Homework 6
100 points
There are
two problems in this homework.
Problem 1
should be submited in the standard format we’ve used many times: 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. (You are encouraged
to save paper here, you may print this section with a small font, double-sided
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.
Problem 2
will be presented in a slightly different, more polished style. Please refer to that specific problem for
details.
Problem 1
The dataset Phillips.dta contains information on the
civilian unemployment rate and the cpi inflation rate. The data is available from 1948 through 2010,
and was downloaded via FRED.
Part 1
a) import
the dataset and let STATA know it is time series with the command tsset year.
b) Estimate
an AR(1) model fot the unemployment rate.
(That is, regress unemp on a single lag of unemp.) Do this for observations of the year>=1951.
You should use the “lag operator” in STATA to do this (L.unemp).
c) Calculate
the BIC with the command estat ic.
d) Repeat
b) and c) for an AR(2) and AR(3).
e) Use
the BIC to determine what is the optimal lag length (q) for unemployment in
this AR(q)?
f)
What is the predicted unemployment rate for 2011
according to the AR(1) model? (Use the
coefficients and the data to calculate the expected value for 2011.) What is it for the AR(2) and AR(3) models?
g) The
actual unemployment rate in 2011 was 9.0.
What is the difference between the predicted values and actual for the
AR(1), AR(2) and AR(3) models.
Part 2)
a) Add
the lag of the cpi_inf rate to the AR(2) regression. Continue to execute with year>=1951. Is
the lag inflation statistically significant?
b) Predict
the unemployment rate 2011 in using the ADL model from 2a. Compare it to the actual level.
c) The
inflation adjusted Phillips curve proposes that the unemployment rate falls
when we encounter unexpected
inflation. Let’s propose that the
expected value of inflation for time t is the actual value of inflation for
time t-1. This means the difference
between actual inflation and expected inflation for time t will be inft-inft-1. Create a variable called d_inf that equals the change in inflation. Us the syntax D.cpi_inf
to help you do this. While you’re at it,
also create d_unemp that equals the change in unemployment.
d) Regress
unemp on d_inf. Report the coefficient
and p-value. Is it of the expected sign?
Part 3)
a) At
a level of α=.05, do unemp and cpi_inf have unit roots? Execute Dickey-Fuller tests for each as we
did in class. Note that the critical
value for a 5% test for a dataset of our size is approximately -2.92.
b) It
appears you cannot reject a unit root for unemp. Let’s try an Augmented Dickey-Fuller test for
unemployment. That is, include a lag of
the change in unemployment in your Dickey-Fuller regression (we created this
above, it’s called d_unemp). Can you
reject a unit root now?
Problem 2
This problem is intended to be
more open-ended than previous assignments, so you can get a feel for what it’s
like to do an actual project. I am
providing some basic guidance so you’ll have some idea of what I want to see,
but the specifics of what you choose to do will be up to you. As always, your write-up should be your own
work. You may talk with other students
about the project, but this is your problem to solve.
You will have two datasets to
choose from to complete this part of the assignment. Use only one of these, not both.
n
The dataset names.dta contains information
regarding job postings and resumes of applicants. This dataset is the basis of a remarkable
(and quite famous) paper by Bertrand and Mullinathan published in 2004. You will probably want to use the variable call_back
as your dependent variable.
n
The dataset seatbelts.dta is a panel dataset
containing state-specific information about motor vehicle fatalities over a 15
year period. This dataset formed the
basis of a paper by Cohen and Einav in 2003.
Each dataset has a description
file detailing the variables it contains.
Presentation
Rules:
All responses must be typed.
