Output gaps. Some evidence from the UK, France and Germany.

Barrell, Ray ; Sefton, James

As the UK economy recovers from the recent recession, there is again widespread concern at the re-emergence of the spectre of inflation. Recent increases in base rates were primarily aimed at reassuring markets that inflation will be controlled. It is therefore of use to be able to calculate whether or not inflationary pressures are liable to re-emerge in the near future. Our macroeconomic, model based, forecast on page 8 of this Review is one way that this could be done. This note investigates a number of other approaches.

The output gap is one of the principal indicators of inflationary pressures used in the current debate. The gap measures the amount of production over and above that which could be expected if the economy were operating at its sustainable level. When we experience above potential output we would anticipate that prices would rise until aggregate demand was reduced sufficiently. Many economists therefore have taken, or are quickly taking, a stand on the size of the output gap, so much so that Gavyn Davis (The Independent, January 9) compiled a list of 'gapologists', the leading proponents of this science.

The output gap is also applied in the estimation of cyclically adjusted budget deficits, and we have utilised them extensively in this context in Barrell, Morgan, Sefton and in't Veld (1994). In order to monitor deficits it is necessary to adjust the actual deficit to take into account the stage of the business cycle. In a recession, government tax income is always reduced and expenditure always increases because of items such as unemployment benefits and social security payments. In calculating the cyclically adjusted budget balance an attempt is made to estimate the budget deficit that would have prevailed if there was no output gap. Hence it may be possible to judge changes in the stance of fiscal policy if we can estimate the size of the output gap.

Given its importance, it is unfortunate that the output gap cannot be measured directly. A variety of techniques for estimating it are in common use. In this note we attempt to review these methods and comment on their merits and deficiencies. We review the different methods that have been in use at different times by the IMF and the OECD. We will also suggest a different approach which avoids most of the pitfalls of the earlier methods, but is econometrically more difficult to implement.

Potential output and output gaps

Measuring potential output and output in relation to potential are important in our analysis of the macroeconomic environment. When the gap is zero there is neither excess demand nor excess supply, then the economy can be seen as in equilibrium at its supply determined potential. The equilibrium levels of unemployment and output are obviously inextricably linked, as disequilibrium pressure in the labour market will spill over into the market for output, and vice versa. Most current theories of the labour market define the equilibrium, or sustainable, level of unemployment as that which is consistent with stable wage inflation. In this situation we would expect the expected wage to equal the actual wage, and hence there should be no pressure for it to depart from its expected trajectory.

The growth of potential output has often been seen as a constant, driven by technology and labour force growth. Maddison (1982) estimated the growth in output for most of the OECD countries over the last 150 years and his work supported this empirical observation. Events in the 1970s persuaded most economists that the growth in potential output should be seen as a stochastic or random process around this historical average. Shocks to the economy come in various forms, and some may affect the supply potential of the economy, while others may cause the economy to cycle around potential. It is reasonably clear that the 1974 oil price shock lowered potential output permanently in the OECD area, but it may not have lowered the subsequent potential or average growth rate. If this is the case then we should model it as a step decrease in the level of potential output. However, the economy takes time to adjust to such a supply-side shock, but when measuring potential output we are interested in the long run or permanent effects of such a shock. Any trend extraction technique we use should be able to deal with such changes in the trend output level, Chart 1 illustrates the problem they face. If we place a linear trend through the data it would suggest an estimate of around 1.4 per cent for the growth in potential output in the UK over the 1970s. This is well below the historical average of 2 per cent. This can be contrasted to the alternative estimate of a linear trend with growth rate of 2 per cent plus a jump in 1974, caused by adjustment to the oil price shock. Similarly the 1980s could be modelled as a linear trend of 2 per cent plus some positive supply shocks due perhaps to the fall in oil prices in 1985/86 and to labour market restructuring.

