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A Summary of Alternative Methods for
Estimating Potential GDP
*March 2004*
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*Notes*
In the figures in this paper, the shaded vertical bars indicate periods
of recession.
Unless otherwise indicated, all years referred to in this paper are
calendar years.
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Preface
For the Congressional Budget Office (CBO), estimating the potential
output of the economy and projecting future levels of that output are
integral parts of producing short-term economic forecasts and
medium-term economic projections. Potential output is an estimate of
"full-employment" gross domestic product, or the level of GDP attainable
when the economy is operating at a high rate of resource use. Rather
than being a technical ceiling on production, potential GDP is a measure
of the economy's maximum sustainable output, in which the in-tensity of
resource use is neither adding to nor subtracting from inflationary
pressure. There are many ways to compute the economy's productive
potential. Some methods rely on purely statistical techniques.
Others--including CBO's method--rely on statistical procedures grounded
in economic theory.
This paper examines those methods, highlighting the pros and cons of
various approaches. In CBO's view, its method--which calculates
potential GDP using a growth model--provides an appropriate balance of
advantages and disadvantages and offers the best structure for
projecting GDP. CBO's basic procedure remains the same as that outlined
in previous reports, although the agency will continue to examine
alternative procedures.
Robert Arnold of CBO's Macroeconomic Analysis Division wrote this paper,
with assistance from Robert Dennis and John Peterson. Christian Spoor
edited the paper, and Leah Mazade proofread it. Maureen Costantino took
the cover photograph and prepared the paper for publication. Annette
Kalicki prepared the electronic versions for CBO's Web site.
Douglas Holtz-Eakin
Director
March 2004
CONTENTS
Introduction <#pt1>
CBO's Method for Estimating Potential Output <#pt2>
Other Methods for Estimating Potential Output <#pt3>
Advantages and Disadvantages of the Different Methods <#pt4><
*Figures*
1. GDP and Potential GDP
2. Okun's Law: The Output Gap and the Unemployment Gap
3. The Unemployment Gap and the Change in Inflation
4. Growth in Real GDP and Trend Growth Computed Using Deterministic
Time Trends and the Hodrick-Prescott Filter
Introduction
Assessing current economic conditions, gauging inflationary pressure,
and projecting long-term economic growth are central aspects of
producing the Congressional Budget Office's (CBO's) economic forecasts
and baseline budget projections. Those tasks require having a summary
measure of the economy's productive capacity. That measure--known as
potential output--is an estimate of "full-employment" gross domestic
product, or the level of GDP attainable when the economy is operating at
a high rate of resource use.
Although potential output measures the productive capacity of the
economy, it is not a technical ceiling on output that cannot be
exceeded. Rather, it is a measure of sustainable output, in which the
intensity of resource use is neither adding to nor subtracting from
inflationary pressure. If actual output exceeds its potential level,
then constraints on capacity begin to bind, restraining further growth
and contributing to inflationary pressure. If output falls below
potential, then resources are lying idle and inflation tends to fall.
Besides being a measure of aggregate supply in the economy, potential
output is also an estimate of trend GDP. The long-term trend in real
(inflation-adjusted) GDP is generally upward (see Figure 1 <#figure1>)
as more resources--primarily labor and capital--become available and as
technological change allows more-efficient use of existing resources.
Real GDP also displays short-term variation around that long-term
trend--largely because of the influence of the business cycle but also
because of random shocks whose sources are difficult to pinpoint.
Analysts often want to estimate the underlying trend, or general
momentum, in GDP by removing such short-term variation. A separate but
related objective is to remove the fluctuations that arise solely from
the effects of the business cycle. Potential GDP serves both purposes.
Figure 1.
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GDP and Potential GDP
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(Billions of chained 2000 dollars)
Graph
Source: Congressional Budget Office.
Note: The y axis is plotted using a logarithmic scale.
