The output gap

68 Pages·2000·1.18 MB·English

The output gap: measurement,
comparisons and assessment
Research Paper No. 44
June 2000
Iris Claus, Paul Conway, Alasdair Scott
Reserve Bank of New Zealand
RESERVE BANK OF NEW ZEALAND: Research Paper No. 44 1
© 2000 Reserve Bank of New Zealand
First printing 2000
Published by the Reserve Bank of New Zealand,
PO Box 2498, Wellington, NEW ZEALAND
The views here are those of the authors and do not necessarily reflect official positions of the Reserve
Bank of New Zealand. All errors, omissions, and views expressed in this paper are the sole responsibility
of the authors. This Research Paper may not be wholly or partially reproduced without the permission
of the Reserve Bank of New Zealand. Contents may be used without restriction provided due
acknowledgement is made of the source.
1. Claus, Iris
2. Conway, Paul
3. Scott, Alasdair
ISSN 0110 523X
2 RESERVE BANK OF NEW ZEALAND: Research Paper No. 44
Acknowledgements
We are especially grateful to the co-authors of some of the Discussion Papers on which this Research
Paper is based: David Frame, Victor Gaiduch and Ben Hunt. In addition, we would like to acknowledge
the support and insightful comments of Adrian Orr. The valuable assistance of Dean Minot is also
appreciated. Finally, we would like to thank colleagues who have commented on earlier versions of this
work: Anne-Marie Brook, Aaron Drew, Gaylene Hunter, John McDermott, Chris Plantier and Christie
Smith.
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Contents
Figures and tables 6
Summary 7
Chapter 1 The output gap and its measurement 9
1.1 The concept of the output gap 9
1.2 Measurement of the output gap 10
1.3 Three output gap models used at the Reserve Bank 13
1.4 Data and results 20
Chapter 2 Assessing the different output gap measures 24
2.1 Time domain analysis 24
2.2 Frequency domain analysis 31
2.3 Conclusion 37
Chapter 3 The use of the output gap under uncertainty 38
3.1 Measures of the output gap and inflation 38
3.2 Output gap uncertainty and monetary policy rules 44
3.3 Is the output gap still useful? 46
3.4 Conclusion 50
References 51
Appendix A1 Estimation techniques 55
Appendix A2 Data and data sources 61
Appendix A3 The Fourier and wavelet transforms 62
Appendix A4 Integration tests 67
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Figures and tables
Figure 1 Artificial series with different trends 12
Figure 2 Time series used in the estimation of the output gap measures 21
Figure 3 Measures of potential output 23
Figure 4 Measures of the output gap 23
Figure 5 Peaks and troughs in the output gap measures 25
Figure 6 Phase behaviour of the MV and UC output gap measures 30
Figure 7 Phase behaviour of the MV and SVAR output gap measures 30
Figure 8 Phase behaviour of the UC and SVAR output gap measures 31
Figure 9 Estimated spectral densities of the output gap measures 33
Figure 10 Wavelet decompositions 34
Figure 11 Adjusted measures of the output gap 35
Figure 12 Measures of the output gap and inflation 39
Figure 13 Actual and predicted changes in inflation 41
Figure 14 Actual and forecast changes in inflation 43
Figure 15 The efficient frontiers 49
Figure A1 Periodic time series and spectral density 63
Figure A2 Time series of three different frequencies and spectral density 64
Figure A3 Wavelet coefficients 66
Table 1 Descriptive statistics 26
Table 2 Descriptive statistics (cont.) 27
Table 3 Correlation statistics 28
Table 4 Concordance statistics 29
Table 5 Spectral mass within business cycle frequencies 33
Table 6 Estimation results 40
Table 7 Variance decomposition of the change in inflation 42
Table 8 Out-of-sample forecasts of inflation changes 44
Table 9 Statistical properties of simulated output gap errors 47
Table A1 Integration tests for the SVAR model 58
Table A2 Integration tests for the inflation models 67
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Summary
In recent years, many central banks have moved to pursue explicit inflation targets. Because of the long
lags between policy actions and inflation outcomes, indicators of future inflationary pressures play an
important role in guiding monetary policy aimed at achieving price stability. The output gap is
considered to be a key indicator of future (domestic) inflation; hence it has an important role in a
forward-looking inflation-targeting framework.
