ECON 306 – Homework 3 The following two problems will require a lot of calculations in STATA (or however you opt to
execute the calculations). It will generate many pages of output. Here is how your should
organize it. The first pages should contain your answers to all the questions, along with
showing any key algebraic equations or explanations you need to use along the way. After
that, include a printout of the output from the regressions you executed in support of your
answers. Highlight any numbers in this output that you used in the first section. (To save paper,
you may print this section double-side and/or with 2-up format.) Last, include a copy of the DO
file that contains the commands you asked STATA to execute. Be sure you organize these in a
way that will be clear to the reader.
1. (52 points total, 4 points each part) With this assignment you will find a STATA data file
called boston.dta. For reference, the variables in this file are:
nox = nitric oxides concentration (parts per 10 million)
rm = average number of rooms per dwelling
age = proportion of owner-occupied units built prior to 1940
dis = weighted distances to five Boston employment centers
ptratio = pupil-teacher ratio by town
lstat = percent lower status of population
medv = median value of owner-occupied homes (in thousands of dollars)
Open this dataset within STATA (only STATA can open it). Before you begin answering
the following, it’s not a bad idea to ask STATA to summarize the data using the command
summarize. You should also start a log file to store your results.
a.) Run the following regression: MEDV 0 1 * RM
b.) Hypothesize the sign of the bias, if any, resulting from excluding age from the
regression. Explain your reasoning. (There is no wrong answer as long as you make
a sensible story.)
c.) Use the data to verify (or not) your claim from b). Break down the bias into its
pieces.
d.) Now, run the regression:
MEDV 0 1 * NOX 2 * RM 3 * AGE 4 * DIS 5 * PTRATIO 6 * LSTAT
e.) At a level of α=.05, for which, if any, values of βi, would you reject the null
hypothesis that βi=0? f.) What is the predicted medv with nox=0.5, rm=4, age=60, dis=3, ptratio=20,
and lstat=10?
g.) Redo (f) but with nox=0.6. What is the difference in predicted medv between these
two communities? Compare this with the coefficient of nox.
h.) Ceteris Peribus, compared to (f), what is the impact of reducing the pupil-teacher
ratio to 18?
i.) What percentage of the variation in medv is explained by the six X-variables?
Now change the measurement of nox. Use the ‘gen’ command:
gen noxppm=nox/10
and then use this in place of nox in the regression command
regress medv noxppm rm age dis ptratio lstat
j.) Compare the coefficient, standard error, and t-ratio for noxppm to that of nox.
Interpret the difference between this model and the previous.
k.) Also compare the and remaining coefficients. Interpret the difference between this model and the original regression model.
Now change the variable age to newage
gen newage=100-age
and then use this in place of age in the original regression command. That is,
execute:
regress medv nox rm newage dis ptratio lstat
l.) Compare the coefficient, standard error, and t-ratio for newage to that of age.
Interpret the difference between this model and the previous.
m.) Also compare the and remaining coefficients. Interpret the difference between this model and the original regression model. 2. (48 points total. 5 points each part, +3 for free.) For the following problem, use the
STATA dataset called crime.dta. This data set was compiled by Christopher Cornwell
and William Trumbull to study factors that influence crime rates. The data set contains
observations for 90 counties in North Carolina for 1981. The definitions of the variables
represented in the data set are:
crmrte=crime rate
prbarr=probability of arrest
prbconv=probability of conviction
prbpris=probability of a prison sentence
avgsen=average sentence in days
polpc=number of police per capita
density=population density
pctmin=percent minority
pctymle=percent young males
wmfg=average weekly wage in manufacturing
wcon=average weekly wage in construction
wtuc=average weekly wage in transportation,utilities,and communications
wtrd=average weekly wage in wholesale and retail trade
wfir=average weekly wage in finance,insurance,and real estate
wser=average weekly wage in services
wfed=average weekly wage in federal government
wsta=average weekly wage in state government
wloc=average weekly wage in local government
According to the economic model of crime rates, lower crime rates are associated with
better labor markets (higher wages), more police presence and tougher sentences, and
lower population density. We will use this data set to examine these hypotheses. Use a
significance level of α=.05 for all hypothesis tests.
a.)
b.)
c.)
d.) Run a regression of crmrte on all of the other variables. Call this Model 1.
Do any t-statistics indicate a variable is not statistically significant? Which?
Interpret the F-statistic STATA has calculated for Model 1.
Test the hypothesis that the coefficients on wfed and wsta are equal to each other.
Use the t-test method described in the lectures. What transformation do you need to
do here? Be specific.
e.) Test the hypothesis that the coefficients on wfed, wsta and wloc are all equal to
each other. Do this by writing down the formula for the relevant F-statistic.
Calculate it (by running the appropriate restricted regression) and test the hypothesis.
Report these results. This restricted version of the regression will be called Model 2. f.) Return to Model 1. Now test the hypothesis that pctmin and pctymle both equal
zero. Do this by writing down the formula for the relevant F-statistic. Calculate it
(by running the appropriate restricted regression) and test the hypothesis. Report
these results. This restricted version of the regression will be called Model 3.
The model could potentially be simplified by replacing all the wage variables with an
average. Specifically, let us define
wmfg wcon wtuc wtrd wfir wser wfed wsta wloc
9
Generate this variable.
avgwage g.) Return to Model 1 and run using avgwage in place of the individual wage variables.
Check the validity of this restriction. As before, do this by writing down the formula
for the relevant F-statistic. Calculate it (by running the appropriate restricted
regression) and test the hypothesis. Report these results. This restricted version of the
regression will be called Model 4.
h.) Let’s focus our attention on the coefficient for the variable polpc. How does the
value of this coefficient change – as well as its statistical significance –as we move
from model to model? To answer this, write down a table containing the results for
this coefficient for each of the four models. In this table, include the coefficient
values, the values of the t-statistic (for a hypothesis that the coefficient=0,) and
whether you’d reject the hypothesis.
i.) What do your results in the last question imply about the relationship between the
number of police and the crime rate. Are you confident in these results based on the
work you have done? Why or why not?