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Potential output plays a role in several aspects of CBO's economic
forecast. In particular, CBO uses potential output to set the level of
real GDP in its medium-term (10-year) projections. In doing so, CBO
assumes that any gap between actual GDP and potential GDP that remains
at the end of the short-term (two-year) forecast will close during the
following eight years. CBO also uses the level of potential output to
gauge inflationary pressure in the near term. For example, an increase
in inflation that occurs when real GDP is below its potential (and
monetary growth is moderate) can probably be attributed to temporary
factors and is unlikely to persist. Finally, potential output is an
important input in computing the standardized-budget surplus or deficit,
which CBO uses to evaluate the stance of fiscal policy.^(1) <#F1>
There are many ways to estimate the trend in GDP (and other economic
data) as well as to compute the economy's productive potential. Some
methods rely on purely statistical techniques. Others, such as CBO's
method, rely on models guided by economic theory. Many methods used to
compute potential output do not benchmark their trends to inflation or
any independent measure of capacity and therefore cannot be interpreted
as estimating the level of maximum sustainable output. That is, they
provide a measure of /trend/ output but not /potential /output.
Measures of potential GDP were initially devised to guide decisions
about monetary and fiscal policy, generally for a one- to two-year
horizon. If the economy was estimated to be below potential--meaning
that labor or capital was not fully employed--then monetary or fiscal
policy could be used to speed up the growth of output without incurring
the risk of significantly higher inflation. The concept of potential
output was seen as a tool to help policymakers manage aggregate demand
and thus maintain steady economic growth.
A spectrum of opinion exists among economists about the usefulness of
measures of potential GDP for monetary and fiscal policy and for
economic projections. Some economists do not think that the idea of
potential output is useful, arguing that:
* The concept is based on a flawed view of the causes of inflation,
even in the short run. According to this argument, inflation is
determined by growth in the money supply, not by where the economy
is in the business cycle.
* Potential GDP is so unstable and varies so much that it is
impossible to estimate accurately, especially for recent years,
and thus is not a helpful guide for policymaking or forecasting.
* Policies to manage demand generally do more harm than good because
of lags, uncertainties, and political pressures. Hence, the size
of the gap between actual and potential output ought to be
irrelevant to policymakers.
The experience of the late 1990s supported the position of people making
those arguments, because virtually all initial estimates of potential
GDP indicated a need for tighter policy to avoid inflation, but higher
inflation never materialized. More-recent experience, however, has
tended to support the opposite opinion: the fiscal and monetary policies
put in place in response to the 2001 recession and its aftermath--which
were predicated on the view that demand had fallen below its
potential--appear to have been timely and to have helped moderate the
downturn.
In CBO's view, the value of potential GDP is not restricted to
short-term fiscal and monetary policy. Potential output calculated with
a growth model is a useful concept for gauging the economy's productive
capacity and offers the best basis for projecting GDP over the 10-year
horizon required by the budget process. Carefully estimated, potential
GDP can provide the user with a reasonable sense of the economy's
potential for growth.
Any estimate of potential output, however, has shortcomings of which
users should be aware. First, such estimates are based on one or more
statistical relationships and thus contain an element of randomness. The
uncertainty surrounding an estimate of potential GDP can be reduced--but
not eliminated. Second, all of the methods used to compute potential GDP
have an "end-of-sample" problem. That is, estimating the trend in a data
series is especially difficult near the end of a data sample, making the
estimate most uncertain for the period of greatest interest: the recent
past. Third, all economic data are subject to revision, and data for
recent history are subject to the largest revisions.
CBO's Method for Estimating Potential Output
CBO's estimate of potential output is based on the framework of a
textbook model of long-term economic growth, the Solow growth model.^(2)
<#F2> The model attributes the growth of real GDP to the growth of labor
(hours worked), capital (an index of capital services emanating from the
stock of productive assets), and technological progress (total factor
productivity). CBO estimates trends --that is, removes the cyclical
changes--in the labor and productivity components by using a variant of
a relationship known as Okun's law. (In principle, other "detrending"
methods could be used to extract the trends in those inputs.)
