Chapter 3: Macroeconomic Facts Instructor’s Manual
Chapter 3: Macroeconomic Facts
Problem 1
The three methods of detrending are linear detrending, flexible detrending (for instance, the Hodrick-Prescott filter) and differencing.
Actual time series data have to be detrended before they can be analyzed for business cycle analysis because we want to isolate that component of a time series data that occurs at business cycle (i.e., high) frequency and leave out the growth (or low frequency) component.
Problem 2
a. A recession is defined as the period from a peak to the successive trough in a business cycle.
b. An expansion, on the other hand, is the period from a trough to the immediately succeeding peak.
c. A business cycle peak is the point at which the growth rate of GDP begins to decline.
d. A business cycle trough is when the growth rate of GDP starts to increase again.
Problem 3
A procyclical variable is one that has a positive correlation coefficient with GDP, while a countercyclical variable is one that has a negative correlation coefficient with GDP. Whenever the cyclical component of any time series is investigated, any trends in the data must first be removed in order to isolate the cyclical component of the data. If this is not done, then the results will be biased. This is the importance of detrending time series data.
Problem 4
Total consumption, total investment, and imports are procyclical. Unemployment is countercyclical. Exports and inflation are acyclical.
Problem 5
a. The correlation coefficient can be used to measure coherence, meaning the strength of the relationship between two different variables, or persistence, meaning the strength of the relationship between a single variable and its past values.
b. A positive relationship (positive correlation) exists between X and Y.
c. Procyclical means that a variable has a positive correlation with GDP, while countercyclical means that a variable has a negative correlation with GDP. If X is GDP, then Y is procyclical.
Problem 6
a. Figures 2 and 3 below show the scatterplot of Consumption and Employment against GDP for Legonia. Notice how consumption moves along with GDP, and unemployment moves in the opposite direction to GDP. Hence consumption is procyclical and the unemployment rate is countercyclical.
Figure 2: Scatter Plot of Consumption against GDPFigure 3: Scatter Plot of Unemployment Rate against GDP
b. The average GDP is 30, average consumption is 20, and average unemployment rate is
2.4.
c. Correlation coefficients are:
Corr(GDP, Consumption) = 0.71, Corr(GDP, Unemployment Rate) = -0.99.
Thus the unemployment rate is more strongly correlated with GDP (the negative sign means it is countercyclical).
d. Persistence is measured by the autocorrelation coefficient. For that, we need to plot GDP(t) against GDP(t-1). The table below constructs these two series for the years 1998-2001. Note that we lose one year's observation, that of 1997, since there is no data for the year 1996 to go with it.
Year / GDP(t) / GDP(t-1)1998 / 25 / 15
1999 / 35 / 25
2000 / 40 / 35
2001 / 35 / 40
Our objective is to find the slope of the line (which equals the autocorrelation coefficient) going through the scatter plot of GDP(t) against GDP(t-1). It is 0.95.
Problem 7
a. In 1992, the total number of people unemployed were:
10% of labor force = 10% of 20,000 = 2,000.
Similarly, in 2002, the unemployment rate was 12% of a labor force of 25,000; hence 3,000 people were unemployed.
b. The labor force participation rate is that percentage of the population who are in labor force. In 1992 this figure was 80% and in 2002 it was 83.33%.
c. Employment per person is obtained by dividing total employment by the total population. It was 0.72 in 1992 and 0.73 in 2002.
Between 1992 and 2002, the unemployment rate increased from 10% to 12%, and the employment rate increased from 72% to 73%. The unemployment rate is the percentage of the labor force who are looking for work but are not currently employed, whereas the employment rate is the percentage of the population who are employed. Since both the rates increased, it must be the case that not only did the total population increase, the labor force increased substantially, too (one possible reason could be increased participation by women as happened in the U.S. in the late 1960s).
Problem 8
The labor force participation rate has increased dramatically since the 1950s (see Box 3.2 Panel C in the text). Most of this increase is the result of the large increase in participation by women in the labor force. Before, when many women worked at home, their production was not included in GDP. One of the important reasons for the large increase in GDP since the 1950s is that as more women have entered the workforce, their output has been and continues to be counted when calculating GDP.
