Econ B S2

Question 1

How many explanatory variables in a simple vs multiple regression model?

Answer 1

Simple - 1

Multiple - 2 or more

Question 2

What is the population model also known as?

Answer 2

The true model

Question 3

Note

Answer 3

model must be linear in parameters

Question 4

How are beta estimates interpreted?

Answer 4

They are partial effects of Xi on Y

Question 5

What is CLM1?

Answer 5

The mode of population can be written in the form (see form) where betas are unknown parameters of interest and u is unobservable random error

Question 6

What is CML2? What does it mean?

Answer 6

The explanatory variables x1->xk are non-stochastic.

It refers to the choosing of inputted x-values (ie. x=5, x=10). It is appropriate for experimental settings but these rarely arise in economics

Question 7

What is CML3?

Answer 7

The error has an expected value of 0

Question 8

Why does error arise?

Answer 8

Because a model won’t be able to find every influence on y in an economic model therefore this term captures these omitted factors

Question 9

What is CML4?

Answer 9

In the sample (and tf population), none of the IVs are constant and there are no exact linear combinations between the IVs

Question 10

What is perfect collinearity? What is it’s implication?

Answer 10

If an IV is an exact linear combination of another, this is perfect collinearity tf model can’t be estimated by OLS

Question 11

Under what other circumstance does CLM4 also fail?

Answer 11

If n is less than k+1

Question 12

What is CLM5?

Answer 12

Each disturbance:

a) has same finite variance σ^2
b) is uncorrelated with every other disturbance uj

Question 13

What does it mean that each disturbance has same finite variance?

Answer 13

Means the variance is the same for all combinations of outcomes of the explanatory variables

Question 14

What does it mean that each disturbance is uncorrelated with every other disturbance (example)?

Answer 14

ie. if interests rates are UNUSUALLY high this period (this observation), they will still be expected as average for the next period

Question 15

What is CML6?

Answer 15

The population error u is normally distributed with mean=0 and variance=σ^2

u~N(0,σ^2)

Question 16

What is the strongest assumption of the CLMs and why?

Answer 16

CLM6 - since u is the sum of many different factors affecting y, we can use central limit theorem to conclude that u has an approximate normal distribution

Question 17

What are the two weaknesses of the assumption with CLM6?

Answer 17

• the factors in u can have very different distributions in the population
• the argument assumes all unobserved factors affect y in a separate, additive fashion

Question 18

How can we prove the OLS estimator is unbiased?

Answer 18

Using CLM1-4

Question 19

How can it be proved that the OLS estimator is the best linear unbiased estimator?

Answer 19

Using CML1-5, the Gauss-Markov Theorem states it

Question 20

How can we prove the OLS estimator is the Minimum Variance Unbiased Estimator?

Answer 20

Using CLM1-6, it can be proved it is the MVUE in the class of all linear and non-linear estimators