Potential Output: Concepts and Measurement - Department of Labour

Labour Market Bulletin 1995:1 Pages 72–115 

Potential Output: Concepts and Measurement 

DARREN GIBBS 1 

This paper is concerned with the concept of potential output—the economy’s sustainable 

level of economic activity. The paper outlines the significance of potential output 

for policymakers, and surveys methods which have been devised to estimate potential 

output empirically. Preliminary analysis for New Zealand suggests that the sustainable 

rate of economic growth currently lies in the range of 3–4 percent per annum. However, 

for many reasons, considerable uncertainty is attached to these estimates. This limits 

the usefulness of these measures in policymaking. 2 

1 Introduction 

THIS PAPER IS CONCERNED with the practical measurement of ‘potential 

output’. The concept is a familiar one to economists. Put simply, potential 

output is the level of economic activity at which aggregate demand and 

aggregate supply is consistent with a stable inflation rate. In a dynamic context, 

the economy’s ‘potential growth rate’ can be similarly defined. (The terms 

‘potential growth rate’ and ‘sustainable growth rate’ are often used interchangeably.) 

By calculating the level and rate of growth of potential output, and 

comparing the results with observed output trends, one can obtain a measure of 

the degree of spare capacity in the economy, and the rate at which capacity is 

expanding. 

The development of empirical measures of the degree of spare capacity in the 

economy, and the economy’s potential growth rate, is important for a number of 

reasons. The most common use of such measures is as a guide for monetary and 

fiscal policy, and as a source of information for use in developing forecasts of 

economic growth. If reliable, they would provide an important guide for 

policymakers in determining whether developments in the real economy are 

consistent with the maintenance of price stability. In the New Zealand context, 

they could also assist fiscal policymakers in determining whether spending 

decisions and tax settings are consistent with the Fiscal Responsibility Act 1994. 3 

1 

Darren Gibbs is an economist at the Reserve Bank of New Zealand. He has worked 

previously as an adviser in the Labour Market Policy Group of the Department of Labour. 

2 

The paper has benfited from comments made by colleagues at the Reserve Bank and the 

Department of Labour. However, all views expressed are those of the author, and not 

necessarily those of the Reserve Bank or the Department of Labour. 

3 

Although most economists would share this view the consensus regarding the usefulness 

of empirical measures of potential output is not unanimous. For example, Plosser and 

Schwert (1979) invoke the Lucas (1976) critique to argue that ‘these models cannot be used 

to predict the future path of output under different policy regimes. It would seem, therefore, 

that modelling “potential output” is an exercise with little merit, serving only to perpetuate 

the idea that its use as a policy guide can be justified through economic theory’ (p 185).

Darren Gibbs 

73 

These measures are also relevant for labour market analysts and commentators. 

In addition to their use in developing employment and wage projections, 

which rely on forecasts of the overall level of activity, they also play a part in 

informed decision-making regarding the feasibility of various labour market 

policy settings. For instance, a knowledge of how close to capacity the economy 

is can tell us about the extent to which efforts to reduce unemployment, or 

trends in employment growth, are likely to result in upward pressure on wages 

or prices. 

The aim of this paper is to present a brief survey of the techniques that have 

been used overseas to measure potential output, and to apply several of these 

techniques in order to estimate preliminary potential output series for New 

Zealand. Section 2 defines what is meant by the term ‘potential output’, and 

outlines more fully why the concept is of interest to central banks, governments 

and private sector businesses. The main techniques used by economists to 

empirically measure potential output are then discussed in section 3. Section 4 

presents the results obtained when applying a number of these techniques to 

New Zealand data, and section 5 uses econometric techniques in an effort to 

select which of the estimates is preferable. The paper ends with a brief 

conclusion, which summarises the main ideas and results and suggests possible 

directions for future research. 

2 Economic growth and potential output 

Following World War II, a stable economic environment saw standards of living 

in most OECD countries grow rapidly. 4 

For many years New Zealand also 

enjoyed strong economic growth and almost everybody who wanted a job was 

able to find work. However by the late 1960s economic performance had begun 

to deteriorate in most OECD countries, and the extent of deterioration was 

particularly marked in the case of New Zealand. Whereas New Zealand’s 

standard of living was ranked third in the developed world in 1950 (behind the 

United States and Canada), by 1975 it had dropped to fifteenth. During the 

decade following the first oil shock in 1973, New Zealand’s economic 

performance slumped significantly. Growth during 1975 to 1984 averaged little 

more than 1.5 percent; and our relative standard of living dropped further to 

twenty-first place on the OECD ladder. 

The deterioration in economic performance prompted a serious rethink of 

economic policy. As a consequence, since the mid 1980s, successive governments 

have implemented a comprehensive programme of economic and financial 

reform. These reforms have included: the deregulation of the banking industry; 

the freeing of controls on international capital flows (including the floating of the 

4 

The term ‘standard of living’ as used here refers only to measured pecuniary benefits as 

proxied by GDP.

74 

Labour Market Bulletin 1995: 1 

exchange rate); the removal of a complex system of export subsidies, import 

licences and quotas; a programme of tariff reductions; the commercialisation 

(and in most cases privatisation) of State-owned market industries; the granting 

of operational independence to the Reserve Bank to pursue the sole target of 

price stability; legislation designed to improve the ability of employers and 

employees to negotiate more flexible and mutually beneficial employment 

relationships; and, latterly, legislation binding the Government to conduct fiscal 

policy in a manner which is both transparent and prudent. All together these 

‘supply-side’ policies are designed to improve the efficiency with which scarce 

resources are allocated within the economy, thus raising productivity growth and 

increasing New Zealand’s long-term sustainable rate of output growth. 

In undergoing these reforms New Zealand has incurred substantial 

adjustment costs. However with economic growth reaching 6.0 percent in the 

year to March 1995, employment recovering strongly, and inflation and current 

account pressures broadly in check, many economists now agree that the fruits 

of these reforms are beginning to be seen. Consequently, the focus of attention 

has now turned to the following question: what is the economy’s sustainable rate 

of growth? 

Although the concept of potential output is widely used in economic analysis, 

there has been a considerable divergence of opinion as to its precise definition 

and, as we shall see in section 3, as to the best method of measuring it. Taken 

literally, the term means the maximum possible output of an economy if all of 

its resources are ‘fully employed’. For example, at one extreme we could define 

potential output as the level of GDP that could be produced if everybody of 

working age worked 24 hours per day, every day of the year. Alternatively, the 

term could be defined as some ‘normal’ level of production given ‘average’ 

factor utilisation rates. 

The definition considered in most recent studies, however, is somewhat more 

restrictive. The contemporary approach is to define the potential output of an 

economy as the maximum level of output obtainable without generating an increase 

in inflation. Thus, calculations of potential output are based either explicitly or 

implicitly on estimates of the ‘natural rate of unemployment’—the rate of 

unemployment which prevails when expectations of inflation are realised, and 

toward which the economy will tend to converge following a disturbance 

(Friedman, 1968). 

Clearly, this concept is somewhat different from one that represents the 

maximum attainable level of output with a given set of inputs. The importance 

of defining potential output in a manner that is consistent with stable inflation 

was recognised by Okun (1962) in his seminal paper on potential output. Okun 

argued that: 

. . . potential GNP . . . is not a measure of how much output could be generated by 

unlimited amounts of aggregate demand. The nation would probably be most

Darren Gibbs 75 

productive in the short run with inflationary pressures pushing the economy. But the 

social target of maximum production and employment is constrained by a social 

desire for price stability and free markets. The full employment goal must be 

understood as striving for maximum production without inflationary pressure . . . 

(p 99). 

There are a number of reasons why central banks and governments, and more 

generally the private sector, require accurate measures of the degree of spare 

capacity in the economy and the economy’s long-term sustainable growth rate. 

The Reserve Bank’s need for economy-wide estimates of potential output reflects 

its statutory responsibility to maintain stability in the general level of prices. 

Although previous Reserve Bank research has been quite successful in providing 

estimates of the inflationary consequences of an increase in, say, unit labour costs 

or the world price of tradeable goods, reliable estimates of the impact of 

domestic demand have proved more elusive, partly because researchers have 

been unsure of how to capture the influence of ‘excessive’ demand pressures. 

Simple economic theory tells us that if demand for goods and services in an 

economy outstrips supply at a given price level, then the price level will rise. But 

what level of demand is consistent with stable prices? If the Reserve Bank 

mismeasures the level of potential output and calculates a positive output gap 

(demand exceeds sustainable supply) when in fact the gap is negative 

(sustainable supply exceeds demand), the consequent (ex-post procyclical) 

monetary policy tightening will tend instead to amplify the business cycle (and 

the perturbations in inflation that stem from it), offsetting some of the efficiency 

and allocative gains that a stable price environment may be expected to deliver. 

Similarly, if the Reserve Bank observes a rise in the rate of output growth, it 

needs to distinguish whether this is purely a positive demand shock (and 

therefore possibly inflationary) or simply the result of the economy responding 

to faster growth in the capacity of the economy to supply (and therefore not 

inflationary). Likewise, if the Reserve Bank observes a fall in actual output 

growth, it needs to distinguish whether this is the result of a negative demand 

shock (and therefore possibly deflationary) or a negative supply shock (and 

therefore possibly inflationary). If policymakers wish to operate monetary policy 

in the least-cost manner possible (thus maximising the benefits), it is imperative 

that they have tools which will enable them to attempt to make such distinctions. 

The concept of potential output is also important from the perspective of the 

Government. In the short term, an assessment of the degree of excess demand 

or excess capacity in the economy will influence the fiscal policy stance. As with 

monetary policy, an over-expansionary stance at a time when excess demand 

conditions are evident or an over-contractionary stance when the spare resources 

are plentiful will tend to amplify the business cycle. In the medium term, views 

regarding the economy’s sustainable growth potential (and thus tax base) are 

also required to guide the formulation of the Government’s fiscal strategy. This

76 


is particularly important in the case of New Zealand where the Fiscal 

Responsibility Act requires the Government to conduct fiscal policy in a 

transparent and prudent manner, and to achieve specific reductions in the net 

public debt to GDP ratio. The calculation of ‘cyclically adjusted’ fiscal balances 

based on measures of potential output is standard practice in most other OECD 

countries (see, for example, Giorno et al, 1995). With regard to labour market 

policy, measures of potential output may also be of assistance in identifying the 

factors underlying unemployment and thus guide the appropriate policy 

responses. That part of unemployment which is identified as being unrelated to 

cyclical variation in economic activity will clearly require a different policy 

response from that which merely reflects the impact of a temporary shock to the 

economy. 

The importance of accurately estimating the economy’s sustainable growth 

rate is not restricted to the public sector. To the extent that demand for some 

types of goods and services is related to the size of the aggregate economy, 

private sector investors must also form views on the economy’s sustainable 

growth rate to guide them in cost-benefit analysis and in making decisions 

regarding the timing of investments. This is particularly important for those 

investment projects in which there is a considerable time lag between the project 

planning and approval phase and project completion. For example, the planning 

and construction of hydroelectric power stations can take seven to eight years. 

Over this length of time, relatively small errors in the projection of annual 

economic growth can accumulative into large deviations in the expected size of 

the economy, with the result that the project may be completed either years 

before or after the capacity is required. 

