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 . 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

2

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

2

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

2

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:

= Β0 + Β1 −1 + Β2 + Β3 + Β4 +

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?

= Β0 + Β1 + 2 +

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.

= 0 + 1 −1 + 2 + 3 −1 + 4 +

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

2

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.