Economics homework help

Economics homework help
market
Financial
The entire problem set 3
J. Edward Taylor Fall 2020
Your Name __________________________________
ARE 106
Quantitative Methods
Problem Set 3
Due before midnight on Friday, December 11, 2020
Financial Markets and COVID-19
The data set “financial_data_ps3.dta” contains daily information on the closing price of the S&P 500 stock,
gold, bitcoin, as well as the interest rate on the U.S. 10-year Treasury note since January 2015 to October
2020. These data were retrieved from Yahoo finance. The following table defines the variables in this data
set:
Variable Variable name in Stata Description
Date date Year-month-day
Time trend timetrend Numerical variable that goes from 1 to T
Closing price of S&P 500 stock sp500_close Closing price in US dollars
Closing price of gold gold_close Closing price in US dollars
Closing price of bitcoin bitcoin_close Closing price in US dollars
Interest rate on the U.S. 10-year
Treasury note
treasury_close Interest rate
Before you begin, however, please read through these important instructions:
• Be sure to write your name on this page! Please submit your assignment by Midnight (CA time)
Friday December 11th. (Note: You will lose a full grade point (e.g., from A- to B-) for turning in
your assignment one day late. No submissions will be accepted after Saturday December 12th.)
The submission process involves two steps, both of which are required to receive full credit for the
Problem Set:
o Part 1: Upload your Stata do-file to the Problem Set 3 Assignment on Canvas. You will
lose a full grade point if you do not submit the Stata do file.
o Part 2: Upload your PDF via Gradescope. If you have any questions about how to upload
via Gradescope, please consult this helpful page:
https://help.gradescope.com/article/ccbpppziu9-student-submit-work
• You are permitted to discuss the assignment with your classmates, but all estimation and writeup should be done independently. Assignments like this are designed for you to generate your
own ideas, and this should be reflected in your submitted work. We will be looking out for
evidence that each student is submitting their own work and not that of classmates.
J. Edward Taylor Fall 2020
• Enter your answers onto this document in the space provided. More than enough space is
provided, so do not worry about filling up the space! Focus more on the quality of your
responses than on the quantity of words used in the responses.
• You have a few options for how to enter your responses. This PDF is fillable, which means
you can type out your responses in the boxes provided. (Note: It is highly recommended that
you print your final document as a PDF file and read over your submission to make sure
everything is as you want it before uploading to Gradescope.) You can also handwrite your
responses on a printed copy of the document, scan that document as a PDF, and upload the
submission. Alternatively, you could handwrite answers using a tablet. If you choose to
handwrite your responses, be sure to keep your handwriting within the boxes provided for each
question. Answers outside of the boxes are liable to be missed by Gradescope, resulting in
unnecessary points lost.
• When typing out equations, you may use lower-case letters in parentheses instead of subscripts.
For example, Y(i) is accepted in place of 𝑌𝑌𝑖𝑖. If you are handwriting your responses, please use
subscripts for full credit.
• In order to open “financial_data_ps3.dta”, go to “File – Open”, and locate your local drives
where this dtafile is saved.
o For Windows users, your local drives should be under “This PC” – “C on {your
computername}.”
o For Mac users, “This PC” – “[folder name] on [your computer name].” The folder is
theone which you set up first in “Preference – General tab” in Microsoft Remote
Desktop Appwhen you install Stata. You should move “financial_data_ps3.dta” to this
folder.
• All the Stata commands have useful documentation with examples. If you want to see these
documents, you can type “help [command name].”
o For example, if you type “help reg” in Stata, a new window will be open and provide
a detailed information on syntax, options, and examples for reg command.
J. Edward Taylor Fall 2020
1. [5 points] The S&P 500 is an index of stock prices for the largest corporations in America. It includes
all the FAANG (Facebook, Amazon, Apple, Netflix, Google) stocks, but it also includes “old economy”
stocks like United Airlines, Hilton Hotels, and Carnival Cruises. Estimate an OLS regression to predict
the S&P 500 price at close of each trading day, based on its close price the previous day and a time
trend. That is, use the model to capture basic dynamics that is Professor Taylor’s preferred starting
model (see ppt for CH 9). Report your results. Hint: before running the regression, make sure to declare
the data to be a time series by typing tsset timetrend in Stata.1
Variables Estimated
Coefficient
Standard Error t-statistic 95% Confidence Interval
Lower Upper
S&P 500 (t-1)
Time trend
Constant
Sample size
𝑅𝑅2
1 timetrend is a numerical variable that goes from 1 to T, where T is the total number of days in the dataset.
J. Edward Taylor Fall 2020
2. [5 points] Is there evidence of serial correlation in this model at 5% of significance? Please write
down the auxiliary model, the null hypothesis, the test statistic and the critical value. DO NOT USE
THE CANNED COMMAND THAT DOES THIS TEST IN STATA! We want to see how you did it.
J. Edward Taylor Fall 2020
3. [5 points] Briefly explain how the Newey West procedure addresses the serial correlation problem.
J. Edward Taylor Fall 2020
4. [5 points] Now re-estimate this basic dynamics model using the Newey West procedure with 6 lags.2
(It is fairly common to set the number of lags equal to the integer part of T1/4, which satisfies the
conditions in Newey and West’s seminal paper.) Report your results and compare them to the results you
got using OLS.
Variables Estimated
Coefficient
Standard Error t-statistic 95% Confidence Interval
Lower Upper
S&P 500 (t-1)
Time trend
Constant
Sample size
𝑅𝑅2
What changed, what did not change, and why?
