For serious macroeconomists, the magnitude (or existence) of the output gap is a central factor for determining the appropriate policy actions (see for instance Weidner and Williams). In several recent posts, I've discussed the variety of approaches to estimating the output gap [0] [1]. A recent symposium on Projecting Potential Growth published by the Federal Reserve Bank of St. Louis is an excellent resource for anybody who wants to think seriously and carefully about the challenges in estimating this variable. In the lead article entitled "What Do We Know (And Not Know) About Potential Output?", the authors John Fernald and Susanto Basu write:

To keep the discussion manageable, we confine our discussion of potential output to neoclassical growth models with exogenous technical progress in the short and the long run; we also focus exclusively on the United States. We make two main points. First, in both the short and the long run, rapid technological change in producing equipment investment goods is important. This rapid change in the production technology for investment goods implies that the two-sector neoclassical model -- where one sector produces investment goods and the other produces consumption goods -- provides a better benchmark for measuring potential output than the one-sector growth model. Second, in the short run, the measure of potential output that matters for policymakers is likely to fluctuate substantially over time. Neither macroeconomic theory nor existing empirical evidence suggests that potential output is a smooth series. Policymakers, however, often appear to assume that, even in the short run, potential output is well approximated by a smooth trend. Our model and empirical work corroborate these two points and provide a framework to discuss other aspects of what we know, and do not know, about potential output.

It's important to understand that potential GDP as discussed by Fernald and Basu is not "a 'forecast' for output and its growth rate in the longer run (say, 10 years out)" which they refer to as a 'steady-state measure'..." -- this is the concept that conforms better with the CBO and OECD estimates of potential. For Fernald and Basu, and most of the others who work in this area...

[p]otential output is the rate of output the economy would have if there were no nominal rigidities but all other (real) frictions and shocks remained unchanged. In a flexible price real business cycle model, where prices adjust instantaneously, potential output is equivalent to actual, equilibrium output.

That last sentence clearly and simply explains why economists steeped in the RBC tradition eschew any macrostabilization policy. It's simply not necessary (see [2], [3]).

I do have a minor quibble here; in many New Keynesian models, monopolistically competitive behavior characterizes either or both product and factor markets. One could define output in the absence of nominal rigidities as that "natural output" and output in the absence of nominal rigidities and departures from competitive markets as "potential output". This is the terminology used in for instance Edge et al. (2007) and Justiniano and Primiceri (2008) (the latter discussed in this post). But one is free to define terms as one desires, as long as terms are clearly defined, and in any event, the "competitive markets" case is not typically considered in these types of exercises.

Fernald and Basu argue that a two sector model (incorporating differential rates of productivity growth for the consumption and investment goods producing sectors) with only technology shocks leads to a better fitting model of output than a single sector model. The main point here is not that technology shocks are the only important type of shocks perturbing the economy (although they argue they are the most important); rather their point is that allowing for two sectors and differential productivity growth can alter one's view about the evolution of the potential GDP, and hence of the output gap. In their DSGE, potential output is more variable than that obtained using a single sector model (closely related to the CBO and OECD production function approaches). Hence, the resulting implied output gaps exhibit smaller variability.

Implications of the crisis and recession

What about the practical concerns of where potential (or "natural") GDP is going? Fernald and Basu provide an extremely useful overview of some of the arguments -- some of which will be familiar to Econbrowser readers -- that potential GDP will move in a substantially altered trajectory in the wake of this crisis. Writing at the end of 2008:

Several arguments suggest that potential output growth might currently be running at a relatively rapid pace. First, and perhaps most importantly, TFP growth has been relatively rapid from the end of 2006 through the third quarter of 2008 (see Table 2). During this period output growth itself was relatively weak, and hours per worker were generally falling; hence, following the logic in Basu, Fernald, and Kimball (2006), factor utilization appears to have been falling as well. As a result, in both the consumption and the investment sectors, utilization-adjusted TFP (from Fernald, 2008) has grown at a more rapid pace than its post-1995 average. This fast pace has occurred despite the reallocations of resources away from housing and finance and the high level of financial stress.

Second, substantial declines in wealth are likely to increase desired labor supply. Most obviously, housing wealth has fallen and stock market values have plunged; but tax and expenditure policies aimed at stabilizing the economy could also suggest a higher present value of taxes. Declining wealth has a direct, positive effect on labor supply. In addition, as the logic of Campbell and Hercowitz (2006) would imply, rising financial stress could lead to increases in labor supply as workers need to acquire larger down payments for purchases of consumer durables. And if there is habit persistence in consumption, workers might also seek, at least temporarily, to work more hours to smooth the effects of shocks to gasoline and food prices.