3 How is potential output measured? 

A number of alternative techniques for measuring potential output have been 

applied in the literature. These techniques range from the simple univariate 

smoothing techniques commonly used in the 1960s and early 1970s, to more 

complex structural techniques based on the ‘production function’ which became 

dominant in the late 1980s. More recently, techniques have been developed 

which provide a middle ground to these two extremes and which allow one to 

exploit relevant empirical information suggested by economic theory without 

imposing a rigid (and quite possibly incorrect) structure. This section briefly 

discusses the theory and methodology underlying the main techniques used, and 

summarises the main advantages and disadvantages associated with each. 

3.1 Simple univariate techniques 

Univariate techniques use information on actual output to estimate potential 

output—no other information (such as trends in factor inputs) is used. The most


common procedure for estimating potential output is to fit a trend either to 

actual output or through its peaks. The choice between these two methods 

implies different views of the business cycle. The essential point is whether the 

gap between potential output and actual output over some cyclically neutral 

historical period is, on average, zero or positive. In the latter case there is 

presumably scope for appropriate macroeconomic policies to increase the mean 

level of output; but in the former case macroeconomic policies may be able to 

decrease the variability of output, but not increase its mean (assuming that initial 

macroeconomic policy settings are structurally optimal). 5 

The most attractive feature of these essentially theory-free estimates is their 

simplicity. The main univariate techniques are the trends through peaks 

approach, the linear time trend approach, and the Hodrick-Prescott filter 

approach. Discussion of the latter is reserved until later in this section where a 

more general application of filtering techniques is outlined. 

Trends through peaks approach 

The trends through peaks approach is one of the most popular techniques 

considered in the literature, and was the accepted methodology in the 1960s and 

early 1970s. To apply this approach, seasonally adjusted output is first graphed. 

It is then assumed that ‘major’ peaks in the series represent output where 

resources in the economy are utilised at 100 percent of capacity. A straight line is 

drawn between each of the major peaks, and is then extrapolated (using the 

same slope as the line connecting the previous two peaks) beyond the last one. 

This line is taken to be potential output. The output gap is represented by the 

difference between the line representing potential output, and actual output. 

Because the approach results in a succession of discrete changes in a linear time 

trend, it is also sometimes referred to as the ‘split time trend’ method. 

This approach reflected the prevailing economic thinking at that time. The 

supply side of the economy was seen as deterministic, with changes in demand 

seen as the prime factor underlying observed business cycles. By focusing on the 

peaks of cycles, potential output was defined as the maximum possible output 

in a physical capacity or engineering sense; and so the calculated output gaps 

were almost always negative (ie actual output was below potential). As Laxton 

and Tetlow (1992) note, this reflected a belief that the unbridled economy tends 

towards inefficient outcomes, and that the goal of macroeconomic policy should 

be to offset this tendency. 

As growth through the 1960s was relatively constant, and inflation was low 

and stable, the conceptual link between the output gap and inflation which had 

5 

As Laxton et al (1994) note, if the short-run Phillips curve is asymmetric, trend output 

will lie below potential output. In this circumstance, a policy aimed at decreasing the 

variability of output will also increase mean output.

78 


been identified by Okun was ignored. However with the advent of greater 

variability in growth and inflation in the early 1970s, the practical shortcomings 

of this approach were exposed. 

Christiano (1981) identifies three such shortcomings. First, deciding what 

constitutes a major peak is purely a matter of judgment, and the assumption that 

each major peak represents the same intensity of resource utilisation is bold. 

Secondly, it is unreasonable to assume that potential output grows at a constant 

arithmetic rate between peaks, and that structural breaks only occur at the peaks. 

Thirdly, the potential output line which follows the most recent peak, a period 

particularly important for policy purposes, is subject to substantial revision 

when a new peak occurs. Hence, potential output estimates created using this 

technique will be unreliable when the economy is suspected to have undergone 

a structural shift, or when the rate of capital accumulation and/or growth in the 

labour force have changed. This latter shortcoming seems particularly applicable 

to New Zealand. 

As the ‘natural rate’ concept became more widely accepted in the economics 

profession in the mid 1970s, and the predictions made by the trends through 

peaks estimates proved increasingly misleading, the use of this method became 

less widespread. However, up until recently, the trends through peaks method 

was still used by the OECD to decompose actual output into trend and cycle 

when constructing fiscal policy indicators (see Giorno et al, 1995). 

Linear time trend approach 

The initial response of researchers to the demise of the trends through peaks 

approach was to estimate linear time trends that were calculated to run through 

the centre of the business cycle. While this was an advance, in that this approach 

utilised all the information contained in the actual output series (rather than just 

the peaks) and allowed for the possibility of both negative and positive output 

gaps, this technique generally assumed that actual output was equal to potential 

output on average over the business cycle, for which there was no guarantee 

(particularly over small samples). Not surprisingly, therefore, this approach also 

yielded implausible estimates of potential output. 

As world economic growth began to slow down in the mid 1970s, in response 

to the oil price shocks and lower growth rates in measured productivity, 

researchers began to turn their attention to the impact of supply-side influences 

on economic activity. Initially however most work continued to assume that the 

supply side of the economy evolved only gradually. Rather than seek to explain 

these developments explicitly, researchers tended to resort to the use of such 

tools as moving averages, spline functions and shift dummies. Indeed, Laxton 

and Tetlow quote a Bank of Canada research memorandum describing the 

method used for specifying total factor productivity:


To put it starkly, given the data and research, both a sharp eye and a flexible 18-inch 

ruler were applied to the data in a manner consistent with existing priors. (From 

Gosselin et al, 1981.) 

It soon became clear that more sophisticated techniques were required. New 

structural approaches began to be developed which sought to explain growth in 

terms of factor inputs. In retrospect, it seems surprising that this advance was 

so long in coming given that the theoretical growth models based on such 

relationships had been developed as far back as the late 1940s by Harrod (1959) 

and Domar (1947). 

3.2 Multivariate structural techniques 

Unlike the approaches discussed above, multivariate techniques make use of 

variables other than just actual output to derive estimates of potential output. 

Typically these techniques involve relating potential output to trends in the 

quantity (and in some cases quality) of labour and/or capital inputs. In this 

section, approaches are outlined based on the seminal work of Okun (1962); the 

output/capital approach; the inversion of input demand functions; and the 

production function approach. 

Okun’s approach 

A simple, widely used and long standing method of calculating potential output 

is based on the seminal work of Arthur Okun (1962). Okun’s method relies less 

on economic theory than it does on an empirical regularity, and is based on a 

simple relationship linking the gap between actual and potential output with the 

gap between actual and natural rates of unemployment. This approach, 

therefore, directly links the estimation of potential output to a judgment or 

estimate of the natural rate of unemployment. 

In Okun’s original work, using US data from 1947Q2 to 1960Q1, the natural 

rate of unemployment was assumed (relatively uncontroversially) to be 4 

percent. Therefore, using Okun’s method, potential output equals actual output 

when aggregate demand is exactly at the level that yields an unemployment rate 

of 4 percent. If aggregate demand is lower, part of the potential output is not 

produced—there is unrealised potential or a gap between actual and potential 

output. 6 

6 

Okun argued that to the extent that low utilisation rates and accompanying low profits 

and personal incomes hold down investment in plant, equipment, research, housing and 

education, the failure to use one year’s potential fully can influence future potential 

output. Because today’s actual output influences tomorrow’s productive capacity, success 

in the stabilisation objective promotes more rapid economic growth. This recognition that 

history can affect the future constitutes an early expression of the hysteresis ideas which 

are prevalent in recent literature.

80 


Okun employed three different methods of relating output to the unemployment 

rate. The most widely known method was based on a regression linking 

quarterly changes in the unemployment rate (U t 

, expressed in percentage points) 

and quarterly percentage changes in GNP (Q t 

). That is: 

( U U ) 

t 

− = α + β 

t−1 

( Q − Q ) 

t 

Q 

t−1 

t−1 

According to the estimates from this equation, the unemployment rate will rise 

by α percentage points from one quarter to the next if real GNP is unchanged, 

as secular gains in productivity and growth in the labour force push up the 

unemployment rate. For each extra 1 percent of GNP, unemployment is β 

percentage points lower. Furthermore, from a position where actual and 

potential output are equal, these estimates imply that output must grow by α β 

percent per quarter in order to stabilise the unemployment rate. Thus, given the 

assumption that the unemployment rate will not change when the economy 

grows at its potential rate, α β provides an estimate of the potential growth rate. 7 

As Okun himself acknowledged, his methodology is very simplistic. A 

number of weaknesses have been identified in the literature. First, in making a 

direct connection between unemployment and output Okun assumed that the 

influence of slack economic activity on average hours, labour force participation 

and productivity are all proxied by the unemployment rate. 

Secondly, the method relies on the assumption that the same statistical 

relations prevailing in the historical data would have applied if the economy had 

been operating at full employment. No correction is made for factors such as 

working age population growth or increased immigration, which would imply 

more unemployment for any given level of output (we correct for this in our 

empirical estimates later in the paper by defining output in per capita terms). 

Thirdly, the natural rate of unemployment is determined by assumption, and 

assumed to be constant over the relevant time period. 8 This led Gordon (1979) 

to argue that: 

The original Okun/Heller concept . . . should have been called not potential output, 

but arbitrarily defined full employment output (p 187). 

7 

Christiano (1981) slightly extends Okun’s original approach by allowing unemployment 

rate changes to depend on various lagged values of GNP growth. Assuming that the 

estimated lag coefficients would have held if the economy had been operating at full 

employment, Christiano derives estimates of potential output and output gaps. 

8 

This problem can be eliminated by separately estimating a series for the natural rate of 

unemployment which varies through time. Techniques to achieve this will be discussed 

later when we outline the more complex multivariate approaches to the measurement of 

potential output which routinely estimate a time-varying natural rate of unemployment as 

part of the general approach.


Fourthly, Plosser and Schwert (1979) demonstrate both theoretically and 

empirically that Okun’s procedure of inverting a regression of unemployment on 

output is valid only if the correlation coefficient is equal to ±1. 

Finally, a more significant problem with the technique is that it can result in 

potential output series which display unreasonable volatility. Indeed, in a recent 

study by the OECD (1994) using an Okun’s Law based technique, they found 

that the potential output series derived for some countries was more volatile 

than the actual output series on which they were based. 

Because of these shortcomings, the reliability of potential output estimates 

obtained using these techniques also suffered as output and inflation became 

more variable in the 1970s. As noted by Adams et al (1987): 

. . . because these approaches tend to deal somewhat mechanically with any change 

in economic conditions, they are not well suited to separating permanent from 

transitory influences. These approaches tend to extrapolate any change in growth 

automatically, provided it is maintained long enough, and, even when they produce 

correct judgments about historical developments in potential output, they do not 

identify the underlying determinants. Such methods are, therefore, unreliable for 

forecasting, particularly when the economic environment is undergoing substantial 

change. 

Adams’ last comment is particularly pertinent in the case of New Zealand. 

The output-capital ratio approach 

Whereas Okun’s measure relies solely on the labour market as an indicator of 

the output gap, this approach hinges on the existence of a stable proportional 

relation between the stock of capital and potential output. The method assumes 

that fluctuations in the observed output/capital ratio are largely due to 

deviations in output from its potential level. 

