ECO 375–Homework 2 University of Toronto Due: 17 November, 2019 Late assignments will not be accepted For full credit, please show your work 1 Theoretical Problems 1. True or false: First indicate whether the following statements are true or false and then justify your answer. (a) In the simple linear regression model if the R2 is equal to one, then the linear relationship between the variables is exact and residuals are all zero. (b) In the simple linear regression model, if Var(Y ) = Var(X) then the estimated slope in a regression model of Y on X is approximately equal to the estimated slope in a regression model of X on Y . (c) The fact that R2 is equal to zero indicates that variables are unrelated. (d) A crucial assumption of the linear model is that the sum of the residuals is zero. (e) The fact that residuals in the linear model estimated by least-squares have zero mean is a consequence of assuming that the expected value of the error term is zero. (f) The assumption that the error term is normally distributed is necessary to demonstrate that the least-squares estimator is unbiased. 2. Take Y = log (W ). Assume the log-linear model Y = β0 + β1X + U , with E (U) = 0. Prove the following: (a) Show that if E (U |X) = 0, then Cov (X,U) = 0. (b) Assume Cov (X,U) = 0. Show that β1 = Cov (X,Y ) /V ar (X). (c) Suppose β̂1 is the OLS estimator of β1. Show that β̂1 p→ β1 + Cov(X,U)V ar(X) . (d) Assume Cov (X,U) = 0. What is the estimated approximate percentage change in W for a change in X, say from X = x0 to X = x1? And what is the estimated exact percentage change in W? (e) Assume Cov (X,U) = 0. Show that exβ̂ − 1 is a biased estimator for exβ − 1. Show that exβ̂ − 1 is a consistent estimator for exβ − 1. 1 2 Computer Based Problems 1. Determinants of Income. Use the dataset “ANES2016.dta” for this question. The data are drawn from the American National Election Survey of 2016 (available at https://electionstudies.org/data-center/2016-time-series-study/). The dataset includes log of income (loginc), gender indicator (female), indicators for black and hispanic (black, hispanic), age, five education dummy variables, numbered educ0 through educ4 (from “high school dropout” to “graduate or professional school”), among others. (Note the data labels on the variables.) (a) Take educ0, “high school dropout,” to be the base level of education and estimate the following model using OLS: loginci = β0 + β1femalei + β2blacki + β3agei + β4age 2 i + β5educ1i+ β6educ2i + β7educ3i + β8educ4i + εi Assume all assumptions of the classical linear regression model hold. How should the coefficient on educ1 be interpreted? What about educ4? (b) Run the regression again, but now take educ1, not educ0, to be the base case. First, write down this regression equation, estimate the model parameters, and interpret the estimated coefficient on educ4. Is it possible to obtain the same result using the regression estimated in item (a)? If it is not ...

1. ECO 375–Homework 2
University of Toronto
Due: 17 November, 2019
Late assignments will not be accepted
For full credit, please show your work
1 Theoretical Problems
1. True or false: First indicate whether the following statements
are true or false and then justify
your answer.
(a) In the simple linear regression model if the R2 is equal to
one, then the linear relationship
between the variables is exact and residuals are all zero.
(b) In the simple linear regression model, if Var(Y ) = Var(X)
then the estimated slope in a
regression model of Y on X is approximately equal to the
estimated slope in a regression
model of X on Y .
(c) The fact that R2 is equal to zero indicates that variables are
unrelated.
(d) A crucial assumption of the linear model is that the sum of
the residuals is zero.

2. (e) The fact that residuals in the linear model estimated by
least-squares have zero mean is
a consequence of assuming that the expected value of the error
term is zero.
(f) The assumption that the error term is normally distributed is
necessary to demonstrate
that the least-squares estimator is unbiased.
2. Take Y = log (W ). Assume the log-linear model Y = β0 +
β1X + U , with E (U) = 0. Prove
the following:
(a) Show that if E (U |X) = 0, then Cov (X,U) = 0.
(b) Assume Cov (X,U) = 0. Show that β1 = Cov (X,Y ) /V ar
(X).
(c) Suppose β̂1 is the OLS estimator of β1. Show that β̂1
p→ β1 + Cov(X,U)V ar(X) .
(d) Assume Cov (X,U) = 0. What is the estimated approximate
percentage change in W
for a change in X, say from X = x0 to X = x1? And what is the
estimated exact
percentage change in W?
(e) Assume Cov (X,U) = 0. Show that exβ̂ − 1 is a biased
estimator for exβ − 1. Show that
exβ̂ − 1 is a consistent estimator for exβ − 1.
1
2 Computer Based Problems