Problem 9
It is possible for both employment and unemployment to rise at the same time, but there must be a large enough increase in the labor force to accommodate increases in both of these categories.
Problem 10
Workers who have been unemployed for long periods of time may become discouraged and stop looking for work. When this happens they are no longer counted as unemployed and dropped out of the labor force. Also, many workers may consider themselves "underemployed" because they are either not working full time and would like to be or are working at a job that is below their skill level. As a result of these factors, the unemployment rate reported by the Bureau of Labor Statistics underestimates the actual unemployment rate within the economy.
Problem 11
When using the base year method of calculating GDP, the growth results will be sensitive to the choice of the year whose prices are used as base year prices. This is because there are often changes in relative prices from year to year. As a result, different goods will be weighted more or less heavily depending upon which base year is chosen. Chain-weighting GDP is one method of smoothing out these differences by calculating GDP for two different base years and averaging the results. The base year prices chosen are always the prices at the beginning of the period and the end of the period. For example, when calculating GDP growth from 2000-2001 the growth rate of GDP between 2000-2001 must be calculated using 2000 prices as the base year, then again using 2001 prices as the base year. These two different results must then be averaged to get chain-weighted GDP.
Problem 12
a. Year Nominal GDP Real GDP
1997 $ 600 $ 600
1998 $ 1,190 $ 790
1999 $ 1,475 $ 930
b. Growth rate between 1997-1998 was 31.7%.
Growth rate between 1998-1999 17.7%.
c. Year Nominal GDP Real GDP
1997 $ 600 $ 920
1998 $ 1,190 $ 1,190
1999 $ 1,475 $ 1,405
Growth rate between 1997-1998 was 29.3%.
Growth rate between 1998-1999 was 18.1%.
The answers to parts b and c of this problem are different because the relative prices of the three goods have changed and, as a result, each good is weighted more or less heavily depending on which year is used as the base year.
e. Chain weighted GDP growth between 1997-1998 = (31.7 + 29.3)/2 = 30.45%.
Chain weighted GDP growth between 1998-1999 = (17.7 + 18.1)/2 = 17.9%.
Problem 13
a. 1997 GDP Deflator = 100
1998 GDP Deflator = 150.1
1999 GDP Deflator = 158.6
b. Inflation 1997-1998 = 50.1%
Inflation 1998-1999 = 5.7%
c. 1997 GDP Deflator = 65.2
1998 GDP Deflator = 100
1999 GDP Deflator = 105
Inflation 1997-1998 = 53.4%
Inflation 1998-1999 = 5%
Once again, the answers to parts b and c are different because the relative prices of the three goods have changed, and as a result each good is weighted more or less heavily depending on which year is used as the base year.
d. Chain-weighted inflation between 1997-1998 = (50.1 + 53.4)/2 = 51.75%.
Chain-weighted inflation between 1998-1999 = (5.7 + 5)/2 = 5.35%
Problem 14
A Laspeyres index measures the current cost, relative to the past cost, of a given bundle of goods consumed in the past (for example, the CPI). A Paasche index measures the current cost, relative to the past cost, of the currently consumed bundle of goods and services (for example, the GDP deflator). A Superlative index takes the average of the Laspeyres and Passche index for two consecutive years (for example, the GDP price index and the PCE price index). Laspeyers indicies tend to overstate inflation because they ignore the substitution that takes place of cheaper goods for more expensive goods. Paasche indicies tend to overstate inflation for the same reason. A Superlative index is far superior but is tedious to calculate.
Problem 15
The CPI uses a fixed bundle of goods from year to year. Because the CPI ignores the substitution that takes place when goods increase in price, it tends to overstate the true effects of inflation. In addition, the CPI includes foreign goods in its calculations and ignores good that are not typically consumed by households.
Problem 16
Because the CPI uses a fixed bundle of goods from year to year, it ignores the substitution that takes place when goods increase in price. As a result, it tends to overstate the true amount of inflation. The CPI is widely used in calculating the size of cost of living adjustments made in labor contracts and also by the federal government. Because of this, the federal government provides cost of living adjustments to social security and other transfer payment recipients that are larger than the actual amount of inflation. This bias in the CPI costs the government billions of dollars a year.
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