class: center, middle, inverse, title-slide

# Final Review Questions
## ECON 480 • Econometrics • Fall 2020
### Ryan Safner<br> Assistant Professor of Economics <br> <a href="mailto:safner@hood.edu"><i class="fa fa-paper-plane fa-fw"></i>safner@hood.edu</a> <br> <a href="https://github.com/ryansafner/metricsF20"><i class="fa fa-github fa-fw"></i>ryansafner/metricsF20</a><br> <a href="https://metricsF20.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i>metricsF20.classes.ryansafner.com</a><br>

---

# Major Models and Extensions

- Causality
  - Fundamental problem of causal inference
  - DAGs, controlling

--

- Multivariate OLS
  - Omitted Variable Bias
  - Variance/Multicollinearity

--

- Categorical data
  - Using categorical variables as dummies
  - dummy variable trap
  - interaction effects

---

# Major Models and Extensions

- Nonlinear Models
  - quadratic model, polynomial models, logarithmic models

--

- Panel Data
  - pooled model
  - fixed effects
  - difference-in-difference models

---

# 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

`$$\widehat{Wages}_i=\beta_0+\beta_1 \, Education_i + \beta_2 \, Age_i + \beta_3 \, Experience_i + \epsilon_i$$`

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 `\(\hat{\beta_2}\)` and `\(\hat{\beta_2}\)`? How can we measure this?

---

# Question 3

`$$\widehat{Cholesterol_i}=\beta_0+\beta_1 \, Treated_i+u_i$$`

- `\(Treated_i\)` 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

`$$\widehat{Y}_i=\beta_0+\beta_1 \, Red_i+\beta_2 \, Orange_i+\beta_3 \, Yellow_i+\beta_4 \, Green_i+\beta_5 \, Blue_i$$`

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 `\(\beta_6 \, Purple_i\)`?

---

# 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

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

--

- 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 `\(\text{Ice Cream Cones}_i^3\)`?

---

# 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 generated

---

# Question 9

`$$\widehat{\text{Divorce Rate}_{it}}=\beta_0+\beta_1 \text{Divorce Law}_{it}+\alpha_i+\theta_t+\epsilon_{it}$$`

--

- 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

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

- Suppose Maryland passes a law (and other States do not) that affects crime rates

--

- 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?

Notes for current slide

Notes for next slide

Final Review Questions

ECON 480 • Econometrics • Fall 2020

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/metricsF20
metricsF20.classes.ryansafner.com

Major Models and ExtensionsCausalityFundamental problem of causal inference
DAGs, controlling

Major Models and Extensions

Causality
- Fundamental problem of causal inference
- DAGs, controlling
Multivariate OLS
- Omitted Variable Bias
- Variance/Multicollinearity

Major Models and Extensions

Causality
- Fundamental problem of causal inference
- DAGs, controlling
Multivariate OLS
- Omitted Variable Bias
- Variance/Multicollinearity
Categorical data
- Using categorical variables as dummies
- dummy variable trap
- interaction effects

Major Models and ExtensionsNonlinear Modelsquadratic model, polynomial models, logarithmic models

   

Major Models and Extensions

Nonlinear Models
- quadratic model, polynomial models, logarithmic models
Panel Data
- pooled model
- fixed effects
- difference-in-difference models

Question 1

What are the two conditions for a variable to cause omitted variable bias if it is left out of the regression?

Question 2

Suppose and are highly correlated

Question 2

Suppose and are highly correlated

Does this bias and ?

Question 2

Suppose and are highly correlated

Does this bias and ?
What will happen to the variance of and ? How can we measure this?

Question 3

is a dummy variable

Question 3

is a dummy variable
What is ?

Question 3

is a dummy variable
What is ?
What is ?

Question 3

is a dummy variable
What is ?
What is ?
What is the average cholesterol level for someone who recieved treatment?

Question 4

Suppose observation can be either Red, Orange, Yellow, Green, Blue, Purple

Question 4

Suppose observation can be either Red, Orange, Yellow, Green, Blue, Purple

What is ?

Question 4

Suppose observation can be either Red, Orange, Yellow, Green, Blue, Purple

What is ?
What is ?

Question 4

Suppose observation can be either Red, Orange, Yellow, Green, Blue, Purple

What is ?
What is ?
What is the average value of for shapes?

Question 4

Suppose observation can be either Red, Orange, Yellow, Green, Blue, Purple

What is ?
What is ?
What is the average value of for shapes?
Why can't we add ?

Question 5

is a dummy variable

Question 5

is a dummy variable

What is ?

Question 5

is a dummy variable

What is ?
What is ?

Question 5

is a dummy variable

What is ?
What is ?
What is ?

Question 5

is a dummy variable

What is ?
What is ?
What is ?
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

Question 6

What is the marginal effect of eating 1 more Ice Cream Cone?

Question 6

What is the marginal effect of eating 1 more Ice Cream Cone?
What if we start with 1 Ice Cream Cone?

Question 6

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?

Question 6

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?

Question 6

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 ?

Question 7

Interpret in context.

Question 7

Interpret in context.

Interpret in context.

Question 8Explain what an F-test is used for
   

Question 8

Explain what an -test is used for
Explain how an -statistic is generated

Question 9

Question 9

Why do we need and ?

Question 9

Why do we need and ?
What sorts of things are in ?

Question 9

Why do we need and ?
What sorts of things are in ?
What sorts of things are in ?

Question 10

Suppose Maryland passes a law (and other States do not) that affects crime rates

Question 10

Suppose Maryland passes a law (and other States do not) that affects crime rates
What must we assume about Maryland over time?

Question 10

Suppose Maryland passes a law (and other States do not) that affects crime rates
What must we assume about Maryland over time?
What is the average crime rate for other states before the law?

Question 10

Suppose Maryland passes a law (and other States do not) that affects crime rates
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?

Question 10

Suppose Maryland passes a law (and other States do not) that affects crime rates
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?

Major Models and ExtensionsCausalityFundamental problem of causal inference
DAGs, controlling

Paused

Help

Keyboard shortcuts

↑, ←, Pg Up, k	Go to previous slide
↓, →, Pg Dn, Space, j	Go to next slide
Home	Go to first slide
End	Go to last slide
Number + Return	Go to specific slide
b / m / f	Toggle blackout / mirrored / fullscreen mode
c	Clone slideshow
p	Toggle presenter mode
t	Restart the presentation timer
?, h	Toggle this help

Esc	Back to slideshow