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# Final Review Questions
## ECON 480 · Econometrics · Fall 2019
### 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/metricsf19"><i class="fa fa-github fa-fw"></i> ryansafner/metricsf19</a><br> <a href="https://metricsF19.classes.ryansafner.com"> <i class="fa fa-globe fa-fw"></i> metricsF19.classes.ryansafner.com</a><br>

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# Major Models and Extensions

- Multivariate OLS
    - Omitted Variable Bias
    - Variance/Multicollinearity
    - Causal inference/DAGs, controls, proxies
- Categorical data
    - Using categorical variables as dummies
    - dummy variable trap
    - linear probability model `\((Y\)` is a dummy)
    - interaction terms `\(X_1 \times X_2\)`
- Nonlinear Models
    - quadratic model, polynomial models, logarithmic models
- Panel Data
    - fixed effects (two-way group effects and time 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?

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# Question 2

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

`\(Education_i\)` and `\(Age_i\)` are highly correlated

--

- Does this bias `\(\hat{\beta_1}\)` and `\(\hat{\beta_2}\)`?

--

- What will happen to the variance of `\(\hat{\beta_2}\)` and `\(\hat{\beta_2}\)`? How can we measure this?

---

# Question 3

`$$\widehat{Cholesterol}=\beta_0+\beta_1Treated+u_i$$`

- `\(Treated_i\)` is a dummy variable `\(=1\)` if person received treatment, `\(=0\)` if did not

--
- 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

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

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

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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 `\(=1\)` if meal is breakfast, `\(=0\)` if not

--

- 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?

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Final Review Questions

ECON 480 · Econometrics · Fall 2019

Ryan Safner
Assistant Professor of Economics
safner@hood.edu
ryansafner/metricsf19
metricsF19.classes.ryansafner.com

Major Models and ExtensionsMultivariate OLSOmitted Variable Bias
Variance/Multicollinearity
Causal inference/DAGs, controls, proxies

Categorical dataUsing categorical variables as dummies
dummy variable trap
linear probability model (Y is a dummy)
interaction terms X1×X2

Nonlinear Modelsquadratic model, polynomial models, logarithmic models

Panel Datafixed effects (two-way group effects and time 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

and are highly correlated

Question 2

and are highly correlated

Does this bias and ?

Question 2

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 if person received treatment, if did not

Question 3

is a dummy variable if person received treatment, if did not
What is ?

Question 3

is a dummy variable if person received treatment, if did not
What is ?
What is ?

Question 3

is a dummy variable if person received treatment, if did not
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 if meal is breakfast, if not

Question 5

is a dummy variable if meal is breakfast, if not

What is ?

Question 5

is a dummy variable if meal is breakfast, if not

What is ?
What is ?

Question 5

is a dummy variable if meal is breakfast, if not

What is ?
What is ?
What is ?

Question 5

is a dummy variable if meal is breakfast, if not

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 ExtensionsMultivariate OLSOmitted Variable Bias
Variance/Multicollinearity
Causal inference/DAGs, controls, proxies

Categorical dataUsing categorical variables as dummies
dummy variable trap
linear probability model (Y is a dummy)
interaction terms X1×X2

Nonlinear Modelsquadratic model, polynomial models, logarithmic models

Panel Datafixed effects (two-way group effects and time effects)
difference-in-difference models

   

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