Economics homework help

• J. Edward Taylor Fall 2020
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
• 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.
• You are permitted to discuss the assignment with your classmates, but all estimation and write- up 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.
• 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 COVID- 19 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.

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