Econ B S2 Flashcards
How many explanatory variables in a simple vs multiple regression model?
Simple - 1
Multiple - 2 or more
What is the population model also known as?
The true model
Note
model must be linear in parameters
How are beta estimates interpreted?
They are partial effects of Xi on Y
What is CLM1?
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
What is CML2? What does it mean?
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
What is CML3?
The error has an expected value of 0
Why does error arise?
Because a model won’t be able to find every influence on y in an economic model therefore this term captures these omitted factors
What is CML4?
In the sample (and tf population), none of the IVs are constant and there are no exact linear combinations between the IVs
What is perfect collinearity? What is it’s implication?
If an IV is an exact linear combination of another, this is perfect collinearity tf model can’t be estimated by OLS
Under what other circumstance does CLM4 also fail?
If n is less than k+1
What is CLM5?
Each disturbance:
a) has same finite variance σ^2
b) is uncorrelated with every other disturbance uj
What does it mean that each disturbance has same finite variance?
Means the variance is the same for all combinations of outcomes of the explanatory variables
What does it mean that each disturbance is uncorrelated with every other disturbance (example)?
ie. if interests rates are UNUSUALLY high this period (this observation), they will still be expected as average for the next period
What is CML6?
The population error u is normally distributed with mean=0 and variance=σ^2
u~N(0,σ^2)
What is the strongest assumption of the CLMs and why?
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
What are the two weaknesses of the assumption with CLM6?
- 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
How can we prove the OLS estimator is unbiased?
Using CLM1-4
How can it be proved that the OLS estimator is the best linear unbiased estimator?
Using CML1-5, the Gauss-Markov Theorem states it
How can we prove the OLS estimator is the Minimum Variance Unbiased Estimator?
Using CLM1-6, it can be proved it is the MVUE in the class of all linear and non-linear estimators
