SAMENVATTING ONDERZOEKSMETHODEN
SCHAKELJAAR HANDELSWETENSCHAPPEN
2023 – 2024
Inhoud
WEEK 0: Inleiding tot OPO en econometrie ............................................................................7
HOOFDSTUK 1: introductie tot econometrie .............................................................................7
1. Wat is econometrie?.........................................................................................................7
2. Waarom gebruiken we econometrie? ................................................................................7
3. Mogelijke valkuilen bij het schatten van een model (niet uitputtend) ...................................8
4. Noodzaak van een goed onderliggend model .....................................................................8
5. Omitted variables .............................................................................................................8
6. Extreme observatie ..........................................................................................................9
7. Regressielijn ....................................................................................................................9
8. Overzicht ....................................................................................................................... 10
9. Terminologie en notatie: ................................................................................................. 10
9.1. variabelen en parameters ......................................................................................... 10
9.2. Afhankelijke en verklarende variabelen ..................................................................... 11
10. Meetschaal (meetniveau) van variabelen ....................................................................... 11
WEEK 1: Introductie OPO & basisprincipes OLS ...................................................................... 12
HOOFDSTUK 1: Basisprincipes OLS ....................................................................................... 12
1. Hoe ongekende waardes van parameters bepalen? ......................................................... 12
1.1. Univariate (= enkelvoudige) regressie .................................................................. 12
1.2. OLS: Ordinary Least Squares / GKK: Gewone Kleinste Kwadraten ......................... 13
2. Eigenschappen en assumpties ................................................................................... 14
2.1. Steekproef VS. Populatie .................................................................................... 14
2.2. Steekproef distributie van 𝛽 ................................................................................ 14
2.3. Precisie van OLS schattingen .............................................................................. 15
2.4. Basisaannames van de OLS-methode: de klassieke aannames............................ 15
2.5. OLS-schattingen zijn BLUE (Gauss-Markov) ......................................................... 16
WEEK 2: Meervoudige regressie en Dummy Variabelen ........................................................... 17
HOOFDSTUK 1: Meervoudige (= multivariate) regressie ........................................................... 17
1. Univariate regressie vs multivariate regressie .................................................................. 17
2. OLS schatting................................................................................................................. 18
1
,HOOFDSTUK 2: de fit van het model ....................................................................................... 19
1. Decompositie van variatie .............................................................................................. 19
2. Coëfficiënt van de determinatie: R² ................................................................................. 20
3. KISS principe.................................................................................................................. 20
4. R² adjusted .................................................................................................................... 21
5. Kwaliteit van het model .................................................................................................. 21
6. Voorbeelden in STATA ..................................................................................................... 22
HOOFDSTUK 3: Dummy variabelen ........................................................................................ 23
1. Type variabelen in regressie analyse ................................................................................ 24
1.1. Afhankelijke variabele Y ...................................................................................... 24
1.2. Onafhankelijke variabele X ................................................................................. 24
2. Dummy Variable trap ................................................................................................. 25
3. Dummy variable interpretatie ..................................................................................... 26
4. Dummy variabelen in intercept ................................................................................... 27
4.1. Voorbeeld 1: verschillen in studieresultaten ........................................................ 27
4.2. Voorbeeld 2: Wijnconsumptie in BE, FR en GE ..................................................... 28
4.3. Voorbeeld 3: aankoopprijzen van auto’s .............................................................. 29
5. Dummy variabelen in intercept en/of slope(s) ............................................................. 30
5.1. Interactie effecten (= moderator effecten) ........................................................... 32
5.2. Voorbeelden Stata.............................................................................................. 32
WEEK 3: Toetsen van hypothesen (t-test en f-test) & normaliteit van residuen .......................... 33
HOOFDSTUK 1: Hypothese testing ......................................................................................... 33
1.1. Wat is (statistische) hypothese testing? .................................................................... 33
1.2. Hypothese bewijzen vs verwerpen ............................................................................ 33
1.3. Hoe hypothese formuleren ....................................................................................... 33
1.4. One-sided versus two-sided ..................................................................................... 34