The identification of potential output allows us to separate the causes of fluctuations in output into those coming from the supply-side, causing equilibrium output to change, and those coming from variations in demand. Most Keynesian economists have associated output fluctuations with changes in demand, but this view was challenged in the late-1970s and the 1980s by the development of theories of Real Business Cycles. At first these analyses seemed to suggest that all the observed variation in output could be put down to supply shocks and their consequences, with output closely following potential. However, as McCallum (1990) suggests, these models should now be seen as a reminder that a 'portion of the output and employment variability that is observed in actual economies is probably not generated by erratic monetary and fiscal policy makers'. It is now generally considered that we can make a distinction between supply shocks that permanently change the level, but not the growth rate, of potential output, and demand shocks that only have a temporary effect on the level of output. The existence of these two types of shocks, and their implications for the measurement of potential output, are discussed in Blanchard and Quah (1989). The prevailing consensus is that any approach to estimating potential output must first decompose fluctuations into those due to supply-side and those due to demand-side shocks. Blanchard and Fisher (1989) stress that the co-movement of economic time series can contain valuable information on this decomposition. For example, a demand-side shock to output would be reflected in or correlated with changes in consumption, whereas a supply-side shock would be expected to cause a change to the level of investment, and hence output. Methods for estimating gaps can be designed which utilise this information.

Given the theoretical importance of the output gap, it is unfortunate that its measurement is so problematic. This will always be the case however when we are trying to separate out 'high frequency' events such as the business cycle from 'low frequency' events or persistent phenomena such as the trend in potential output. As Watson (1986) points out, a time series of 30 years could contain a significant number of examples of cycles of periods of less than 5 years, yet only a few examples of cycles of 10 years or more. Therefore we have more information in a finite sample on the shorter cycles, and correspondingly less information on longer cycles and the permanent shocks (which can be regarded as infinitely long cycles). Techniques for trend extraction have to address this problem directly, and filters for trend extraction are designed to remove specific frequencies and, in particular, cycles from the data under consideration.

This note examines a number of ways of extracting trends, and uses them to produce output gaps for the UK, France and Germany. We look at the broken deterministic trend approach developed by the NBER, and used until recently by the OECD, as well as at the simple symmetric filter advocated by Hodrick and Prescott (1980). Both these methods use only information contained in the output series and assume that the average growth rate of potential GDP varies over time. We suggest estimating trend output using a VAR based multivariate filter which utilises and extends the techniques suggested by Beveridge and Nelson (1981). This method models the co-movement between the selected time series to help differentiate between demand and supply-side shocks, and then extracts the long-run component of the supply-side shocks. It implicitly assumes that the average long-run growth of GDP remains constant over time. We also look at the commonly used, and economically justifiable, application of the aggregate production function to the calculation of potential output. This approach is now in use by both the OECD and the IMF.

Methods For estimating output gaps

We wish to investigate methods that allow us to extract from output those events that had a persistent but ultimately transitory effect on the equilibrium level of output. The 1970s, for instance, may have seen rather low growth of potential, in part because of worsening labour market conditions in a number of countries, while the 1980s may have produced higher potential growth, in part because of high levels of investment. We would want all our trend extraction methods to take account of local variations in trend growth, at least in as far as they are relevant for policy purposes. Each method implicitly contains a model of potential output growth and we will discuss them. Output gap estimates are frequently used in the policy debate, and we consider it a failing that some estimates suffer from an end of sample bias. A method might produce very plausible and robust estimates of the output gap in the middle of the data period, but might also be particularly sensitive to small changes in the implementation of the method at the end of the sample, and we will point out where this is the case.

The NBER benchmark method

The traditional analysis of Burns and Mitchell (1946) has been widely applied, for instance by Friedman and Schwartz (1963), and it was used for some time by the OECD, whose method is set out in Chouraqui et al. (1990). The method requires that the observer can identify the timing of peaks (or troughs) in the economic cycle. Once this is done it is relatively easy to estimate the trend. For instance the OECD benchmark scenario was based on a measure of mid-cycle trend output. Estimation of trend growth is based on a simple semi-log model:

ln(y) = [a.sub.0] + [summation over i] [a.sub.i] T[D.sub.i] + e (1)

where ln(y) is the natural logarithm of real GDP, [a.sub.i] the ith trend growth coefficient and T[D.sub.i] the ith segment of the broken time trend, while T is a time trend and [D.sub.i] takes the value one in the ith segment but is zero elsewhere. Business cycles are assumed to start on the first year following a peak, when the growth rate displays a local maximum, and to end in the year of the next observed peak. Equation (1) also contains a constant term because it is necessary to estimate the initial level of the trend at the start of the sample. This technique has the advantage that it is simple and mechanical, but it does depend on a rather arbitrary or subjective choice of the timing of the cycle, and it appears that in many applications a large amount of judgement has been used.

