Problem Set 1 - Answers
(due Monday, January 9)

1. Let's compare the 10 recessions that the U.S. has experienced since the end of the WWII. Your task is to complete the table below (parts a. through c.), and then answer questions using the data in the table (parts d through f).

a. Complete the Beginning and End columns. Go to www.nber.org click on Recessions and Recoveries, the NBER Business Cycle Dating Committee, and related topics then click on US Business Cycle Expansions and Contractions. Calculate the duration of each recession. Do not count the peak month (the recession begins at the end of the month).

b. Complete the Cumulative Output Fall column. You can use this spreadsheet which contains the quarterly real GDP (this data was used to generate the first figure in packet one). For each recession, calculate the percentage cumulative output fall by calculating the percent change from the beginning quarter of the recession (peak) to the final quarter of the recession (trough). For example, for the percent cumulative output fall during the first recession was calculates as "=(B13-B9)/B9*100".

c. Finally, complete the Increase in Unemployment Rate column. You will need to obtain statistics on the unemployment rate in the U.S. Go to the web site of the Bureau of Labor Statistics (BLS): www.bls.gov. In the middle of the page you will see the latest BLS numbers. Under the unemployment rate, click on the dinosaur icon ()  next to the "current unemployment rate." This will take you to a table with 10 years of historical data. However, we want all of the data. Therefore, click on "More Formatting Options" and then specify years range from 1948 to 2005 and view of the data as "Column Format." Click retrieve data. Copy the table into Excel. For each recession calculate the change in the unemployment rate from the beginning (peak) to the end (trough).

d. In your view, which recession has been most severe? Explain. (Note that the answer depends on your subjective weighing of duration, output fall and unemployment.)

In my view, the recession of 1973 stands out as the most severe. It is one of the two longest post-war recessions and has the second largest drop in output and the second largest increase in the unemployment rate. While the 1957 recession experienced a greater output fall, it was only half as long as the 1973 recession. Similarly, while the 1948 recession experienced a greater increase in the unemployment rate, output fell by only half of the percentage of 1973. In summary, the 1973 recession was severe on all counts: duration, output fall and the increase in the unemployment rate.

e. How does the most recent recession compare in severity to others?

By many measures the 2001 recession is the mildest recession on record. Its duration was only 8 months which makes it the second shortest. Output actually increased during this recession (!) which is unprecedented, and the increase in the unemployment rate was the lowest (tied only with the 1990 recession).

f. The recession known as the "Great Depression" started in August 1929 and ended in March 1933. During that time GDP fell by nearly 50%, and the unemployment rate went from 3% in 1929  to nearly 25% in 1933 . Given what you now know about other recessions, do you think that the recession of 1929-1933 deserves the "Great Depression" name?

Absolutely. The Great Depression lasted 43 months, nearly three times as long as the longest post-WWII recession. The cumulative drop in output was nearly 16 times larger than during the worst post-WWII recession. Most striking, however, is the increase in the unemployment rate by 22 percentage points which is five times more than during the worst post WWII recession. In summary, the Great Depression stands out as a truly exceptional decline in economic activity.

2. The table below shows per capita GDP in 2004 and the annual growth of per capita GDP over the last 25 years for selected countries. (A complete list of countries is available here.) Answer the following questions:

a. If over the next 25 years the Chinese economy grows at the same rate as it did during the last 25 years, what will its level of GDP per capita be? (Hint: GDP per capita in China next year would be 1,162*(1 + 0.0826), two years from now it would be 1,162*(1+0.0826)² and x years from now 1,162*(1+0.0826)^x .)

If China were to grow at the same rate as it did during the last 25 years, in the next 25 years its GDP per capita will be 1,162*(1.0826)²⁵=8,450, i.e. about the current level of Portugal.

b. If China grows at the same rate as it did during the last 25 years, when will it achieve the current level of U.S. GDP per capita? (Hint: You will also need to refresh your equation solving skills. In particular, recall that when solving an equation you can manipulate your equation by taking the natural logarithm of both sides. Also, recall that ln(a^x)=x*ln(a).)

We need to find x so that
1,162*(1.0826)^x=36,790
 1.0826^x=31.66
x*ln(1.0826)=ln(31.66)
x=43.5
If China were to grow at the same rate as it did during the last 25 years, it will take less than 44 years for China to achieve the current level of GDP in the U.S.

b. If both China and the U.S. grow at the same rate as they did during the last 25 years, how many years will it take for China to have a per capita GDP equal to that of the U.S.?

We need to find x so that
1,162*(1.0826)^x=36,790*(1.0206)^x
 1.0826^x=31.66*1.0206^x
x*ln(1.0826)=ln(31.66)+x*ln(1.0206)
x=59
It would take about than 59 years for China to catch up with the U.S.

c. If both the U.S. and Mexico grow at the same rate as they did during the last 25 years, will Mexico ever catch up with the U.S.? Will the gap between the U.S. and Mexico narrow or widen?

Mexico grows at a slower rate than the U.S. Therefore, if the current trend continues, Mexico will never catch up with the U.S.  Instead the income gap between the two countries will widen.

d. If China and Mexico grow at the save rate as they did during the last 25 years, when will China be richer than Mexico?

We need to find x so that
1,162*(1.0826)^x=5,968*(1.0067)^x
 1.0826^x=5.136*1.0067^x
x*ln(1.0826)=ln(5.136)+x*ln(1.0067)
x=22.5
It would take only 23 years for China to catch up with Mexico.