multincolinearitatea econometrie

7/30/2019 Multincolinearitatea Econometrie

1/16

1Prof. dr. Monica ROMAN


2/16

Definition Consequences

Detecting

Selection of independent variables Examples

References



3/16

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


4/16

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



5/16

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



6/16

The perfect collinearity.

The regression coefficients can not be

computed using OLS The XX matrix is not invertable!



7/16

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.



8/16

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



9/16

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.



10/16

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!



11/16

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



12/16

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.



13/16

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.



14/16

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.



15/16

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



16/16

16

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


multincolinearitatea econometrie

Documents