The log linear trend approach is based on rather strong assumptions, and in particular it assumes that trend output growth is constant between structural break points, but can vary radically between cycles. Actual output cycles around this trend because demand shocks push the economy away from equilibrium. At the peak the supply determined trend suddenly breaks, giving a new underlying growth rate for the economy. However despite the improbability of this scenario, Campbell and Mankiw (1987) do demonstrate that this specification can have as much explanatory power as a more believable stochastic model. The approach also has the advantage that it allows the user to specify the points at which supply shocks change the level of potential output.

There are two problems with the practical implementation of this approach, especially if we are interested in evaluating the current situation. Unfortunately if a break point is placed near the end of the sample, then there is little data to estimate the trend growth coefficient over the last period. This is a particularly serious problem at the present conjuncture as most economies in Europe are just recovering from a recession. If a structural break was placed at the previous peak, around 1987 for most of these economies, this model would predict almost negative growth in potential output over the period since 1987. There are two possible solutions to this end point problem, neither of them particularly satisfactory. We could use our macro-forecast of output over the future in order to locate the next cyclical peak, or we could avoid the problem and not place a break point near the end of the sample. In the former case our estimate of the current level of potential output would be very heavily influenced by our forecast for potential output, while in the latter case we could be ignoring useful information on the evolution of output. It is also necessary to estimate the initial level of trend output, [a.sub.0]. This will cause similar problems at the beginning of the period but of course this is less critical in the analysis of current policy problems.

Hodrick-Prescott filter

The Hodrick-Prescott filter has been commonly used, in part because it is easy to apply. The trend is defined as the time series which minimises the size of the output fluctuations centred on it, subject to a constraint limiting the maximum allowable change in the growth rate of trend output. If the maximum allowable change in the rate of growth is zero, then the trend must be a straight line. As the maximum allowable change increases so the trend line is allowed to bend to achieve a better fit. The trend is defined as the solution to the problem,

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

where [Epsilon] is an arbitrarily chosen small number.

As King and Rebelo (1989) and Harvey and Jaegar (1993) demonstrate, the solution to this problem is equivalent to applying a linear filter to the original GDP time series. The choice of the parameter [Epsilon] should depend on one's views on the variance of trend relative to that of output, and hence it should be varied from application to application. However this is seldom done, and the most commonly used values in the application of the Hodrick-Prescott filter tend to completely remove all stochastic or deterministic cycles shorter than three years, and pass through to the trend all cycles longer than 20 years. In between the filter only reduces the magnitude of the observed cycle in proportion to the cycle length. Over the 1980s the major cycle in GDP lasted for around 8-10 years for most major economies, which was rather longer than the average of the post-war period. As a result the standard application of the Hodrick-Prescott filter would interpret this movement in GDP as a change in potential output and not a business cycle. Although this might be a correct deduction, it is simply the result of an arbitrary choice for [Epsilon] and is not based on statistical or economic inference. The filter also has the property that it can induce fake cycles into the data by taking a moving average of a random process. This so-called 'Yule-Slutsky' effect is difficult to avoid if the output series is very noisy.

