The Output Gap: Neoclassical Synthesis, New Classical and New Keynesian

It has been interesting to me how much excited commentary has been elicited by my posts on output gaps. [0],
[1], [2], [3] 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.


Recap


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). [4] And there are primarily time series methods, discussed in this post.


Other Approaches


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 [5]). 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.


ogap1.gif

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).


ogap2.gif

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.)


Last Words


Of course, overarching all these measures, keep in mind Simon van Norden’s caution [6] 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).

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27 thoughts on “The Output Gap: Neoclassical Synthesis, New Classical and New Keynesian

  1. nelson46

    Professor Menzie,
    Could you take a moment to help explain why the HP filtered output model of figure 1 is so unlike the first graph of observed vs potential output. I am not going to understand the math, but the basic logic, if that works, would be helpful to know. Perhaps reading at a later date what HP indtend to filter, I’m sorry for not being one of your students, I’ve had 3 courses of economics, all undergrad. Please accept my desire for further understanding.

  2. S

    Austrian synthesis in this context would clearly incorporate a GDP deflator for the home equity extraction – in this instance. Then such a measur might be relevant. Otherwise output gap analysis is psuedo science. To ignore the role of leverage in inflating GDP is a head scratcher.

  3. MattYoung

    Consumers invest in methods of consumption, and under technological pressure will unexpectedly change their Kalman filter model of consumption.
    The output gap best represents the value of consumption a consumer group is willing to give up in order to invest in a better model of consumption. This consumer group is performing a Ramsey best subgraph of consumption that fits the new model of consumption.
    So, in order to find out what changed in the consumption model we have to correlate the depth of the output gap with the range of investments made under the old equilibrium conditions. Identifying what part of the old consumption model the consumer abandoned identifies the exact component of consumption in which the consumer expects to invest in.
    In 1996 the consumer was willing to re-invest in telecom deregulation. Look at that output gap.
    In 2008 the consumer is willing to re-invest in something much bigger. Find out what. Find out, specifically, what common structure of the old consumption model the current output gap is most correlated with.
    Even more specifically, find out what the consumption model looked like in June 2008, as a Kalman filter. Then match the output gap to the component of the old Kalman filter model, in terms of fixed investment. You will identify the component of the Kalman filter that the consumer changed. The consumer changes the smallest component state that maximally reduces the capital cost of consumption
    But you have to construct Kalman consumption models then reconstruct these models as Ramsey graphs.

  4. DickF

    Menzie wrote:
    I spent a few hours trying to figure out what the Austrian View of potential GDP, but for the life of me I havent been able to determine what observables determine potential in that framework
    The output gap would be better defined as the amount of pain government intervention inflicts on economic actors.
    Perhaps an analogy will help explain the Austrian view. Assume a doctor in the 1700s was attempting to determine the optimal amount of blood to let from a patient. After studying the new medicine that did not believe in blood-letting he stated, I spent a few hours trying to figure out what the new medicine view of optimal blood-letting was, but for the life of me I havent been able to determine what observables determine potential in that framework
    Some physicians are more interested in healing the patient than measuring the pain.

  5. Buzzcut

    Some physicians are more interested in healing the patient than measuring the pain.
    Indeed, one of Taleb’s throwaway catchphrases is that it wasn’t until the 1990′s that doctors saved more people than they killed.
    Not sure to the extent that that is true, but it is certainly truthy.

  6. DickF

    Buzzcut wrote:
    Indeed, one of Taleb’s throwaway catchphrases is that it wasn’t until the 1990′s that doctors saved more people than they killed.
    Buzzcut,
    I would say that most economists would actually like to come up with a theory that would improve the economy but most economic theories harm the economy so your criticism is well taken. :-)

  7. Menzie Chinn

    nelson46: The HP filter is described briefly in this post.

    MattYoung: Forgive me, but I don’t want to implement the procedure myself, but would welcome seeing how somebody imbued with the Austrian spirit does it.

