Download Transforming Economic Data

Chapter 3
Macroeconomic Facts
Introduction
• Two kinds of regularities in economic data:
- Relationships between the growth components
in different variables.
- Relationships between the cycles.
• The relationships can be described by
persistence and coherence.
• Detrending helps us to uncover hidden patterns
in the data.
• Business Cycle
2
Transforming Economic Data
• Measuring Variables
- Time series
- Relationships between diff. time series
- Predict future
- Government policy
3
Transforming Economic Data
• Separating Growth From Cycles
- Data are measured at different intervals
annual, quarterly, monthly and etc.
- To make the data more amenable to analysis, we
transform it by seasonal adjustment or
detrending.
4
Transforming Economic Data
• The trend is the low-frequency component of a
time series.
The theory of economic growth
• The deviation of the series from its trend is
called the high-frequency component.
The theory of business cycle
5
Transforming Economic Data
• Removing a Trend
- Fitting a trend line to a set of points and
defining the cycle as the differences between
the original series and the trend.
- Before fitting a trend, we typically take the
logarithm of the original series.
Why?
6
Transforming Economic Data
• Removing a Trend
- Suppose “Y” is growing at a constant,
compound rate.
- Compound growth (exponential growth) means
that annual increments to the series themselves
contribute to growth in subsequent year.
Y is nonlinear but log of Y is linear.
See Figure 3.1 A.
7
How to Construct a Linear Trend
8
Figure 3.1
Transforming Economic Data
• Removing a Trend
- Many economics variables have an underlying
growth rate that is constant, but it fluctuate
randomly around this underlying rate from one
year to the next.
- Linear detrending is to fit the best straight line
through the graph of the logarithm.
- The fitted line is called the linear trend (lowfrequency) and the deviations from the fitted
line are called the linear cycle (high-frequency).
9
How to Construct a Linear Trend
10
Figure 3.1
Transforming Economic Data
• Detrending Method
- The linear trend has the disadvantage that the
trend itself is assumed constant.
- If a series is detrended using the linear method,
the series may deviate from its underlying
growth rate in the long run.  we need to fit a
flexible trend.
11
Transforming Economic Data
• Detrending Method
- A third method of revealing the high-frequency
relationship is to look at a growth rates of data
rather than at the raw data itself
differencing
DGDP1987
GDP1987  GDP1986

GDP1986
12
Transforming Economic Data
• Importance of Detrending
- Detrending reveals relationships between time
series that exist at on frequency but not at
another.
- Many relationship can be easily observed from
the high-frequency component.
- See Figure 3.2
13
High and Low Frequencies Compared
14
Figure 3.2
High and Low Frequencies Compared
15
Figure 3.2
Transforming Economic Data
• Quantifying Business Cycles
- The business cycle is an irregular, persistent
fluctuation of real GDP around its trend growth
rate.
- It is accompanies by highly coherent comovements in many other economic variables.
16
Transforming Economic Data
• Quantifying Business Cycles
- One tool used to describe business cycles is the
correlation coefficient.
- It is used to measure the strength of a
relationship between two variables (coherence)
and the strength of the relationship between a
single variable and its own history
(persistence).
17
Transforming Economic Data
• Peaks and Troughs
- The common features of business cycles are
peaks, troughs, expansions and recessions.
Ex: GDP
- Peak: the point at which the growth rate of
GDP begins to decline.
- Trough
- Expansion: the period between a trough and its
subsequent peak.
- Recession
18
A Stylized Business Cycle
19
Figure 3.3
©2002 South-Western College Publishing
Transforming Economic Data
• Peaks and Troughs
- Real data do not display the kinds of
regularities as in figure 3.3.
- The regularities in economic data are statistical.
- No two business cycles are exactly alike, so we
aim at their average behavior and relationship.
20
Transforming Economic Data
• The Correlation Coefficient
- Scatter Plot : a graph in which each each point
represents an observation from two different
variables at a given time. (See Figure 3.4)
- Statistician have developed a way of
quantifying the relationship between two
variables in a scatter plot with a single number
 the correlation coefficient.
21
Transforming Economic Data
• The Correlation Coefficient
  x  x  y
n
 xy 
i 1
i
y
i