1.5. Hypothesis testing: intuïtie ....................................................................................... 34
HOOFDSTUK 2: Normaliteit van residuen ............................................................................... 36
1. Normaliteitsassumptie voor ui: 𝒖𝒊 ~𝑵(𝟎, 𝝈²) .................................................................. 36
2. Testen voor normaliteit van de resttermen ....................................................................... 36
2.1. Grafisch: histogrammen van de resttermen............................................................... 36
2.2. Grafisch: via Kernel density ...................................................................................... 37
2.3. Statistisch: Shapiro-Wilk test voor normaliteit ........................................................... 37
2.4. Statistisch: test voor Skewness & Kurtosis ................................................................ 37
3. Normaliteitsassumptie niet voldaan................................................................................ 38
HOOFDSTUK 3: De t-test ....................................................................................................... 38
2
, 1. T-test: t-statistiek ........................................................................................................... 38
2. Kritische t-waarde & t-distributie..................................................................................... 39
Drie elementen van de t-test ........................................................................................... 39
3. Significatieniveau ........................................................................................................... 40
4. Confidence interval (= betrouwbaarheidsinterval) ........................................................... 41
5. P-waarde ....................................................................................................................... 42
5.1. Hoe interpreteren? ................................................................................................... 42
6. T-test in STATA ................................................................................................................ 42
6.1. LINCOM COMMANDO ............................................................................................. 44
HOOFDSTUK 4: de F-test ....................................................................................................... 46
1. Full model versus restricted model ................................................................................. 46
2. Testen van restricties op meerdere parameters................................................................ 46
3. Procedure F-test ............................................................................................................ 47
4. F-test in STATA................................................................................................................ 49
4.1. Meest gebruikte vormen van F-testen ....................................................................... 50
4.2. Relatie tussen R² en F............................................................................................... 51
WEEK 4: Extreme observaties en functionele vormen .............................................................. 52
HOOFDSTUK 1: verschillende stappen bij een regressie analyse ............................................. 52
1. Stap 0: Check de data .................................................................................................... 52
2. Stap 1: Check de OLS assumpties en doe de nodige correcties ........................................ 52
3. Stap 2: check de meaningfulness van het model ............................................................. 53
4. Stap 3: Interpreteer de geschatte coëfficiënten ............................................................... 54
HOOFDSTUK 2: Extreme observaties ...................................................................................... 54
1. Probleem ....................................................................................................................... 54
2. Detectie ......................................................................................................................... 55
3. Correctie ....................................................................................................................... 57
3.1. Corrigeren met dummy Variabelen ........................................................................... 57
3.2. Corrigeren met extreme observaties ......................................................................... 58
HOOFDSTUK 3: Verkeerde functionele vormen ....................................................................... 58
1. Probleem ....................................................................................................................... 59
2. Detectie ......................................................................................................................... 60
3. Correctie ....................................................................................................................... 62
3.1. Keuze juiste functionele vorm ................................................................................... 63
WEEK 5: keuze van onafhankelijke variabelen ......................................................................... 64
HOOFDSTUK 1: Keuze onafhankelijke variabelen .................................................................... 64
1. Probleem: Omitted variables (underfitting) ...................................................................... 64
3
, 2. Detectie van omitted variables (underfitting) ................................................................... 65
3. Correctie omitted variables (underfitting) ........................................................................ 66
4. Irrelevant variables (overfitting) ....................................................................................... 66
Hoofdstuk 2: Multicollineariteit .............................................................................................. 67
1. Probleem 1: perfecte multicollineariteit .......................................................................... 67
2. Probleem 2: Imperfecte multicollineariteit ...................................................................... 68
3. Detectie van probleem multicollineariteit........................................................................ 70
4. Correctie MC ................................................................................................................. 73
WEEK 6: Heteroscedasticiteit en autocorrelatie ...................................................................... 74