An example of the use of this method is contained in Panic (1978). First he 

constructs an output/capital ratio series ( Q t 

K ), and then he fits a least squares 

t 

linear trend to the actual output/capital series, to yield a ‘capacity’ output/ 

capital series, as follows: 

⎛ Qt 

⎞ 

⎜ ⎟ = α0 + α1t+ 

e 

⎝ K ⎠ 

t 

t 

where Q t 

and K t 

represent output and the capital stock at time t and e t 

is a 

random error. The capacity output/capital ratio is taken to be the points on a line 

with the time derivative α 1 

raised just enough so that it touches only one of the 

observed Q t 

Q 

c 

t 

K data points. The adjusted trend ratio ( ) 

t 

K is the assumed capacity 

t 

output/capital ratio. From here, a series measuring potential output is simply 

Q 

c 

t 

. 

given by K t ( K ) 

t

82 


As with the other approaches that we have described so far, this approach is 

computationally relatively simple to apply. However a major weakness in this 

approach is that it relies exclusively on capital stock series, which are among the 

least reliable series available. 9 Estimates of the capital stock generally rely on an 

initial starting value for the capital stock, updated using gross investment data, 

allowing for an assumed rate of depreciation. There is a variety of problems 

associated with such estimates including: the reliability of initial capital stock 

estimates; the use of accounting rather than economic rates of depreciation; 

capital vintage effects; scrapping rates; and the use of capital definitions that 

exclude components such as human capital. 

Inverted input demand approach 

Approaches have also been derived which rely on the inversion of estimated 

input demand functions. One such approach is based on first estimating the 

desired quantity of labour or capital input as a function of output and other 

variables. Next, given the estimated demand function, the desired input level is 

replaced with the actual input level in the equation, and the equation is solved 

for output. On the assumption that the relationship between desired input and 

output holds at efficient points in production, the output series computed in the 

second step of the procedure can be taken as an estimate of potential output. 

Christiano (1981) provides two examples of the use of this approach. The first, 

calculated by the US Council of Economic Advisors (CEA, 1979), relies on a 

labour demand function. The following labour demand function relating the 

labour input gap to current and lagged output gaps is the basis for this approach: 

⎛ L ⎞ 

t 

log 

⎜ 

p ⎟ 

⎝ L ⎠ 

= 

where: 

t 

n 

∑ 

s= 

0 

⎛ Q 

bs 

log 

⎜ 

⎝ Q 

t−s 

p 

t−s 

⎞ 

⎟ 

⎠ 

L t 

= hours demanded measured in efficiency units 10 

L p t 

= full employment (or potential) hours demanded in efficiency units 

Q t 

= actual output 

Q p t 

= capacity (or potential) output 

and where t = 1, . . ., T and n and T are finite numbers. It is assumed that the 

sum of the b coefficients approximately equals unity. 

10 

Efficiency units are derived by weighting hours for different sub-groups according to 

their relative wage. 

9 

In the case of New Zealand there are no official capital stock data. The only estimates 

available are those estimated by the Reserve Bank of New Zealand and the Research Project 

on Economic Planning at Victoria University. Both are estimated using the perpetual 

inventory approach.


p 

⎛ Qt 

Assuming that labour productivity ⎜ ⎞ 

p 

⎟ 

⎝ Lt 

⎠ follows a simple time pattern, 

Christiano rearranges the above equation to express actual labour input as a 

function of actual output and that time pattern, and obtains estimates of the b s 

coefficients. Using these coefficients and an independent measure of L p t 

, 11 the 

demand equation can be inverted to yield an estimate of the output gap as a 

function of lagged values of the input gap. 

A second approach which makes use of a capital (or investment) demand 

function was proposed by Hickman (1964). In this approach the demand for 

capital, K * t 

, is expressed as: 

* * * 

t 0 1 t 2 t 3 

log K = α + α logQ + α log P + α t 

where Q t * and P t * represent permanent income and relative output prices at time 

t. (The model assumes annual data.) 

Assuming that the capital stock follows a partial adjustment process, and that 

both permanent income and relative output prices depend linearly on current 

and lagged values of actual output and actual prices respectively, it is possible 

to estimate Q t * as a function of capital and output price series. 

The relative advantage of the inverted demand function approaches discussed 

above is that although, computationally, they are slightly more burdensome than 

the other approaches discussed so far, they do go some way towards addressing 

some of the weaknesses in the simpler approaches. They are also simpler to 

apply than the next technique we will discuss, which requires us to estimate the 

underlying production function. However, as is usually the case, the search for 

computational simplicity requires a trade-off to be made with theoretical 

desirability. Strong assumptions need to be made about functional forms and the 

time behaviour of various variables. 

There are a number of difficulties with applying these approaches to New 

Zealand data. In the case of the labour demand approach, sufficiently disaggregated 

data over a long enough time period is either extremely unreliable or 

simply unavailable. Without this disaggregation, the approach differs little from 

that suggested by Okun; and the capital demand approach has all the limitations 

that were discussed earlier in the context of the output/capital ratio approach. 

The production function approach 

The final approach that we shall discuss in this section is the production function 

approach which, at least on theoretical grounds, is by far the most desirable. The 

essence of the production function approach is an explicit modelling of output 

in terms of the underlying factor inputs, which involves the specification and 

11 

Christiano derives a measure of potential hours demand by applying cyclically adjusted 

participation and unemployment rates to eight age-gender groups in the population. 

Hours are converted to efficiency units by valuing them using relative wages. This is often 

known as ‘Perry weighting’, based on Perry (1971).

84 


estimation of production functions linking output to factor inputs, as well as the 

determination of the quantity and quality of inputs. The non-accelerating 

inflation constraint is usually introduced by relating the potential level of factor 

inputs to the natural level of unemployment. 

Adams et al (1987) identify four components to the production function 

approach. First, a two factor production function, relating the output of the 

private business sector to the inputs of labour and capital and to total factor 

productivity. Secondly, a pair of equations that relate the intensities with which 

labour and capital are used over the business cycle to the ratio of actual to 

normal output. Thirdly, a pair of equations which are used to determine the 

potential levels of the factor inputs. 12 And fourthly, an equation or wage-price 

model that is used to determine the natural rate of unemployment. 

This approach relies heavily on the production function, but does not require 

the explicit modelling of the demand for and supply of factor inputs and total 

factor productivity. The approach assumes that, in the short term, the potential 

inputs of factors are determined principally by the behaviour of unemployment 

relative to its natural rate, and output relative to its normal level. It is further 

assumed that the growth in factor inputs and total factor productivity 

underlying the projections of potential output can be based on judgments about 

the macroeconomic environment supplemented by explicit views on key 

relationships. 

Variants of the production function approach are used by both the International 

Monetary Fund (IMF) (Adams et al, 1987; Adams and Coe, 1990) and 

the Organisation for Economic Cooperation and Development (OECD) (Torres 

and Martin, 1990). 

Adams et al (1987) identified four major advantages that the production 

approach has over the more traditional approaches discussed so far. First, it 

allows for an explicit accounting for growth in terms of the contributions of 

factor inputs and total factor productivity. Secondly, it explicitly accounts for the 

links between the product and factor markets that underlie relationships such as 

Okun’s Law, without imposing a constant Okun coefficient. Thirdly, it allows one 

to analyse the impact of various disturbances including, for example, an increase 

in energy prices. Finally, it can be adapted for forecasting purposes to determine 

the underlying rates of economic growth that may be envisaged, and the effects 

of such factors as changes in the natural rate of unemployment. 

However, as with all the approaches discussed so far, this approach also has 

disadvantages. First, its theoretical supremacy is at the cost of computational 

12 

These equations relate the inputs of factors to the deviation of the unemployment rate 

from its natural rate, to the ratio of actual to normal output, and to a number of factor 

specific circumstances. Potential inputs are found by determining the levels of input when 

unemployment is at its natural rate and output is at its normal level (hence introducing the 

inflation constraint).


simplicity. The approach requires that an assumption be made regarding the 

mathematical form of the production function. Typically, the Cobb-Douglas and 

CES specifications are used as well as a variety of more flexible forms, though 

economists have had a great deal of difficulty agreeing on which form is best. 

Furthermore, in addition to the need to measure the quantity of inputs used 

in the process (which, as already outlined, is a feature of structural approaches), 

the approach also requires that some estimate is made of the quality of factor 

inputs. Studies as early as that of Solow (1957) have found that the physical 

quantity of inputs provides a poor explanation of actual movements in output. 

Indeed, this study found that factor inputs could explain only one-third of 

growth with the ‘Solow residual’ or total factor productivity accounting for the 

remainder. It is this residual that captures changes in the quality of inputs and 

production processes. As Laxton and Tetlow note: 

One important advantage of the production function approach over the time trend 

approach is that it is easy to keep track of the major contributing factors to potential 

output. That is, variations in its underlying determinants such as labour force 

growth, capital formation, and trend total factor productivity. For this reason the 

production function approach was seen as an attractive framework for organising the 

data. However, there remained a problem. Since economists had no useful model of 

the determinants of productivity, the resulting estimates were still essentially 

exogenous time trends (p 7). 

The use of ad hoc polynomial time trends as regressors in production functions 

to explain productivity (see, for example, Perloff and Wachter, 1979), together 

with their quantitative importance to the results, constituted a very significant 

weakness in the empirical application of the production function approach. 

Moreover estimates derived from these techniques proved to be very sensitive 

to the type of approach used. Together these factors severely limited the practical 

usefulness of the estimates. 

Although the recent theoretical development of the endogenous growth 

literature has provided some insights and stimulated debate regarding the 

determinants of long-run growth, endogenous growth theory has received little 

attention in empirical research to date. 

Partly in response to the above problems, a new literature emerged in the 

early 1980s in which changes in potential output and the natural rate of 

unemployment were treated as stochastic (rather than deterministic) phenomena. 

3.3 Stochastic filtering techniques 

Laxton and Tetlow (1992) argue that there is insufficient knowledge about the 

true structure of the economy to make the structural approach practical. 

Moreover, researchers using structural techniques have tended to concentrate on 

highly stylised models focusing on specific, easily identifiable shocks, and have

86 


tended to cling too long to obsolete estimates of potential output or to overinterpret 

apparent changes in potential output. 

Laxton and Tetlow argue that potential output is best characterised as being 

driven by a stochastic process so that in addition to the myriad of policy, demographic, 

and commodity price shocks there are regular unidentifiable shocks, 

some of which have lasting effects on potential output. Given the extensive 

programme of economic and financial reform in New Zealand over the last ten 

years, and the change in behaviour and decision-making patterns (and thus 

structural relationships) that are likely to have taken place, it seems particularly 

reasonable to reach this conclusion in the case of New Zealand. 

They also note a tendency to use much more judgment and more structured, 

but less detailed, macroeconomic models. This they attribute to: 

. . . a by-product of the realisation that, although economists have a broad grasp of 

the relationships between macroeconomic activity and such observables as potential 

output, the structural form of these relationships remains elusive. This would seem 

to call for a method of measuring potential output that reflects general beliefs 

concerning the nature of these relationships, without imposing too much formal 

structure (p 12). 

It is the difficulty of finding sufficient evidence to arrive at a consensus on 

structure that has spawned astructural methods of measurement such as the 

Hodrick-Prescott filter, at least as complementary tools in much the same way 

as VAR models can be seen as complementary to structural macroeconomic 

models. The Hodrick-Prescott filter is a popular technique for smoothing time 

series data and for this reason it worth discussing it in its own right. However, 

it is also interesting because it encompasses the deterministic time trend as a 

special case and it provides the basis for the multivariate filter technique 

suggested by Laxton and Tetlow which is discussed later in this section. 