Read the attached short article from The Economist magazine. Address the following questions.

11. What is the Kyoto Protocol? When does it become outdated? What is the current state of international negotiations on climate change?

12. What are the main reasons why countries hesitate to commit to multilateral environmental agreements?

13. What are possible ways to overcome the impasse in reducing greenhouse gas emissions?

14. Explain/discuss your personal opinion about what is a feasible and efficient measure to reduce the carbon footprint. (Note: you can use external references to support your answer)

http://www.economist.com/node/21528247

On January 1, 2016, Gless Textiles issued $27 million of 8%, 10-year convertible bonds at 101. The bonds pay interest on June 30 and December 31. Each $1,000 bond is convertible into 40 shares of Gless’s no par common stock. Bonds that are similar in all respects, except that they are nonconvertible, currently are selling at 99 (that is, 99% of face amount). Century Services purchased 15% of the issue as an investment

Three players live in a town, and each can choose to contribute to fund a streetlamp. The value of having the streetlamp is 3 for each player, and the value of not having it is 0. The mayor asks each player to contribute either 1 or nothing. If at least two players contribute then the lamp will be erected. If one player or no players contribute then the lamp will not be erected, in which case any person who contributed will not get his money back.

a. Write out or graph each player’s best-response correspondence.

b. What outcomes can be supported as pure-strategy Nash equilibria?

Countries X and Y differ in population growth rates and rates of investment.

Country X: investment is 10% of GDP, population grows at 1% per year

Country Y: investment is 25% of GDP, population grows at 3% per year.

Both countries have the same rate of depreciation (5%).  Use the Solow model to calculate the ratio oftheir steady state levels of income per capita, assuming α =1/2. Interpret your answer.

2.   In Country 1 the rate of investment is 2%, and in Country 2 it is 12%. The two countries have thesame rate of depreciation, and there is no growth in its labor force. Assuming that the value of is 1/3,what is the ratio of steady-state output per worker in Country 1 to steady-state output per worker inCountry 2? What would the ratio be if the value of were 2/3?  Explain the change in your answer. 3.

