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Download quarterly, seasonal adjusted data on US real GDP, personal consumption expenditures, and gross private domestic investment for the period 1960Q1-2015Q4. You can find these data in the BEA NIPA Table 1.1.6, ?Real Gross Domestic Product, Chained Dollars". Make sure you follow the instructions given in the first page.

1. Take the natural logarithm of each series (=ln(series)") and plot each against time. Which series appears to move around the most? Which series appears to move the least?
2. The growth rate of a random variable x, between dates t ? 1 and t is defined as:

x xt ? xt?1 gt = xt 1

Calculate the growth rate of each of the three series (using the raw series, not the logged series) and write down the average growth rate of each series over the entire sample period. Are the average growth rates of each series approximately the same?

1. We argued in class that the first difference of the log is approximately equal to the growth rate: gtx ? lnxt ? lnxt?1
Compute the approximate growth rate of each series this way. Comment on the quality of the approx- imation.
2. The standard deviation of a series of random variables is a measure of how much the variable jumps around about its mean (=stdev(series)"). Take the time series standard deviations of the growth rates of the three series mentioned above and rank them in terms of magnitude.
3. The National Bureau of Economic Research (NBER) declares business cycle peaks and troughs (i.e. recessions and expansions) through a subjective assessment of overall economic conditions. A popular definition of a recession (not the one used by the NBER) is a period of time in which real GDP declines for at least two consecutive quarters. Use this consecutive quarter decline definition to come up with your own recession dates for the entire post-war period. Compare the dates to those given by the NBER.

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1. Honors & Bonus. The most recent recession is dated by the NBER to have begun in the fourth quarter of 2007, and officially ended after the second quarter of 2009, though the recovery in the last three years has been weak. Compute the average growth rate of real GDP for the period 2003Q1- 2007Q3. Compute a counterfactual time path of the level of real GDP if it had grown at that rate over the period 2007Q4- 2010Q2. Visually compare that counterfactual time path of GDP, and comment (intelligently) on the cost of the recent recession. Answer the following question using the St. Louis?s FRED database I showed you in class.
2. Williamson, 5th edition, problem 2.16. Sometimes economists are interested in the length of time that the unemployed have been out of work. Why is the median duration of unemployment a convenient summary? Plot this variable, and comment on how it has evolved over time, particularly during the last recession.

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This question was answered on: Feb 21, 2020

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