HOOFDSTUK 1: Heteroscedasticiteit ...................................................................................... 74
1. Probleem ....................................................................................................................... 74
2. Detectie ......................................................................................................................... 76
2.1. Detectie via scatter graphs waarin verband tussen X en Y variabelen wordt bekeken ... 76
2.2. Detectie via rvfplot & added variable plots waarin resttermen tov geschatte Y waardes
worden geplot ................................................................................................................ 76
2.3. Detectie via Predicted² en Resid² .............................................................................. 77
2.4. detectie via box plots voor categorische OV .............................................................. 78
2.5. Statistische testen voor HS ...................................................................................... 78
3. Correctie ....................................................................................................................... 82
3.1. Bron van Heteroscedasticiteit .................................................................................. 82
3.2. Robuuste standard errors ......................................................................................... 82
HOOFSTUK 2: Autocorrelatie en tijdsreeksen.......................................................................... 83
1. Tijdsreeksen................................................................................................................... 83
2. Probleem ....................................................................................................................... 83
2.1. Autocorrelatie (serial correlation) ............................................................................. 83
2.2. Pure VS impure autocorrelatie .................................................................................. 84
2.3. Impure of valse serial correlation .............................................................................. 84
2.4. Gevolgen autocorrelatie ........................................................................................... 84
3. Detectie ......................................................................................................................... 85
3.1. Grafisch: plots ......................................................................................................... 85
3.2. Autocorrelatie functie (ACF) van de restterm ............................................................. 87
3.3. Partiële ACF (PACF) van de restterm ......................................................................... 87
3.4. Durbin-Watson test .................................................................................................. 88
3.5. Breusch-Godfrey LM test for autocorrelation............................................................. 89
4. Correctie ....................................................................................................................... 90
4.1. Pure vs. Impure autocorrelatie .................................................................................. 90
4
SCHAKELJAAR HANDELSWETENSCHAPPEN
2023 – 2024
Inhoud
WEEK 0: Inleiding tot OPO en econometrie ............................................................................7
HOOFDSTUK 1: introductie tot econometrie .............................................................................7
1. Wat is econometrie?.........................................................................................................7
2. Waarom gebruiken we econometrie? ................................................................................7
3. Mogelijke valkuilen bij het schatten van een model (niet uitputtend) ...................................8
4. Noodzaak van een goed onderliggend model .....................................................................8
5. Omitted variables .............................................................................................................8
6. Extreme observatie ..........................................................................................................9
7. Regressielijn ....................................................................................................................9
8. Overzicht ....................................................................................................................... 10
9. Terminologie en notatie: ................................................................................................. 10
9.1. variabelen en parameters ......................................................................................... 10
9.2. Afhankelijke en verklarende variabelen ..................................................................... 11
10. Meetschaal (meetniveau) van variabelen ....................................................................... 11
WEEK 1: Introductie OPO & basisprincipes OLS ...................................................................... 12
HOOFDSTUK 1: Basisprincipes OLS ....................................................................................... 12
1. Hoe ongekende waardes van parameters bepalen? ......................................................... 12
1.1. Univariate (= enkelvoudige) regressie .................................................................. 12
1.2. OLS: Ordinary Least Squares / GKK: Gewone Kleinste Kwadraten ......................... 13
2. Eigenschappen en assumpties ................................................................................... 14
2.1. Steekproef VS. Populatie .................................................................................... 14
2.2. Steekproef distributie van 𝛽 ................................................................................ 14
2.3. Precisie van OLS schattingen .............................................................................. 15
2.4. Basisaannames van de OLS-methode: de klassieke aannames............................ 15
2.5. OLS-schattingen zijn BLUE (Gauss-Markov) ......................................................... 16
WEEK 2: Meervoudige regressie en Dummy Variabelen ........................................................... 17
HOOFDSTUK 1: Meervoudige (= multivariate) regressie ........................................................... 17
1. Univariate regressie vs multivariate regressie .................................................................. 17
