M10 - Multiple Regression

Question 1

Problem 1 in multiple regr
Omitted variables bias

“Bias of the estimations of b1, when regressor … is …. and there is positive/ negative …. of both regressors”

Positive bias:
Negative bias:

Answer 1

Problem 1 in multiple regr
Omitted variables bias

“Bias of the estimations of b1, when regressor X2 is OMITTED and there is positive/ negative CORRELATION of both regressors”

Positive bias: b2>0 and corr(x1,x2) > 0
Negative bias: b2 <0 and corr() <0

Question 2

Prob 2: Multi-collinwarity

What is it?

Disadv
Which measures?

Answer 2

High degree of correlation between explanatory variables (correlations > .9)

• inaccurate estimates
• high standard errors

Test with VIF - Variance inflation factor
Or tolerance

Question 3

Tolerance

Answer 3

Are there correlations with other regressors?

Yes, if tolerance < 0.2/0.1 and VIF > 10

Question 4

VIF

Answer 4

Variance inflation factor

How much has the variance of an estimated coeff increased due to collinearity?

If totally uncorr:1
Rises with correlation

Question 5

Solution for multi- collinearity

Answer 5

• eliminate critical variables –> loose info
• increase sample size –> not always possible
• leave it as it is
• aggregate the critival IV into 1 factor

Question 6

Prob 3: too many regressors?

Answer 6

Better include too many variables than too less

Question 7

Standardiuation

When?
For what?

Gleichung

Answer 7

To make coeff comparable

When they have different units

Question 8

Can OLS also estimate non-linear relships?

Answer 8

Yes, if the relship is linear in the parameters.

E.g.:
Log transforation
Quadratic terms
Interaction terms

Question 9

Logarithmic transformation

Model 1 -3

Answer 9

Log transf makes coeff linear

• -> we can estimat it using OLS
• -> test the restriction b1+b2 =1

Model1:
Lny = b0+b1 lnx + u
B1 is the % change in y when x is changed by 1% –> ELASTICITY

Model 2:
Lny = b0+b1x + u
B1 is the approx % change in y when x is chabged by 1 unit

Model 3:
Lny = b0+b1 lnx + u
B1 is the change in y resulting from a multiplication of x with e

Question 10

Why determine elasticity rather than absolute effect size?

Elasticity is a …. quantity.
–> no …. of …. have to be taken into account

–> facilitates …. and improves …..

Answer 10

Why determine elasticity rather than absolute effect size?

Elasticity is a DIMENSIONLESS quantity.
–> no UNITS of MEASUREMENT have to be taken into account

–> facilitates INTERPRETATION and improves COMPARABILITY

Question 11

Log transformation

What kinds of variables are included with transf?
Which are included withiut transf?

Adv:

Answer 11

Include with tranfs/ in log form:

• strictly positive variables (money, income)
• indication of sizes (population)

Include withiut transf?

• percentage variables
• time periods

A logarithmic transformation turns a right-skewed distribution into a normal distribution.

Question 12

Rj² = 1 means what

Answer 12

means that the variable can be expressed as a linear combination of all other variables and is therefore not needed

Question 13

Specification in multiple regression

• problems with that

Answer 13

• which variables are included/ignored?
• whats their funtcional relship?
• are they correlated among each other?
• multi- collinearity
• omitted variable bias
• too many regressors
• wrong functional form

Question 14

Transformation

what does it mean when beta1 + beta 2 are

• smaller than 1
• equal to 1
• bigger than 1

Answer 14

=1 constant economies of scale