Hodrick-Prescott filter approach 

The rationale for using the Hodrick-Prescott (HP) filter (Hodrick and Prescott, 

1980) is that it can help to decompose an observed shock into a supply and a 

demand component. This is done by making the identifying assumption that 

supply shocks have permanent or lasting effects on output while demand shocks 

tend to be temporary. Of course, if the temporary demand component contains 

a great deal of persistence it is very difficult to distinguish between the two, 

particularly at the end of the sample. Moreover, there is also the possibility of 

supply shocks which are temporary (eg due to climatic factors such as the 1992 

electricity crisis). Furthermore, the two sources of shock need not be independent. 

In endogenous growth models, cycles and growth are part of the same 

process. Nevertheless, as noted earlier, since supply shocks and demand shocks 

have inherently different implications for inflation we need some way of 

disentangling demand shocks from supply shocks.


The HP filter is derived by minimising the sum of the squared deviations of 

a variable (in this case, output), Q t 

, from its trend τ, subject to a smoothness 

constraint, λ, that penalises squared variations in the growth of the trend series. 

That is, the HP filter is calculated to minimise: 

T 

T−1 

QHP = 

∑ t − τ t + λ ∑ 

τ t − τ − τ t − τ t 

t= 

1 

t= 

2 

[ + 1 1 −1 

] 

2 

( Q ) ( ) ( ) 

Thus, the calculated HP trend series is a function of the smoothness constraint, 

and of both past and future values of output. The user can determine the 

smoothness in the trend series by choosing an appropriate value for the 

smoothness parameter. Higher values of λ imply a larger weight on the 

smoothness of the series, so that in the limit, as λ becomes arbitrarily large, the 

trend series will converge on a linear time trend. As Laxton and Tetlow note, this 

would be consistent with an extreme Keynesian model in which supply shocks 

are deterministic, and variations in output come almost entirely from demand 

shocks. Conversely, a very small value of λ will effectively eliminate the penalty 

function, and thus the HP trend series will be equal to the actual series. This 

would be consistent with an extreme real-business-cycle model in which most 

variations in output are also variations in potential or trend output, and hence 

are driven by supply shocks. 

King and Rebelo (1989) show that the optimal value of λ is a function of the 

ratio of the variances of these shocks and that, for some data generating process 

of permanent and temporary shocks, the HP filter is an optimal (minimumvariance) 

linear inverse filter. However, there is considerable debate concerning 

the relative variance of supply and demand shocks. In practice, users of the HP 

filter have tended to set λ = 1600 when smoothing quarterly data following the 

initial approach of Hodrick and Prescott. An alternative approach is to choose λ 

so as to generate an output gap series which is consistent with the results of 

other business cycle dating techniques. 

Relative to the trends through peaks or linear time trend approach, the HP 

filter approach has the advantage that it allows for structural change to occur at 

any point in the series (although the rate of change is constrained by the choice 

of λ). However, this approach still has a number of weaknesses. 

First, the choice of λ can have a large effect on the conclusion reached, as can 

the choice of sample period chosen. If an ‘average’ level of λ is chosen, any 

dramatic change in the actual series will tend to be attributed to both demand 

and supply disturbances. Even if this attribution is correct on average, in the case 

of pure positive demand shocks the technique will tend to understate the 

amount of excess demand in the economy, while understating the amount of 

excess supply in the case of pure positive supply shocks. For example, during a 

period of disinflation when monetary conditions are being tightened, the HP 

2

88 


filter will tend to understate the amount of excess supply in the economy. 

Secondly, as with the trend through peaks approach, the level of uncertainty 

in the estimates will be greater at the end of the sample, precisely where it 

matters the most. This is because, if the effects of demand shocks are persistent, 

it will be difficult to distinguish between permanent and temporary shocks; and 

at the end of the sample there is almost no information available about the effects 

of the latest shocks. 

Finally, the level of potential output produced by this simple detrending 

technique is clearly not consistent with the traditional equilibrium notion of 

potential output. There is no guarantee that the sample period chosen is 

cyclically neutral, particularly when dealing with small samples. For these 

reasons, Laxton and Tetlow suggest that very large confidence intervals should 

be placed around potential output estimates that are derived solely through the 

use of univariate techniques. Despite these problems, the HP filter is a very 

popular tool for obtaining estimates of potential output. 

The multivariate filter approach 

Laxton and Tetlow (1992) have suggested the use of a multivariate filter to 

overcome some of the problems with the univariate HP procedure. 

This approach attempts to retain the computational simplicity of the Hodrick- 

Prescott filter approach, but supplements that approach with additional 

information based on established economic relationships. Therefore the approach 

can be thought of as quasi-structural in that it makes use of theoretical 

relationships and/or empirical regularities, without needing to impose 

restrictions based on imperfect representations of the true structure. 

The specific multivariate filter approach suggested by Laxton and Tetlow 

relies on the short-term output-inflation relationship (the Phillips curve) and the 

output-unemployment relationship (Okun’s Law) to attribute the proportion of 

a given shock that can be deemed as originating from a supply disturbance. 

These relationships are specified as follows: 

( −1 , −1) 

π , 

( −1 −1) ( −1 −1) 

π = π + BL ( ) Q − τ + ε 

t et t Q t t 

U − τ = C( L) U − τ + D( L) 

Q − τ + ε 

t U, t t U, t t Q, t U, 

t 

where π is the inflation rate, π e is the expected inflation rate, Q is the log of 

output, U is unemployment, τ i,t 

is the trend value for variable I, and J(L) are 

polynomial lag operators. The generalised problem is, therefore, to minimise: 

T 

T 

T 

T−1 

Q MVF = ∑ ηε 2 

t Q t + ∑ θε 2 

t t + ∑ γ ε 2 

, π , t U , t + λ ∑ τ t − τ t − τ t − τ t 

t= 

1 

t= 

1 

t= 

1 

t= 

2 

[( + 1 ) ( −1) 

] 

subject to the Phillips curve and Okun’s Law equations. That is, estimates of 

potential output are then chosen in a way that helps to improve the fit of the 

2


inflation rate equation and the unemployment rate equation. If there is useful 

explanatory power in these equations, then the data on inflation and unemployment 

will help in the identification of potential output. Of course, the procedure 

can be developed to take account of other known relationships such as changes 

in the yield curve, the import penetration rate, real unit labour costs, or any 

other relationship that may offer insights which help to separate out the trend 

from the cycle. 

Laxton and Tetlow further generalise the HP optimisation by allowing for 

time varying weights on the various terms in the optimisation process (these are 

given by {η,θ,γ}). This means that users have the option of exercising judgment 

to increase or decrease the weight attached to a particular piece of information 

at a particular time. For example, one may wish to attach very little weight to 

the inflation equation during a period covered by wage and price controls, or 

attach a very high weight on actual output when there is good reason to believe 

that actual and potential output are close to coinciding. (In this way, benchmarks 

are established for the potential output series.) There are a number of ways of 

choosing the relative weights. Laxton and Tetlow suggest that a sensible 

approach is to base them on the relative uncertainty in the relationships. 

Laxton and Tetlow conducted Monte Carlo tests under various assumptions 

about the relative importance of demand and supply shocks to compare the 

performances of the HP and multivariate filters. Their results indicated that the 

multivariate filter improves on the estimates of the HP filter regardless of the 

proportion of output stemming from supply disturbances, but the extent of the 

improvement varies negatively with the proportion of shocks coming from 

supply sources. The HP filter does best when supply shocks are prevalent; but 

since the multivariate filter uses information on inflation, it improves the 

estimates most when supply shocks are less dominant. However, their results 

also suggest that although the multivariate filter performs better than the HP 

filter, there is still considerable uncertainty in the estimates. 

3.3 Summary 

As we have seen, there are number of empirical methods that have been used to 

calculate potential output, and the policy conclusions reached can be sensitive 

to the methods chosen. Simple time trend techniques appear to be too inflexible 

to generate plausible estimates while, in practice, structural techniques are too 

rigid and rely on unreliable data and unjustifiable assumptions. The multivariate 

filter approach, which represents something of a middle ground, has several 

desirable characteristics which attempt to overcome the problems. Nevertheless, 

none of the techniques surveyed is free from serious deficiencies. Therefore, the 

relative desirability of each approach is ultimately an empirical question. This 

also suggests that policymakers should not place too great a reliance on one 

single measure.

90 


These conclusions are shared by Laxton and Tetlow. They note that regardless 

of the method used estimates of potential output should be interpreted with 

caution, since the confidence bands around such estimates are quite wide. This 

is seen as especially important when these estimates are used to guide 

macroeconomic policy decisions. This view is emphasised by the results of the 

preliminary empirical work discussed in the remainder of this paper. 

4 Empirical estimates of potential output for New Zealand 

In this section we apply a selection of the techniques discussed in section 3 to 

estimate preliminary potential output series for New Zealand. The section 

describes how each series was constructed and uses graphical techniques to first 

compare the results of those techniques which are similar in nature, and then 

compare the results obtained across completely different techniques. A statistical 

comparison of the derived output gaps is reserved for section 5. 

4.1 Data 

A variety of data has been used in constructing the potential output series 

described in this section. The measure of actual output used was the seasonally 

adjusted quarterly production-based real GDP statistics produced by Statistics 

New Zealand (QGDP). These data are officially available for the period 1977Q2 

to 1994Q1, though the National Bank has backdated this data to 1965Q4. For 

those techniques based solely on QGDP (ie the univariate techniques) a potential 

output series covering the whole of the period 1965Q4 to 1994Q1 was calculated. 

As noted above, the multivariate estimates of potential output require a 

variety of additional data series as inputs into the estimation process. The 

construction of these additional series is discussed as they arise. The start dates 

for the potential output series derived from these approaches were dependent 

on the availability of these additional series. The estimated multivariate potential 

output series typically start in the early 1970s. 

For the purposes of the discussion in this section and the statistical analysis 

that follows we focus on the single period 1977Q2–1994Q1—the period during 

which official data are available on movements in actual output. In the interest 

of brevity we concentrate mainly on reporting the final output from these 

techniques (ie the estimated potential output series and the associated output 

gaps), and not on the intermediate estimation results from which they were 

constructed. 

4.2 Simple univariate estimates 

Given the dubious theoretical quality of these measures, the only technique 

utilised under this heading is the trend through peaks approach. As noted earlier, 

a particular difficulty with this approach is establishing what constitutes a 

significant peak; and how to project out the potential output line past the last


significant peak. We use two variants to derive two alternative series. In the first, 

the potential output line is extrapolated past the last peak (the December quarter 

1986 GST induced boom) at the same slope as that connecting the previous two 

peaks (ie the standard approach). In the second, we extrapolate on the basis of 

the average slope during the period 1965Q4–1982Q2. 

Figure 1 illustrates the estimated series potential output series (tp1 and tp2) 

and the corresponding output gaps. Note that these gaps are by definition 

always negative. 

While both these series indicate the development of a substantial output gap 

over the early 1990s, only tp2 suggests that this gap closed significantly by 

March 1994 (to less than 2 percent of GDP). 

4.3 Structural multivariate estimates 

Multivariate estimates of potential output (and thus the output gap) were 

constructed using three of the techniques described in section 3. The techniques 

used were the labour input related Okun approach, the capital input related 

output-capital ratio approach, and the combined input related general 

production function approach. These are discussed in turn. 

