### Potential Output: Measuring the Gap

There's been quite a bit of discussion recently about the output gap. I want to make a simple point in this post, how the gap is measured can have a big impact on the estimate of the state of the economy, and hence on the need for policy. Below, three different gap measures are presented, one that measures a large gap and hence implies the need for a large stimulus, one that measures a "medium size" gap, and one where the gap is absent altogether. In fact, according to this model we have already exceeded the full employment level of output.

In the first model, the trend is assumed to be linear, i.e. Y_{trend} = b_{0} + b_{1}*t. Recall that the gap is measured as (Y - Y_{trend}), i.e. as the distance between the red and blue lines in the following diagram showing the estimated trend for GDP (click on figures for larger versions):

To highlight recent movements, here's the same picture for the last 10 years:

Thus, this model of the trend calls for lots of stimulus.

In the second model, the trend is assumed to be quadratic, i.e. Y_{trend} = b_{0} + b_{1}*t +b_{2}*t^{2}:

Again, here's the last ten years:

**Quadratic Trend - Last 10 Years**

The value of the current output gap in this model, as is clear in the second diagram, is smaller than for a linear trend model. However, it is still quite large and stimulus would still be called for, particularly given that actual output (the blue line) is running parallel to trend rather than making up ground.

However, there's a problem with this method of measuring the gap. One way to think of these models is that variation in the red line arises from supply shocks, and variation around the red line -- shown by the blue line -- represents demand shocks. Thus, under this interpretation, the first two models assume that all variation in the economy is due to demand shocks. This is clearly incorrect -- certainly supply shocks matter too -- and therefore these models may not give a very good measure of the gap.

The last model uses the HP filter popularized in the Real Business Cycle literature to overcome this problem (lambda = 1600, the standard value for quarterly data). This model allows the trend to be variable (stochastic), i.e. it allows the trend to reflect supply shocks:

The last 10 years for the HP trend model:

The results for the HP model tell us that we are now above trend! That doesn't seem believable to me (but I've never liked the HP filter, so no surprise, but some people might buy into this).

There are other ways to measure the underlying trend for GDP, and hence there are other ways to measure the gap, but they will generally be near one of these three outcomes so I won't cover those in any detail. There are also questions such as which potential output level to target, today's or one in the future. If, say, policy takes a year to be fully realized, and in the meantime the trend in model three begins to recover, as it likely would, how large is the gap to be targeted?

Unfortunately, there is no perfect way to choose among the gap models (the problem is that you have one time-series, output, and you are trying to extract two things, a trend and a cycle, and that can't be done without an assumption of some sort -- and when assumptions are involved, there's room to argue about their validity). If I had to choose, it would be somewhere between the first and second models. That is, I think the long-run trend for GDP is lower than the pre-crisis track we were on, but not as low as the more dour among us believe (and, to be clear, I endorse the stochastic trend model, but from the accumulated econometric evidence I've seen, I think aggregate demand shocks are the more important source of variation in output over time -- e.g. the movement in the trend in model three is much too large). In any case, I think there's enough uncertainty about the size of the gap, and enough asymmetry in the errors -- assuming model three when model one is actually true is worse than the other way around -- to justify aggressive policy actions to help the economy.

Posted by Mark Thoma on Saturday, February 18, 2012 at 06:36 PM in Economics, Fiscal Policy, Methodology, Monetary Policy |
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