Transcript 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
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Transforming Economic Data
• Measuring Variables
- Time series
- Relationships between diff. time series
- Predict future
- Government policy
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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.
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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
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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?
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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.
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How to Construct a Linear Trend
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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).
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How to Construct a Linear Trend
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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.
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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
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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
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High and Low Frequencies Compared
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Figure 3.2
High and Low Frequencies Compared
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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.
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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).
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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
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A Stylized Business Cycle
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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.
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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.
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Transforming Economic Data
• The Correlation Coefficient
  x  x  y
n
 xy 
i
y
i
i 1

 x  x  y  y
2
i
2
i
 xy

 x y
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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
 xt
t 1
 x
t 1
x  x  x
2
t
t
t 1
 xt 1

 xt 1

2
• See Figure 3.5
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Transforming Economic Data
• Coherence
- A second important feature of economic time
series is that they tend to move together
coherence.
 x
T
 xy 
t

 x yt  y
t 1

 x  x  y  y
2
t
2
t
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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
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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.
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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
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Labor Force Participation Since 1950
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Box 3.2A
Labor Force Participation Since 1950
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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
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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.
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34
From GDP Growth to GDP
Index of real GDP and the chain weighting
method.
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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)
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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.
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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)
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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)
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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.
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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.
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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.
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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.
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Growth and Inflation: Pre- and Postwar
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Figure 3.7
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Homework
Question 4, 6, 7, 12, 13
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END