FIGURE 1: Estimated potential output and output gap series—trends through 

peaks approach 

20 

Output gap (%) 

15 

10 

5 

0 

-5 

-10 

-15 

-20 

10000 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 

8000 

6000 

4000 

2000 

0 

Output ($m 82/83) 

June years 

tp1: output gap (left axis) 

gdp (right axis) 

tp2: potential output (right axis) 

tp2: output gap (left axis) 

tp1: potential output (right axis)

92 


Labour input related approaches 

Two potential output series were estimated using solely labour market data. The 

first approach relied on relating the size of the output gap to the deviation of 

the actual employment rate (one minus the actual unemployment rate) from the 

estimated ‘natural rate’ of employment (one minus the natural rate of 

unemployment), where the natural rate of unemployment is that rate at which 

the labour market is in equilibrium and there is no pressure for nominal wages 

to rise. The natural rate of unemployment is usually taken to represent that part 

of unemployment not explained by purely cyclical factors (in other words, the 

part of unemployment due to frictional, structural, and classical unemployment). 

This technique relies on Okun’s assumption that the influence of slack economic 

activity on average hours, labour force participation and productivity are all 

proxied by the unemployment rate. 

Obtaining an accurate measure of the unobserved natural rate of unemployment 

is no easier than estimating the unknown rate of growth in potential 

output. Two approaches have been commonly applied in the literature. The first 

involves directly estimating a reduced form model for the unemployment rate, 

including both ‘natural’ and cyclical factors as determinants. For example, 

studies have related the actual unemployment rate to actual output; the real 

exchange rate; real consumer wages; the marginal tax on wages; the unionisation 

FIGURE 2: Estimated natural unemployment rate 

12 

10 

Unemployment rate (%) 

8 

6 

4 

2 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

June years 

1987 

1988 

1989 

1990 

1991 

1992 

1993 

Estimated natural rate 

Actual unemployment rate


FIGURE 3: Estimated potential output and output gap series—labour input 

methods 

20 

15 

10000 


10 

5 

0 

-5 

-10 

-15 

-20 

8000 

6000 

4000 

2000 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 


June years 

yl1: output gap (left axis) 




yl1: potential output (right axis) 

rate; the real unemployment benefit; the minimum wage rate; and the volume of 

world trade. The natural rate of unemployment is then obtained by solving out 

the equation with the cyclical factors eliminated. 

An alternative approach involves the estimation of a Phillips curve or twoequation 

wage-price model. This model is subsequently solved for an 

unemployment rate that is consistent with stable inflation. 

It was decided to adopt the Phillips curve approach in this paper. However, 

the estimated natural unemployment rate series also displayed unreasonable 

volatility. This was removed by passing the series through the Hodrick-Prescott 

filter, producing the natural unemployment rate series depicted in Figure 2. 

Clearly this methodology is deficient. However, its use was necessitated by 

the absence of better estimates of the natural rate of unemployment (which is a 

major task in its own right). Although the true natural rate series is likely to be 

less smooth, the estimated natural rate of 7.75 percent as of March 1994 seems 

plausible; however recent falls in unemployment (to 6.3 percent in June 1995) 

combined with only moderate wage growth suggest that it was likely to have 

been lower than this by mid 1995. 

The second labour input related potential output series estimate is based 

directly on Okun’s model relating the levels of output and unemployment as

94 


FIGURE 4: Estimated potential output and output gap series—capital input 

methods 

20 

15 

10000 


10 

5 

0 

-5 

-10 

-15 

8000 

6000 

4000 

2000 


-20 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 

June years 

yk1: output gap (left axis) 


yk2: potential output (right axis) 

yk2: output gap (left axis) 

yk1: potential output (right axis) 

discussed in section 3. The technique involves regressing the employment rate 

on output per working age person, and a time trend. This yields an estimate of 

the potential per capita growth rate which, when combined with the rate of 

growth in the working age population, results in an estimate of the total potential 

growth rate. Using this approach, the estimated output elasticity of the 

employment rate was 0.35 (which compares well with Okun’s original estimate 

of 0.35–0.40), while the estimated potential per capita growth rate was around 2 

percent per annum. 

Having obtained this estimate (which is expressed as a growth rate) the level 

of potential output is then calculated by choosing one time period at which the 

level of actual output and potential output are assumed to coincide (ie a 

benchmark). In this case, March 1985 was chosen as the benchmark (almost all 

of the more sophisticated estimates which are discussed later in this section 

support this choice). 

Figure 3 illustrates the estimated series potential output series derived from 

applying the above techniques (yl1 and yl2), and the corresponding output gaps. 

While both techniques produce output gaps which display a similar trend, the 

variance of yl2 is considerably greater than that associated with yl1. Both


estimates suggest that a negative output gap existed in March 1992, with the 

more intuitively plausible yl1 measure suggesting that a negative output gap of 

around 1.5 percent of GDP remained in the 1994 March quarter. 

Capital input related approaches 

Two techniques of relating solely capital inputs to output were applied. The first 

approach, similar in nature to that used to derive yl1 above, was to relate 

deviations in actual from potential output to deviations in capacity utilisation 

from historical norms. The capacity utilisation series used was that collected in 

the Quarterly Survey of Business Opinion (produced by the New Zealand 

Institute of Economic Research). 

The second approach used was the output/capital ratio approach discussed 

in section 4 which relies on the assumption of a stable proportional relationship 

between the stock of capital and potential output. Annual capital stock estimates 

for the non-government sector (excluding dwellings) produced by the Research 

Project on Economic Planning (Philpott, 1994) were interpolated to produce 

quarterly capital stock estimates through to March 1993; and capital stock data 

for the remaining year of the sample were estimated from SNA data with the 

rate of depreciation set at 1.8% per quarter. 13 

Figure 4 illustrates the estimated potential output series derived from applying 

the above techniques (yk1 and yk2), and the corresponding output gaps. 

As the figures illustrate, the two estimates are highly correlated. The yk1 

measure suggests that the economy has been operating at above potential since 

1993. Also note that yk2 is similar to the trend through peaks estimates in that 

the estimated output gap is by construction always negative. Both series suggest 

that the degree of spare capacity has declined sharply over the last two years. 

The production function approach 

The previous two approaches related potential output to either some measure of 

labour input or some measure of capital input. By contrast, the production 

function approach relates potential output to both labour and capital inputs, and 

by so doing should yield better estimates of potential output. 

Only one potential output series was estimated using this technique. The 

functional form chosen for the estimated production function was the constant 

elasticity of substitution (CES) function. The estimated function was of the 

following form: 

⎡ 

LF E H 

Q= PWA• ⎛ ⎝ ⎜ ⎞ 

⎟ • ⎛ PWA⎠ 

⎝ ⎜ ⎞ 

⎟ • ⎛ −ρ 

⎛ 

LF⎠ 

⎝ ⎜ ⎞⎞ 

⎢α⎜ 

⎟⎟ + − • 

⎝ 

E ⎠⎠ 

⎣⎢ 

( 1 α)( QCU K) 

1 

ρ 

−ρ 

⎤ 

⎥ 

⎦⎥ 

13 

This rate was chosen based on previous work at the Reserve Bank (See Brooks and 

Gibbs, 1991).

96 


where 

Q = actual output 

PWA = population of working age 

LF = labour force 

E = employment 

H = hours worked 

QCU = capacity utilisation 

K = capital stock 

The function implies that output is a function of: the population of working age; 

the labour force participation rate; the employment rate; hours per employee; 

and the utilised capital stock. All labour force data were taken from the 

Household Labour Force Survey, while the capacity utilisation and capital stock 

series used were the same as noted earlier in this section. 

A potential output series based on the above function was estimated. First, 

the production function was estimated so as to yield estimates of the parameters 

α and ρ. Secondly, these parameters were used to create the predicted values 

from the regression with the following adjustments: the actual series of labour 

FIGURE 5: Estimated potential output and output gap series—production 

function method 

20 

15 

10000 

10 

5 

0 

-5 

-10 

-15 

-20 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 


8000 

6000 

4000 

2000 

0 


June years 

pf1: output gap (left axis) 


pf1: potential output (right axis)


force participation rates was replaced with a series in which all observations 

were equal to the average rate of participation over the sample period; the actual 

series of employment rates was replaced with the estimated ‘natural’ employment 

rates derived earlier in this section; the actual series of hours worked per 

employee was replaced with a series in which all observations were equal to the 

average hours per employee over the sample period; and the actual series of 

capacity utilisation was replaced by a series in which all observations were equal 

to the average rate of capacity utilisation over the sample period. 14 The influence 

of technology was proxied as is standard in these techniques by adding back the 

residuals to the above predicted values. 

Figure 5 illustrates the estimated potential output series and the estimated 

output gaps obtained by following the above approach. 

As Figure 5 illustrates, the output gap derived from the production function 

based estimate of potential output is similar to the others derived so far. The mid 

1980s is identified as a period in which output was above potential, while the 

early 1990s is identified as a period during which output was well below potential. 

Output is estimated to have moved above potential in late 1993/early 1994. 

4.4 Stochastic filtering approaches 

Four filtering approaches were applied following the methodology discussed in 

section 3. The first relies on the conventional Hodrick-Prescott filter, while the 

remaining three involve various forms of the multivariate filter which include 

progressively greater degrees of ‘outside’ information. 

Hodrick-Prescott filter 

The first approach tried was a straightforward application of the Hodrick- 

Prescott filter. As noted in section 3, the only parameter that must be chosen is 

the smoothness constraint (λ). Three variations of the constraint were applied 

yielding three different potential output series. The first variation involved 

setting λ to equal 1600—the value recommended by Hodrick and Prescott. The 

second variation involved setting λ to equal 200. This results in greater nonlinearity 

of the potential output series so that supply shocks are assumed to be 

more dominant than in the case when λ is equal to 1600. The third variation 

involved setting λ to equal 100,000. This results in greater linearity of the 

potential output series so that demand shocks are assumed to be more dominant 

than in the case where λ is equal to 1600. 

Figure 6 illustrates the three estimated potential output series (hp1600, hp200, 

hp100,000) obtained by following the above approach, and the estimated output 

gaps. 

14 

As noted earlier, these assumptions require that the period covered is cyclically neutral. 

Moreover, these assumptions could be improved by modelling the trend of each of these 

series individually.

98 


FIGURE 6: Estimated potential output and output gap series— 

Hodrick-Prescott method 

20 


15 

10 

5 

0 

-5 

-10 

-15 

-20 

10000 

8000 

6000 

4000 

2000 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 


June years 

hp200: output gap (left axis) 

hp100,000: output gap (left axis) 

hp200: potential output (right axis) 

hp100,000: potential output (right axis) 


gdp: (right axis) 

hp1600: potential output (right axis) 

The output gaps illustrated in Figure 6 once again display the same broad 

trends as those estimated earlier. The impact of variations in the smoothness 

constraint can be seen clearly. When l is equal to 200, the estimated potential 

output series is more closely correlated with the actual output series so that the 

absolute size of the estimated output gap tends to be smaller. By contrast, when 

l is equal to 100,000, the estimated potential output series is a near linear trend 

and the absolute size of the estimated output gaps tends to be larger. All series 

suggest that actual output rose above potential output during 1993, but this is 

less pronounced in the case of the hp200 filter. 

