# Big Assignment 4

### A number of organizations and governments are considering policies to supply students with access to free computers, in an effort to boost learning outcomes. Suppose that you want to learn about the effect of having a free computer on test scores. For a sample of high school students, you collect data on test scores (`test` ), parent’s income (`inc`), and whether they have a computer at home (`comp`).

### Part A:
#### Suppose that a local organization held a lottery, and offered computers at random to a number of students, indicated by freecomp. Suppose that among the population who were not offered a free computer, 60% have a computer, whereas after the lottery, 90% of people offered a computer had a computer. Compare the specifications

\begin{align}
test=\beta_0+\beta_1comp+u
\end{align}

#### or

\begin{align}
test=\beta_0+\beta_1freecomp+u
\end{align}


#### Both tell you something different about the effect of computers on test scores. Describe the limitations of each approach.

Click here to type you answer to part A. 

### Part B: 
#### You are concerned that household income may be correlated with test scores for a variety of reasons. Suggest an alternate specification that holds income constant, and discuss how you anticipate it changing inference using each estimated $\beta_1$ above.

Click here to type you answer to part B. 

### Part C:
#### Propose a “Treatment on the treated” estimator for the free computer lottery.

Click here to type you answer to part C. 

### Part D: 
#### You think computers might have two different effects on test scores. On the one hand, they are a productive tool which can help learning. On the other hand, they open up recreational opportunities (like social networking) which may not be very useful for learning. As a result, you wonder what the effects of a free computer would be if you could hold recreational screentime constant. That is, you would like to estimate
\begin{align}
test=\beta_0+\beta_1freecomp+\beta_2screentime+u
\end{align}

#### However, in practice you cannot observe screentime. You have two options:  

#### - either you can just use whether they have a smart phone as a proxy variable for screentime (variable `Smartphone`), 

#### -or you can ask the students to report how much screentime they spend per day (`repscreentime`).
#### Describe algebraically how each approach will affect estimation of $\beta_1$ and $\beta_2$ in the equation for part D, and the analogue to MLR4 which is necessary to grant unbiased estimates. Discuss different potential forms for any measurement error, and the likely consequences of that measurement error.

Click here to type you answer to part D. 

### Part E:

#### Suppose instead that the organization offered free computers to the students whose parent’s income was in the bottom 20% of the school. Write down a regression equation which will implement a regression-discontinuity estimator to learn the impact of receiving a free computer. Discuss why results from that estimator may be different from the results from the randomized lottery in part A.


Click here to type you answer to part E. 

5022ad95ea6c796c7ac4744bad83fb13de7692bb
ipynb
Jupyter Notebook
Fall-19/ProblemSet4/Assignment_4_new.ipynb
sungsy12345/ENVECON-118
b2b62f49115f37e3a3c1f13b7ac6a3550c4c0600
BSD-3-Clause
2020-09-10T13:45:34.000Z
2021-11-01T21:41:59.000Z
Fall-19/ProblemSet4/Assignment_4_new.ipynb
sungsy12345/ENVECON-118
b2b62f49115f37e3a3c1f13b7ac6a3550c4c0600
BSD-3-Clause
2021-01-22T17:02:59.000Z
2021-06-20T14:03:54.000Z
Fall-19/ProblemSet4/Assignment_4_new.ipynb
sungsy12345/ENVECON-118
b2b62f49115f37e3a3c1f13b7ac6a3550c4c0600
BSD-3-Clause
2019-11-06T20:55:27.000Z
2021-06-20T08:14:41.000Z
Qwen/Qwen-72B
1. YES
2. YES