bij start (slimheid). → het is
niet omdat er correlatie is dat er een oorzakelijk verband is
! Correlation does not imply causation!
Chapter 2 & 3: review statistics
An empirical problem
Policy question: what is the effect on test scores of reducing class size by one student per class? By 8
students per class? (effect van klasgrootte op testscores)
Hoe operationaliseer (meet) je klasgrootte? Kijk naar het niveau van de data. Wij hebben geen data op
microniveau (per lln), bij ons zijn de observaties per district: 1 obs = 1 district, en we hebben 420
districten dus n=420.
5
, Hoe goed een leerling het doet = testscore, Y = gemiddelde testscore van alle leerlingen in het district
Klasgrootte X = totaal # lln in district / totaal # lkr in district → Student-teacher-ratio STR
Y = testscore (max 700), X = STR
De gemiddelde klas-grootte is
dus 19.6
Mediaan STR = 19.7, de helft is
groter en de helft is kleiner dan
40% percentiel heeft de eigenschap dat 40% van de klasgroottes kleiner zijn dan dat percentiel, en dus
60% groter.
- 10% percentiel = 1ste deciel | 25% percentiel = 1ste kwartiel | 75% percentiel = 3de kwartiel
- Percentiel = kwantiel, kwantielen worden gewoon in cijfers uitgedrukt tussen 0-1, dus het 75%
percentiel is 0,75 kwantiel
→this table doesn’t tell us anything about the relationship between test scores and the STR. Het is een
beschrijvende statistiek = univariaten (It focuses on describing the distribution, mean, median, and
standard deviation of a single dataset, rather than examining relation-ships between variables)
deze grafiek toont de relatie tussen X en Y (het is dus
niet meer univariaat). De beide variabelen hun relatie
wordt berekend dus bivariaat.
We zien een negatief verband, als X stijgt daalt Y Grotere
klassen hebben lagere test scores
Hoe kunnen we dit kwantificeren? De correlatie
berekenen
Initial analysis: compare districts with small (STR < 20)
and large (STR > 20) class sizes:
Standard deviatie hebben we nodig om de standard
error SE te berekenen. (SE(∆̂)= de typische fout die je
maakt)
Estimation of ∆ ? = ∆̂ = 7.4 (657.4 – 650.0)
∆̂: omdat het een schatting is van het verschil, want we werken met steekproeven dus het zijn
schatting dat we doen. En bij schatting is er altijd schattingsfout. Het echte verschil (∆) kennen we niet
en gaan we nooit kennen
6