3. 1. Determinants of Income. Use the dataset “ANES2016.dta” for
this question. The
data are drawn from the American National Election Survey of
2016 (available at
https://electionstudies.org/data-center/2016-time-series-study/).
The dataset includes log of income (loginc), gender indicator
(female), indicators for black
and hispanic (black, hispanic), age, five education dummy
variables, numbered educ0 through
educ4 (from “high school dropout” to “graduate or professional
school”), among others. (Note
the data labels on the variables.)
(a) Take educ0, “high school dropout,” to be the base level of
education and estimate the
following model using OLS:
loginci = β0 + β1femalei + β2blacki + β3agei + β4age
2
i + β5educ1i+
β6educ2i + β7educ3i + β8educ4i + εi
Assume all assumptions of the classical linear regression model
hold. How should the
coefficient on educ1 be interpreted? What about educ4?
(b) Run the regression again, but now take educ1, not educ0, to
be the base case. First,
write down this regression equation, estimate the model
parameters, and interpret the
estimated coefficient on educ4. Is it possible to obtain the same
result using the regression
estimated in item (a)? If it is not possible, explain why. If it is
possible, explain how.

4. (c) Test whether age has significant impacts on income. Based
on the estimated results,
what is the (approximated) effect of an increase in age from 34
to 35 on income? In
which age do we expect to see the maximum income level
(holding all other covariates
constant)?
2. Economic Convergence. The idea that poor countries grow
faster than richer countries
is a result central to many neoclassical growth models. This
idea is often referred to in
the literature as (absolute) β-convergence. Empirically, papers
such as the influencial study
by Robert J. Barro (1991, “Economic Growth in a Cross Section
of Countries,” published
at the Quarterly Journal of Economics) demonstrate how β-
convergence can be tested on
a cross-section of economic data. For an early survey of the
literature, see Sala-i-Martin
(1994. “Cross-sectional Regressions and the Empirics of
Economic Growth,” published at the
European Economic Review).
To investigate this issue, let yi,t represent the GDP per capita of
country i at year t, and
consider the following regression model:
log
(
yi,t+k
yi,t
)

5. = α+ β log(yi,t) + ui,t. (1)
The dependent variable measures the (approximate) growth rate
of GDP per capita of country
i between year t and t+k. The model assumes that the growth
rate depends on the initial level
of income per capita yi,t, and on other (unobserved) factors ui.t.
If β < 0, richer countries are
expected to have smaller growth rates than poorer countries,
leading to the β-convergence.
Please use the Penn World Tables dataset, “PWT data.dta” for
this question (the original
data is available at https://www.rug.nl/ggdc/productivity/pwt/).
For the remainder of this
question, let t = 1975 and t+ k = 1995. A description of
variables is provided below:
2
Variable Description
GDP1975 Real GDP of country i in 1975
GDP1995 Real GDP of country i in 1995
POP1975 Population of country i in 1975
POP1975 Population of country i in 1995
HCI1975 Human capital index of country i in 1975
GCF1975 Gross capital formation shares of country i in 1975
(a) Assume the Gauss-Markov assumptions are valid. Estimate
equation (1) using ordinary
least squares. Interpret the results. Do you find evidence in
favor or against the β-
convergence?

6. (b) Now we will add the human capital index for country i at
time t, HCi,t into the model:
log
(
yi,t+k
yi,t
)
= α+ β1 log(yi,t) + β2HCi,t + ui,t (2)
If β1 < 0, then the group of countries are said to be
conditionally β-convergent. Estimate
equation (2) using OLS. Based on the estimated results, do you
find evidence in favor
of conditional economic convergence? Interpret the results and
compare them with the
results you found in (a).
(c) Now add one more variable to the regression - share of gross
capital formation in country
i:
log
(
yi,t+k
yi,t
)
= α+ β1 log(yi,t) + β2GCFi,t + β3HCi,t + ui,t (3)
Interpret the results. Do your conclusions from (b) change? Are
both types of capitals

7. jointly important to explain future growth?
3. Monte Carlo Simulation. Simulate the following model in
STATA:
Y = β0 + β1X + U
where
β =
(
β0
β1
)
=
(
−10
5
)
X ∼ U (0, 1) ,
that is, X is uniformly distributed between 0 and 1; and
U ∼ N(0, 5).
For each simulation, generate a data set {yi, xi : i = 1, ..., n}
with n = 100 observations. Then,
for each sample, estimate β using OLS, make the tests described
below, and save the p-values.
Run m = 1000 simulations.

