Variables Estimated Coefficient
Standard Error t-statistic 95% Confidence Interval Lower Upper
S&P 500 (t-1)
Time trend
Constant
Sample size
π π 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
π π 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 βsafe havenβ 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:
πππππππππ‘π‘ = Ξ0 + Ξ1πππππππππ‘π‘β1 + Ξ2π‘π‘πππ‘π‘πππ‘π‘πππππππππ‘π‘ + Ξ3πππππππππππ‘π‘πππππ‘π‘ + Ξ4πππ‘π‘πππ‘π‘πππππππ π π‘π‘ + πππ‘π‘ 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 βthin airβ (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 βnew digital gold.β 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? πππππ‘π‘πππππππππ‘π‘ = Ξ0 + Ξ1πππππππππ‘π‘ + π½π½2π‘π‘πππ‘π‘πππ‘π‘πππππππππ‘π‘ + πππ‘π‘
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.
πππππ‘π‘πππππππππ‘π‘ = πΎπΎ0 + πΎπΎ1πππππ‘π‘πππππππππ‘π‘β1 + πΎπΎ2πππππππππ‘π‘ + πΎπΎ3πππππππππ‘π‘β1 + πΎπΎ4π‘π‘πππ‘π‘πππ‘π‘πππππππππ‘π‘ + πππ‘π‘
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 assetsβbut 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
π π 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.
Your Name:
Standard ErrorSP 500 t1:
tstatisticSP 500 t1:
LowerSP 500 t1:
UpperSP 500 t1:
Estimated CoefficientTime trend:
Standard ErrorTime trend:
tstatisticTime trend:
LowerTime trend:
UpperTime trend:
Estimated CoefficientConstant:
Sample size:
fill_18:
Standard ErrorConstant:
tstatisticConstant:
LowerConstant:
UpperConstant:
3:
Estimated CoefficientSP 500 t1_2:
Standard ErrorSP 500 t1_2:
tstatisticSP 500 t1_2:
LowerSP 500 t1_2:
UpperSP 500 t1_2:
Estimated CoefficientTime trend_2:
Standard ErrorTime trend_2:
tstatisticTime trend_2:
LowerTime trend_2:
UpperTime trend_2:
Estimated CoefficientConstant_2:
Standard ErrorConstant_2:
tstatisticConstant_2:
LowerConstant_2:
UpperConstant_2:
Sample size_2:
fill_18_2:
What changed what did not change and why:
a:
b:
Estimated CoefficientSP 500 t1_3:
Standard ErrorSP 500 t1_3:
tstatisticSP 500 t1_3:
LowerSP 500 t1_3:
UpperSP 500 t1_3:
Estimated CoefficientTime trend_3:
Standard ErrorTime trend_3:
tstatisticTime trend_3:
LowerTime trend_3:
UpperTime trend_3:
Time trendRow1:
Estimated CoefficientRow3:
Standard ErrorRow3:
tstatisticRow3:
LowerRow3:
UpperRow3:
Time trendRow2:
Estimated CoefficientRow4:
Standard ErrorRow4:
tstatisticRow4:
LowerRow4:
UpperRow4:
Estimated CoefficientConstant_3:
Standard ErrorConstant_3:
tstatisticConstant_3:
LowerConstant_3:
UpperConstant_3:
Sample size_3:
fill_29:
details on your tests null hypothesis test statistic critical value Use a significance level of 5:
6:
hypothesis test statistic critical value:
tests null hypothesis test statistic critical value:
Test statistic:
Degrees of freedom for critical value m:
Critical value:
What do you conclude:
Test statistic_2:
Degrees of freedom for critical value m_2:
Critical value_2:
What do you conclude_2:
Explain providing enough details on your tests null hypothesis test statistic critical value:
time trend as well:
VariablesRow1:
Estimated CoefficientRow1:
Standard ErrorRow1:
tstatisticRow1:
LowerRow1:
UpperRow1:
VariablesRow2:
Estimated CoefficientRow2:
Standard ErrorRow2:
tstatisticRow2:
LowerRow2:
UpperRow2:
VariablesRow3:
Estimated CoefficientRow3_2:
Standard ErrorRow3_2:
tstatisticRow3_2:
LowerRow3_2:
UpperRow3_2:
VariablesRow4:
Estimated CoefficientRow4_2:
Standard ErrorRow4_2:
tstatisticRow4_2:
LowerRow4_2:
UpperRow4_2:
VariablesRow5:
Estimated CoefficientRow5:
Standard ErrorRow5:
tstatisticRow5:
LowerRow5:
UpperRow5:
Estimated CoefficientConstant_4:
Standard ErrorConstant_4:
tstatisticConstant_4:
LowerConstant_4:
UpperConstant_4:
Sample size_4:
fill_38:
test statistic critical value:
Estimated CoefficientSP 500 t1:
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