 x  x  y  y
2
i
2
i
 xy

 x y
22
Transforming Economic Data
• Persistence
If we plot the value of deviation of GDP from
trend in one year against its own value in the
previous year, these deviations follow a straight
line.
T
x x 
t t 1
 x
t 1
t
 xt
 x
t 1
x  x  x
2
t
t
t 1
 xt 1

 xt 1

2
• See Figure 3.5
23
Transforming Economic Data
• Coherence
- A second important feature of economic time
series is that they tend to move together
coherence.
 x
T
 xy 
t 1
t

 x yt  y

 x  x  y  y
2
t
2
t
24
Transforming Economic Data
• Coherence
- If a time series goes up (down) when GDP goes
up (down), we say the series is procyclical.
ex. Consumption, Investment
- A series that moves in the opposite direction to
GDP is countercyclical.
ex. Unemployment
- See BOX 3.1
25
26
Table 3.1
Measuring Unemployment
• Labor force: people who are working or
looking for work.
• Out of labor force: people who are not
employed and are not looking for a job.
• Labor force participation rate: the labor
force expressed as a percentage of the civilian
population over the age of 16.
27
Measuring Unemployment
• Employment Rate:
the fraction of the population employed.
employed
adult population
• Unemployment Rate:
the fraction of the labor force looking for a job.
unemployed
labor force
28
Labor Force Participation Since 1950
29
Box 3.2A
Labor Force Participation Since 1950
30
Box 3.2B
Measuring Unemployment
• Does a increase in the employment rate
imply a decrease in the unemployment rate ?
employed
employment rate =
adult population
employed

labor force + out of labor force
unemployed
unemployment rate =
labor force
31
32
Table 3.2
©2002 South-Western College Publishing
Measuring GDP Growth
- Real GDP was measured by the base-year
method.
- Recently, the Commerce Department has
switched to the chain weighted method as an
alternative to reduce the relative price effects.
33
34
From GDP Growth to GDP
Index of real GDP and the chain weighting
method.
35
Measuring Inflation
• Inflation is the average rate of change of the
price level.
• Five measures of the price level
- The consumer price index (CPI)
- The producer price index (PPI)
- The GDP deflator
- The GDP price index
- The personal consumer expenditure (PCE)
36
Measuring Inflation
• A price index is a weight average of the prices
of many different commodities where weights
are constants that are multiplied by each price
and that sum to one.
• The weights denotes importance.
37
Different Kinds of Price Indices
• Three alternative kinds of price indices:
- Laspeyres (CPI, PPI GDP deflator)
past consumed bundle
- Paasche (GDP deflator)
current consumed bundle
- Superlative (GDP price index, PCE)
38
The CPI and the PPI
• CPI tried to measure the average cost of living
of a representative household.
• PPI tried to measure the average cost of the
inputs of a representative producer.
• Many economists watch the PPI closely since
price increases that occur in the PPI often
eventually end up in the CPI
 PPI is the leading indicator of inflation.
• Shortage: It overstates inflation. (Laspeyres)
39
The GDP Deflator and
the GDP Price Index
• Corresponding to the Commerce Department’s
switch from a base-year to a chain weighted
measure of growth, there has been a switch
from the GDP deflator to the GDP price index.
• Example: Table 3.3, 1999-2000
• For GDP price indices, inflation is measured as
the average of the percentage change in the
price indices obtained from using adjacent
years as the base.
40
The PCE Price Index
• Like the GDP price index, PCE is a Superlative
index.
• Like the CPI, the PCE includes only those
commodities that represent personal
consumption expenditures by households.
41
Inflation and the Business Cycle
• Many time series are strongly procyclical (e.g.,
consumption) or strongly countercyclical (e.g.,
unemployment).
• Inflation is neither procyclical nor
countercyclical.
See Figure 3.6.
42
Inflation and the Business Cycle
•
•
•
•
Figure 3.7
1920-40 : Inflation seems to be procyclical.
1940-90: Inflation seems to be countercyclical.
Keynes believed that the Great Depression was
caused by the demand shocks and inflation
would be procyclical.
• Real business cycle theorists assert that most
business fluctuations occur as a result of
changes in productivity, and they predict that
inflation should be countercyclical.
43
Growth and Inflation: Pre- and Postwar
44
Figure 3.7
©2002 South-Western College Publishing
Homework
Question 4, 6, 7, 12, 13
45
END