ECON 351 Assignment 2 - Queen's University · ECON 351 Assignment 2 Instructor: ... The results of our analysis will not be used for commer- ... 2hs degree2 + u (3) i.

ECON 351 Assignment 2

Instructor: Maggie JonesQueen’s University, Department of Economics

Due: October 14th, 2016

Note: Students may work in groups of up to three. Please make sure you clearly list eachmember of your group on the front page of the assignment. You are strongly encouraged towork out all the problems on your own before meeting with your group. 5 points (out of 100) willbe allocated to the presentation of your assignment, i.e., if you pass in something that is illegibleor difficult for the TAs to read for any other reason then you will lose 5 points. Also, pleasemake sure your assignment has a cover page. You can download the standard assignment coverpage from the economics website. Attach your computer do-file(s) at the end of the assignment,but do not print out your log file.

1. [50 pts] Suppose you are an advisor for one of the local high schools in Kingston that isconsidering implementing a school lunch program to boost student performance. Fortu-nately, there is already a federal program in the U.S. that provides free lunch to low incomestudents. Several high schools in Michigan have participated in the program and have col-lected data on their students’ outcomes, and the percent of students who participate inthe free lunch program, which is available for you to analyze.

(a) [15 pts] The first specification you consider is to simply regress the percentage oftenth graders who pass their standardized math exam on the percentage of studentswho are eligible for the lunch program:

math = β0 + β1lunch program + u (1)

i. Derive the OLS estimators β̂0 and β̂1 by hand

ii. If we assume that E(u|x) = 0 (i.e. SLR. 4), is the slope estimator β̂1 unbiased?

iii. Before estimating the regression in stata, what sign do you expect on β̂1 (i.e. doyou expect it to be positive or negative) and why?

(b) [20 pts] Download the student data set MEAP93.dta and estimate equation 1 usingthe regress command

i. Report and interpret the coefficient estimates, β̂0 and β̂1ii. Are these coefficient estimates what you expected?

iii. If the sign of the coefficient estimate differs from what you expected, what is thelikely reason? Hint: you can refer to the assumption made in part (ii) of (a).

iv. What quantity in your output tells you the portion of the variance in math scoresthat is explained by the varation in participation in the lunch program (i.e. whatis the name of this quantity)?

v. What is the value of the quantity you described in part (b) iv)?

vi. If the quantity you found in part (b) v) is small, why do you think this is thecase?

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vii. Calculate the standard error of the regression, σ̂

viii. Does stata report this value under a different name from “the standard error ofthe regression”?

ix. How does the standard error of the regression relate to the standard error esti-mates for β̂0 and β̂1?

(c) [15 pts] Examine the remainder of the control variables in the data set

i. What are some additional control variables that you think make sense to add tothe regression and why?

ii. Add them to the regression and estimate it; report the coefficient on “lunch”,β̂1.

iii. Is the coefficient on lunch different from part (b)? If so, why do you think thisis the case?

iv. Is the coefficient on lunch what you expect it to be, i.e. is it the same sign asyou expected from part (a)? If not, why?

2. [45 pts] Visit the website https://usa.ipums.org/usa/ and go to the IPUMS Registration

tab on the left side to register for access to the data. This should bring you to a pagewhere you have to click Apply for Access to reach the application page. When you arefilling out the application you may enter a version of the following statement into theResearch Statement text box:

“For my introductory econometrics course we are learning about the effect of educationand immigration on wages and we want to use the IPUMS USA data to examine thesequestions. We will be using this data for the next 3 months and will be adding to ouranalysis throughout the course. The results of our analysis will not be used for commer-cial purposes and will be used solely for the purpose of learning about the econometrictechniques and tools required to learn about the effects of immigration and education onwages.”

Once you have been granted access to the data (this may take up to a day), log in toyour account and go to the select data option at the top of the page, and then clickselect samples. Choose the 1% sample of the 2000 census and then proceed to selectthe following variables:

• statefip

• countyfips

• sex

• age

• marst

• race

• bpl

• language

• school

• educ

• empstat

• labforce

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• occ

• wkswork1

• uhrswork

• looking

• inctot

• incwage

• migrate5

We won’t use all these variables for assignment 2, but we will be using this dataset through-out the course, so some of the variables may seem irrelevant at first.

When you’re finished selecting all the variables above, you can click the View Cart buttonwhich will bring you to a page with a green Create data extract button. Click it andthen make sure you select the data in stata format. The page will look like this atfirst:

Click the Change button under “data format”, which will bring you to a screen like this:

Choose the stata format. You are now ready to click on the submit extract button:

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Note that your request will not be available immediately, so I suggest you submit your datarequest before attempting any other parts of the assignment. I will not accept assignmentsthat are late because you submitted your data request the day the assignment was due.

(a) [5 pts] Once you have the data, open the do file assignment2.do and change my filepaths to your own. Also note that I have called my data file us_2000_census_1p_sample.dta,so you will either need to change your data file to this name or change the file pathto reflect what your dataset is called.

i. Write a brief description of the purpose of this do-file at the top of the file usingthe \* *\ notation

ii. Add smaller commentary using \\ or * to quickly remind yourself of eachfunction being used

iii. Run the do-file to create the smaller data file that we will use for this exercise

(b) [10 pts] Start a new do-file that loads the new dataset you created in part (a),us_census_clean.dta. Be sure to include the preliminary commands that we dis-cussed in the tutorial and that can be found in tutorial2.do. As you work throughthe remainder of this exercise, continue to add your commands to your do-file so thatat the end of the question you have a do-file that you can run that will create all theresults you need to answer this question.

i. Create a scatter plot with average income from wages on the y-axis and thepercent of the county with a high school degree on the x-axis

ii. Based on your scatter plot, do you think assumption SLR. 5 holds in this data?i.e., do you think Var(u|x) = σ2 for each value of x?

(c) [12.5 pts] Suppose you think the relationship between the average income fromwages and the high school graduation rate were linear:

incwage = β0 + β1hs degree + u (2)

i. Estimate equation 2 using OLS and report your estimates, β̂0, β̂1, and the R2

ii. What is the effect of increasing high school graduation rates by 5 percentagepoints on wages?

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iii. After using the regress command to estimate equation 2, use the commandpredict yhat, xb to create a new variable called “yhat”, the fitted values ofthe regression.

iv. Recreate the scatter plot and include a line with the fitted values:

twoway (scatter incwage hs_degree, sort) (line yhat hs_degree, sort)

(d) [12.5 pts] Now, suppose you think the functional form should be:

incwage = β0 + β1hs degree + β2hs degree2 + u (3)

i. Create a new variable that is the square of hs_degree

ii. Estimate equation 3 using OLS and report your estimates, β̂0, β̂1, β̂2, and theR2

iii. What is the effect of increasing high school graduation rates by 5 percentagepoints on wages?

iv. After using the regress command to estimate equation 2, use the commandpredict yhat2, xb to create a new variable called “yhat2”, the fitted values ofthe new regression.

v. Recreate the scatter plot and include a line with the fitted values:

twoway (scatter incwage hs_degree, sort) (line yhat2 hs_degree, sort)

(e) [5 pts] Do you think equation 2 or equation 3 is a better specification? Why?

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