Average Annual Growth Rates of Population by Country Group

1950-2000 2000-2050

More Developed 0.8%

0.0%

Less Developed 2.1%

0.8%

Least Developed 2.4%

2.1%

Using the data from the above table (Weil, 3rd edition, Table 5.2, page 136) where the only change is in

the growth rate of population between the two time periods.  Assume that rate of depreciation =5% and α

=1/2.   Use the Solow model to calculate how much the change in population growth between the period1950-2000 and 2000-2050 would affect the steady state level of output per worker fora) the most developed countries compared to the least developed countries. Verbally, interpret your

answers.b) Suppose that in the least developed group of countries, between the two above time periods, thesavings rate increases from 1% to 2% how would your answer for the least developed countrieschange.  Graphically illustrate your answer being careful to label your graph.

4.     Consider the Solow model with population growth, as presented in class and in the Weil text.  Thereare two countries 1 and 2 are the same in every respect except that population grows at n1 in country 1and n2 in country 2 and  n1 > n2.  Assume that the population growth rate depends on the level ofoutput per capita (and therefore the level of capital per capita) and is given by

ℎ  = {

1,  < ∗2,  ≥ ∗

(k* represents some hypothetical level of capital per worker and not the steady state).Draw a diagram for this model.  Assume that at (n1 + δ)k*> sy and that  (n2 + δ)k*< sy.  Explain what thediagram says about the steady states of the model.

[HINT: the phenomenon described in this question is similar to the situation of what happens to the steadystate when we assume that savings rate depends on income – endogenous savings rate on page 71-74 andFigure 3.9 in Weil. In this question, instead of savings, population growth depends on income andtherefore capital per worker.]