2. OLS schatting................................................................................................................. 18
1
,HOOFDSTUK 2: de fit van het model ....................................................................................... 19
1. Decompositie van variatie .............................................................................................. 19
2. Coëfficiënt van de determinatie: R² ................................................................................. 20
3. KISS principe.................................................................................................................. 20
4. R² adjusted .................................................................................................................... 21
5. Kwaliteit van het model .................................................................................................. 21
6. Voorbeelden in STATA ..................................................................................................... 22
HOOFDSTUK 3: Dummy variabelen ........................................................................................ 23
1. Type variabelen in regressie analyse ................................................................................ 24
1.1. Afhankelijke variabele Y ...................................................................................... 24
1.2. Onafhankelijke variabele X ................................................................................. 24
2. Dummy Variable trap ................................................................................................. 25
3. Dummy variable interpretatie ..................................................................................... 26
4. Dummy variabelen in intercept ................................................................................... 27
4.1. Voorbeeld 1: verschillen in studieresultaten ........................................................ 27
4.2. Voorbeeld 2: Wijnconsumptie in BE, FR en GE ..................................................... 28
4.3. Voorbeeld 3: aankoopprijzen van auto’s .............................................................. 29
5. Dummy variabelen in intercept en/of slope(s) ............................................................. 30
5.1. Interactie effecten (= moderator effecten) ........................................................... 32
5.2. Voorbeelden Stata.............................................................................................. 32
WEEK 3: Toetsen van hypothesen (t-test en f-test) & normaliteit van residuen .......................... 33
HOOFDSTUK 1: Hypothese testing ......................................................................................... 33
1.1. Wat is (statistische) hypothese testing? .................................................................... 33
1.2. Hypothese bewijzen vs verwerpen ............................................................................ 33
1.3. Hoe hypothese formuleren ....................................................................................... 33
1.4. One-sided versus two-sided ..................................................................................... 34
1.5. Hypothesis testing: intuïtie ....................................................................................... 34
HOOFDSTUK 2: Normaliteit van residuen ............................................................................... 36
1. Normaliteitsassumptie voor ui: 𝒖𝒊 ~𝑵(𝟎, 𝝈²) .................................................................. 36
2. Testen voor normaliteit van de resttermen ....................................................................... 36
2.1. Grafisch: histogrammen van de resttermen............................................................... 36
2.2. Grafisch: via Kernel density ...................................................................................... 37
2.3. Statistisch: Shapiro-Wilk test voor normaliteit ........................................................... 37
2.4. Statistisch: test voor Skewness & Kurtosis ................................................................ 37
3. Normaliteitsassumptie niet voldaan................................................................................ 38
HOOFDSTUK 3: De t-test ....................................................................................................... 38
2
, 1. T-test: t-statistiek ........................................................................................................... 38
2. Kritische t-waarde & t-distributie..................................................................................... 39
Drie elementen van de t-test ........................................................................................... 39
3. Significatieniveau ........................................................................................................... 40
4. Confidence interval (= betrouwbaarheidsinterval) ........................................................... 41
5. P-waarde ....................................................................................................................... 42
5.1. Hoe interpreteren? ................................................................................................... 42
6. T-test in STATA ................................................................................................................ 42
6.1. LINCOM COMMANDO ............................................................................................. 44
HOOFDSTUK 4: de F-test ....................................................................................................... 46
1. Full model versus restricted model ................................................................................. 46
2. Testen van restricties op meerdere parameters................................................................ 46
3. Procedure F-test ............................................................................................................ 47
4. F-test in STATA................................................................................................................ 49
4.1. Meest gebruikte vormen van F-testen ....................................................................... 50
4.2. Relatie tussen R² en F............................................................................................... 51
WEEK 4: Extreme observaties en functionele vormen .............................................................. 52
HOOFDSTUK 1: verschillende stappen bij een regressie analyse ............................................. 52