STATA tables that are cut and pasted in are NOT acceptable. You need to create summary tables that
present the information in a reader-friendly fashion. Imagine you are writing this up for your new
boss, who doesn’t have time to go through countless pages of STATA output. You need to distill the essential information
you want to convey in a few easy to read tables. Here’s an example I have fabricated out of
thin air.
|
Dependent Variable: Independent |
Model 1 |
Model 2 |
Model 3 |
|
Bowl Cleaned ≥1 per |
25.12 (.005) |
21.23 (.008) |
15.11 (.001) |
|
Food per day |
1.378 (.034) |
1.455 |
1.144 (.021) |
|
Food per day ^2 |
-.00034 (.002) |
-.00045 (.003) |
|
|
Water Temperature |
-.15 (.14) |
n=435, p-values in parenthesis,
using robust standard errors.
I believe to do a thoughtful job analyzing
these datasets will take a minimum of 2-3 typed pages (not including any
tables). I am not setting a page
requirement, but if you are coming in low, you probably aren’t thinking hard
enough.
Answer the Following
a) Which
dataset are you using?
b) What
is your dependent variable?
c) What
is the question you want to use the dataset to try and answer? What is your key
independent variable(s)? [State these very clearly. It is important you know exactly what it is
you are trying to accomplish before you try to accomplish it.]
Example:
Does cleaning a fishbowl increase the lifespan of a goldfish? My wife says yes. Easy for her to say. When’s the last time she cleaned Ludwig’s bowl? Try never.
That’s right, never. But I
digress.
d) What
is your expected answer to the question? [This is your chance to develop your
ideas as to what you think the relationship between the variables is.]
Example:
[Yours should be much longer and thoughtful.]
I think a thick layer of organic compounds (aka “scum”) on the inside of
a fishbowl is a sign of a healthy biosphere.
A fish will benefit from the rich broth of nutrients a non-cleaned bowl
will provide. Those that provide a
“sterile,” or “habitable,” environment are doing their fish a disservice. Thus,
I expect there to be a negative relationship between cleaning a bowl and the
lifespan of a goldfish.
e) What
control variables do you think you should use?
For each, what do you think would be the relationship between these
control variables and the dependent/key independent variables? Alternatively, how would the omission of these variables
impact your central analysis?
Example:[Your’s
should be much longer and thoughtful.] I think I should control for food
consumption. Fish need food to
survive. Giving the fish food should
increase its lifespan. It is also
possible that people who feed their fish periodically will be more likely to clean the
fishbowl. I thus expect omitting food
consumption will lead to a positive bias in the coefficient on cleaning the
bowl.
f)
What is the functional form of your
regression? Why have you chosen this
form?
Example:
I have cross-sectional data from 435 random selected households. I have no reason to believe that any of the
CLRM assumptions aren’t being met, so I will use OLS to estimate the
model. I will use robust standard errors
in case there is heteroskedasticity of unknown form. The only novel functional form issue is that
I will include a quadratic term for food, in case very high food consumption is
bad for fish. I’ve heard rumors that
Timmy Jorgenson gave his fish like a pound of food before vacation and when he
got back he’d swelled up to the size of a cantaloupe. For real.
But I digress.
g) Run
your regressions. You should have
several different variations of the model, using different control variables
and possibly slightly different functional forms. Compile the important numbers in a table, as
I did above.
h) Describe
your results. Obviously, you should
highlight the signs and significance levels of your key variables, and any
interesting findings for the control variables.
How do the findings change based on specification of the model? Are the results consistent with your initial
guess?
i)
Propose (at least one) interaction that includes
your key independent variable. Why do
you think this interaction is potentially important? You should present these results in a table,
as well. Be sure to interpret these
results carefully.
j)
Conclude your paper by summing up your major
findings. Suggest related questions
you’d be interested in and ways you would want to try to investigate the ideas
here more thoroughly.
Example:
Well, despite my hopes, I can only conclude that washing a fish’s bowl
increases a fish’s life expectancy. Poor Ludwig. I guess that raspy gasping sound he makes
isn’t him trying to say hello. I’ll make
it up to him by buying him a steak. Now
that Ludwig can see out of his bowl, I shall turn my attention towards
analyzing what types of films fish like to watch. I’m pretty sure it’s a toss up between killer space robots and killer space aliens. Ludwig, it’s movie night!