    DickF: Thank you for your comment; I am glad that some things in this world are reliably predictable. However, I nonetheless did not see your description of how to define the output gap in the Austrian view. The absence of an empirically implementable counterpart to the theoretical construct of sustainable output, for instance, will necessarily make it difficult to validate — or invalidate — this approach.

  8. DickF

    Since real GDP can be measured (though it is debatable how accurate it is) it is a consistent, measurable number. On the other hand there are many “potential” GDP numbers depending on the economic assumptions. Doesn’t this mean that it would be more accruate to call this “Forecast GDP” than “Potential GDP?” It is only potential if the assumptions made are correct and since there is no agreement on what assumptions are accurate this is a very soft number. Therefore, output gap is a very soft number depending on the assumptions you use for your forecast.
    But I realize that Output GAP was a term coined by Keynes and is a good buzz word, so I will not suggest it be changed.

  9. dkawaii

    Perhaps an analogy will help explain the Austrian view. Assume a doctor in the 1700s was attempting to determine the optimal amount of blood to let from a patient. After studying the new medicine that did not believe in blood-letting he stated, I spent a few hours trying to figure out what the new medicine view of optimal blood-letting was, but for the life of me I havent been able to determine what observables determine potential in that framework
    Some physicians are more interested in healing the patient than measuring the pain.

    Whereas, the Austrians are more like the faith healers, who would rather let their child die than to use that new fangled penicillin.

  10. Rich Berger

    Menzie-
    To put DickF’s question in a different form: how do we verify that potential GDP is correct?

  11. Inflation is the Enemy

    Econobrowser…”…interpreted as the level of output that would prevail if markets were perfectly competitive.”
    Then the solution is to make markets as competitive as possible, not continuously expand credit (using forced savings) in a long run attempt to compensate for a non competitive environment.
    “…estimated using a state space model, and (in the baseline approach) Bayesian priors.”
    There is the problem of using Gaussian algorithms to model non Bell curve phenomena. This type of misapplication is what sank Long Term Capital Management, and more recently almost the entire financial system.

  12. MikeR

    Menzie, thanks for the well referenced post.
    You post a lot about the output gap. I suppose economists are concerned with both the trend (average) and the volatility (proxied by the output gap).
    In my view, and I think DickF would agree, there is a tradoff between the two. Stimulus might reduce the output gap, but at the expense of a lower long term trend. I suspect you feel that there does not have to be a tradeoff.

  13. DickF

    Menzie wrote:
    DickF: Thank you for your comment; I am glad that some things in this world are reliably predictable. However, I nonetheless did not see your description of how to define the output gap in the Austrian view. The absence of an empirically implementable counterpart to the theoretical construct of sustainable output, for instance, will necessarily make it difficult to validate — or invalidate — this approach.
    Menzie,
    I totally agree. The output gap can neither be validated nor invalidated. I normally don’t enter the discussion about the output gap.
    Rich, Thanks. An important question.

  14. Menzie Chinn

    DickF: But you can validate or invalidate the output gap estimates, by seeing if inflation accelerates or decelerates in response to lagged output gaps, after controlling for expected inflation and supply shocks. In other words, I don’t know what you’re talking about.

    Inflation is the enemy: So we should break down all the firms in the economy into yeoman-producer household firms, so that the demand curves facing all agents in the economy are perfectly flat?

  15. all-the-T-bills-in-China

    Menzie, I feel sure that you are being dishonest or disingenous when you say that you spent hours trying to determine an Austrian version of the output gap. 15 minutes study should have sufficed to determine the Austrian view that “The only function of economic forecasting is to make astrology look respectable” (Galbraith)
    Your comment about ‘sustainable credit boom’ suggest that you don’t understand Austrian Business Cycle Theory. It does appear that you enjoy making snide comments about its adherents.
    Hopefully I’m wrong. If Austrian theorists are so benighted, it shouldn’t take an intellectual of your caliber more than a few paragraphs to demonstrate to the rest of us the mistakes in their view of the business cycle.

  16. Menzie Chinn

    all-the-T-bills-in-China: My statement was an honest description of my bewilderment. I freely admit to my intellectual limitations, but I do not admit to dishonesty. In any case, I think of conceptualizing potential GDP and an output gap as a separate enterprise from forecasting.

