The other day I googled

*graph of hodrick-prescott trend for GDP*. First thing that turned up was Stephen Williamson (of the St. Louis Fed)'s HP Filters and Potential Output. Unusual for a Williamson post, I could follow most of it.

Let me provide some background here, from A Summary of Alternative Methods for Estimating Potential GDP (PDF). First, under

**CBO’s Method for Estimating Potential Output**:

CBO’s estimate of potential output is based on the frame-work of a textbook model of long-term economic growth, the Solow growth model.

Next, under

**Other Methods for Estimating Potential Output**:

Statistical filters (such as centered moving averages, bandpass filters, the Hodrick-Prescott filter, and the Kalman filter) are often used to extract the trend from GDP directly.

Finally, under

**Advantages and Disadvantages of the Different Methods**:

The statistical approaches also have their drawbacks. For the filtering methods, three shortcomings are significant. First, many of the filters do not benchmark their trends to any external measure of capacity. Therefore, unlike CBO’s results, their results can be interpreted astrendGDP but not aspotentialGDP. In other words, they do not yield an estimate of the level of output that is consistent with stable inflation.

(Emphasis in the original.)

The difference is significant. Potential output is supposed to show what GDP would be if the economy was running at the level where something (demand, maybe) isn't causing inflation, but it would be causing inflation if anybody put in just an ounce more effort. Or, as CBO has it, potential output is

an estimate of “full-employment” gross domestic product, or the level of GDP attainable when the economy is operating at a high rate of resource use.

Although potential output measures the productive capacity of the economy, it is not a technical ceiling on output that cannot be exceeded. Rather, it is a measure of sustainable output, in which the intensity of resource use is neither adding to nor subtracting from inflationary pressure.

A year back I was having trouble with The Myth of ‘Jobless Recoveries’, a guest post by Laurence Ball, Daniel Leigh, and Prakash Loungani, at

*Econbrowser*.

Eventually I worked it out. The trouble turned out to be that the Econbrowser post was my first experience with "the statistical approaches" that "do not benchmark their trends to any external measure of capacity." After that, I started doing some Hodrick-Prescott calculations and understood that post a little better.

Anyway, Stephen Williamson writes

In studying the cyclical behavior of economic time series, one has to take a stand on how to separate the cyclical component of the time series from the trend component. One approach is to simply fit a linear trend to the time series (typically in natural logs for prices and quantities). The problem with this is that there are typically medium-run changes in growth trends (e.g. real GDP grew at a relatively high rate in the 1960s, and at a relatively low rate from 2000-2012). If we are interested in variation in the time series only at business cycle frequencies, we should want to take out some of that medium-run variation. This requires that we somehow allow the growth trend to change over time. That's essentially what the HP filter does.

Williamson then quotes Paul Krugman:

When applied to business cycles, the HP filter finds a smoothed measure of real GDP, which is then taken to represent the economy’s underlying potential...

But Williamson says Krugman has it wrong. Williamson says the same thing the CBO says -- Hodrick-Prescott shows the trend of actual GDP, not the trend of potential GDP:

The HP trend is no more a measure of potential than is a linear trend fit to the data. The HP trend was arrived at through a purely statistical procedure... How then could the HP trend be a measure of potential GDP? To measure potential GDP requires a model.

Stephen Williamson then turns about-face. He says, let's use the Kydland-Prescott model (which introduced the HP calculation to economists) to figure potential output:

If the model is Kydland and Prescott's, there is a clear answer to what potential is - it's actual GDP (and certainly not the HP trend). That model doesn't have a government in it, and was not intended for thinking about policy. What Kydland and Prescott's work does for us, though, is to allow us to consider the possibility that, for some or all business cycle events, there may be nothing we can or should do about them.

Think of actual GDP as the trend of potential GDP, Williamson says, and consider the possibility that there may be nothing we can do about our declining economy. Reminds me of something written by a guy calling himself Adam Smith in

*The Roaring '80s*:

...the Keynesian revolution gave some hope that nations could do something about the 'economic blizzards' that had previously been considered as random as the weather.

Williamson is one of those who see the economic blizzards as like weather we can do nothing about.

*Can and should*do nothing about. Why is this guy at the Fed?

Why is he even an economist?

Williamson's third graph:

Williamson's Third: The Log of Real GDP and the HP Trend Since 2000 |

In its attempt to fit the actual time series, the HP filter has done away with part of what we might want to think of as the recession, and real GDP in the first quarter of 2012 was more than 1% above trend.

By 2012, actual GDP is above trend. The output gap is gone, because the Hodrick-Prescott calculation pushed the trend line down in response to the Great Recession.

It is a fluke in the calculation. It doesn't mean everything is back to normal. It doesn't mean unemployment is back to normal. It doesn't mean the economy is booming again. It is a fluke in the calculation.

But you know what I think? I think that's where James Bullard got his "wealth shock" view. From a fluke in the calculation.

**// Update 16 September 2014:**My conclusion (

*Bullard got his 'wealth shock' view from a fluke in the H-P calculation*) is confirmed in the July 2012 article Blog review: HP Filters and business cycles by Jérémie Cohen-Setton and Yury Yatsynovich:

"James Bullard pointed to these [Hodrick-Prescott] estimates – together with the fact that we don’t see deflationary pressures (see our review here) – as evidence that advanced economies are operating near potential, if not above."

"Tim Duy points that St. Louis Federal Reserve President James Bullard ... likes to rely on this technique to support his claim that the US economy is operating near potential."

But there is an "end point problem" with the HP calculation:

" Luís Morais Sarmento – economist at Banco de Portugal – explains that the end point problem results from the fact that the series smoothed by the HP-filter tend to be close to the observed data at the beginning and at the end of the estimation period."

And this:

"Tim Duy points that if you don’t deal with the endpoint problem, you get that actual output is above the HP trend..."

Yeah. I noticed this "end point problem" too. See How to Change the Past.

## 1 comment:

Art

It is a problem, you once made a great comment to Tom about doing Macro, and not Micro.

CBO’s estimate of potential output is based on the frame-work of a textbook model of long-term economic growth, the Solow growth model.

Solow’s own reactions are the most notable, since Solow’s growth model is acknowledged by Finn Kydland and Edward Prescott, the originators of these models, as its fountainhead (Kydland and Prescott 1991: 167–8).

Solow’s reaction to the fact that his growth model was used as the basis of modern neoclassical macroeconomics was one of bewilderment:

The puzzle I want to discuss – at least it seems to me to be a puzzle, though part of the puzzle is why it does not seem to be a puzzle to many of my younger colleagues – is this. More than forty years ago, I […] worked out […] neoclassical growth theory […] [I]t was clear from the beginning what I thought it did not apply to, namely short-run fluctuations in aggregate output and employment […] the business cycle […] The question I want to circle around is: how did that happen? (Solow 2001: 19)

Solow, R. M. (2001) ‘From neoclassical growth theory to new classical macroeconomics,’ in J. H. Drèze (ed.), Advances in Macroeconomic Theory, New York: Palgrave.

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