# Gapologists giving answers with too many holes

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The Independent Online
Calculating the output gap is the latest fad among macro-economists, a fad that was unknown a decade ago but which now underpins policy analysis from every quarter. My impression is that the gap has a much larger role in the Bank of England's thin king on monetary policy than is apparent from reading the Inflation Report or the Governor's speeches. And Alan Budd, chief economist at the Treasury, is a self-confessed gapologist.

The bug is also on the loose in the City. Many economists (and I do not necessarily exclude myself from this) quote their own estimates of the gap as if they were handed down from the Mount in tablets of stone. As is very common in economics, people become intensely wedded to their own estimates of the gap, just because they wielded the computer keyboard themselves.

There is no doubt that there is something particularly beguiling about one's own calculations relative to anyone else's. And because the output gap is superficially easy to calculate, some analysts who should not ordinarily be allowed out with a set of log tables have become obstinately attached to their own estimates.

The purpose of this article, which I have prepared with Philippe Gudin de Vallerin, my colleague at Goldman Sachs, is to debunk the growing mythology surrounding gap calculations by explaining exactly what it is and showing how hard it is to measure withany precision.

Conceptually, the gap is quite easy to define - it is simply the difference between the actual level of output at any given time and the"capacity" of the economy. Capacity in this instance is not the absolute maximum level of output that the economy could produce if machines and workers were straining at every leash. In fact, this physical maximum is a meaningless concept, since it would always be possible for firms to induce machines and labour to work harder or longer if cost were no object. But aftera certain point inflation would rise and/or the output would no longer be profitable to produce.

For our purpose, economic capacity is instead defined to mean that amount of output that the economy can produce while leaving inflation pressures constant. Strictly, we should also want the balance of payments and the real exchange rate to be in equilibrium, and the share of profits normal, but these provisos are rarely mentioned. Put more loosely, economic capacity is the amount of output that the supply side of the economy can comfortably deliver when all of the dials in the system are reading normal.

Estimating the trend One way of estimating this amount of output is to assume that over many years economic growth will be broadly determined by the supply side, so that the capacity of the economy can be defined by the long-term trend for output. It follows that the output gap can then be calculated as the deviation from that trend, and the problem then becomes one of estimating the trend.

But this is not easy. We may be on fairly safe territory in estimating the trend for periods in the past (say up to five years ago), but calculations for more recent dates are highly uncertain, since we never know in advance when the trend might be changing. There are two ways round this, neither particularly satisfactory. The first is to use a statistical technique that permits the trend to vary over time, with recent levels of output being allowed to have some influence on the trend estimate. One suchstatistical technique in increasing use is the so-called "Hodrick Prescott filter". Some analysts employ this technique to fit trends and imagine that this is the end of the story.

It is not. Any trend-fitting technique of this sort is entirely arbitrary, since the user has to decide how much weight to give to recent observations when allowing the trend to vary over time. If we choose to give recent observations zero weight, we simply get a straight line trend, as if drawn with a ruler. If instead we choose to give recent figures infinite weight, we get a trend estimate that follows all the nooks and crannies of the series itself. The statistician can provide anything in between a ccording to whim.

In the table we show two estimates of the output gap at the end of 1994 derived from the Hodrick Prescott method, one assuming a straight line trend, and the other allowing the trend to vary a little over time. The former estimate says that the current level of output is about 0.8 per cent below trend, while the latter says it is 0.8 per cent above trend. Neither estimate should be considered reliable, since there is no way of knowing which of these estimates - or any other that the statistician could derive - is the one to choose.

An alternative way of proceeding is to choose the date when the economy was last at mid-cycle (1990 in the UK case), and extrapolate the trend from there by assuming that previous long-term growth rates in the economy have been maintained. This extrapolation method suggests that output is now 2.4 per cent below trend, and that it will still be well below trend throughout the rest of this year. This is the type of estimate that inflation optimists are using at present to argue that the recent tightening in monetary policy was premature.

But these estimates are vulnerable to the possibility that the trend growth in output since 1990 may have changed. Some economists believe it may have changed upwards, arguing that the supply-side reforms of the 1980s are finally bearing fruit. Others fear it may actually have changed downwards owing to scrapping of capacity during the recession, and to a slowdown in growth of the labour force for demographic reasons. In order to allow for these possibilities, we need to use a more fundamental economicmethod for estimating capacity that directly takes account of the availability of spare labour and underutilised machinery.

In the graph, we estimate how much additional output could be produced if plant capacity were normal, and unemployment were at the"natural" rate necessary to hold wage inflation constant. (The former is estimated from CBI survey data, while the latter isestimated as the five-year moving average of the unemployment rate. Other methods for estimating the natural unemployment rate would result in very different estimates for the output gap, so again this method is subject to much uncertainty.)

According to this "fundamental" method, the output gap is now exactly zero, and the gap will turn positive - ie, output will be above trend - this year. The reason for this is that unemployment has fallen much more sharply than it did at the same stage in previous recoveries, so the labour market has already tightened considerably.

As the graph shows, the contribution of capital (ie, spare machinery) to the output gap is now quite similar to what it was in 1985-86, the equivalent point in the last upswing. By contrast, the contribution of labour is much smaller, and has indeed already dwindled away to nothing.

If this last piece of gapology proves accurate, then inflation has already troughed, and the authorities might once again have tightened policy too late.

Different estimates of the UK output gap End 1994 End 1995

Methodology Linear trend -0.8% 0.7% Varying trend 0.8% 1.4% Extrapolated trend -2.4% -1.0% Economic fundamentals 0.1% 1.4% Negatives imply output below capacitySource: Goldman Sachs