    So, once again, please send me your references for implementable calculations of potential GDP in an Austrian framework. I look forward to being enlightened.

  17. jult52

    Menzie – Since I was one of the commenters who motivated you to put up this post, I want to thank you for your entry.
    My objection to the idea of potential GDP is not theoretical. It was practical and about the inputs. What are the distortions due to sectoral shifts, demographic and cultural changes, time lags in price changes and imprecision in statistical measurement that could render whatever model of potential GDP growth used inaccurate?
    Put another way: we can all agree that potential GDP growth is somewhere between +7% and -5%. But what reason is there to believe that the potential GDP growth is 1% rather than 2% over a relatively short span of time (say 2006-2009)?
    BTW, your coblogger has stated that he suspects US potential GDP growth is negative. I’d be interested in hearing your response.

  18. SvN

    Menzie;
    A very interesting and useful post; many thanks. I hope I can add a couple of marginally useful remarks.
    Regarding the validation of output gaps: in many mainstream models of inflation, the output gap is effectively “the component of real output that helps explain innovations in inflation.” This seems to be the main (only?) way in which output gap measures have been objectively verified to date. The results are not good. In Orphanides and van Norden (2005 JMCB) we found that the relationships between output gaps and inflation was unstable and that none of the gaps we looked at could perform significantly better than real output growth. I’d be interested to know whether anyone is aware of more encouraging results.
    Second, I wanted to comment on the differences between the “time-series” and “production function” approaches. As you know, many in the profession strongly favour the latter over the former due to its strong microfoundations. However, the latter approach typically requires distinguishing actual and trend levels of TFP and labour inputs. (If we use the dual approach to the production function, we instead get to detrend real wages and interest rates.) The problem of atheoretic detrending is therefore again present and not in an innocuous way. The reliability problems that this causes at the end of sample are also compounded in this case by more severe data revisions problems; both capital stock and TFP measures are subject to relatively large and highly persistent revisions for several years after original estimates are released. I’ve yet to see a good study of the importance of these effects; I’m wondering whether any readers of this blog can suggest some.
    SvN

  19. MikeR

    jult52,
    Although I agree with Menzie about the nature of the current recession, I also agree with your statement: “But what reason is there to believe that the potential GDP growth is 1% rather than 2% over a relatively short span of time (say 2006-2009)?”
    Economics just does not lend itself to precise estimates or forecasts. Even past GDP numbers are just estimates.
    However, I think the stock market sell off over the past two weeks is a recognition by the market that the recession will last into 2010.

  20. A.West

    For an overview of how to compare and contrast Keynesian and Austrian models, consult Roger Garrison’s “Time and Money” which dwells at length on the production possibility frontier. His website might supply a summary by powerpoint. I’m not sure that his model is rightly considered orthodox Austrian. Hayek seemed interested in models, while Mises said measuring GDP was pointless and impossible, while George Reismann suggested that GDP is far too netted, ignoring how much of the economy is involved in the production of intermediate goods.

  21. Anonymous

    Interesting. I’m not so deep into macro but now I wonder: Would the notion of “potential output” be the macro equivalent of the also fuzzy and unobservable “fundamental value” of financial assets? I guess the difference is that one could at least in principle observe it (asking everybody about their preferences and technologies), whereas in financial assets, one would have to examine a probabilitz space which one cannot do even in principle. Still I don’t agree with your insistence on measurability and implementability. Ok, just musing aloud, back to work… ;-)

  22. jmh

    Menzie,
    The reason why there is no potential GDP in the austrian tradition is b/c most of the work in their macroeconomics was either completed before Keynes or as an alternative to him.
    If you’re looking for one possible source for inspiration, I would highlight what Mises and Rothbard call the Evenly Rotating Economy. But this is more of a artificial construct to think about an equilibrium economy before adding in such things as central banking. If I were an Austrian looking to create a potential GDP measure, I would probably just use the HP filter as a decent approximation.
    Suffice it to say there is no potential GDP measure for Austrians b/c I’m not quite sure they see the value in such a measure. They aren’t particularly fond of GDP in the first place or quantitative measures. You could say the PPF or the ERE are examples of equilibrium output growth, but the Austrian focus is more on the disequilbrating forces rather than the equilibrium and they really don’t go through the effort to calculate such things b/c the equilibrium is less their focus.
    Again, as a market observer, an HP filter is probably sufficient to identify an output gap, but I wouldn’t say that it has any Austrian story behind using it. Other than that it works well enough.