The output gap is simply the difference between actual output and potential output. In turn, potential
output is the level of economic activity that is consistent with no inflation pressures in the economy. In
this sense, potential output is the level of activity that the economy can sustain, given its productive
capacity. All else equal, if the output gap is positive through time, so that actual output is greater than
potential output, then inflation will begin to increase in response to demand pressures in key markets.
The converse will apply if the output gap is negative.
Given its importance, the output gap has been the focus of considerable research effort at the Reserve
Bank of New Zealand during the last few years. This research has been conducted on three fronts. First,
various techniques for estimating potential output and the output gap have been developed. Second,
the resultant estimates have been rigorously compared to assess their similarities and differences. The
third research direction has investigated the policy implications of the significant uncertainty associated
with these estimates of the output gap. This Research Paper presents the results of this ongoing work.
The volume is organised into three chapters that cover these themes.
The first chapter discusses the theoretical foundations of the output gap and various ways in which it
has been measured. Potential output is determined by factors such as the level of technology, the
abundance and quality of productive resources and the microeconomic environment. However, for a
number of reasons, it has generally proved impracticable to estimate potential output on the basis of
these fundamentals. At the Reserve Bank, three models have been developed that infer the level of
potential output from observable macroeconomic data. These models decompose real output into a
trend and a cyclical component. The trend is interpreted as a measure of the economy’s potential
output (supply) and the cycle is interpreted as a measure of the output gap (demand).
The first model, the multivariate filter, produces the measure of the output gap used in the Reserve
Bank’s economic projections. The multivariate filter augments a common time-series filter with condi-
tioning information from structural economic relationships. Specifically, information from inflation,
RESERVE BANK OF NEW ZEALAND: Research Paper No. 44 7
unemployment and surveyed capacity utilisation is used to help decompose actual output into
measures of potential output and the output gap.
The multivariate filter imposes some restrictions on the dynamics of potential output and the output
gap. Two alternative estimation techniques used at the Reserve Bank are less restrictive in this respect.
Both of these techniques estimate potential output and the output gap within a system of equations.
The first alternative technique is based on a structural vector autoregression methodology. This tech-
nique uses a system consisting of output, employment and capacity utilisation to identify potential
output and the output gap. The second technique employs a multivariate unobserved components
approach. This technique decomposes observed output into three unobserved components: a perma-
nent trend (potential output), a trend-reverting cyclical component (the output gap) and random noise.
The cyclical component is assumed to be related to an underlying cycle in the economy, which is also
present in unemployment and capacity utilisation.
In chapter 2, the estimated output gaps from these models are compared using a variety of different
techniques. This analysis suggests that the various output gap measures share some important similari-
ties. In particular, all of the output gaps ‘co-move’ and, more often than not, are in agreement about
the state of the cycle, especially during the 1970s and 1990s. During the 1980s, however, the output
gaps are less similar, highlighting the difficulties of distinguishing supply and demand shocks during this
period of economic reform in New Zealand. During the 1990s the output gap estimates appear to
converge, which may imply the emergence of a more regular growth cycle in the New Zealand econo-
my. Although the output gap measures tend to indicate consistently whether the economy is in excess
demand or supply, there is often substantial disagreement about the severity of cycles. In other words,
there is uncertainty about the magnitude of the output gap.
This highlights the uncertainty that is an inherent feature of output gap estimates. The policy implica-
tions of this uncertainty are investigated in chapter 3. Despite uncertainties, the output gap estimates
are found to be significant determinants of inflationary pressures. Furthermore, the various output
gaps are reasonably proficient at forecasting near-term changes in inflation. This chapter goes on to
consider the implications of output gap uncertainty on simple rules for conducting monetary policy.
This analysis suggests that policymakers should temper the aggressiveness of their response to move-
ments in the output gap in light of associated uncertainty. However, even in the presence of uncertainty,
the output gap still has a valuable role to play in the policy process. Using the output gap to guide
policy actions leads to greater macroeconomic stability than does basing policy actions solely on cur-
rent, observable data.
The output gap provides a link between the real economy and inflation and remains an important
indicator of future inflationary pressures at the Reserve Bank of New Zealand. However, because a
range of other factors also influence inflation, the output gap takes its place in a broad inflation-
targeting framework. Hence, the output gap is always viewed in context with other indicators. If it is
used in this way, and not accorded spurious accuracy, it has a valuable role to play.