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1
List the determinants of aggregate demand in the textbox below. (Check lesson 3.03 for help.)
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2
List the determinants of short-run aggregate supply in the textbox below. (Check lesson 3.02 for help.)
.
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3 For the question below, write an explanation of the short-run effect (including the determinant of AD or AS
. that is causing the shift, the line that shifts (AD or AS), the direction of the shift (left or right), and the
impact on output and price level (increase or decrease) and submit a properly drawn and labeled
aggregate demand and aggregate supply graph for the scenario. Make sure your name and assignment
number are written on each page of graphs you submit. All text must be written in the text box provided.
An economic crisis increases the degree of excess capacity in a nation.
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4 For the question below, write an explanation of the short-run effect (including the determinant of AD or AS
. that is causing the shift, the line that shifts (AD or AS), the direction of the shift (left or right), and the
impact on output and price level (increase or decrease) and submit a properly drawn and labeled
aggregate demand and aggregate supply graph for the scenario. Make sure your name and assignment
number are written on each page of graphs you submit. All text must be written in the text box provided.
Congress passes a sweeping health care reform bill that provides free medical insurance for all Americans.
Once the President signs it into law, the government will provide every American with a policy that will pay
up to 80% of every medical bill a patient incurs. This change does not impact consumer income.
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5. P1Y1 in this economy reflects that there is
an inflationary gap with high employment.
an inflationary gap with low employment.
a recessionary gap with high employment. a recessionary gap with low employment.
long-run equilibrium in this economy.
6. At P1Y1, if taxes decrease then consumer spending will
decrease and AD will shift right to long-run equilibrium.
decrease and AD will shift left to long-run equilibrium.
increase and AD will shift right to long-run equilibrium.
increase and AD will shift left to long-run equilibrium.
cannot be determine with information given.
7. If workers are more educated, then short-run aggregate supply will
increase and output and price level will increase as well.
decrease and output and price level will decrease as well.
increase and output will increase but price level will decrease.
increase and output will decrease but price level will increase.
decrease and output will decrease but price level will increase.
8. If Congress increases personal and business taxes to decrease the national debt, then
output and price level will increase.
output will increase and price level will be indeterminate.1
List the determinants of aggregate demand in the textbox below. (Check lesson 3.03 for help.)
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2
List the determinants of short-run aggregate supply in the textbox below. (Check lesson 3.02 for help.)
.
Fon
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3 For the question below, write an explanation of the short-run effect (including the determinant of AD or AS
. that is causing the shift, the line that shifts (AD or AS), the direction of the shift (left or right), and the
impact on output and price level (increase or decrease) and submit a properly drawn and labeled
aggregate demand and aggregate supply graph for the scenario. Make sure your name and assignment
number are written on each page of graphs you submit. All text must be written in the text box provided.
An economic crisis increases the degree of excess capacity in a nation.
Fon
Font
t
Famil
Siz
y
e
4 For the question below, write an explanation of the short-run effect (including the determinant of AD or AS
. that is causing the shift, the line that shifts (AD or AS), the direction of the shift (left or right), and the
impact on output and price level (increase or decrease) and submit a properly drawn and labeled
aggregate demand and aggregate supply graph for the scenario. Make sure your name and assignment
number are written on each page of graphs you submit. All text must be written in the text box provided.
Congress passes a sweeping health care reform bill that provides free medical insurance for all Americans.
Once the President signs it into law, the government will provide every American with a policy that will pay
up to 80% of every medical bill a patient incurs. This change does not impact consumer income.
Fon
Font
t
Famil
Siz
y
e
5. P1Y1 in this economy reflects that there is
an inflationary gap with high employment.
an inflationary gap with low employment.
a recessionary gap with high employment. a recessionary gap with low employment.
long-run equilibrium in this economy.
6. At P1Y1, if taxes decrease then consumer spending will
decrease and AD will shift right to long-run equilibrium.
decrease and AD will shift left to long-run equilibrium.
increase and AD will shift right to long-run equilibrium.
increase and AD will shift left to long-run equilibrium.
cannot be determine with information given.
7. If workers are more educated, then short-run aggregate supply will
increase and output and price level will increase as well.
decrease and output and price level will decrease as well.
increase and output will increase but price level will decrease.
increase and output will decrease but price level will increase.
decrease and output will decrease but price level will increase.
8. If Congress increases personal and business taxes to decrease the national debt, then
output and price level will increase.
output will increase and price level will be indeterminate.help.)
.
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2
List the determinants of short-run aggregate supply in the textbox below. (Check lesson 3.02 for help.)
.
Fon
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Famil
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3 For the question below, write an explanation of the short-run effect (including the determinant of AD or AS
. that is causing the shift, the line that shifts (AD or AS), the direction of the shift (left or right), and the
impact on output and price level (increase or decrease) and submit a properly drawn and labeled
aggregate demand and aggregate supply graph for the scenario. Make sure your name and assignment
number are written on each page of graphs you submit. All text must be written in the text box provided.
An economic crisis increases the degree of excess capacity in a nation.
Fon
Font
t
Famil
Siz
y
e
4 For the question below, write an explanation of the short-run effect (including the determinant of AD or AS
. that is causing the shift, the line that shifts (AD or AS), the direction of the shift (left or right), and the
impact on output and price level (increase or decrease) and submit a properly drawn and labeled
aggregate demand and aggregate supply graph for the scenario. Make sure your name and assignment
number are written on each page of graphs you submit. All text must be written in the text box provided.
Congress passes a sweeping health care reform bill that provides free medical insurance for all Americans.
Once the President signs it into law, the government will provide every American with a policy that will pay
up to 80% of every medical bill a patient incurs. This change does not impact consumer income.
Fon
Font
t
Famil
Siz
y
e
5. P1Y1 in this economy reflects that there is
an inflationary gap with high employment.
an inflationary gap with low employment.
a recessionary gap with high employment. a recessionary gap with low employment.
long-run equilibrium in this economy.
6. At P1Y1, if taxes decrease then consumer spending will
decrease and AD will shift right to long-run equilibrium.
decrease and AD will shift left to long-run equilibrium.
increase and AD will shift right to long-run equilibrium.
increase and AD will shift left to long-run equilibrium.
cannot be determine with information given.
7. If workers are more educated, then short-run aggregate supply will
increase and output and price level will increase as well.
decrease and output and price level will decrease as well.
increase and output will increase but price level will decrease.
increase and output will decrease but price level will increase.
decrease and output will decrease but price level will increase.
8. If Congress increases personal and business taxes to decrease the national debt, then
output and price level will increase.
output will increase and price level will be indeterminate.

