Final Review Questions

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# Final Review Questions
## ECON 480 • Econometrics • Fall 2021
### Ryan Safner Assistant Professor of Economics <a href="mailto:safner@hood.edu">safner@hood.edu</a> <a href="https://github.com/ryansafner/metricsF21">ryansafner/metricsF21</a> <a href="https://metricsF21.classes.ryansafner.com"> metricsF21.classes.ryansafner.com</a>

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# Major Models and Extensions

.smallest[
- Causality
  - Fundamental problem of causal inference, potential outcomes
  - DAGs, controlling
]

.smallest[

- Multivariate OLS
  - Omitted Variable Bias
  - Variance/Multicollinearity
]

.smallest[
- Categorical data
  - Using categorical variables as dummies
  - dummy variable trap
  - interaction effects
]

---

# Major Models and Extensions

.smallest[
- Nonlinear Models
  - quadratic model & polynomial models
  - logarithmic models
]

.smallest[
- Panel Data
  - pooled model
  - fixed effects
  - difference-in-difference models
]

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# 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?

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# 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 .hi-purple[bias] `$\hat{\beta_1}$` and `$\hat{\beta_2}$`?

- What will happen to the .hi-purple[variance] of `$\hat{\beta_1}$` and `$\hat{\beta_2}$`?
  - How can we measure this?

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# 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?

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# 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 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 `$Green$` shapes?

- Why can't we add `$\beta_6 \, Purple_i$`?

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# 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?

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# 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 if we *start* with 1 Ice Cream Cone?

- What if we *start* with 4 Ice Cream Cones?
--

- What amount of ice cream cones will *maximize* utility?

- How would we know if we should add `$\text{Ice Cream Cones}_i^3$`?

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# 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.

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# Question 8

- Explain *what* an `$F$`-test is used for;

- Explain *how* an `$F$`-statistic is estimated (roughly).

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# 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 `$\theta_t$`?

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# 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?