Inhoudsopgave
1 Basisprincipes van econometrie...................................................................................................... 4
1.1 Introductie..................................................................................................................................... 4
1.2 Ordinary Least Squares (OLS)..................................................................................................... 5
1.1.1 Gauss-Markov assumpties..................................................................................................... 6
2 Basisprincipes en categorische variabelen....................................................................................7
1.3 Basis regressiemodel................................................................................................................... 7
1.4 Multiple regression........................................................................................................................ 8
2.1.1 Goodness of fit....................................................................................................................... 8
2.1.2 Rvf-plot................................................................................................................................... 8
1.5 Dummy-variabelen........................................................................................................................ 9
2.1.3 Gebruik van dummy-variabelen.............................................................................................. 9
3 Formele specificatie en enkelvoudige hypothesetest..................................................................10
1.6 Removing the unit scale: standardized coefficients....................................................................10
1.7 Transforming our variables: Logarithmic transformations...........................................................10
3.1.1 Polynomials.......................................................................................................................... 10
3.1.2 Logarithms............................................................................................................................ 11
1.8 Normaliteit-testing....................................................................................................................... 12
3.1.3 Normaliteit residu’s: visuele inspectie...................................................................................12
3.1.4 Normaliteit residu’s: statistische testen.................................................................................12
1.9 Enkelvoudige hypothesis testing................................................................................................. 13
3.1.5 T-test.................................................................................................................................... 13
3.1.6 Confidence intervals............................................................................................................. 14
3.1.7 Nullity testen van een parameter.......................................................................................... 14
4 Testen van hypotheses op meerdere paramaters........................................................................15
1.10 Hypothesetesting op meerdere parameters: T-distribution & F-distribution..............................15
4.1.1 2-parameter Equality............................................................................................................ 15
4.1.2 2-parameter Restriction........................................................................................................ 16
4.1.3 M-parameter Nullity: Joint F-test...........................................................................................16
4.1.4 M-parameter Nullity: Joint F-test – a Special Case...............................................................16
4.1.5 M-parameter Restriction....................................................................................................... 17
1.11 Hypothesetesting Special Cases: Testing Parameter Stability.................................................17
4.1.6 Chow-test............................................................................................................................. 17
4.1.7 Alternatief voor Chow-test: dummy-variabelen.....................................................................18
1.12 Hypothesetesting Special Cases: Formal Specification Error Test using RESET-test..............19
, 4.1.8 Visuele inspectie: Partial Plots.............................................................................................. 19
4.1.9 Statistische inspectie: Ramsey’s RESET test.......................................................................19
1.13 Extreme observaties................................................................................................................. 20
4.1.10 Ex ante: Visuele inspectie................................................................................................... 20
4.1.11 Ex post: Visuele inspectie................................................................................................... 20
4.1.12 Ex post: Dfbeta’s................................................................................................................ 20
4.1.13 Ex post: Standardized Dfbeta’s.......................................................................................... 21
4.1.14 Ex post: Studentized Residuals.......................................................................................... 21
4.1.15 Extreme observaties oplossen............................................................................................ 21
5 Multicollineariteit en modeldiagnose............................................................................................. 22
1.14 Multicollineariteit....................................................................................................................... 22
5.1.1 Perfecte multicollineariteit..................................................................................................... 22
5.1.2 Non-perfecte multicollineariteit............................................................................................. 22
5.1.3 Multicollineariteit detecteren.................................................................................................23
5.1.4 Multicollineariteit oplossen.................................................................................................... 23
1.15 Model specification en diagnostic testing..................................................................................24
5.1.5 Main causes of bias in OLS.................................................................................................. 24
5.1.6 Underfitting........................................................................................................................... 24