Applied Econometrics Exam 1 (100 points) 1. [70 points] You wish to predict the sale price of single-family residences in Massachusetts using
property features (commonly called a “hedonic pricing model”). You collect price and property features
data on properties sold in the state for the year 2010 and obtain the following regression:
Pricei = 14407.60 – 759.92*houseagei + .24*lotsizei + 354.35*bldareai + 12015.61*roomsi + µi
(6433.23) (89.67)
(.115)
(265.39)
(8516.47)
Observations = 2691 R2 = 0.49 F = 65.10 Where:
houseage = age of the house (in years)
lotsize = total square feet of the land
bldarea = total square feet of the interior of the house
rooms = total number of rooms in the house
A. [6 points] How would you categorize, or label, this dataset? Defend your answer.
B. [6 points] What is the interpretation of the constant term in this regression? Why is it included?
C. [8 points] How do we interpret the coefficient on lotsize? Why is the coefficient on lotsize
nominally small if we expect it to have a large impact on the price of a house?
D. [6 points] What is the predicted price of a house that is 7 years old, with a lot size of 800 square
feet, a building interior of 400 square feet, and 5 rooms? Will this predicted price be close to the
actual price? Why or why not?
E. [6 points] Explain what is meant that the value of the R 2 = .49. What is one good reason and one
bad reason to use R2 as a measure of the “goodness of fit” of a regression?
F. [10 points] Test the significance of each independent variable in the model using α = .05. Are
these findings expected? Why or why not, and what could explain your findings? G. [8 points] Construct a 95% confidence interval for houseage in the model above. What this
measure is telling us? How will consistency in your OLS estimation affect your confidence
intervals?
H. [10 points] After thinking about your model further, you wish to add median income as variable
in your regression. You collect data on the median income of each census tract in Massachusetts
in the year 2010, and match that to your housing data. Assuming you believe that your original
form of the model suffered from omitted variable bias, in what direction would you expect your
estimates to change with the inclusion of median income? Defend your answers. I. [10 points] Suppose you ran the same model as above only using log(price) instead of price and
obtain an R2 of 0.54 and an F-statistic of 68.17. Based on this information, are we able to say
which version (level or log) of the model is better? Explain why or why not. 2. [10 points] The following questions are based on airline data collected from routes in the U.S. for the
year 2000. You are interested in examining the determinants of ticket prices. 0 avg. one-way fare, $
200
400 600 You decide to generate a scatter diagram to visually assess if the average one-way fare for a route is
related to the distance of that route. 0 1000 2000 3000 distance, in miles Based on this scatter diagram, would OLS be BLUE if we ran a regression of the average one-way fare for
a route on the distance of that route? Explain why or why not and if this would affect any estimated
coefficients. 3. [20 points] Suppose that 5 years ago, a new job training program was introduced in Massachusetts
that accepted 1000 applicants. For $200, participants would undergo a 6-week training program that
would teach them about basic computer skills, resume building, interviewing, and job searching. Now, 5
years later, you wish to survey some of these participants to see if the training has helped them.
You create a simple survey asking participants how much they though the job training helped them in
their professional life on a scale of 1 to 5 (with 5 being most helpful and 1 being least helpful), how much
they currently earn per month, and how many jobs they are currently working.
You mail out 100 surveys to known participants, and after waiting several weeks you receive 32
responses. You wish to use the income and number of job responses to predict how favorably a participant viewed the training (using the 1 through 5 scale above). If you estimate your model using
OLS, do you believe that any of our Classical Linear Model assumptions would be violated? If so, explain
which ones, why they are violated, and what potential problems that could pose for your estimation.