ES1004 Econometrics by Example
Lecture 4: Multicollinearity
Dr. Hany Abdel-Latif
Swansea University, UK
Gujarati textbook, second edition
21st May 2016
Dr. Hany Abdel-Latif (2016) ES1004ebe Lecture 3 Multicollinearity 1 / 23
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ES1004 Econometrics by Example, Summaries of Introduction to Econometrics
Nature of Multicollinearity. Basic Idea. CLRM assumes no exact linear relationship among explanatory variables A6 perfect multicollinearity.
Typology: Summaries
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ES1004 Econometrics by Example
Lecture 4: Multicollinearity
Dr. Hany Abdel-Latif
Swansea University, UK
Gujarati textbook, second edition
21st May 2016
Meaning Nature of Multicollinearity
CLRM Assumptions
A 1 : model is linear in parameters A 2 : regressors are fixed non-stochastic A 3 : the expected value of the error term is zero E (ui |X ) = 0 A 4 : homoscedastic or constant variance of errors var (ui |X ) = σ^2 A 5 : no autocorrelation, cov (ui , uj ) = 0 , i 6 = j A 6 : no multicollinearity; no perfect linear relationships among the X s A 7 : no specification bias
Meaning Nature of Multicollinearity
Perfect Multicollinearity I
Yi = β 1 + β 2 X 2 i + β 3 X 3 i + · · · + βk Xki + ui (1)
if, for example, X 2 i + 3 X 3 i = 1 we have perfect collinearity for X 2 i = 1 − 3 X 3 i then we cannot include both X 2 i and X 3 i in the same regression model we cannot estimate the regression coefficients
Meaning Nature of Multicollinearity
Perfect Multicollinearity II
examples of perfect collinearity if we introduce income variables in both dollars and cents in the consumption function dummy variable trap: when including as many dummies as the number of groups with the presence of the intercept
in practice, exact linear relationships among regressors is a rarity
Imperfect Collinearity Consequences
Multicollinearity and OLS Estimation
OLS estimators still BLUE high R^2 but will have insignificant coefficients regression coefficients are very sensitive to small changes in the data, especially of the sample is relatively small
if two variables are highly collinear it is very difficult to isolate the impact of each variable separately on the regressand
Imperfect Collinearity Example 1
Modelling Expenditure: Data
Imperfect Collinearity Detection
Testing for Collinearity
there is no unique test for multicollinearity
(^1) high R^2 but few significant t ratios (^2) high pairwise correlations among explanatory variables (^3) high partial coefficients (^4) significant F -test for auxiliary regressions (^5) high variance inflation factor [low tolerance factor]
Imperfect Collinearity Example 2
Married Women’s Hours of Work: Data
Mroz (1987) Econometrica, 55, 765- assessing the impact of several socio-economic variables data in Table 4.4 [see Piazza] cross-sectional data on 753 married women in 1975 325 married women did not work [i.e., zero hours of work]
Imperfect Collinearity Example 2
Married Women’s Hours of Work: Variables II
hhours R hours worked by husband hwage R husband’s hourly wage, 1975 kids618 R number of kids between ages 6 and 18 kidsl6 R number of kids under age 6 wage R estimated wage from earnings mothereduc R mother’s years of education mtr R marginal tax rate facing a woman unemployment R unemployment rate in county of residence
Imperfect Collinearity Example 2
Married Women’s Hours of Work: A priori
we would expect a positive sign R education, experience, father’s education, mother’s education negative sign R age, husband’s age, husband’s hours of work, husband’s wage, marginal tax rate, unemployment rate, number of kids under 6
Imperfect Collinearity Example 2
Dependent Variable and Sample
Imperfect Collinearity Example 2
Insignificant Coefficients
Imperfect Collinearity Example 2
Variance Inflation Factor VIF
Imperfect Collinearity Example 2