5.1.7 Overfitting............................................................................................................................. 24
5.1.8 Variabelen: include or not?................................................................................................... 25
6 Heteroskedasticiteit......................................................................................................................... 26
1.16 Gevolgen van heteroskedasticiteit............................................................................................ 26
1.17 Heteroskedasticiteit detecteren................................................................................................. 27
6.1.1 Visuele inspectie................................................................................................................... 27
6.1.2 Statistische inspectie............................................................................................................ 27
1.18 Heteroskedasticiteit oplossen................................................................................................... 28
7 Autocorrelatie.................................................................................................................................. 29
1.19 Oorzaken van autocorrelatie..................................................................................................... 29
1.20 Gevolgen van autocorrelatie..................................................................................................... 30
1.21 Autocorrelatie detecteren.......................................................................................................... 30
7.1.1 Visuele inspectie................................................................................................................... 30
7.1.2 Statistische inspectie............................................................................................................ 31
1.22 Autcorrelatie oplossen.............................................................................................................. 32
7.1.3 Lagged variables.................................................................................................................. 32
1.23 Autocorrelatie oplossen in STATA............................................................................................ 33
,
, 1 Basisprincipes van econometrie
1.1 Introductie
Omitted variable bias: Onterecht variabelen uit het model halen, kan voor vertekening zorgen
Cross-section: Iets bestuderen op één moment
Panel data: Eén fenomeen meerdere keren observeren overheen de tijd
Pooled data: Meerdere fenomenen bestuderen overheen tijd
Spurious correlations: Correlatie ≠ causaliteit gebruik gezond verstand hiervoor
β0: Constante term, intercept
β1: Helling, rico
Als β1 = 450, dan betekent het dat als X met één eenheid stijgt, Y gaat stijgen met 450 eenheden
Extreme observaties gaan ervoor zorgen dat de regressielijn naar zich toe wordt getrokken
Regressielijn: Een lijn door de puntenwolk, een lijn die het gemiddelde gaat weergeven van de
punten (observaties)
Variabelen: Informatie in de data
Zoals bijvoorbeeld ‘C’ en ‘I’
Parameters: Ongekende coëfficiënten
Zoals bijvoorbeeld β0 & β1
Y-variabele: Afhankelijke, endogene, verklaarde variabele
X-variabele: Onafhankelijke, exogene, verklarende, voorspellende variabele
Lagged: Vertraagd
Error-term:
o Storingsterm, residual of residu
o Hetgeen we niet kunnen verklaren, is compleet random
1 Basisprincipes van econometrie...................................................................................................... 4
1.1 Introductie..................................................................................................................................... 4
1.2 Ordinary Least Squares (OLS)..................................................................................................... 5
1.1.1 Gauss-Markov assumpties..................................................................................................... 6
2 Basisprincipes en categorische variabelen....................................................................................7
1.3 Basis regressiemodel................................................................................................................... 7
1.4 Multiple regression........................................................................................................................ 8
2.1.1 Goodness of fit....................................................................................................................... 8
2.1.2 Rvf-plot................................................................................................................................... 8
1.5 Dummy-variabelen........................................................................................................................ 9
2.1.3 Gebruik van dummy-variabelen.............................................................................................. 9
3 Formele specificatie en enkelvoudige hypothesetest..................................................................10
1.6 Removing the unit scale: standardized coefficients....................................................................10
1.7 Transforming our variables: Logarithmic transformations...........................................................10
3.1.1 Polynomials.......................................................................................................................... 10
3.1.2 Logarithms............................................................................................................................ 11
1.8 Normaliteit-testing....................................................................................................................... 12
3.1.3 Normaliteit residu’s: visuele inspectie...................................................................................12
3.1.4 Normaliteit residu’s: statistische testen.................................................................................12
1.9 Enkelvoudige hypothesis testing................................................................................................. 13
3.1.5 T-test.................................................................................................................................... 13
3.1.6 Confidence intervals............................................................................................................. 14
3.1.7 Nullity testen van een parameter.......................................................................................... 14
4 Testen van hypotheses op meerdere paramaters........................................................................15
1.10 Hypothesetesting op meerdere parameters: T-distribution & F-distribution..............................15
4.1.1 2-parameter Equality............................................................................................................ 15