Multivariate filter approach—the bivariate filter 

We now supplement the information generated by the pure Hodrick-Prescott 

filter with information derived from the evolution of inflation using the 

multivariate filter approach discussed in section 3. 

The procedure was applied as follows. First, an initial ‘Phillips curve’ was 

estimated whereby today’s inflation is described as a function of expected 

inflation (this was estimated assuming adaptive expectations using a fourth 

order autoregressive model) and the history of output gaps (the Hodrick-Prescott 

output gap derived above was used in the first iteration). The information


FIGURE 7: Estimated potential output and output gap series—bivariate filter 

method 

20 

15 

10000 


10 

5 

0 

-5 

-10 

-15 

-20 

8000 

6000 

4000 

2000 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 


June years 

bf200: output gap (left axis) 

bf100,000: output gap (left axis) 

bf200: potential output (right axis) 

bf100,000: potential output (right axis) 



bf1600: potential output (right axis) 

contained in this regression was than embedded within the Hodrick-Prescott 

minimisation formula to yield a bivariate estimate of potential output which was 

based on both the observed behaviour of output and the observed behaviour of 

inflation. Next, the Phillips curve was re-estimated with the initial Hodrick- 

Prescott derived output gap being replaced by the new estimated bivariate 

output gap. The bivariate filter was then re-estimated using the information from 

this updated regression. This iterative procedure was repeated until the 

coefficients in the re-estimated Phillips curve converged. 

As noted in section 3, the procedure can be generalised to allow independently 

determined weights to be placed on the various terms in the minimisation 

problem. This facility was used so as to effectively give zero weight to developments 

in inflation during the 1982–84 wage and price freeze, and to the 1986 and 

1989 GST induced increases in indirect tax. 

As with the potential output estimates derived using the pure Hodrick- 

Prescott approach three variations of the smoothness parameter were used, so 

that three different bivariate filters were derived. Figure 7 illustrates the three 

estimated potential output series (bf1600, bf200, bf100,000) obtained by following 

the above approach, and the estimated output gaps.

100 


FIGURE 8: Comparison of the HP1600 and BF1600 filters 

4 

6 

2 

5 


0 

-2 

-4 

-6 

4 

3 

2 

1 

0 

Inflation rate (%) 

-8 

-1 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 

June years 



Inflation rate (right axis) 

The general pattern of the bivariate output gaps is similar to the Hodrick- 

Prescott derived estimates. However, unlike the Hodrick-Prescott estimates, the 

bivariate estimates suggest that the output gap remained negative (ie output 

below potential) at the end of the sample period. The influence of adding the 

inflation process to the filtering problem is best illustrated in Figure 8 which 

graphs the hp1600 and bf1600 filters against the quarterly inflation rate. 

Compared with the hp1600 filter, the bf1600 filter tends to result in a more 

positive (or less negative) output gap when inflation is rising and a more 

negative (or less positive) output gap when inflation is falling. In other words, 

in the latter case declining inflation is interpreted as additional evidence that 

actual output is below potential, with the result that the estimated level of 

potential output is higher and thus the estimated negative output gap is larger. 

Multivariate filter approach: Adding information regarding unemployment 

The multivariate filter is simply a further generalisation of the bivariate filter in 

which we include, in this case, additional information on the evolution of 

unemployment. To be specific, we make use of an estimated Okun relationship 

to map ‘unemployment gaps’ into output gaps. The unemployment gap was 

calculated using the natural rate of unemployment series derived earlier in this 

section. As with the bivariate filter, the initial output gap used in the Okun


FIGURE 9: Estimated potential output and output gap series—multivariate 

filter method 

20 

15 

10000 


10 

5 

0 

-5 

-10 

-15 

-20 

8000 

6000 

4000 

2000 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 


1992 

1993 

June years 

mfa200: output gap (left axis) 

mfa100,000: output gap (left axis) 

mfa200: potential output (right axis) 

mfa100,000: potential output (right axis) 



mfa1600: potential output (right axis) 

equation was that derived using the Hodrick-Prescott method. The information 

contained in the Okun regression was than embedded within the Hodrick- 

Prescott minimisation formula (along with the Phillips curve regression) to yield 

a bivariate estimate of potential output which is based on both the observed 

behaviour of output and the observed behaviour of inflation and unemployment. 

As with the bivariate filter, an iteractive technique was used to generate 

successive replacement output gaps in the Phillips curve and Okun equation, 

until the estimated coefficients converged. 

As with the potential output estimates derived using the previous filtering 

techniques three variations of the smoothness parameter were used, so that three 

different multivariate filters were derived. Figure 9 illustrates the three estimated 

potential output series (mfa1600, mfa200, mfa100,000) obtained by following the 

above approach, and the estimated output gaps. 

The general pattern of the multivariate output gaps is similar to the bivariate 

filter estimates. However, the size of the negative output gap is more pronounced 

in the late 1980s and early 1990s than that estimate derived from the 

bivariate filter. Note also that the mfa200 measure suggests that potential output 

fell in absolute terms in 1991. This is consistent with accelerated capital 

scrapping and a rising natural unemployment rate.

102 


FIGURE 10: Comparison of the BF1600 and MFA1600 filters 

4 

2 


0 

-2 

-4 

-6 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 

June years 



unemployment gap (left axis) 

The influence of adding the information regarding unemployment to the 

filtering problem is best illustrated in Figure 10 which graphs the bf1600 and 

mfa1600 filters against the estimated unemployment gap (a negative unemployment 

gap implies that actual unemployment is above the estimated natural rate). 

Compared with the bf1600 filter, the mfa1600 filter results in a more negative (or 

less positive) output gap when the actual unemployment rate is assessed as 

above the natural rate. This is because the presence of a negative unemployment 

gap is interpreted as additional evidence that actual output is below potential, 

with the result that the estimated level of potential output is higher and thus the 

estimated negative output gap is larger. 

The multivariate filter: Adding information regarding the yield curve 

The final estimates that we shall consider involve a further extension of the 

above approach so as to include additional supplementary information on the 

evolution of the yield curve. Specifically, we seek to relate the yield gap between 

90-day bank bills and five-year government bonds (expressed as a deviation 

from a moving mean) to the output gap. The estimated ‘IS curve’ implies that 

high short-term rates relative to long-term rates (a negatively sloped yield curve) 

are associated with a negative output gap. This may reflect the fact that a


FIGURE 11: Estimated potential output and output gap series—multivariate 

filter method 

20 

15 

10000 


10 

5 

0 

-5 

-10 

-15 

-20 

8000 

6000 

4000 

2000 

0 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 


1992 

1993 

June years 

mfb200: output gap (left axis) 

mfb100,000: output gap (left axis) 

mfb200: potential output (right axis) 

mfb100,000: potential output (right axis) 



mfb1600: potential output (right axis) 

tightening in monetary policy (resulting in a positive yield gap: short rates 

exceed long rates) tends to temporarily depress economic growth during the 

transition to low inflation; or the fact that a positive yield gap may cause some 

people to expect interest rates to fall in the near future with the result that some 

investment projects are delayed (see Ebert, 1994). 

The information contained in the IS regression was than embedded within the 

Hodrick-Prescott minimisation formula (along with the Phillips curve and Okun 

regression) to yield a multivariate estimate of potential output which is based on 

both the observed behaviour of output and the observed behaviour of inflation, 

unemployment and the yield curve. Again, an iterative technique was used to 

generate successive replacement output gaps in the IS regression until the 

estimated coefficients converged, and three variations of the smoothness parameter 

were used so that three different multivariate filters were derived. Figure 

11 illustrates the three estimated potential output series (mfb1600, mfb200, 

mfb100,000) obtained by following the above approach, and the estimated output 

gaps. 

The general pattern of the multivariate output gaps is similar to the previous 

estimates. However, the size of the negative output gap is less pronounced in the

104 


FIGURE 12: Comparison of the MFA1600 and MFB1600 filters 

4 

6 

2 

0 

-2 

-4 

-6 

1977 

1978 

1979 

1980 

1981 

1982 

1983 

1984 

1985 

1986 

1987 

1988 

1989 

1990 

1991 

1992 

1993 


5 

4 

3 

2 

1 

0 

-1 

-2 

Yield gap (%) 

June years 



yield gap (right axis) 

late 1980s and early 1990s than the estimates using the previous multivariate 

filter. The influence of adding the information regarding the yield gap to the 

filtering problem is illustrated in Figure 12 which graphs the mfa1600 and 

mfb1600 filters against the yield gap. 

Compared with the mfa1600 filter, the mfb1600 filter tends to result in a less 

positive output gap the more positive the yield gap. This is because the presence 

of a positive yield gap is interpreted as additional evidence that actual output is 

below potential, with the result that the estimated level of potential output is 

higher and thus the negative output gap is larger. 

Potential growth rates implied by each measure 

Table 1 presents the estimated potential growth rate over the year to March 1994 

(the actual growth rate was 5.4 percent in the numbers used in this study though 

this has since been revised up to 6.0 percent) and the estimated output gap (as a 

proportion of GDP) as at March 1994 for each of the 19 potential output series 

generated in this section of the paper. 15 

15 

The size of the output gap is only reported for those measures that are broadly 

consistent with the ‘natural rate’ as opposed to the maximum physical capacity definition 

(eg output gaps for the trends through peaks approach can only be negative so the sign on 

the gap term is of no significance).


TABLE 1: Estimated potential growth rates and magnitude of output gap 

Method used Growth rate Output gap 

tp1 2.21 

tp2 1.06 

yl1 4.05 -1.52 

yl2 3.54 

yk1 3.16 3.43 

yk2 1.52 

pf1 1.39 1.34 

hp1600 1.73 3.41 

hp200 3.55 1.52 

hp100,000 1.10 3.53 

bf1600 3.55 -0.25 

bf200 5.42 -1.10 

bf100,000 1.50 -0.20 

mfa1600 2.79 -0.90 

mfa200 4.19 -1.95 

mfa100,000 1.62 -1.83 

mfb1600 3.76 -0.76 

mfb200 4.94 -1.75 

mfb100,000 1.66 -0.35 

As Table 1 illustrates the various measures produce vastly different 

conclusions regarding the potential growth rate over the year to March 1994, and 

the size and sign of the output gap. If, for example, mfa200 is the correct estimate 

of potential output then, assuming the potential growth rate over the year to 

March 1995 is the same as in 1994, this would imply that the economy could 

sustain a further 6.1 percent before the output gap termed positive and pressures 

on inflation developed. 16 On the other hand, if pf1 is the correct estimate of 

potential output, then the estimates suggest that inflationary pressures are likely 

to have been developing since the beginning of last year. The question is, how 

does one select which (if any) is the best estimate? 

5 Econometric properties of estimated output gaps 

In section 4 we estimated 19 different output gaps. Given that the different 

estimates led to different conclusions, the usefulness of these measures will be 

limited; unless one estimate can be isolated as being superior to the rest, or the 

range of valid alternatives can at least be narrowed down. In this section we 

make use of both correlation and regression analysis in an attempt to do 

just that. 

16 

The estimate of 6.1 percent is calculated by summing last period’s output gap and the 

negative of the estimated potential growth rate.

