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Use the dataset here Download the dataset herefor this question.
The data set has,
EXRATE: the exchange rate for the Mexican Peso (pesos per dollar), the value for the rate is taken at the end of the month
LAGEXRATE: the lagged exchange rate
MXINFL: the Mexican inflation rate
USINFL: the U.S. inflation rate. The observations run from January 2015 to December 2020. There is also a trend variable, T, which is 1 in the first period and increases by 1 each period. The file also has a column indicating the year and another indicating the month.
Details on the data sources will be available with the key.
a) Construct a histogram of the exchange rate. Use the option breaks=5. Based on the histogram (i) the data are highly left skewed (ii) the data are highly right skewed (iii) the distribution is approximately uniform (iv) the distribution is approximately bell shaped.
[ Select ] [“(i)”, “(iv)”, “(ii)”, “(iii)”] .
b) Now construct a histogram of the exchange rates before 2020. That is, exclude the last 12 observations from your graph. Does your graph for the pre 2020 observations have the same basic appearance as for the entire data set?
[ Select ] [“No, the graphs are noticeably different”, “Yes, the graphs are similar.”] .
c) Create a new variable that is the difference in the inflation rates. Take the Mexican inflation rate and subtract the U.S. inflation rate to get the difference. Find the summary statistics for this new variable. What is the mean for this variable?
[ Select ] [“0.1106”, “0.086”, “0.0782”, “0.0954”] .
d) Other things equal, if country A has persistently higher inflation than country B we expect that country A’s currency will depreciate. That is, country A’s currency will buy fewer units of country B’s currency over time. Regress the exchange rate on the lagged exchange rate and the difference in the inflation rates. Are the results consistent with previous sentences in part (d)? That is, do the estimated coefficients have the signs implied by the previous statements about inflation and currency depreciation? Reminder: the exchange rate is specified as Pesos/Dollar.
[ Select ] [“No”, “Yes”] .
e) Conduct a test for autocorrelation. The test leads you to the conclusion that the errors are
[ Select ] [“correlated”, “not correlated”] .
f) If you conclude that the errors are correlated use the Cochrane-Orcutt procedure to estimate the coefficient on the difference in inflation rates. If you conclude the errors are not correlated, just report the OLS estimate for the coefficient on the difference in inflation rates. The estimated coefficient is [ Select ] [“0.3652”, “0.3708”, “0.3513”, “0.3431”] .
g) Exchange rates will also fluctuate with trade policy changes. Create a dummy variable (aka indicator variable) for the Trump administration. This will be 1 for November 2016 through October 2020; while the inauguration takes place in January, markets tend to adjust in anticipation of future changes so use the time frame stated. Before November 2016 this variable will be 0 and after October 2020 this variable will also be 0.
Run an OLS regression where EXRATE is the dependent variable and the three explanatory variables are the lagged exchange rate, the difference in the inflation rate and the dummy variable. Based on the signs of the estimated coefficients does it appear that the Trump administration led to a strengthening of the dollar or a weakening of the dollar? Reminder: strong dollar means lots of Pesos per dollar and weak dollar means few Pesos per dollar. [ Select ] [“weaker dollar”, “stronger dollar”] .
h) Create a plot of the exchange rate against time or against a default index in R. That is, create a plot of the exchange rates where the left most value is the exchange rate from the first period and then the values are ordered by time such that the last value, the right most value, is from the last period in the data set. Immediately after creating the plot give the following command to R, abline(v=22.5, col=”red”, lwd=2). This creates a vertical line between the October and November 2016 values. Also, run this line of code, abline(v=52.5, col=”blue”, lwd=2). This creates a vertical line between the February and March 2020 values which are pre and post COVID-19 related quarantine implementations. Suppose you were regressing the exchange rate on the time trend up until before the COVID-19 quarantines; that is, until March 2020. You are no longer including a lagged value in the regression but instead using T as the explanatory variable. Based on the plot you just created choose the best statement. (i) it appears appropriate to include a dummy variable for the Trump administration but not an interaction term (ii) it appears appropriate to include an interaction term but not the dummy variable (iii) it appears appropriate to include both the dummy variable and an interaction term (iv) it appears that neither the dummy variable nor the interaction term belong in the model.
[ Select ] [“(i)”, “(ii)”, “(iv)”, “(iii)”] .
i) Create a dummy variable (indicator variable) for the first four months of the COVID quarantine period. That is, a variable which is 1 for the months of March-June 2020 and 0 for all other months. Regress the exchange rate on the lagged exchange rate, the difference in the inflation rates and the two dummy variables. There are four explanatory variables in your model, one is a dummy for the Trump administration and the other is an indicator for the first 4 months of quarantine. This is an OLS regression.
Do the errors appear to be heteroskedastic? You can use a combination of plots and formal tests to answer this.
[ Select ] [“NO”, “YES”] .
j) Test the hypothesis that the errors are correlated. Use ?=.1 for this test. Do you reject or fail to reject the null hypothesis of independent errors?
[ Select ] [“Fail to reject”, “Reject”] .
k) Based on your regression results does the quarantine appear to have had an impact on the exchange rate?
[ Select ] [“NO”, “YES”] .
l) Using this last model what is the estimated standard deviation of the residual?
[ Select ] [“0.53 dollars”, “0.49 pesos”, “0.87 pesos”, “0.35 dollars”, “0.7 pesos”] .