Stephen Williamsonがここで紹介した名目GDP目標懐疑論の補強材料としてHPフィルタを使用したのに対し、主たる論争相手となったサムナーのみならず、Marcus Nunesがその使用法に疑義を唱えた。そのNunesの疑義にDavid GlasnerデロングTim Duyが反応し、さらにはクルーグマンが自らのIt's baaack論文邦訳)を持ち出してその議論に加わった。すると今度は当のWilliamsonがクルーグマン反応し、以下のようなことを書いた。

Kydland and Prescott's approach to studying business cycles was to: (i) Define the raw time series that we are trying to explain as the deviations of actual time series from HP trends. (ii) Simulate a calibrated model on the computer to produce artificial time series. (iii) HP filter the artificial time series and ask whether these time series look much like the raw time series we are trying to explain.

Here's what Paul Krugman has to say about HP filters:

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, with deviations from this smoothed measure representing unsustainable temporary deviations from potential.

I'm not sure if this is just Krugman's misunderstanding, or if this is widespread. In any case, it seems important to correct the misunderstanding.

What is the economy's "underlying potential" anyway? It's the level of aggregate real GDP that we could achieve if, within the set of feasible economic policies, policymakers were to choose the policy that maximizes aggregate economic welfare. 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. I did not use any economics to arrive at the two charts above - only a few lines of code. How then could the HP trend be a measure of potential GDP?

To measure potential GDP requires a model. The model will define for us what "feasible economic policies" and "aggregate economic welfare" are. If we used Kydland and Prescott's procedure, above, we might construct a model, calibrate and simulate it, and argue that the model produces time series that fit the actual data. We might then feel confident that we have a good model, and use that model to measure potential output. Maybe the model we fit to the data is a Keyesian model, which implies an active role for monetary and fiscal policy. Maybe it's a model with a well-articulated banking and financial sector, with an explicit role for monetary policy.

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.


  1. 説明したいと思う原系列データを、実際の時系列データのHPトレンドからの乖離として定義する
  2. コンピュータでカリブレートしたモデルのシミュレーションを行い、人工的な時系列データを生成する
  3. その人工的な時系列データにHPフィルタを掛け、その時系列データが、説明したいと思う原系列と類似しているかどうかを調べる




経済の「潜在力」とはそもそも何か? それは、実現可能な経済政策の中から、政策当局者が総経済厚生を最大化する政策を選択した場合に達成できる実質GDPの水準である。HPフィルタによる潜在力の測定は、データの線形トレンド近似による測定と何ら変わるところは無い。HPトレンドは純粋に統計的な手順により求められる。上で示した2つの図を描くのに、私は経済学を一切用いなかった。コードを数行書いただけだ。どうしてそのHPトレンドが潜在GDPの測定値になるというのか?