Okun's law postulates an inverse relationship between the size of the
output gap (the percentage difference between GDP and potential GDP) and
the size of the unemployment gap (the difference between the
unemployment rate and the natural rate of unemployment) (see Figure 2
<#figure2>).^(3) <#F3> According to that relationship, actual output
exceeds its potential level when the rate of unemployment is below the
"natural" rate of unemployment; actual GDP falls short of potential when
the unemployment rate is above its natural rate.
Figure 2.
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Okun's Law: The Output Gap and the Unemployment Gap
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Graph
Source: Congressional Budget Office.
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For the natural rate of unemployment, CBO uses its estimate of the
nonaccelerating inflation rate of unemployment (NAIRU).^(4) <#F4> That
rate corresponds to a particular notion of full employment--the rate of
unemployment that is consistent with a stable rate of inflation. The
historical estimate of the NAIRU derives from an estimated relationship
known as a Phillips curve, which connects the change in inflation to the
unemployment rate and other variables, including changes in productivity
trends, oil price shocks, and wage and price controls. The historical
relationship between the unemployment gap and the change in the rate of
inflation is strong (see Figure 3 <#figure3>) and fairly stable. When
the unemployment rate is below the NAIRU, inflation tends to rise, and
when it exceeds the NAIRU, inflation tends to fall.
Figure 3.
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The Unemployment Gap and the Change in Inflation
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(Percentage points)
Graph
Source: Congressional Budget Office.
Notes: Inflation is measured using the consumer price index for all
urban consumers.
Unlike the other figures in this report, this figure uses annual data.
------------------------------------------------------------------------
CBO estimates an Okun's Law relationship for hours worked and total
factor productivity (TFP). It uses regression equations that link each
variable to the same set of explanatory variables (including the
unemployment gap) to capture the effects of fluctuations in the business
cycle. It also uses several time trends, which constrain the growth of
the potential variables to a constant rate over one or more specified
historical periods. CBO then calculates the potential levels of hours
worked and TFP from the predictions of the equations when the
unemployment gap is set at zero. Those potential levels are combined
with the capital input to compute potential GDP.^(5) <#F5>
Unlike the labor input and TFP, the capital input does not need to be
cyclically adjusted to create a "potential" level--the unadjusted
capital input already represents its potential contribution to output.
Although use of the capital stock varies greatly during the business
cycle, the potential flow of capital services will always be related to
the total size of the capital stock, not to the amount currently being
used.
Other Methods for Estimating Potential Output
CBO's approach is just one of a host of methods available for estimating
potential GDP, each of which has strengths and weaknesses. The major
methods include:
* / Labor productivity growth accounting./ This approach is similar
to CBO's method except that it models potential output as a
function of labor and labor productivity.^(6) <#F6> This approach
is simpler than CBO's approach because it avoids the need to
estimate and project the capital input. It is favored by people
who believe that capital is impossible to measure accurately. The
inputs (labor and labor productivity) can be cyclically adjusted
by using Okun's law or another detrending method.
* / Statistical filtering techniques./ Statistical filters (such as
centered moving averages, bandpass filters, the Hodrick-Prescott
filter, and the Kalman filter) are often used to extract the trend
from GDP directly.^(7) <#F7> These methods do not generally use
Okun's law and do not require judgments about trend breaks.
However, they do require analysts to make assumptions about how
the filters are structured, including the values of one or more
parameters.
* / Simultaneous econometric models./ Some researchers have
specified full simultaneous systems of equations that describe the
behavior of variables such as output, employment, productivity,
and inflation.^(8) <#F8> The parameters of these equations can be
estimated using statistical techniques, and under certain
assumptions, the equations can be used to calculate potential output.
* / Multivariate time-series models./ This category includes
statistical methods of estimation known as vector autoregressions
(VARs) and structural VARs.^(9) <#F9> These models are similar to
the econometric models described above in that they estimate the
parameters of econometric equations using statistical techniques.
However, they differ in that they impose far fewer restrictions on
the structure of, and relationships between, equations in the
system than the econometric models do.