1. Stap 0: Check de data .................................................................................................... 52
2. Stap 1: Check de OLS assumpties en doe de nodige correcties ........................................ 52
3. Stap 2: check de meaningfulness van het model ............................................................. 53
4. Stap 3: Interpreteer de geschatte coëfficiënten ............................................................... 54
HOOFDSTUK 2: Extreme observaties ...................................................................................... 54
1. Probleem ....................................................................................................................... 54
2. Detectie ......................................................................................................................... 55
3. Correctie ....................................................................................................................... 57
3.1. Corrigeren met dummy Variabelen ........................................................................... 57
3.2. Corrigeren met extreme observaties ......................................................................... 58
HOOFDSTUK 3: Verkeerde functionele vormen ....................................................................... 58
1. Probleem ....................................................................................................................... 59
2. Detectie ......................................................................................................................... 60
3. Correctie ....................................................................................................................... 62
3.1. Keuze juiste functionele vorm ................................................................................... 63
WEEK 5: keuze van onafhankelijke variabelen ......................................................................... 64
HOOFDSTUK 1: Keuze onafhankelijke variabelen .................................................................... 64
1. Probleem: Omitted variables (underfitting) ...................................................................... 64
3
, 2. Detectie van omitted variables (underfitting) ................................................................... 65
3. Correctie omitted variables (underfitting) ........................................................................ 66
4. Irrelevant variables (overfitting) ....................................................................................... 66
Hoofdstuk 2: Multicollineariteit .............................................................................................. 67
1. Probleem 1: perfecte multicollineariteit .......................................................................... 67
2. Probleem 2: Imperfecte multicollineariteit ...................................................................... 68
3. Detectie van probleem multicollineariteit........................................................................ 70
4. Correctie MC ................................................................................................................. 73
WEEK 6: Heteroscedasticiteit en autocorrelatie ...................................................................... 74
HOOFDSTUK 1: Heteroscedasticiteit ...................................................................................... 74
1. Probleem ....................................................................................................................... 74
2. Detectie ......................................................................................................................... 76
2.1. Detectie via scatter graphs waarin verband tussen X en Y variabelen wordt bekeken ... 76
2.2. Detectie via rvfplot & added variable plots waarin resttermen tov geschatte Y waardes
worden geplot ................................................................................................................ 76
2.3. Detectie via Predicted² en Resid² .............................................................................. 77
2.4. detectie via box plots voor categorische OV .............................................................. 78
2.5. Statistische testen voor HS ...................................................................................... 78
3. Correctie ....................................................................................................................... 82
3.1. Bron van Heteroscedasticiteit .................................................................................. 82
3.2. Robuuste standard errors ......................................................................................... 82
HOOFSTUK 2: Autocorrelatie en tijdsreeksen.......................................................................... 83
1. Tijdsreeksen................................................................................................................... 83
2. Probleem ....................................................................................................................... 83
2.1. Autocorrelatie (serial correlation) ............................................................................. 83
2.2. Pure VS impure autocorrelatie .................................................................................. 84
2.3. Impure of valse serial correlation .............................................................................. 84
2.4. Gevolgen autocorrelatie ........................................................................................... 84
3. Detectie ......................................................................................................................... 85
3.1. Grafisch: plots ......................................................................................................... 85
3.2. Autocorrelatie functie (ACF) van de restterm ............................................................. 87
3.3. Partiële ACF (PACF) van de restterm ......................................................................... 87
3.4. Durbin-Watson test .................................................................................................. 88
3.5. Breusch-Godfrey LM test for autocorrelation............................................................. 89
4. Correctie ....................................................................................................................... 90
4.1. Pure vs. Impure autocorrelatie .................................................................................. 90
4