8. (a) In each simulated data, perform the following hypothesis
test: H0: β1 = 5 vs H1:
β1 6= 5, and save the p-value. In what fraction of the
simulations can you reject the null
hypotheses? Most likely, you will find that the fraction of
rejections is not too far from
5%. Why is that true for this test?
(b) Now, in each simulated data, perform the following
hypothesis tests:
3
i. H0: β1 = 4.5 vs H1: β1 6= 4.5, and
ii. H0: β1 = 0 vs H1: β1 6= 0,
and save the corresponding p-values. In what fraction of the
simulations can you reject
each null hypotheses? Are those fractions close to 5%? Which
one is greater? Why are
these results expected for these tests?
Provide your do file and log file as part of your submission.
4
Theoretical ProblemsComputer Based Problems
Microbiology On Line Lecture
Assignments to Chapter 10
Infectious Diseases on Skin
Dr. I. Iliev
I. DISEASE AT GLANCE: Cutaneous Anthrax: Provide full
information to following:

9. Causative Agent:
Virulence Factors:
Portal of Entry:
Signs and Symptoms:
Incubation Period:
Susceptibility:
Treatment:
Prevention:
II. CLINICAL CASE STUDY: A Painful Rush. Please answer to
your best all questions ate the end of this case.
A mother brings her 3 year old daughter to pediatrician
describing that the girl has fever and chills for 3 days. The girl
also has a large, intensely red patch with a distinct margin on
her leg and a nearly swollen lymph node. When the nurse, and
later the physician touches the area it is firm and warm, and the
girl screams in pain. Based on these observations, doctor makes
a presumptive diagnosis and begin treatment.
1. Is it necessary to confirm the diagnosis with lab test? Why or
why not?
2. What was the diagnosis? Treatment?
3. How is this case different from impetigo?
4. What is the agent causing this girl’s condition?
5. How may the girl have contracted the condition?
6. What component(s) of the agent stimulated the fever and the
lesion?
7. Why is important for doctor to begin immediate treatment?
III. What do we know about Chickenpox and Shingles? Is it
viral or bacterial disease? Provide details for the following:
cause; virulence factors, portal entry, signs and symptoms,
incubation period, treatment and prevention.
IV. CRITICAL THINKING: A week after spending their
vacation rafting down Colorado River, all five members of
Jones family developed cold sores on their lips. At the local

10. hospital doctor told them that the lesions were caused by a
herpesvirus. Both Mr. and Mrs. Jones were stunned: Isn’t true
that herpes is a sexually transmitted disease (STD)? How could
it have affected their young children?
Assignment 9
Wound Infections
Biology 200 (Microbiology), on line, CRN….
Dr. I. Iliev
I. LEARNING OBJECTIVE
One of the most common bacterial infection on wounds are
Group A Streptococcal infections. Describefor “Flesh-Eating
disease” also known as Necrotizing Fasciitis the following:
Sign and Symptoms -
Incubation Period -
Causative Agent -
Pathogenesis -
Epidemiology -
Treatment -
Prevention–
The following disease is due to anaerobic condition. Describe
the conditions that lead to the development of anaerobic wound
infection. Key word: “Lockjaw”. Name the disease and provide
to your best knowledge the following information:
Sign and Symptoms –
Incubation Period -
Causative Agent –
Pathogenesis -
Epidemiology -
Treatment –
Prevention–

11. II. CASE STUDY:
Human bite infections can be dangerous because some of normal
mouth microbiota, not invasive when are growing alone,
suddenly can invade and destroy tissue when growing together
with Pasteurella orBartonella microbes (usually that comes from
animal bites). It cause high fever and rash. Questions:
1. What Gram-negative organism commonly infects wounds
caused by animal bites?
2. What is the most common cause of chronic localized lymph
node enlargement in young children?
3. Why are members of the normal mouth microbiota a cause of
serious infection in human bite?
III. CRITICAL THINKING AND APPLICATIONS:
An army field nurse, working in a mobile hospital ask all the
time the ambulance EMT and driver: “Was the soldier wounded
in a field of animals, cows, etc.?” Why the nurse is asking this
question?