Advantages and Disadvantages of the Different Methods
The first two approaches--CBO's method and the labor productivity growth
accounting method--have several key advantages. First, they look
explicitly at the supply side of the economy. Potential output is a
measure of productive capacity, so any estimate of it is likely to
benefit from explicit dependence on factors of production. For example,
if growth in the available pool of labor increases, then both of those
methods will show an acceleration in potential output (all other things
being equal). Under CBO's approach, an increase in investment spending
would also be reflected in faster growth in productive capacity.
Second, both of those methods permit a transparent accounting for the
sources of growth. In other words, they allow analysts to divide the
growth of actual or potential GDP into the contributions made by each of
the factor inputs. For CBO's model, that means labor, capital, and TFP;
for the labor productivity model, it means labor and labor productivity.
Third, by using a disaggregated approach, those two methods
(particularly CBO's procedure) can reveal more insights about the
economy than a more aggregated model would. For example, CBO's model
allows analysts to identify the separate contributions made by hours
worked, the stock of productive assets, and total factor productivity to
the robust growth of potential GDP during the late 1990s. By looking at
the different contributions, CBO determined that investment by
businesses (especially in information technology) was the primary source
of the acceleration in growth of potential output.
CBO's growth model and the labor productivity accounting method have
disadvantages as well. The simplicity of those two approaches can be a
drawback at times. CBO's model imposes some parameters--most notably,
the weights on labor and capital in the production function--rather than
estimating them econometrically. Although that approach is standard in
the growth- accounting literature, it requires making some strong
assumptions that may not be consistent with the data.
Another point of contention--particularly regarding CBO's approach--is
the use of deterministic time trends to cyclically adjust many variables
in the model. Some analysts assert that relying on fixed time trends
provides a misleading view of the cyclical behavior of some economic
time series. They argue, on the basis of empirical studies of the
business cycle, that using variable rather than fixed time trends is
more appropriate for most data series.
Finally, both CBO's growth model and the labor productivity accounting
approach are based on an estimate of the amount of slack in the labor
market, which in turn requires an estimate of the natural rate of
unemployment or the NAIRU. Such estimates are highly uncertain. Few
economists would claim that they can confidently identify the current
NAIRU to within a percentage point. CBO's method and the labor
productivity accounting approach are not very sensitive to possible
errors in the average level of the estimated NAIRU, but they are quite
sensitive to errors in identifying how that level changes from year to
year.
The three statistical approaches--statistical filtering, simultaneous
econometric models, and multivariate time-series models--have a key
advantage in that they are more flexible than the other methods in how
they estimate the trends in the data series and the values of
parameters. The filtering techniques, for example, do not require any
judgments about when trend growth changes during the sample. Because
they follow the data more closely, those methods tend to identify
changes in trends more quickly (see Figure 4 <#figure4>). The
econometric-model and time-series-model approaches allow the data to
determine the strength of the relationships among variables and
equations within the model. The three statistical approaches also allow
the values of estimated parameters to change as the economy evolves.
Figure 4.
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Growth in Real GDP and Trend Growth Computed Using Deterministic Time
Trends and the Hodrick-Prescott Filter
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(Percentage change from previous year)
Graph
Source: Congressional Budget Office.
Notes: Deterministic time trends assume break points at business-cycle
peaks (excluding the peaks in 1981 and 2001).
The Hodrick-Prescott filter uses a smoothing parameter of 1,600.
------------------------------------------------------------------------
The statistical approaches also have their drawbacks. For the filtering
methods, three shortcomings are significant. First, many of the filters
do not benchmark their trends to any external measure of capacity.
Therefore, unlike CBO's results, their results can be interpreted as
/trend/ GDP but not as /potential/ GDP. In other words, they do not
yield an estimate of the level of output that is consistent with stable
inflation. Moreover, the filtering methods do not produce cyclically
adjusted estimates of GDP, meaning that they do not attempt to remove
the effects of business-cycle fluctuations from the variable being
filtered. For example, a filtered estimate of real GDP slows
considerably during each recession and accelerates afterward (see Figure
4 <#figure4>). A cyclically adjusted measure of trend GDP would not
display that type of cyclical fluctuation.