The Hodrick-Prescott filter has a major flaw when used for the analysis of current economic events. At the end of the sample, the optimal trend will always follow the actual series more closely than elsewhere. At the end of the sample there is only a small reduction in the sum of squares from following the actual series into a supposed trough. There is no requirement for the trend to then change direction suddenly into the next peak outside the sample. By contrast, in mid sample, if the trend followed the cycle into a trough, there would be a large cost to closely following the series into the next peak as this would require a considerable change in direction. The optimal path in this case would lie along an average line somewhere between the peak and trough. This feature also makes it difficult to pick up sudden changes in the level of potential output, and supply-side driven shifts in potential output are smoothed out over a number of years either side of the shock that causes them. Unfortunately there is very little one can do to minimise these failings. In order to avoid end point biases one could use forecasts so that the trend distortion takes place beyond the period of interest and therefore is no longer at the end of the sample. However, the consequent estimate of the gap is very dependent on the subjective forecast.

Potential output and the production function

Potential output is defined to be level of output that would have prevailed if the economy had been experiencing equilibrium employment with normal utilisation of capacity. In this situation we would observe equilibrium in the goods and labour markets. The equilibrium level of employment is often defined as equal to measured supply of labour minus the non accelerating wage inflation rate of unemployment (NAWRU), the maximum sustainable level of employment that is consistent with stable wage inflation. It is therefore necessary to estimate the underlying aggregate production function and the equilibrium level of employment in order to estimate potential output directly. This method is currently in use by both the IMF (1993) and the OECD (1994). They both assume a two factor input Cobb-Douglas production function,

Y = A(t)[K.sup.a][L.sup.(l - a)], (4)

where Y is output, K is capital in use, L is labour in use, and A(t) is an exogenous times series describing the rate of technical progress. By taking logs, this can also be written as

log Y = log A + a log K + (l - a) log L (4[prime])

Potential output is then calculated as the level of output that is consistent with normal capacity utilisation and an estimate of the NAWRU. Potential output can be written as

log [Y.sup.*] = [Alpha] + gt + alog[K.sup.*] + (l - a)log[L.sup.*]

where [K.sup.*] = [K.sub.*]CU, where CU is capacity utilisation, and [L.sup.*] is sustainable employment.

These estimates of trend output have an advantage over those based on trends and filters because they depend on a more theoretical model with less immediate reliance on econometric techniques. If the capital stock is known, and the labour market equilibrium can be calculated, then the levels of factor inputs available in equilibrium (or on trend) can be input into the production function to enable the calculation of trend output. A production function can allow for (a considerable degree of) factor substitution, and a change in relative factor prices could affect the estimate of trend output.

The application of this technique by the IMF and the OECD is somewhat more problematic than it might at first appear. The use of a Cobb-Douglas production function, with the labour shares based on the national accounts, fixes the substitution elasticity. Within this rather restricted framework there are still serious measurement problems. Even if it is possible to make an adequate measure of the capital stock. (i.e. one that covaries strongly with the actual stock with no trend in the measurement error), changes in management techniques may alter the feasible level of utilisation.

More problems are encountered in measuring the rate of technical progress A(t). The method most commonly used, for instance by the IMF and the OECD, is to assume that log A(t) is the residual from equation (4[prime]). This estimate is very noisy and therefore needs to be smoothed. The IMF use a split-trend method to fit this series, while the OECD chose to smooth A(t) using a Hodrick-Prescott filter.

More severe problems are encountered in the estimation of the level of sustainable employment, in part because the evaluation of labour market equilibrium is problematic. Minford and Riley (1994) argue that in the UK sustainable unemployment (i.e. the NAWRU) is now around 2 1/2 per cent, or well under a million. In the same volume Barrell, Pain and Young (1994) calculate that the NAWRU in the UK varied over the 1980s but by the early-1990s it was no lower than 7-8 per cent. If labour has a 66 per cent share in output, then this difference alone would cause the implied output gap estimates to differ by 3 to 4 per cent of GDP. In Giorno et al. (1995) the OECD produces a similar estimate of the NAWRU than Barrell, Pain and Young (1994) by first adjusting the actual level of unemployment by the degree of wage inflation before detrending using the Hodrick-Prescott filter. Once again this estimate will affect the evaluation of potential output.

