L2 Flashcards
What is Bias?
Difference between expected value of an estimator and the population parameter that it is estimating
Difference between B1 and ^B1:
B1 is a constant
^B1 is a random variable with sampling distribution: E(^B1) and Var(^B1)
What makes an estimator unbiased?
E(^B) = B
Draw the bias table
Corr
Bias
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What is the Kitchen Sink Regression problem?
Temptation to include all available variables.
Irrelevant Variables
Have no effect on unbiasdeness, can affect variance of OLS estimators
Most important when selecting variables is theorectical relevance
Consider the model:
wage = B0 + B1 female + u
What is B0?
Avg wage in the sample for men
Consider the model:
wage = B0 + B1 female + u
What is B1?
Difference in avg wages in sample between men and women
Consider the model:
wage = B0 + B1 female + u
What is B0 + B1?
Avg wage in sample for women
Consider the model:
wage = 0.62 - 2.27 female + 0.51 educ
Why is B1 negative?
We can believe there are ommited variables, makes no sense if evertyhing else is 0 for a women to have a negative wage
Collinearity in dummies
Cannot include dummies for all model groups (so choose base group)
Consider the model:
log(wage) = B0 + B1 married + B2 female + B3 (married x female)
What is B0?
Intercept for base group, in this case -> single male
Consider the model:
log(wage) = B0 + B1 married + B2 female + B3 (married x female)
What is B0 + B1?
Intercept for married men
Consider the model:
log(wage) = B0 + B1 married + B2 female + B3 (married x female)
What is B0 + B2?
Intercept for single women
Consider the model:
log(wage) = B0 + B1 married + B2 female + B3 (married x female)
What is B0 + B1 + B2 + B3?
Intercept for married women
Consider the model:
log(wage) = B0 + B1 married + B2 female + B3 (married x female)
What is B3?
Difference in marriage premium between men and women
Larger u variance -> larger ^B1 variance
More variation in u -> harder to estimate B1
Sum ( xi - avg(x) ) increases as N increases
Larger samples -> better estimations
Sum ( xi - avg(x) ) reflects x variance
Larger x variance is good
T-statistic tells us what?
How far the estimated parameter is from the true value
Normality of the errors
Assume u ~ iid (0, sigma^2)
Large samples
If H0: B1 - B2
Show t
t= Ô - O / se(Ô)
Ô = B1 - B2
se(B1-B2) != se(B1) - se(B2)
What is the F-test for?
Understand how much worse does the restricted model fit the data, when compared to the unrestricted
What does the F-test measure?
Change in SSR between models
F-test formula
F = SSR (R) - SSR (UR) / SSR (UR)
cheat sheet
Is F always larger than 0?
Yes
F-stat for parameter exclusion is equal to square of t-stat in what case
1- parameter exclusion (2-sided H)
3 types of Functional Form Misspecification
1 - Omitting higher powers of variables
2 - Omit variable interactions
3 - Using levels instead of logs
What does FFM lead to?
Biased OLS coefficients ( can be tested )
What does RESET test consist of?
Estimate model
Compute predicted values
See if predicted values in different powers have significance
What does Davidson and Mckinnon test consist of?
Compare two models, e.g.:
y = B0 + B1 x + u
y = B0 + B1 log(x) + u
Use fitted values of other in each:
y = B0 + B1 x + B2 (^y)
y = B0 + B1 log(x) + B2 (^y)
Where the fitted are not significant in the other model, we reject
If after Davidson and Mckinnon we cannot decide between models, what is the tie-breaker?
R-squared