Second, the filters require analysts to make judgments about the values
of parameters without providing guidance about satisfactory values. The
Hodrick-Prescott filter, for example, requires users to choose a
smoothing parameter, which entirely determines how much variation the
final estimate will display.
Third, those methods suffer from what is commonly known as the
end-of-sample problem. They typically compute the trend value for a
certain date using data from both before and after that date--that is,
they "average" both past and future values to calculate the trend.
Hence, those methods have trouble identifying the trend at the end of
the sample (during recent history) because fewer and fewer future values
are available to include in the average. Of course, recent history is
the period that policymakers are often most interested in because of its
bearing on the future.
With respect to the econometric and time-series models, the main
disadvantage is that they are highly aggregated and can obscure some
underlying relationships in the economy. In a sense, that disadvantage
is a mirror image of the key advantage of CBO's method, which allows the
sources of growth to be accounted for transparently. The econometric
models are largely black boxes--they may indicate, for example, that the
growth of potential output has accelerated, but they give no insight
into why.
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1. <#t1> See Congressional Budget Office, /The Cyclically Adjusted and
Standardized-Budget Measures/ (March
2004).
2. <#t2> See Congressional Budget Office, /CBO's Method for Estimating
Potential Output: An Update/ (August
2001).
3. <#t3> The natural rate of unemployment is the rate of unemployment
that prevails when the labor market is in equilibrium and the only
source of unemployment is job turnover (workers shifting between jobs
and searching for new jobs).
4. <#t4> For a description of CBO's procedure for estimating the
NAIRU, see Congressional Budget Office, /The Economic and Budget
Outlook: An Update/ (August 1994),
Appendix B. See also Congressional Budget Office, /The Effect of Changes
in Labor Markets on the Natural Rate of Unemployment/
(April 2002).
5. <#t5> That method requires CBO to make judgments about when breaks
occur in the trends for growth in TFP and hours worked. CBO allows those
trends to change at business-cycle peaks. Note that the method does not
force the trends to change at each peak; if the data do not call for a
change, the trends will remain constant.
6. <#t6> See, for example, George Kahn, "New Estimates of the U.S.
Economy's Potential Growth Rate," /Contemporary Economic Policy/, vol.
14 (October 1996).
7. <#t7> For examples of various statistical filters, see Mark French,
/Estimating Changes in Trend Growth of Total Factor Productivity: Kalman
and H-P Filters versus a Markov-Switching Framework,/ Working Paper
(Board of Governors of the Federal Reserve System, September 2001);
Kenneth Kuttner, "Estimating Potential Output as a Latent Variable,"
/Journal of Business and Economic Statistics/, vol. 12, no. 3 (July
1994); Jane Haltmaier, /Inflation-Adjusted Potential Output,/
International Finance Discussion Paper No. 561 (Board of Governors of
the Federal Reserve System, August 1996); and Douglas Laxton and Robert
Tetlow, /A Simple Multivariate Filter for the Measurement of Potential
Output,/ Technical Report No. 59 (Ottawa: Bank of Canada, June 1992).
8. <#t8> See Charles Adams and David Coe, "A Systems Approach to
Estimating the Natural Rate of Unemployment and Potential Output for the
United States," /IMF Staff Papers,/ vol. 37, no. 2 (June 1990).
9. <#t9> For examples using this approach, see Ufuk Demiroglu and
Matthew Salomon, /Using Time-Series Models to Project Output Over the
Medium Term/ , Technical Paper 2002-1
(September 2002); Olivier Jean Blanchard and Danny Quah, "The Dynamic
Effects of Aggregate Demand and Supply Disturbances," /American Economic
Review,/ vol. 79, no. 4 (September 1989); Chantal Dupasquier, Alain
Guay, and Pierre St-Amant, /A Comparison of Alternative Methodologies
for Estimating Potential Output and the Output Gap,/ Working Paper 97-5
(Ottawa: Bank of Canada, February 1997); and Pierre St-Amant and Simon
Van Norden, /Measurement of the Output Gap: A Discussion of Recent
Research at the Bank of Canada,/ Technical Report No. 79 (Ottawa: Bank
of Canada, August 1997).
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