Large-scale macro-models that incorporate estimated production functions can also be used to evaluate potential, much as they can be useful in understanding the current conjuncture. They often have production functions for individual sectors, and hence they could be preferable to estimating a single aggregate production function. They also often include a fully coherent model of the labour market, and the NAWRU for each sector is embedded and easily calculated. It is then only necessary to calculate the average level of capacity utilisation in each sector before the potential output of each sector can be aggregated to an estimate of total potential output. Setting up such a model is a huge task but, given that large-scale macro models exist in nearly all the developed economies, it does provide a theoretically coherent and practical way of estimating potential output. However, applications are rare, although the approach currently used by the OECD can be described in this way.

A new approach: Beveridge-Nelson trend cycle decomposition

Most methods for trend extraction in current use have statistical failings, the most important being the end of sample bias. It is also possible to introduce more ancillary information in order shed some light on the evolution of trends. We would advocate an approach that should recognise the stochastic nature of the business cycle, and be able to distinguish between shocks that permanently affect the level of output and those shocks which only have a transitory effect on the level of output. In order to be able to determine the long-run effects of any shock, we should be able to use the information contained in the co-movements of a number of economic time series such as capacity utilisation, sales or employment. If, for instance, a change in output is correlated with a change in employment, then this would suggest a supply-side shock, whereas if it is correlated with consumption then it is more likely to suggest a demand-side shock.

Blanchard and Quah (1989) and King, Plosser, Stock and Watson (1991) suggested estimating a Vector Autoregression (VAR) model subject to some long-run restrictions. These restrictions impose the condition that only supply-side shocks can have a permanent effect on output in the long run. Changes in output could then be decomposed into the changes due to the supply-side shock and changes due to the demand-side shock. The gain from imposing this property and including more a priori knowledge of the economy within the model could outweigh the loss of flexibility, especially when we are using very limited data sets. As King et al. note, this decomposition allows one to estimate changes to potential output as the long-run effects of the supply-side shock. A refinement was made to this technique by Evans and Reichlin (1994). They suggested using a multivariate generalisation of the Beveridge and Nelson (1981) decomposition, and we describe this technique in our Annex. Instead of effectively imposing the decomposition into supply-side and demand-side shocks, they proposed estimating the long-run relations that describe the evolution of potential output. This can be done by estimating the cointegrating vectors contained in the VAR. However, if the data sample is short it is sometimes difficult to find estimates of these long-run relations that are robust to minor specification changes. Despite this problem, this method has the major advantage that it does not require the estimation of any initial conditions and therefore there are no end of sample biases.

The technique is not a simple mechanical one, unlike the Hodrick-Prescott filter. It requires considerable econometric expertise to first estimate the long-run relationships by cointegration techniques. Care is also required in estimation of the short-run dynamic model to ensure that this model is correctly specified. The choice of the set of variables to include in the VAR is an important step in the decomposition. Some of the variables that are included should share a common trend with income, but have different amplitudes in the cycle. In general we attempted to choose conditioning variables so that we might have a 'production' cointegrating vector with output and employment, and a 'demand' cointegrating vector with consumption and investment. Output and consumption, for instance, share a common trend, but output tends to have greater cyclical variation. Other variables should have a common trend with output but be good forward indicators. If output is expected to rise (and expectations are on average correct) then investment will be a useful forward looking common trending variable because we can expect investment now to respond to expected future output. It is also useful to include some non-trending (integrated of order zero) series in the set of conditioning variables. Some such conditioning variable may contain forward looking information, while others may give a good indication of the potential speed of acceleration of output. Capacity utilisation and confidence measures could be included in the former set, while (the change in) unemployment may be a good indicator for the rate of change in output.

Estimates of output gaps

In this section we will compare the output gaps that result from the different methods outlined above. We will also compare our estimates to those of the IMF and the OECD. Table 1 presents estimates from the IMF World Economic Outlook, October 1994, and compares them to estimates produced by the OECD in Giorno et al. (1995). In general these organisations believed output gaps in 1993 were large, at least in the UK and France. If we took account of new data available since the calculation of these figures they would indicate that the output gap in the UK was around 3 per cent at the end of 1994, suggesting that it would be some time before inflationary pressures might emerge. Our own calculations suggest that the output gap in the UK may be considerably lower than this. Table 1 also includes our own estimates of gaps using four methods and more recent data on 1994 than was available to the OECD or the IMF.