106 


TABLE 2: Correlations between estimated output gaps and the change and 

level of inflation 

Change in 

Gap and 

gap and 

change in 

change in 

Change in import import 

Method inflation Inflation penetration penetration 

used 77Q2–94Q1 77Q2–94Q1 77Q2–94Q1 77Q2–94Q1 

tp1 0.1064 0.5815 -0.0013 0.2144 

tp2 0.1577 0.1230 0.0740 0.2272 

yl1 -0.0451 0.7760 -0.0934 0.1426 

yl2 0.0380 0.8218 -0.0545 0.2302 

yk1 0.2735 0.2811 0.0806 0.2046 

yk2 0.1696 0.3681 0.0617 0.2102 

pf1 0.1768 0.4695 0.0612 0.2126 

hp1600 0.2415 0.0272 0.1406 0.2231 

hp200 0.3372 0.1461 0.1932 0.2225 

hp100,000 0.1439 0.1655 0.1052 0.2078 

bf1600 0.3643 0.4530 0.1639 0.2252 

bf200 0.3930 0.3891 0.1650 0.1744 

bf100,000 0.1645 0.2100 0.0790 0.2108 

mfa1600 0.2910 0.6542 0.0986 0.2236 

mfa200 0.2624 0.6744 0.0643 0.1933 

mfa100,000 0.1614 0.3821 0.0590 0.2121 

mfb1600 0.3223 0.5442 0.1377 0.2179 

mfb200 0.2712 0.6226 0.0891 0.1783 

mfb100,000 0.1595 0.2484 0.0701 0.2099 

5.1 Correlation analysis 

From the standpoint of a central bank that is required to maintain price stability, 

the usefulness of the estimated output gap series depends on the strength and 

reliability of its link with inflation. Keeping in mind the theory that the output 

gap should be related to the rate of acceleration in inflation (so that positive 

output gaps are associated with an increasing inflation rate), one way of 

assessing this linkage is to analyse the simple correlation between the output gap 

and the change in inflation. Given that previous Reserve Bank research has found 

stronger correlations between the output gap (or some measure of excess 

demand) and the level of inflation, these correlations were also computed. The 

results are presented in the first two columns of Table 2, which lead to the 

following conclusions. First, in all but one case, the estimated correlation coefficient 

is positive. This is to be expected, and implies that more positive values 

of the output gap are associated with larger changes in the rate of inflation or 

higher levels of inflation itself.


Secondly, focusing on the relationship between the output gaps and the 

change in inflation, the strongest correlations were obtained with those output 

gaps derived using the filtering techniques. Again this is to be expected, given 

that information about the evolution of inflation was used in the construction of 

the underlying output series; though the Hodrick-Prescott derived estimates 

(which did not use this information) produced similar correlations to the 

multivariate filters. The magnitude of these correlation coefficients is comparable 

to those estimated for the G7 economies by Torres and Martin (1990) which 

ranged from 0.27 (for Germany) to 0.53 (for the United States), with an average 

correlation coefficient of 0.41. 

Thirdly, focusing on the relationship between the output gaps and the level 

of inflation, the strongest correlations were obtained with the labour input 

derived output gaps, although the multivariate filter based estimates were not 

far behind. In almost all cases, the correlation coefficient between the estimated 

output gap and the level of inflation was substantially higher than that between 

the output gap and the change in inflation. The relative strength of these 

correlations was further emphasised when they were recalculated over a more 

recent data period (1986Q1–1994Q1). 

Finally, among the filtered output gaps, those estimates based on smaller 

values of λ—the smoothness constraint—typically out-performed those based on 

higher values, with λ = 200, tending to provide the best correlation among each 

type of filter. This result suggests that supply shocks have been more dominant 

than demand shocks over the sample period, which is perhaps not surprising 

given the extent of financial and economic reform. 

Another feature that we might expect to see in a good estimate of the output 

gap is a positive correlation between the output gap and the change in the 

import penetration rate. This reflects the idea that conditions of excess demand 

will typically result in a greater proportion of domestic expenditure on imported 

goods (together with a running down of domestic stocks). Indeed, this type of 

relationship could also have been added to the multivariate filter, in the same 

way that we added data on inflation, unemployment and the yield gap. As 

Torres and Martin found a stronger correlation between the change in the output 

gap and import penetration growth for the G7 economies, these correlation 

coefficients were also calculated. The last two columns of Table 2 present the 

estimated correlation coefficients which lead to the following conclusions. First, 

in almost all cases, the correlation is positive. This is as one would expect, and 

implies that more positive values of the output gap are associated with increased 

import penetration. 

Secondly, focusing on the relationship between the level of the output gap and 

the change in import penetration, the strongest correlations were obtained with 

those output gaps derived using the Hodrick-Prescott and bivariate filtering 

techniques, though in all cases the correlations were relatively weak. The

108 


magnitude of these correlation coefficients is comparable with those estimated 

for the G7 economies by Torres and Martin which ranged from 0.02 (for Canada) 

to 0.33 (for France), with an average correlation coefficient of 0.15. 

Finally, focusing on the relationship between the change in the output gap and 

the change in import penetration, the estimated correlations were in all cases 

higher than those noted above (as in Torres and Martin), and were of a very 

similar magnitude. However, in absolute terms, the strength of the correlation is 

still weak. 

5.2 Regression analysis 

Given the finding that the estimated output gaps are more highly correlated with 

the level, rather than the change, in inflation (particularly over the last decade), 

it was decided to pursue this relationship further using regression analysis. 

In order to compare the explanatory power of the estimated output gaps, the 

following approach was employed. First, a simple reduced form econometric 

equation for quarterly consumer price inflation was estimated, including data on 

unit labour costs, the nominal exchange rate, and world export and import 

TABLE 3: Regression results—the output gap and quarterly consumer 

price inflation (1977Q2–1994Q1) 

Coefficient 

Regression 

Output gap on gap adjusted 

used term t statistic R-squared 

tp1 0.0380 1.602 0.8682 

tp2 0.0650 1.853 0.8702 

yl1 0.1053 1.222 0.8656 

yl2 0.0207 1.186 0.8654 

yk1 0.0845 2.504 0.8764 

yk2 0.0780 2.236 0.8737 

pf1 0.0842 2.337 0.8747 

hp1600 0.1085 2.414 0.8755 

hp200 0.1725 2.826 0.8799 

hp100,000 0.0451 1.689 0.8689 

bf1600 0.1801 3.497 0.8877 

bf200 0.1849 3.353 0.8860 

bf100,000 0.0580 1.965 0.8712 

mfa1600 0.1591 3.527 0.8881 

mfa200 0.1485 3.633 0.8894 

mfa100,000 0.0622 2.061 0.8721 

mfb1600 0.1788 3.362 0.8861 

mfb200 0.1957 3.352 0.8860 

mfb100,000 0.0540 1.916 0.8708


prices. The equation was then re-estimated with the addition of one of the 

estimated output gaps. If the output gap is to be useful for explaining and 

forecasting the inflation process then we would want the estimated coefficient 

on the gap term to be of the correct sign, statistically significant and of a 

plausible magnitude. 17 

The relationship between the estimated output gaps and inflation was 

assumed to be linear in nature (ie the Phillips curve is linear). Recent research 

by Laxton et al (1994) suggests that this assumption may not be valid. Their 

research using pooled data from the G7 countries indicated that the relationship 

may in fact be non-linear (so that larger output gaps have a proportionately 

larger impact on inflation) and quite possibly asymmetric (positive output gaps 

have a different impact on inflation compared with negative gaps). Assuming 

symmetric non-linearity (of the cubic form) tended to worsen the equations’ fit. 

A more extensive testing for other forms of non-linearity and asymmetry was not 

attempted in this paper. However, given the significant policy implications of 

non-linearity (and especially asymmetry) in the output-inflation process, further 

research along these lines appears warranted. 

This procedure gives us 19 possible models, each using a different output gap. 

Table 3 presents the estimated coefficients on the output gap terms, their t 

statistics, and the regression adjusted R-squared for each of the 19 alternative 

models. 

An examination of Table 3 leads to the following conclusions. First, in all 

cases the estimated coefficient on the output gap is positive as expected, and this 

is statistically significant in all regressions except those including the labour 

input derived output gaps. This latter result is interesting since the simple 

correlation between these output gaps and the inflation rate was very strong. 

This suggests that the unit labour cost term in the regression is already capturing 

the same information as these output gap measures. 

Secondly, the estimated coefficients range from 0.0207 to 0.1957, though the 

coefficients of the most significant gaps range from 0.1485 to 0.1957. These 

coefficients imply that a positive output gap equal to 1 percent of potential GDP 

will add around 0.15–0.195 to the quarterly inflation rate or 0.60–0.78 over the 

full year to the annual inflation rate, while a positive output gap equal to 3 

percent of potential GDP will add 0.45–0.59 to the quarterly inflation rate or 

1.80–2.34 over a full year to the annual inflation rate. Bearing in mind the period 

over which these equations have been estimated, these figures seem reasonably 

plausible. Given the Reserve Bank’s target of 0–2 percent annual movements in 

17 

One possibility, not investigated here, is that inflation may respond to the rate at which 

actual output is growing relative to potential in addition to the size of the output gap itself. 

Thus, there may be a distinction between short-run potential output and long-run potential 

output. Both have been found to be important by the Bank of England (1994).

110 


the Consumers Price Index these estimates imply that the Bank would, in the 

absence of inflationary pressures from other sources, need to ensure that actual 

output remained within around 2 percent either side of the estimated potential 

level of output. 18 

Finally, as in the correlation analysis, those estimates based on smaller values 

of λ—the smoothness constraint—typically outperformed those based on higher 

values, with λ = 200, tending to provide the best explanatory power among each 

type of filter. It is interesting to note that the choice of λ = 200 is the preferred 

parameter for Canada—another ‘small’ open economy. Again this result suggests 

that supply shocks have been more dominant than demand shocks over the 

sample period. 

The task now is to assess whether any one model or group of models 

performs statistically better than the rest. This was done by applying the nonnested 

model selection tests developed by Davidson and Mackinnon (1981) and 

Cox (1961 and 1962), known as the J test and Cox test respectively. The basic 

hypothesis that is tested is that Model A is the true model and that Model B is 

not. The testing procedure requires that the reverse hypothesis also be tested, as 

in small samples the procedure can generate conflicting or inconclusive results 

(ie both models are accepted or both models are rejected). Table 4 presents the 

results of the J test while Table 5 presents the results of the Cox test. In both 

tables, the statistics are presented in the form of p (or probability) values so that 

low values of p (say, less than 0.10) indicate the null hypothesis (that Model A is 

the true model) is rejected. Each row of the tables test the null hypothesis that 

Model A is superior to the alternative hypothesis (given by the columns). Cells 

with a p value of less than 0.10 are shaded so as to highlight the key results. 

An examination of Table 4 and Table 5 clearly indicates that the multivariate 

filters (including the bivariate filter) are to be preferred to those estimated using 

other techniques. Indeed, for those multivariate techniques which allow for 

greater non-linearity in the estimated potential output series (ie those where λ = 

1600 or λ = 200) the null hypothesis is accepted against all alternative techniques 

including the more linear forms of the multivariate filter. 

Overall, the tests suggest that there is little difference between the bf1600, 

mfa1600, and mfa200 output gaps. 

5.3 Summary 

The analysis in the previous section suggests that the bf1600, mfa1600, and 

mfa200 output gaps are in a statistical sense equally good at explaining trends 

in inflation. The potential growth rates suggested by these series range from 2.79 

18 

It should be noted that the other variables in the regression, particularly unit labour 

costs, may also capture part of the total cyclical influence. Therefore, the estimated 

coefficient on the output gap term should not be interpreted as the total elasticity with 

respect to cyclical pressures.