  23. Menzie Chinn

    SvN: You always provide excellent insights — thank you for these. I guess that as someone who works on exchange rates, I find the goodness of fit using potential GDP measures (ex post, in sample) pretty good. Admittedly, I do not have as much experience on this point as others, but on the other hand, I have looked across countries more than some other analysts. It’s all a matter of degree, in my mind.

    On your second point that the “production function” approach incorporates some time series aspects, you are completely correct. While we can probably predict the capital stock and labor stock fairly well, the TFP measures are much more problematic. The question is, then, whether to pursue alternative approaches to backing out potential (say from the unemployment rate). So, there are two issues — the conceptual aspect of potential, and the implementation. I think policymakers will always want to infer the measures of potential, so one will have to keep at working at measuring it.

    By the way, Jim Nason has pointed out to me that I neglected the Beveridge-Nelson approach to trend-cycle decomposition. I think it would’ve been useful to note that there is yet another time series approach (which probably has the same problems with end-point data revisions that the other approaches suffer from).

    jmh: Thank you for your comment. I understand the Austrian focus is on disequilibrium and on transition dynamic. My puzzlement is how you can talk about these transition dynamics without having a clear statement about the beginning and end points. Relatedly, A. West‘s point makes sense, and I had glanced at a couple of bits of the book that are online. I did see the graphs of the PPFs. Once again, I wonder how one can provide useful policy analysis without some quantification of beginning and end points (e.g., where is that PPF?).

  24. SvN

    Points to note about the Beveridge-Nelson approach;
    - it’s end-of-sample problem are much, much smaller (I’m tempted to say trivial) than those of the other methods you’ve shown above. This is largely because the Kalman filter and smoother formulas for the BN gap give identical results.
    - it’s “output gap” estimates look very little like those that you’ve shown above. Gaps instead look very small and have only slight persistence.
    - there’s a debate about the *sign* of the output gap with the BN approach. My recollection is that Charles Nelson claimed that the journal editor forced them to change the sign in the published version, but that he thinks it logically requires the opposite sign.

  25. Jmh

    Menzie,
    The Austrian would be opposed to government management of the economy or a central bank. So they would not be in the position to give policy advice or analysis in their own ideal setting.
    The question for the Austrian becomes how do they identify booms and busts. Really there is nothing in their theory that says one way to look at the data is the best. I prefer the approach of Detken and Smets (2004) in ECB working paper No. 364 of using an HP filter. That along with looking at a bunch of other data helps me determine where the economy is (mostly from the perspective of an investor).
    That being said, it doesn’t help answer the normative question of how should an Austrian set interest rates or use fiscal policy b/c mainly the optimal Austrian short-term interest rate is that determined by the market and the optimal fiscal policy is 0. Now as an investor if I were to try to decide if interest rates (or money supply growth) were too easy or too tight, it’s tricky. Outside of pointing out empirical regularities like, recessions in the US tend to follow from negative real money base growth or an inverted yield curve, b/c they don’t have quantitative measures of where interest rates should be, it makes it difficult to determine how easy or loose the Fed is being. In this case, I simplify by using Taylor Rule measures for interest rates. It’s obviously not perfect, but as an investor you don’t need the sophistication.
    So you’re definitely right that Austrians don’t offer a potential GDP in a way that can assist policy analysis.

  26. A.West

    Austrians want the government to get out of the interest rate setting and fiscal policy business. They don’t believe that central planning solves any problems.
    The reasons they give for anti-intervention certainly does assist policy analysis, but it’s not the sort of advice bureaucrats are likely to be receptive to.

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