4.1.2 2-parameter Restriction........................................................................................................ 16
4.1.3 M-parameter Nullity: Joint F-test...........................................................................................16
4.1.4 M-parameter Nullity: Joint F-test – a Special Case...............................................................16
4.1.5 M-parameter Restriction....................................................................................................... 17
1.11 Hypothesetesting Special Cases: Testing Parameter Stability.................................................17
4.1.6 Chow-test............................................................................................................................. 17
4.1.7 Alternatief voor Chow-test: dummy-variabelen.....................................................................18
1.12 Hypothesetesting Special Cases: Formal Specification Error Test using RESET-test..............19
, 4.1.8 Visuele inspectie: Partial Plots.............................................................................................. 19
4.1.9 Statistische inspectie: Ramsey’s RESET test.......................................................................19
1.13 Extreme observaties................................................................................................................. 20
4.1.10 Ex ante: Visuele inspectie................................................................................................... 20
4.1.11 Ex post: Visuele inspectie................................................................................................... 20
4.1.12 Ex post: Dfbeta’s................................................................................................................ 20
4.1.13 Ex post: Standardized Dfbeta’s.......................................................................................... 21
4.1.14 Ex post: Studentized Residuals.......................................................................................... 21
4.1.15 Extreme observaties oplossen............................................................................................ 21
5 Multicollineariteit en modeldiagnose............................................................................................. 22
1.14 Multicollineariteit....................................................................................................................... 22
5.1.1 Perfecte multicollineariteit..................................................................................................... 22
5.1.2 Non-perfecte multicollineariteit............................................................................................. 22
5.1.3 Multicollineariteit detecteren.................................................................................................23
5.1.4 Multicollineariteit oplossen.................................................................................................... 23
1.15 Model specification en diagnostic testing..................................................................................24
5.1.5 Main causes of bias in OLS.................................................................................................. 24
5.1.6 Underfitting........................................................................................................................... 24
5.1.7 Overfitting............................................................................................................................. 24
5.1.8 Variabelen: include or not?................................................................................................... 25
6 Heteroskedasticiteit......................................................................................................................... 26
1.16 Gevolgen van heteroskedasticiteit............................................................................................ 26
1.17 Heteroskedasticiteit detecteren................................................................................................. 27
6.1.1 Visuele inspectie................................................................................................................... 27
6.1.2 Statistische inspectie............................................................................................................ 27
1.18 Heteroskedasticiteit oplossen................................................................................................... 28
7 Autocorrelatie.................................................................................................................................. 29
1.19 Oorzaken van autocorrelatie..................................................................................................... 29
1.20 Gevolgen van autocorrelatie..................................................................................................... 30
1.21 Autocorrelatie detecteren.......................................................................................................... 30
7.1.1 Visuele inspectie................................................................................................................... 30
7.1.2 Statistische inspectie............................................................................................................ 31
1.22 Autcorrelatie oplossen.............................................................................................................. 32
7.1.3 Lagged variables.................................................................................................................. 32
1.23 Autocorrelatie oplossen in STATA............................................................................................ 33
,
, 1 Basisprincipes van econometrie
1.1 Introductie
Omitted variable bias: Onterecht variabelen uit het model halen, kan voor vertekening zorgen
Cross-section: Iets bestuderen op één moment
Panel data: Eén fenomeen meerdere keren observeren overheen de tijd
Pooled data: Meerdere fenomenen bestuderen overheen tijd
Spurious correlations: Correlatie ≠ causaliteit gebruik gezond verstand hiervoor
β0: Constante term, intercept
β1: Helling, rico
Als β1 = 450, dan betekent het dat als X met één eenheid stijgt, Y gaat stijgen met 450 eenheden
Extreme observaties gaan ervoor zorgen dat de regressielijn naar zich toe wordt getrokken
Regressielijn: Een lijn door de puntenwolk, een lijn die het gemiddelde gaat weergeven van de
punten (observaties)
Variabelen: Informatie in de data
Zoals bijvoorbeeld ‘C’ en ‘I’
Parameters: Ongekende coëfficiënten
Zoals bijvoorbeeld β0 & β1
Y-variabele: Afhankelijke, endogene, verklaarde variabele
X-variabele: Onafhankelijke, exogene, verklarende, voorspellende variabele
Lagged: Vertraagd
Error-term:
o Storingsterm, residual of residu
o Hetgeen we niet kunnen verklaren, is compleet random