2 To conduct the Newey West procedure use the Stata command newey. Do not forget to specify the number of lags.
J. Edward Taylor Fall 2020
5. On 20200225, the World Health Organization (WHO) announced that COVID-19 was becoming a
pandemic. On 20200317 U.S. President Trump requested Congress to send Americans direct financial
relief, in the form of stimulus checks and other measures. Please use the variable date in the dataset to
create two dummy variables, one for each of these two events.3 (Hint: They should equal to 0 before
the relevant date and 1 afterwards.) Include the new COVID dummy variables in your basic dynamic
regression to predict S&P 500 prices.
a) [2 points] Write down your model
b) [3 points] Does it make sense to also include the lagged dummy variables? Why or why not?
3 date is a numerical variable with the corresponding date (year-month-day).
J. Edward Taylor Fall 2020
c) [5 points] Report the results in table form
Variables Estimated
Coefficient
Standard Error t-statistic 95% Confidence Interval
Lower Upper
S&P 500 (t-1)
Time trend
Constant
Sample size
𝑅𝑅2
Did COVID-19 affect S&P 500 prices? Did the request for stimulus? Explain providing enough
details on your tests: null hypothesis, test statistic, critical value. Use a significance level of 5%
J. Edward Taylor Fall 2020
6. [5 points] In Question 5, what estimator did you use, and why?
J. Edward Taylor Fall 2020
7. [5 points] People traditionally have viewed gold as a “safe haven” to put their money into at times of
uncertainty. The COVID-19 pandemic obviously ushered in a new era of uncertainty, whereas the
promise of stimulus attempted to alleviate this uncertainty.
Estimate the following equation using the Newey West procedure with the same number of lags as in
question 4:
𝑔𝑔𝑔𝑔𝑔𝑔𝑑𝑑𝑡𝑡 = Β0 + Β1𝑔𝑔𝑔𝑔𝑔𝑔𝑑𝑑𝑡𝑡−1 + Β2𝑡𝑡𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡 + Β3𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑐𝑐𝑡𝑡 + Β4𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑠𝑠𝑡𝑡 + 𝑢𝑢𝑡𝑡
How did COVID-19 pandemic and stimulus affect the demand for gold, as reflected in gold prices?
Are these results significant at 5%? Please explain providing enough details on your tests: null
hypothesis, test statistic, critical value.
J. Edward Taylor Fall 2020
8. [5 points] Bitcoin (BTC) has swept the world with a new and, for many people, confusing asset,
seemingly created from “thin air” (though it really is created by a mathematical equation, which
limits the total supply of BTC to exactly 21 million, unlike the supply of national currencies in the
world, which can be increased infinitely by central banks running their money presses). The COVID19 pandemic created a lot of uncertainty in the world, and governments printed new money to support
their stimulus policies (like the US did to send a $1,200 check that many Americans received this
year).
Estimate a model to test whether the COVID-19 pandemic and the stimulus changed the demand for
BTC, as reflected in BTC prices. (Hint: the model should be similar in spirit to the one estimated in
question 7). How did COVID-19 pandemic and stimulus affect the demand for bitcoin, as reflected in
bitcoin prices? Are these results significant at 5%? Please explain providing enough details on your
tests: null hypothesis, test statistic, critical value.
J. Edward Taylor Fall 2020
9. Some people consider BTC to be the “new digital gold.” If that is true, then BTC and gold prices
could be significantly related to one another.
a) [5 points] Estimate the following equation and test for autocorrelation. What are the statistic and
the critical value?
𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡 = Β0 + Β1𝑔𝑔𝑔𝑔𝑔𝑔𝑑𝑑𝑡𝑡 + 𝛽𝛽2𝑡𝑡𝑡𝑡𝑡𝑡𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑡𝑡 + 𝑢𝑢𝑡𝑡
Test statistic
Degrees of freedom for
critical value (m)
Critical value
What do you conclude?
b) [5 points] Now estimate the following autoregressive distributed lagged model and test for
autocorrelation.
𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡 = 𝛾𝛾0 + 𝛾𝛾1𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑏𝑛𝑛𝑡𝑡−1 + 𝛾𝛾2𝑔𝑔𝑔𝑔𝑔𝑔𝑑𝑑𝑡𝑡 + 𝛾𝛾3𝑔𝑔𝑔𝑔𝑔𝑔𝑑𝑑𝑡𝑡−1 + 𝛾𝛾4𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑑𝑑𝑡𝑡 + 𝜖𝜖𝑡𝑡
Test statistic
Degrees of freedom for
critical value (m)
Critical value
What do you conclude?
J. Edward Taylor Fall 2020
c) [5 points] Using this autoregressive distributed lagged model, test whether gold prices are
significantly correlated with bitcoin prices at a 5% significance level. What do you conclude?
Explain providing enough details on your tests: null hypothesis, test statistic, critical value.
J. Edward Taylor Fall 2020
10. People dream of getting rich by finding a way to predict stock prices. Our data set has information on
S&P 500 stock prices as well as prices of gold, BTC, and the interest rate on the U.S. 10-year Treasury
note. Going into each new day of trading, we know the closing price of each of these assets—but only for
the previous trading day.
a) [5 points] Write down an econometric model to predict the S&P 500 market close based on its
closing price in the previous day, the closing price of gold and BTC in the previous day, and the
interest rate on the U.S. 10-year Treasury note in the previous day. Do not forget to include the
time trend as well.
b) [5 points] Estimate this model using the Newey West procedure and 6 lags. Report your results.
Variables Estimated
Coefficient
Standard Error t-statistic 95% Confidence Interval
Lower Upper
Constant
Sample size
𝑅𝑅2
J. Edward Taylor Fall 2020
c) [5 points] Based on your results, which, if any, of these variables significantly explains S&P 500
performance at 5% level? Please explain providing enough details on your tests: null hypothesis,
test statistic, critical value.