Careful with that HP Filter

Brad DeLong reads Marcus Nunes’ review of Stephen Williamson and concludes:

Marcus Nunes, I think properly, concludes that Williamson’s graph is wrong, because Williamson ignores the fact that there was a rising trend of NGDP during the 1970s, while during the Great Moderation, NGDP was stationary… Furthermore, Scott Sumner questions whether the application of the Hodrick-Prescott filter to the entire 1947-2011 period was appropriate, given the collapse of NGDP after 2008, thereby distorting estimates of the trend…

Williamson is here, Sumner’s reply is here.  DeLong jogged my memory that this topic is trapped in my computer, and this seems a good time to get it out of there.

First off, I am very cautious about mixing pre- and post-1985 data because of the impact of the Great Moderation on business cylce dynamics.  This applies to Jim Hamilton’s reply to my thoughts about the positive impact from housing.  Hamilton points out that prior to the Great Moderation, housing would make significant contributions to GDP growth as the economy jumped back to trend.  True enough; Hamilton might prove correct.  But I would add that large contributions prior to 1985 would typically come in the early stages of the business cycle.  I don’t think the same kinds of cycles are currently at play, and that it is a little late to be expecting a V-shaped boost from housing.

As to the issue of the HP filter, this was on my radar because 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.  As he said today:

The housing bubble and the ensuing financial crisis probably did some lasting damage to the economy, suggesting that the output gap in the U.S. is not as large as commonly believed and that the growth rate of potential output is modest. This helps explain why U.S. growth continues to be sluggish, why U.S. inflation has remained close to target instead of dropping precipitously and why U.S. unemployment has fallen over the last year—from a level of 9.1 percent in June 2011 to 8.2 percent in June 2012.

I think there is more wrong than right in these two sentences.  I don’t see how a slower rate of potential growth necessarily implies lower actual growth in the short run.  Clearly we have many instances of both above and below trend growth over the years. The failure of inflation to fall further can easily be explained by nominal wage rigidities.  And the drop in the unemployment rate, in itself not impressive, should be taken in context with the stagnation of the labor force participation rate.

Bullard likes to rely on this chart as support:


For some reason, Bullard rejects entirely CBO estimates of potential output, which would reveal a smaller output gap then his linear trend decomposition.  My version of this chart:

To deal with the endpoint problem, I used a GDP forecast from an ARIMA(1,1,1) model to extend the data beyond 2012:1.  If you don’t deal with the endpoint problem, you get this:

I believe most people would believe this result (that output is solidly above potential) to be a nonsensical.  By itself, the issue of dealing with the endpoint problem should raise red flags about using the HP filter to draw policy conclusions about recent economic dynamics.

Relatedly, notice that the HP filter reveals a period of substantial above trend growth through the middle of 2008. This should be a red flag for Bullard.  If he wants to argue that steady inflation now implies that growth is close to potential, he needs to explain why inflation wasn’t skyrocketing in 2005.  Or 2006.  Or 2007.  Most importantly, we should have seen the rise in headline inflation confirmed by core-inflation.  The record:

Core-inflation remained remarkably well-behave for an economy operating so far above potential, don’t you think?

At issue is the tendency of the HP filter to generate revisionist history. Consider the view of the world using data through 2007:4:


Suddenly, the output gap disappears almost entirely in 2005. And 2006. And 2007.  Which is much more consistent with the inflation story during that period.

Bottom Line:  Use the HP filter with great caution, especially around large shocks.  Such shocks will distort your estimates of the underlying trends, both before and after the shock.

This post originally appeared at Tim Duy’s Fed Watch and is posted with permission.

2 Responses to "Careful with that HP Filter"

  1. Bob Bronson   July 16, 2012 at 9:12 pm

    Why hasn't someone simply applied the HP filter on a walk-forward basis?

  2. Charlie   August 12, 2012 at 7:35 pm

    Hi Bob,

    Someone did : Mehra, Y.P. (2004, p. 7) ["The Output Gap, Expected Future Inflation and Inflation Dynamics: Another Look," The B.E. Journal of Macroeconomics, Berkeley Electronic Press.]