It has been interesting to me how much excited commentary has been elicited by my posts on output gaps. ,
, ,  I had thought the subject fairly uncontroversial, especially my reliance upon the CBO measure, which is calculated in a conventional manner, and is an object well-understood in mainstream macroeconomics (take your pick — from Hall and Papell to Mankiw). However, it’s clear that there is no such agreement in the blogosphere (which can be taken as an indicator of how dispersed beliefs are in that world). In any case, the reaction tells me that one’s belief in what determines potential GDP defines in large part how one thinks about the workings of the economy, and so I thought it useful to discuss alternative measures coming out of current academic work.
As I’ve discussed earlier (see this post), in some incarnations actual output is potential. This fits into the Classical approach, at least as interpreted in modern textbooks (I’m sure there are many subtleties glossed over here, and certain individuals will provide long and extended disquisitions in the comments section to this post). And, in the New Business Cycle models, output equals potential up to some random error which depends upon expectational errors (and parameters).  And there are primarily time series methods, discussed in this post.
So, what about other approaches? I spent a few hours trying to figure out what the Austrian view of potential GDP, but for the life of me I haven’t been able to determine what observables determine potential in that framework (although I have an inkling it has to do with credit, and the distinction between sustainable and unsustainable credit booms ). So let me recount what some researchers have found, when working in a framework incorporating microfoundations (intertemporally optimizing households, firms), rational expectations (or at least model-consistent expectations), imperfect competition in intermediate product and labor markets, and sticky prices and wages (Calvo pricing); in other words, a New Keynesian model. Here, I’m relying upon a paper by Alejandro Justiniano and Giorgio Primiceri, wherein the authors estimate a dynamic stochastic general equilibrium model to obtain estimates of potential GDP and natural GDP. Note that while I’ve characterized the approach as New Keynesian, as the authors note, the analysis is consistent with the literature “focusing on productivity shocks as sources of sizable business cycles…”
In Figure 1, I depict the CBO measure of the output gap, as reported on January 9, and Justiniano and Primiceri’s measure. The former measure is calculated (see description here; it’s essentially a “production function” approach) using measures of productivity, capital and labor stocks, while the latter is estimated using a state space model, and (in the baseline approach) Bayesian priors. (I thank Giorgio Primiceri for sharing with me his most recent estimates, which are not reported in the paper.) Potential output in their approach is also interpreted as the level of output that would prevail if markets were perfectly competitive.
Figure 1: CBO measure of the output gap (blue), Justiniano-Primiceri baseline measure (red), and Justiniano-Primiceri measure allowing for persistent labor shocks (green), all in log terms. NBER defined recession dates shaded gray; last recession dates assume recession has not ended by 2009Q1. Source: CBO, NBER, and personal communication.
Regarding their measure of potential, and hence the output gap, the authors observe:
According to our estimates, U.S. potential output has evolved quite smoothly in the post-war period. In other words, had markets been competitive, postwar business cycles would have been much less pronounced. A consequence of this finding is that the difference between actual and potential output, the output gap, closely resembles more traditional measures of detrended output, such as Hodrick-Prescott (HP) filtered output or the estimate produced by the Congressional Budget office (CBO).
Potential versus Natural Output
A digression. In their paper, the authors make a distinction between potential output and natural output. The latter is the level of output that would prevail if wages and prices were perfectly flexible. (In the standard textbook treatment of the neoclassical synthesis, potential and natural would be the same.) This distinction is important when reading different papers. For instance, in Javier Andres, David Lopez-Salido, and
Edward Nelson, the output gap is defined as the difference between actual and natural output, and hence looks very different from the CBO or HP-defined output gap for a good reason. The “gap” in this case is between actual output and a flex-price output. For a much more simple model distinguishing between natural output and that which would prevail under perfect competition, see Blanchard and Kiyotaki’s seminal paper, “Monopolistic Competition and the Effects of Aggregate Demand,” American Economic Association 77(4): 647-66; link to working paper version: [pdf].
Extension to persistent labor shocks
In the baseline model, there are white noise shocks to price markups and wage markups, but no “labor supply” shocks of a persistent nature. Incorporation of such shocks to mimic demographic trends leads to a slightly different measure of the output gap, shown as the green series in Figure 1.
I thought I would compare the CBO and J-P series to a pure time series based measure, in this case an HP filtered cycle (for other output gap measures, including quadratic in time, and band-pass, see this post).
Figure 2: CBO measure of the output gap (blue), Justiniano-Primiceri baseline measure (red), and HP filtered cycle based on 1967-2008 data (light green), all in log terms. NBER defined recession dates shaded gray; last recession dates assume recession has not ended by 2009Q1. Source: CBO, NBER, and personal communication.
To sum up, all four measures of the output gap depicted in Figures 1 and 2 are getting diving in 2008Q4.
(I’ve skipped the Mankiw-Reis “sticky information” approach; readers interested in the empirical validity of this approach can refer to a paper by Oli Coibion, a former colleague of mine from our days at the CEA. I’ve also skipped discussing the implied potential GDP from a Casey Mulligan approach because…well, because of this post, not to mention his prediction that “…employment will not drop below 134,000,000” (it’s at 134.58 million as of January.)
Of course, overarching all these measures, keep in mind Simon van Norden’s caution  that the estimates of the output gap will have wider confidence bands as one gets closer to the end of the sample — exactly because of the data revisions that will take place.
A comprehensive survey of issues relating to the use of production function and time series approaches to calculating output gaps is provided in this OECD working paper (large PDF).