Our output gaps for the UK are plotted in Chart 2. All four methods that we employ suggest that the gap had shrunk to less than 2 per cent, and it could be around zero in 1994. The production function based indicator embodies an estimate of sustainable unemployment, and Barrell, Pain and Young (1994) suggest that sustainable unemployment is around 8 per cent, and this is likely to [TABULAR DATA FOR TABLE 1 OMITTED] be reached some time in 1995. Charts 3 and 4 plot output gaps for France and Germany. Our output gaps in the early 1990s suggest that the recession in France was mild and that only around 1 or 2 per cent of spare capacity exists. The production function based approach is particularly problematic for France, as inertia in the labour market is very severe, and it is possible that unemployment could have been above the NAWRU for most of the 1980s (see Barrell, Pain and Young (1994) for a discussion of France). Three of our four methods of trend extraction suggest that there is little spare capacity in (west) Germany, but a production function based approach indicates that it may be considerable. This may reflect the historically high level of unemployment that has been caused by migration into west Germany, a factor that is not picked up by our other filters. Migration may well have changed past relations, and in the future output may grow more rapidly than it has done in he past. Only a production function based approach (or a model based forecast) can pick up recent structural changes of this sort.

Our trend estimation also provides some indications or estimates of the rate of growth of potential output. We have found that all our filters produce an estimate for the UK in the range 2-2.1 per cent growth a year, although temporary factors may raise this. Our estimates for France, at 2.5-2.6 per cent, and for Germany, at 2.3-2.6, are slightly higher, with the larger estimate for Germany coming from the production function. Our calculations for the HP and production function approaches are based on developments over the last five years. These estimates should, of course be treated with caution, and in particular they depend upon the assumption that the trend rate of growth of the labour force will be unchanged. This may be questionable for several reasons. Our forecast for Germany suggests that migration will continue to raise the rate of growth of the workforce above its average in the 1980s, and that this will raise sustainable growth by at least a quarter of a per cent. Our forecasts for the UK and France in this Review are predicated on a belief that government policies to reduce equilibrium unemployment will be effective, albeit slow acting, and we assume that this will add a quarter to a half a per cent to sustainable growth over the next decade.

Conclusions

Extracting evidence on trend output is difficult, and estimates should always be treated as uncertain. Indeed, it is clear that an element of judgement must always enter the calculation of the output gap. However, our estimates suggest that gaps are not particularly large in Europe at present, and hence that caution should be observed in the setting of policy. This conclusion supports that in the forecast section in the Review that was published in May 1994, where it was suggested that capacity utilisation levels indicated an output gap of no more than 3 per cent at that time. Given that growth in 1994 has exceeded most estimates of potential the gap is likely to have shrunk since then.

ANNEX 1. THE MULTIVARIATE TREND EXTRACTION

Our technique is based on that in Evans and Reichlin (1994).

There are three stages to the construction of the trend estimates:

1. The first stage is to estimate any long-run relationships between the selected time series, using for instance the Johansen maximum-likelihood method. This assumes that the times series are all integrated of order one and can be modelled by a finite order VAR. If [X.sub.t] is the vector of the times series at time t, then given the OLS estimates for the following regression,

[Mathematical Expression Omitted]

the number and direction of the long-run relations can be estimated from the long-run matrix [A.sub.p]. We would normally expect to find fewer significant eigenvectors than we have time series in the model.

2. These long-run relationships are then imposed on the structure described above and then it is possible to reestimate the short-run relationships conditional on the set of trends. As there are fewer eigenvectors than there are time series the parameters estimated in the second stage will differ from those in the first stage.

3. The resulting model can then be simulated to run forward in time. The further into the future we take the run the more damped become the dynamic elements, and eventually the cyclical components disappear leaving only the permanent supply-side effects on trend output. This procedure has to be repeated for each time period. The trend value is the estimate of trend output under the assumption that the trend output growth is a constant plus a linear or stochastic component. Further details of methods and datasets used are available from the authors.

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