8 RESERVE BANK OF NEW ZEALAND: Research Paper No. 44
1 The output gap and its
measurement
The first section of this chapter defines the output gap and provides a brief chronology of its develop-
ment. Section 1.2 outlines the different approaches that have been used to measure potential output
and the output gap. Three models of the output gap developed at the Reserve Bank of New Zealand are
discussed in more detail in section 1.3. The results from these three models are presented in section 1.4.
1.1 The concept of the output gap
It is straightforward to define the output gap as the difference between the level of actual output and
potential output. Since we can readily observe actual output, this naturally leads us to focus on the
definition of potential output. Potential output can be defined in terms of the factors of production. For
instance, Artus (1977) defines it as the level of output “that would be realised if the labour force … were
fully employed, and labour and capital were used at normal intensity”. However, this expression is not
particularly succinct – ‘labour force’, ‘fully employed’, and ‘normal intensity’ are all subject to consider-
able variation in interpretation and measurement. This variation, at least in part, explains the lack of a
single, unique definition of potential output.
From a central banking perspective, potential output is typically defined as the level of output that is
consistent with no inflation pressure in the economy. In this framework, the output gap is a summary
indicator of the relative demand and supply components of economic activity. As such, the output gap
provides a measure of the degree of inflation pressure in the economy and is an important link between
the real side of the economy – the production of goods and services – and inflation. All else equal, if the
output gap is positive through time, so that actual output is greater than potential output, then inflation
will begin to move upwards in response to demand pressures in key markets.1
The idea that economic growth tends to fluctuate around a sustainable rate has a reasonably long
history in the economics literature, dating back at least to Fisher (1933). Such an idea established a role
for stabilisation policy, suggesting, for example, that demand management policies could be used to
1 This definition is consistent with Okun (1962), who defines potential output as being “the maximum production without
inflationary pressure; or, more precisely … a point of balance between more output and greater stability”.
RESERVE BANK OF NEW ZEALAND: Research Paper No. 44 9
increase output when it is below its sustainable level. The link to the nominal side of the economy came
with the short-run Phillips curve. In the original specification of the curve, the inverse of the unemploy-
ment rate was used as a proxy for excess demand for labour (Phillips 1958). Low unemployment spelled
high excess demand and upward pressure on wages.
The original version of the Phillips curve has undergone several modifications since 1958. It was trans-
formed from a wage-change equation to a price-change equation, where prices are set by applying a
constant mark-up to unit-labour cost. From the slope of the price-change Phillips curve, policymakers
could then infer how much unemployment would be associated with any target rate of inflation. These
early versions of the Phillips curve reflected the prevailing economic thinking in the 1960s that the
supply side of the economy was deterministic, that is, it grew at a constant rate through time, and that
changes in demand were the prime cause of economic fluctuations.
In the early 1970s price expectations and a stochastic supply side were introduced into Phillips curve
analysis. The demand variable was re-specified more explicitly in terms of excess demand. Originally
defined as an inverse function of the unemployment rate, the demand variable was redefined as the
gap between the ‘natural’ and actual rates of unemployment.2 The adoption of the unemployment
gap in the Phillips curve finally recognised Samuelson and Solow’s (1960) finding that economic fluctu-
ations can arise as the result of both demand and supply shocks. Accordingly, it became necessary to
decompose unemployment into components attributable to changes in supply and demand in order to
formulate appropriate policy responses. The inclusion of price expectations recognised the importance
of expectations in the inflation process and was able to account for shifts in the Phillips curve.
Okun’s (1962) law relates labour market conditions to conditions in the goods market, providing a link
between the unemployment gap and the output gap. With the natural rate hypothesis of Phelps (1967)
and Friedman (1968), this led to the notion that there is an equilibrium level of output consistent with
stable long-run inflation (Modigliani and Papademos 1976).
Clearly, a central problem with the concept of the output gap is that it cannot be directly measured.
The level of potential output is unobservable and has to be inferred from available macroeconomic
data. This is the issue to which we now turn.
1.2 Measurement of the output gap
Three general approaches to measuring potential output and the output gap have been used to varying
degrees. The first, and one that received early favour, was to estimate a production function based on
factor inputs such as capital, labour, and possibly intermediate inputs such as energy. The second
estimation approach uses times-series techniques to decompose actual output into potential output
2 The natural rate is the rate that prevails when expectations are fully realised and incorporated into all wages and
prices.
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