Final Review

ECON 480 • Econometrics • Fall 2022

Dr. Ryan Safner
Associate Professor of Economics

## Major Models & Extensions

• Causality
• Fundamental problem of causal inference, potential outcomes
• DAGs, front-doors/back-doors, controlling
• Multivariate OLS
• Omitted Variable Bias
• Variance/Multicollinearity

## Major Models & Extensions

• Categorical data
• Interpreting dummies, group means
• Using categorical variables as dummies
• dummy variable trap
• interaction effects
• Nonlinear Models & Transforming Variables
• higher-order polynomials
• logs
• standardizing variables
• joint hypothesis (F-tests)

## Major Models & Extensions

• Panel data

• pooled regression & problems
• fixed effects
• Difference-in-differences

• Instrumental variables

## Question 1

What are the two conditions for a variable $Z$ to cause .shout[omitted variable bias] if it is left out of the regression?

## Question 2

$Wages_i=\beta_0+\beta_1 \, Education_i + \beta_2 \, Age_i + \beta_3 \, Experience_i + u_i$

Suppose $Education_i$ and $Age_i$ are highly correlated

• Does this bias $\hat{\beta_1}$ and $\hat{\beta_2}$?
• What will happen to the variance of $\hat{\beta_1}$ and $\hat{\beta_2}$?
• How can we measure this?

## Question 3

$Cholesterol_i=\beta_0+\beta_1 \, Treated_i+u_i$

• $Treated_i$ is a dummy variable $= \begin{cases} 1 & \text{if person received treatment}\\ 0 & \text{if person did not receive treatment}\\ \end{cases}$
• What is $\hat{\beta_0}$?
• What is $\hat{\beta_1}$?
• What is the average cholesterol level for someone who recieved treatment?

## Question 4

$Y_i=\beta_0+\beta_1 \, Red_i+\beta_2 \, Orange_i+\beta_3 \, Yellow_i+\beta_4 \, Green_i+\beta_5 \, Blue_i$

Suppose the color of observation $i$ can be either $\{$Red, Orange, Yellow, Green, Blue, Purple $\}$

• What is $\hat{\beta_0}$?
• What is $\hat{\beta_1}$?
• What is the average value of $Y_i$ for $Green$ observations?
• Why can’t we add $\beta_6 \, Purple_i$?

## Question 5

$\widehat{Utility}_i=\beta_0+\beta_1 \, Eggs_i+\beta_2 \, Breakfast_i+\beta_3 (Eggs_i \times Breakfast_i)$

$Breakfast_i$ is a dummy variable $= \begin{cases} 1 & \text{if meal i is breakfast}\\ 0 & \text{if meal i is not breakfast}\\ \end{cases}$

• What is $\hat{\beta_1}$?
• What is $\hat{\beta_2}$?
• What is $\hat{\beta_3}$?
• We have two regressions (one for Breakfast; one for Not Breakfast)
• how can we determine if the intercepts are different?
• how can we determine if the slopes are different?

## Question 6

$\widehat{Utility}_i=2+4\text{ Ice Cream Cones}_i-1\text{ Ice Cream Cones}_i^2$

• What is the marginal effect of eating 1 more Ice Cream Cone?
• What amount of ice cream cones will maximize utility?
• How would we know if we should add $\text{Ice Cream Cones}_i^3$?

## Question 7

$\ln(GDP_i)=10+2\text{ population (in billions)}_i$

• Interpret $\hat{\beta_1}$ in context.

$\ln(GDP_i)=10+0.1 \, \ln(\text{population}_i)$

• Interpret $\hat{\beta_1}$ in context.

## Question 8

• Explain what an $F$-test is used for.
• Explain how an $F$-statistic is estimated (roughly).

## Question 9

Consider a two-way fixed effects model:

$\text{Divorce Rate}_{it}=\beta_1 \text{Divorce Law}_{it}+\alpha_i+\theta_t+\epsilon_{it}$

for State $i$ at time $t$

• Why do we need $\alpha_i$ and $\theta_t$?
• What sorts of things are in $\alpha_i$?
• What sorts of things are in $\theta_t$?

## Question 10

Suppose Maryland passes a law (and other States do not) that affects crime rates. Consider the following model:

$\text{Crime Rate}_{it}=\beta_0+\beta_1 \, \text{Maryland}_{i}+\beta_2 \, \text{After}_t+\beta_3 \, (\text{Maryland}_i \times \text{After}_t)$

for State $i$ at time $t$

• What must we assume about Maryland over time?
• What is the average crime rate for other states before the law?
• What is the average crime rate for Maryland after the law?
• What is the causal effect of passing the law?

## Question 12

• What are the two conditions required for an instrument to be valid?
• How is this different from the conditions for omitted variable bias?
• How can we test each condition?
• How do we run a two-stage least squares regression?