ECON 3040 - Previous Exams

Previous midterms

Define / calculate (true) mean (from a prob. function)
Same for variance
Properties of mean / variance (if you multiply by $c$, variance is multiplied by $c^2$)
Know what cov. and corr. are measuring (very similar - corr. is between -1 and 1)
Skip blizzard/midterm example
Basic result of CLT, and how it applies to sample average and LS estimator (it makes them Normal)

Estimators (y-bar, LS intercept and slope) are random variables. Explain why
Bias / efficiency / consistency (define these terms either in a sentence or an equation)
Know that $\bar{y}$ and LS is unbiased / efficient / consistent under some assumptions.
GM theorem - establishes efficiency
Define: significance, type I and II error, critical value, confidence interval, p-value
Basics of hypothesis testing
Why t-test instead of z-test, and how the distribution changes from Normal to t when we use $s^2$
$\hat{\sigma}^2$ (biased) and $s^2$ (unbiased)
degrees of freedom

R-square: define it. Pick it out in R output
To derive: take sample variance of both sides of $y = \hat{y} + e$
TSS / ESS / RSS terminology
no fit / perfect fit (draw diagram)
Hypothesis testing: calculate a t-stat, get the decision to reject/fail to reject correct.
Reject H0 when: p-value is small (< 0.05) / t-stat is greater than crit. value (e.g. 1.96) / if hypothesis is outside the C.I.
var(b1) tells us when the LS estimator becomes more efficient (3 things)
Definition of dummy variables
Interpretating the beta on a dummy variable

Issues that arise in the multiple regression model:

No perfect multicollinearity / DVT
- define it
- examples: different units/gender dummy/location dummy
Imperfect multicollinearity - basic definition and consequences
$R^2$ no longer works
- explain why
$\bar{R}^2$ used instead
- explain why it works

Linear vs. non-linear effect
Consequences of missing a non-linear effect
Polynomial regressionn model
- Determine “r”
- Interpret the $b$ by predicting values ($\hat{y}$)
Logs
- Can “linearize” exponential growth (GDP)
- Can “linearize” multiplicative models (Cobb-Douglas)
- approximate percentage changes
- 3 configurations: lin-log, log-lin, log-log
- Intepretations of the $\beta$ in these three configurations

Interaction terms
- $D \times X$ allows for different slopes/lines for different groups
- Test for differences between groups
Dummy-dummy interactions
- different effect for different groups
DiD
- minimum wage example
- fundamental problem of causal inference
- DiD estimator is the $b$ on the dummy-dummy interaction
- Picture