Question

(1) Playing with data: Download quarterly, seasonally adjusted data on US real GDP, personal consumption expenditures, and gross private domestic investment for the period 1947q1 - 2010q2. You can download these series from the Bureau of Economic Analysis (BEA) or the St. Louis Fed FRED database.

(a) Take the natural logarithm of each series (ì=ln(series)î in Excel) and plot each against time. Which series appears to move around the most? Which series appears to move around the least?

(b) The growth rate of a random variable, x, between dates t 1 and t is deÖned as: g x t = xt xt1 xt1 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 post-war sample period. Are the average growth rates of each series approximately the same?

(c) We argued in class that the Örst di§erence of the log is approximately equal to the growth rate: g x t ln xt ln xt1 Compute the approximate growth rate of each series this way. Comment on the quality of the approximation.

(d) The standard deviation of a series of random variables is a measure of how much the variable jumps around about its m (Excel command ì=stdev(series)î). Take the time series standard deviations of the growth rates of the three series mentioned above and rank them in terms of magnitude.

(e) 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 deÖnition of a recession ñnot the one used by the NBER ñis a period of time in which real GDP declines for at least two consecutive quarters. Use this consecutive quarter decline deÖnition to come up with your own recession dates for the entire post-war period. Compare the dates to those given by the NBER (just google ìNBER recession datesîto Önd those dates).

(f) The most recent recession is dated by the NBER to have begun in the fourth quarter of 2007. Compute the average growth rate of real GDP for the period 2003q1 - 2007q3. Compute a counterfactual time path of real GDP if it had grown at that rate over the period 2007q4-2010q2. Use that counterfactual simulation to speculate (intelligently) on the welfare cost of business cycles.

Answer 1

Data source: https://fred.stlouisfed.org

GDPC1	Real Gross Domestic Product, Billions of Chained 2012 Dollars, Quarterly, Seasonally Adjusted Annual Rate
PCEC	Personal Consumption Expenditures, Billions of Dollars, Quarterly, Seasonally Adjusted Annual Rate
GPDI	Gross Private Domestic Investment, Billions of Dollars, Quarterly, Seasonally Adjusted Annual Rate

a)   So, GPDI appears to move around the most with the highest degree of fluctuation and PCEC appears to move around the least, that is, even though it increases sharply over time, the fluctuations along the series are less.

b)   Given the formula of growth rate, Gt = (Xt1 – Xt)/Xt , we calculate the growth rate for each series for each quarter and then take the average of all the growth rate value for each series. We get the following values:
Average growth rate of RGDP = 0.8%
Average growth rate of PCEC = 1.7%
Average growth rate of GDPI = 1.8%
We see that the growth rates of GDPI and PCEC are approximately the same while the growth rate for GDP is comparatively lower.
c)   Computing the first difference of the log series and then taking the average of the values gives us the following results:
Average growth rate of RGDP = 0.8%
Average growth rate of PCEC = 1.6%
Average growth rate of GDPI = 1.6%
So we see that the results are very similar. The quality of approximation is good.
d)   Taking the standard deviation of the series gives us the following results-
SD of RGDP = 0.00980723
SD of PCEC = 0.00983516
SD of GDPI = 0.05
We see SD of RGDP and PCEC is almost same, but SD of PCEC exceeds that of RGDP at the 5th decimal place. So, order of ranking - SD of GDPI > SD of PCEC > SD of RGDP.

e)   With the new definition, the recession date comparison is given in the figure below.

Time Period	Recession (Computed)
1947 Q2	1
1947 Q3	1
1949 Q1	1
1949 Q2	1
1949 Q4	1
1953 Q3	1
1953 Q4	1
1954 Q1	1
1956 Q1	1
1956 Q3	1
1957 Q2	1
1957 Q4	1
1958 Q1	1
1960 Q2	1
1960 Q4	1
1969 Q4	1
1970 Q1	1
1970 Q4	1
1973 Q3	1
1974 Q1	1
1974 Q3	1
1974 Q4	1
1975 Q1	1
1980 Q2	1
1980 Q3	1
1981 Q2	1
1981 Q4	1
1982 Q1	1
1982 Q3	1
1990 Q4	1
1991 Q1	1
2001 Q1	1
2001 Q3	1
2008 Q1	1
2008 Q3	1
2008 Q4	1
2009 Q1	1
2009 Q2	1

Time Period	NBER Recession
1949 Q1	1
1949 Q2	1
1949 Q3	1
1949 Q4	1
1953 Q3	1
1953 Q4	1
1954 Q1	1
1954 Q2	1
1957 Q4	1
1958 Q1	1
1958 Q2	1
1960 Q3	1
1960 Q4	1
1961 Q1	1
1970 Q1	1
1970 Q2	1
1970 Q3	1
1970 Q4	1
1974 Q1	1
1974 Q2	1
1974 Q3	1
1974 Q4	1
1975 Q1	1
1980 Q2	1
1980 Q3	1
1981 Q4	1
1982 Q1	1
1982 Q2	1
1982 Q3	1
1982 Q4	1
1990 Q4	1
1991 Q1	1
2001 Q2	1
2001 Q3	1
2001 Q4	1
2008 Q1	1
2008 Q2	1
2008 Q3	1
2008 Q4	1
2009 Q1	1
2009 Q2	1

f)   Avg GDP growth 2003Q1 - 2007Q3 = 0.8 %

If GDP would have grown at this rate constantly from 2007Q4 to 2010Q2, the overall growth rate of GDP would have increased. The output would have increased and there would have been less fluctuations in the economy.