Are pressures in the economy strong or subdued? The answer to this question is important to a central bank operating an inflationtargeting monetary policy regime, because the degree of pressure in the economy can provide some indication of future inflation. The level of output that is at any time consistent with stable inflation is usually referred to as potential output. The output gap, which measures the difference between actual and potential output, is a commonly used measure of inflationary pressures in the economy.
The output gap is not directly observable, and must therefore be estimated. Different calculation methods, however, often produce different values for the output gap. In this article, a set of alternative methods for estimating the output gap are presented and compared. The different methods show a consistent pattern for the output gap, but there are also important differences. Our study shows that if the assessment of economic pressures is solely based on developments in the output gap as measured by one method, there is a risk of misjudging the economic situation. Assessments of the output gap must therefore also be based on professional judgment and supplementary indicators.
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Assessments of the state of the economy are based on continuous monitoring and analysis of a number of economic indicators that represent different aspects of the economy. In order to summarise and quantify economic pressures, the output gap has proved to be a useful startingpoint. Most inflationtargeting central banks therefore publish estimates of developments in the output gap in addition to inflation projections.
In a situation where employment is high in relation to the total labour force and the capital stock is fully utilised, there will be a tendency for price and wage inflation to rise. Conversely, price and wage inflation will tend to decrease when unemployment is high and capital utilisation is low. This also means that at any given time there exists a level of resource utilisation that would be consistent with stable developments in prices and wages. The corresponding level of output is usually referred to as potential output. The output gap is the difference between actual and potential output. If actual output is higher than potential output, the output gap is positive, indicating pressures in the economy. In isolation, this is usually accompanied by rising inflation. A negative output gap indicates spare capacity and falling inflation.
The output gap is also an important variable in itself, as a measure of economic fluctuations. Over time, economic resources are utilised efficiently when economic growth is stable and the output gap remains close to zero. Employment and unemployment will then be stable.
It may be useful to think of potential output as consisting of two components. On the one hand, a constant rate of increase in the labour force, capital and technological progress will result in steady annual growth in potential output. This component of potential output can be represented by a smooth, deterministic trend that is solely dependent on time. On the other hand, there are a number of reasons for potential output growth to vary over time. Technological advances can result in strong productivity growth and changes in the level of potential output. The supply of natural resources can vary. The labour supply depends on factors such as preferences between work and leisure, institutional factors and demography. Capital stock depends on the level of fixed investment. Changes in these production conditions (the supply side of the economy) might result in changes in potential output beyond those indicated by purely deterministic developments. As a rule, these changes will lead to longterm or permanent shifts in potential output, (although the changes may also be temporary). When these factors are added to the deterministic trend, it becomes clear that potential output can no longer be described as a smooth trend.
If actual output is equal to potential output, the output gap will be zero. This occurs very seldom since the economy is also exposed to more shortterm, cyclical disturbances, which are related to the demand side of the economy.
Actual output can thus be divided into three components:
a deterministic trend,
changes in production conditions (supplyside disturbances of some duration), and
the output gap (temporary demandside disturbances).
This division is useful for two reasons. First, the division shows that variation in economic growth over time may be due to disturbances (shocks) on both the supply side and the demand side of the economy. The output gap and the inflation outlook are only affected by temporary demand shocks (2). Second, the division provides a useful guideline when calculating and interpreting the unobservable variables potential output and the output gap.
Different methods for estimating the output gap can produce different values. This has given rise to a number of studies, including some recently carded out by central banks (3). Historical estimates of the output gap might also change when data are revised and new information emerges (4). The problem of data revisions applies to both actual and potential output, and there is therefore uncertainty concerning both components of the output gap.
In this article, we will focus on estimating and comparing different methods for estimating the output gap and will for the present disregard the problems associated with data revision and new information. In Section 1, the different methods are explained and estimates based on Norwegian data are presented. In Section 2, we review some simple criteria for comparing the alternative estimates. Our conclusions are presented in the third and final section.

Methods for estimating the output gap
A few methods for estimating the output gap have been discussed previously in Norges Bank's quarterly Economic Bulletin, see Froyland and Nymoen (2000). The issue of measuring the output gap has also been discussed in a number of boxes in Norges Bank's Inflation Report, most recently in Inflation Report 2/04. In this article, we will present a set of internationally recognised and commonly used methods, then estimate alternative output gaps using Norwegian data and compare the different methods.
The output gap can be defined as
(1) [ygap.sub.t] = [y.sub.t]  [y.sup.*.sub.t]
The variables are expressed in logarithms, with the output gap, [ygap.sub.t], being the percentage deviation between actual output ([y.sub.t]) and potential output ([y.sup.*.sub.t]).
Chart 1 presents a graphical illustration (5) of the relationship between the output gap and actual and potential output.
Historically, the first, simple methods for estimating the output gap were based on the assumption that output was moving along a linear trend in the long term. The trend was interpreted as an indication of potential output. A linear trend, however, is a very strict assumption that does not allow for possible variations in potential output over time, cf. the above discussion.
Over recent decades, a number of alternative methods for estimating the output gap have been developed. The alternative methods can be categorised in several ways. We have chosen to group the methods into two main categories: univariate methods (methods that use information inherent in GDP only) and multivariate methods (methods that also use additional variables).
1.1 Univariate methods
Univariate methods only use information in the time series itself (here, mainland GDP) to estimate the output gap. Most of these methods calculate a trend as an expression of potential output. Some methods model the output gap directly.
There are many alternative univariate methods, from the very simple to the relatively complicated. Three examples will be reviewed here. The estimates are based on seasonallyadjusted figures from the quarterly national accounts for the period 1978 Q1 to 2004 Q2. In spite of seasonal adjustment of the figures, variations in the quarterly figures result in substantial, random disturbances in the output gaps. Although the calculations are based on quarterly data, in the figures presenting the various output gap, we have aggregated the quarterly figures to annual figures. For 2004, published figures for the first half of the year have been used.
HodrickPreseott filter (HP)
The HodrickPrescott filter is a simple, widely used technical method (6). The HP filter is a method for finding the value of potential output [yt.sup.*] that minimises the difference between actual output and potential output while imposing constraints on the extent to which growth in potential output can vary. The following expression is minimised:
(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
The first term in the equation is the square of the difference between actual output and potential output. The second term is the square of the change in potential output growth. [lambda] is a parameter with values between zero and infinity that determines the extent of permissible variations in potential growth. [lambda] is determined outside the model. In the borderline case where [lambda] is infinite, there will be minimal variation in potential growth. The result is a linear trend with a level of growth that is constant. In the opposite borderline case where [lambda] = 0, the difference between actual output and potential output is as small as possible. These two variables will then be identical and the output gap will be zero at all times.
One advantage of the HP filter is that the method is simple to use. Flexibility in potential output growth is permitted by setting an appropriate value for [lambda]. One disadvantage is that the level of potential output is more affected by variations in actual output at the beginning and at the end of the period than in the rest of the period. This is because the HP filter for any given point...