TABLE 4: Non-nested model selection: J test 

tp1 tp2 yl1 yl2 yk1 yk2 pf1 hp1600 hp200 hp100 bf1600 bf200 bf100 mfa1600 mfa200 mfa100 mfb1600 mfb200 mfb100 

tp1 0.366 0.530 0.752 0.045 0.120 0.102 0.072 0.016 0.372 0.003 0.002 0.271 0.004 0.002 0.212 0.006 0.006 0.313 

tp2 0.887 0.553 0.372 0.091 0.173 0.161 0.139 0.041 0.823 0.006 0.006 0.505 0.006 0.003 0.388 0.009 0.010 0.590 

yl1 0.237 0.142 0.486 0.031 0.073 0.052 0.046 0.015 0.227 0.002 0.003 0.138 0.001 0.001 0.111 0.003 0.003 0.151 

yl2 0.276 0.102 0.451 0.022 0.058 0.049 0.016 0.007 0.080 0.002 0.002 0.085 0.002 0.001 0.086 0.003 0.003 0.010 

yk1 0.405 0.559 0.557 0.356 0.332 0.274 0.240 0.072 0.542 0.020 0.020 0.379 0.021 0.013 0.325 0.025 0.018 0.377 

yk2 0.718 0.504 0.956 0.582 0.152 0.476 0.352 0.080 0.487 0.014 0.016 0.457 0.011 0.009 0.604 0.017 0.021 0.363 

pf1 0.818 0.699 0.687 0.689 0.168 0.754 0.444 0.108 0.479 0.017 0.022 0.425 0.011 0.011 0.488 0.017 0.026 0.466 

hp1600 0.579 0.827 0.816 0.180 0.184 0.714 0.608 0.173 0.395 0.016 0.030 0.962 0.016 0.014 0.787 0.029 0.029 0.991 

hp200 0.307 0.669 0.688 0.234 0.186 0.489 0.523 0.967 0.970 0.022 0.101 0.678 0.052 0.039 0.574 0.098 0.076 0.615 

hp100 0.466 0.445 0.664 0.190 0.064 0.120 0.091 0.065 0.033 0.004 0.007 0.239 0.004 0.003 0.225 0.005 0.007 0.359 

bf1600 0.593 0.974 0.800 0.603 0.500 0.946 0.765 0.494 0.184 0.574 0.697 0.760 0.588 0.340 0.870 0.899 0.418 0.884 

bf200 0.223 0.368 0.684 0.429 0.254 0.444 0.535 0.666 0.953 0.862 0.334 0.636 0.225 0.213 0.543 0.328 0.239 0.542 

bf100 0.870 0.811 0.928 0.407 0.088 0.210 0.151 0.185 0.052 0.495 0.007 0.011 0.006 0.005 0.431 0.008 0.011 0.763 

mfa1600 0.852 0.878 0.334 0.976 0.613 0.654 0.403 0.566 0.714 0.561 0.726 0.472 0.595 0.391 0.623 0.960 0.490 0.716 

mfa200 0.348 0.541 0.554 0.699 0.492 0.799 0.983 0.971 0.903 0.848 0.704 0.938 0.976 0.706 0.895 0.635 0.402 0.818 

mfa100 0.879 0.931 0.952 0.570 0.097 0.332 0.211 0.244 0.056 0.652 0.009 0.012 0.603 0.008 0.006 0.010 0.013 0.380 

mfb1600 0.800 0.693 0.575 0.968 0.371 0.543 0.379 0.683 0.894 0.420 0.386 0.340 0.381 0.341 0.189 0.393 0.571 0.442 

mfb200 0.643 0.993 0.617 0.506 0.222 0.843 0.723 0.614 0.493 0.848 0.230 0.238 0.675 0.231 0.133 0.597 0.541 0.689 

mfb100 0.954 0.784 0.840 0.436 0.079 0.155 0.144 0.165 0.045 0.761 0.007 0.009 0.608 0.006 0.005 0.256 0.008 0.010 

Darren Gibbs 111

112 

TABLE 5: Non-nested model selection: Cox test 

tp1 tp2 yl1 yl2 yk1 yk2 pf1 hp1600 hp200 hp100 bf1600 bf200 bf100 mfa1600 mfa200 mfa100 mfb1600 mfb200 mfb100 

tp1 0.224 0.308 0.688 0.000 0.021 0.008 0.000 0.000 0.166 0.000 0.000 0.109 0.000 0.000 0.075 0.000 0.000 0.166 

tp2 0.871 0.349 0.017 0.001 0.083 0.057 0.033 0.000 0.795 0.000 0.000 0.412 0.000 0.000 0.275 0.000 0.000 0.578 

yl1 0.005 0.000 0.222 0.000 0.000 0.000 0.000 0.000 0.012 0.000 0.000 0.002 0.000 0.000 0.001 0.000 0.000 0.002 

yl2 0.043 0.000 0.169 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 

yk1 0.169 0.440 0.354 0.010 0.160 0.102 0.074 0.001 0.399 0.000 0.000 0.189 0.000 0.000 0.130 0.000 0.000 0.179 

yk2 0.706 0.486 0.952 0.393 0.017 0.412 0.234 0.002 0.479 0.000 0.000 0.432 0.000 0.000 0.575 0.000 0.000 0.343 

pf1 0.801 0.682 0.687 0.585 0.025 0.732 0.343 0.011 0.475 0.000 0.000 0.406 0.000 0.000 0.462 0.000 0.000 0.449 

hp1600 0.448 0.814 0.774 0.000 0.035 0.666 0.540 0.073 0.398 0.000 0.000 0.958 0.000 0.000 0.752 0.001 0.001 0.990 

hp200 0.044 0.591 0.586 0.000 0.030 0.364 0.416 0.963 0.966 0.004 0.027 0.608 0.008 0.003 0.419 0.028 0.007 0.519 

hp100 0.290 0.327 0.553 0.000 0.000 0.032 0.016 0.007 0.000 0.000 0.000 0.147 0.000 0.000 0.114 0.000 0.000 0.259 

bf1600 0.468 0.971 0.793 0.438 0.386 0.940 0.751 0.485 0.178 0.577 0.654 0.750 0.535 0.254 0.860 0.886 0.321 0.874 

bf200 0.003 0.158 0.579 0.11 0.085 0.297 0.426 0.600 0.947 0.838 0.245 0.549 0.121 0.127 0.423 0.222 0.120 0.413 

bf100 0.850 0.783 0.918 0.055 0.001 0.129 0.072 0.066 0.000 0.473 0.000 0.000 0.000 0.000 0.367 0.000 0.000 0.739 

mfa1600 0.826 0.869 0.392 0.974 0.534 0.642 0.402 0.554 0.694 0.566 0.691 0.384 0.590 0.310 0.616 0.955 0.406 0.706 

mfa200 0.098 0.408 0.575 0.602 0.373 0.765 0.982 0.967 0.894 0.838 0.663 0.930 0.974 0.666 0.879 0.579 0.279 0.786 

mfa100 0.869 0.922 0.947 0.371 0.001 0.254 0.130 0.090 0.000 0.635 0.000 0.000 0.590 0.000 0.000 0.000 0.000 0.346 

mfb1600 0.791 0.684 0.592 0.965 0.218 0.534 0.378 0.667 0.883 0.440 0.310 0.235 0.394 0.262 0.094 0.401 0.510 0.451 

mfb200 0.642 0.993 0.629 0.536 0.056 0.831 0.707 0.533 0.392 0.838 0.123 0.120 0.665 0.128 0.041 0.589 0.477 0.679 

mfb100 0.949 0.752 0.808 0.102 0.000 0.82 0.061 0.045 0.000 0.742 0.000 0.000 0.561 0.000 0.000 0.188 0.000 0.000 

Labour Market Bulletin 1995: 1


to 4.19 percent (averaging 3.51 percent); while all the series suggest that a small 

negative output gap still existed in March 1994, ranging from between 0.25 to 

1.95 percent of GDP (averaging 1 percent of GDP). It is comforting that the 

preferred estimates span a range which would be considered plausible by most 

economists. However the lack of precision, which characterises empirical studies 

of this type, severely hinders the usefulness of these measures for policy analysis. 

Nevertheless, if we combine the information about potential growth rates, the 

output gap, and the elasticities of the output gaps in the estimated inflation 

equations, and assume (somewhat heroically) that growth in potential output 

over the year to March 1995 is the same as over the year to March 1994, the 

estimates imply that actual output could grow by between 3.8 percent and 6.1 

percent in the year to March 1995 (in point to point terms) before the output gap 

becomes positive and inflationary pressures emerge. Beyond that, every extra 1 

percent of growth would contribute between 0.59 percent to 0.72 percent to the 

annual inflation rate. 

6 Conclusion 

Empirical measures of the degree of spare capacity in the economy and of the 

economy’s potential (non-inflationary) growth rate are important for a number 

of reasons. Such measures, if robust, are particularly important for monetary and 

fiscal policy, for labour market monitoring, forecasting and policy and for private 

sector planning. 

This paper surveyed a variety of techniques used to measure potential output. 

In the presence of uncertainties surrounding the true structural determinants of 

the supply side of the economy together with poor quality data, the paper argues 

that multivariate filtering techniques are likely to be preferable to more rigid 

structural approaches such as those based on the estimation of production 

functions (especially in the short term). 

This view is supported by preliminary estimates of output gaps with New 

Zealand data. Nevertheless, although statistical techniques identify some 

measures as better than others, these estimates are still imprecise. The current 

potential growth rates preferred by the study range from 2.79 to 4.19 percent 

(averaging 3.51 percent); while all series suggest that a small negative output gap 

still existed in March 1994, ranging from between 0.25 to 1.95 percent of GDP 

(averaging 1 percent of GDP). 

Although the theory hypothesises a relationship between the measured 

output gaps and the change in inflation, the empirical measures derived in this 

paper display a stronger relationship with the level of inflation. Regression 

analysis suggests that between 0.59 percent to 0.72 percent is added to the annual 

inflation rate for each percentage point of GDP in which actual output exceeds 

potential. However, further research aimed at testing for a non-linear or

114 


asymmetric inflationary response to both the change and the level of the output 

gap is required. 

One characteristic of the preferred estimates is that they suggest, perhaps not 

surprisingly, that supply shocks have dominated over the last two decades. 

Given the different inflationary dynamics implied by demand versus supply 

shocks, policymakers would be wise to keep this in mind when seeking to draw 

conclusions regarding recently observed sharp increases in actual output. 

Given the wide range of estimates of potential output which appear 

consistent with the data, estimates must be treated with considerable caution. 

Although further research is likely to yield better estimates than those presented 

here, empirical measures of potential output are unlikely ever to be sufficiently 

robust as to be useful for fine-tuning macroeconomic policy. As Giorno et al 

(1995) argue: 

. . . the OECD has revised its estimation methods to provide a single measure of 

potential output. . . . Nonetheless, it is clear from this work and the wide range of 

analytic and survey based indicators which are available that significant margins of 

error are involved in their estimation and use. Reliance therefore cannot wholly be 

placed on a single measure of potential or trend output, and related indicators must 

therefore be treated with due caution (p 6).


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Potential Output: Concepts and Measurement - Department of Labour

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