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1Prof. dr. Monica ROMAN
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Definition Consequences
Detecting
Selection of independent variables Examples
References
2Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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In certain situations, the dependence among the X variablescan be so strong that it may difficult to estimate the
regression coefficients.
In this situation, we say that the dataset exhibits
it is a violation of the model assumptions!!
Multicolinearity is a matter of paucity of information in
the data.
We dont have enough independent variation in the Xs.
Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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i. colinear variables can have coefficients with largestandard errors
ii. colinear variables can have insignificant ts but
very significant Fsiii. getting a larger sample doesnt necessarily help
much
Prof. dr. Monica ROMAN
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Example:
11109876
10
9
8
7
6
5
x1
x2
11109876
8
7
6
5
4
3
2
x1
y
1098765
8
7
6
5
4
3
2
x2
y
33 Firms:
Y = log net income in millions
X1 = log sales in millions
X2 = log assets in millions
i. it is a violation of the modelassumptions
Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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The perfect collinearity.
The regression coefficients can not be
computed using OLS The XX matrix is not invertable!
6Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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Standard errors of regression coefficientsare large. As a result t statistics for testingthe population regression coefficients aresmall.
Regression coefficient estimates areunstable. Signs of coefficients may beopposite of what is intuitively reasonable.
7Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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1. Pairwise correlations between explanatoryvariables are high Regress Xj on other Xs and get very high R
2
Klein criterion
2. Large overall F-statistic for testingusefulness of predictors but small tstatistics.
3. Variance inflation factors
8Prof. dr. Monica ROMAN
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Variance Inflation Factors Variance inflation factor (VIF): Let 2jR denote the R2 for the multiple
regression ofxj on the other x-variables. Then
2
1
1j
j
VIFR
.
Fact:2
2
1j
j j
x
MSESD VIF
n S
VIFj for variable xj: Measure of the increase in the variance of thecoefficient on xj due to the correlation among the explanatory variables
compared to what the variance of the coefficient on xj would be if xj wereindependent of the other explanatory variables.
9Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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delete some Xs (give up on those partial effects)
combine the highly correlated independent variables into
indices inject variation into the system via
different sorts of data (cross-section vs. time series)
experimentation, if possible!
10Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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The most important decision to be made in MR is theselection of regressors to be included in the model.
Draw up a wish list of variables by:
Consulting subject matter research
Consulting experts in the area Listen carefully for the factors that they use to
forecast
Carefully considering whether variables have anyexplanatory power
Avoiding the mistake of selecting too many variables
Try to limit the list of variables to no more than 10variables and certainly less than 20
11Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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Check for availability of data: Dont over-invest in fancy statistical techniques to
overcome the paucity of data Invest in collecting more data if necessary
We now have to develop a method for selecting a finalregression specification.
Why not just include all of the variables and be done with it?
Each coefficient estimate is subject to error.
So even if the true coefficient is zero or extremely small, theleast squares estimate will be non-zero.
These coefficient sampling errors contribute to prediction
error.
12Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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Rossis Rules: An informal method for variable
selection.i. run a regression on the full set of variables
ii. collect all the variables with small t-statistics in onegroup
iii. test the deletion of this group using a partial F-test
Note: some variables may be so important that they are
always kept in the regression
variables can be highly intercorrelated so that neithervariable contributes significantly (as measured by the t-test) but that they are jointly significant as measured bythe F-test.
13Prof. dr. Monica ROMAN
7/30/2019 Multincolinearitatea Econometrie
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However, you should know about it as it is popular
There are two popular versions of step-wiseregression:
keep adding variables successively until the additionof variables is no longer significant as measured by the F-test.
put all variables in, and delete if you cannot reject
the null that the deleted variables are insignificant.
Both of these techniques can be implemented withgroups of two or more variables as well as onevariable at a time.
14Prof. dr. Monica ROMAN
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Problems with step-wise regression :
i. Avoids subject matter considerations in selectingvariables
ii. Each time a test is performed you run the risk ofa type I error. These multiply over the course ofthe stepwise regression.
iii. There can be real problems with correlated data
due to the one variable at a time emphasis ofmost stepwise regression procedures
iv. You don't really know the true significance level
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Andrei, T., Bourbonnais, R.- Econometrie, Ed.Economica, Bucuresti, 2008- capitolul 9, pag.268-285
Voineagu, V. si colectiv- Teorie si practicaeconometrica, Ed. Meteor Press, 2007, cap.6.3 pag. 294-302
Prof. dr. Monica ROMAN