Nevertheless, there are also reasons to be concerned that potential output growth is currently lower than its pace over the past decade or so. First, Phelps (2008) raises the possibility that because of a sectoral shift away from housing related activities and finance, potential output growth is temporarily low and the natural rate of unemployment is temporarily high. Although qualitatively suggestive, it is unclear that the sectoral shifts argument is quantitatively important. For example, Valletta and Cleary (2008) look at the (weighted) dispersion of employment growth across industries, a measure used by Lilien (1982). They find that as of the third quarter of 2008, "the degree of sectoral reallocation…remains low relative to past economic downturns." Valletta and Cleary (2008) also consider job vacancy data, which Abraham and Katz (1986) suggest could help distinguish between sectoral shifts and pure cyclical increases in unemployment and employment dispersion. The basic logic is that in a sectoral shifts story, expanding firms should have high vacancies that partially or completely offset the low vacancies in contracting firms. Valletta and Cleary find that the vacancy rate has been steadily falling since late 2006.

Third, Bloom (2008) argues that uncertainty shocks are likely to lead to a sharp decline in output. As he puts it, there has been "a huge surge in uncertainty that is generating a rapid slow-down in activity, a collapse of banking preventing many of the few remaining firms and consumers that want to invest from doing so, and a shift in the political landscape locking in the damage through protectionism and anti-competitive policies" (p. 4). His argument is based on the model simulations in Bloom (2007), in which an increase in macro uncertainty causes firms to temporarily pause investment and hiring. In his model, productivity growth also falls temporarily because of reduced reallocation from lower to higher productivity establishments.

Fourth, the credit freeze could directly reduce productivity-improving reallocations, along the lines suggested by Bloom (2007), as well as Eisfeldt and Rampini (2006). Eisfeldt and Rampini argue that, empirically, capital reallocation is procyclical, whereas the benefits (reflecting cross-sectional dispersion of marginal products) are dountercyclical. These observations suggest that the informational and contractual frictions, including financing constraints, are higher in recessions. The situation as of late 2008 is one in which financing constraints are particularly severe, which is likely to reduce efficient reallocations of both capital and labor.

Fifth, there could be other effects from the seize-up of financial markets in 2008. Financial intermediation is an important intermediate input into production in all sectors. If it is complementary with other inputs (as in Jones, 2008), for example, you need access to the commercial paper market to finance working capital needs -- then it could lead to substantial disruptions of real operations.

Finally, the substantial volatility in commodity prices, especially oil, in recent years could affect potential output. That said, although oil is a crucial intermediate input into production, changes in oil prices do not have a clear-cut effect on TFP, measured as domestic value added relative to primary inputs of capital and labor. They might, nevertheless, influence equilibrium output by affecting equilibrium labor supply. Blanchard and Gali (2007) and Bodenstein, Erceg, and Guerrieri (2008), however, are two recent analyses in which, because of (standard) separable preferences, there is no effect on flexible price GDP or employment from changes in oil prices. So there is no a priori reason to expect fluctuations in oil prices to have a substantial effect on the level or growth rate of potential output.

A difficulty for all these arguments that potential output growth might be temporarily low is the observation already made, that productivity growth (especially after adjusting for utilization) has, in fact, been relatively rapid over the past seven quarters.

...

Given wealth effects on labor supply and strong recent productivity performance -- along with the failure of typical proxies for mismeasurement to explain the productivity performance -- there are reasons for optimism about the short-run pace of potential output growth. Nevertheless, the major effects of the adverse shocks on potential output seem likely to be ahead of us. For example, the widespread seize-up of financial markets has been especially pronounced only in the second half of 2008. We expect that as the effects of the collapse in financial intermediation, the surge in uncertainty, and the resulting declines in factor reallocation play out over the next several years, short-run potential output growth will be constrained relative to where it otherwise would have been.

As an aside, I will observe that Jim might have a very different opinion on whether the change in oil prices would have an impact on potential GDP; see Hamilton, JPE 1988.

What does the output gap look like?

The discussion thus far has focused on the definition of output gap as the deviation of output from the natural level of output. While Fernald and Basu do not show their measure of actual output gaps as implied by their model, one can look to another paper (Edge et al. 2007) to see what a somewhat different DSGE produces an output gap (by the way, this segue highlights the fact that there are very many different types of DSGE's out there; gross characterizations are dangerous since there are many dimensions along which each model might differ).

From the Edge et al. (2007) paper, the authors observe:

Nonetheless, there are sharp differences between the FRB/US and DSGE model generated output gaps, partially reflecting differences in the economic concept captured by the two series. The DSGE model's output gap is a driver of inflation, which implies that the path of inflation has an important bearing on the resulting output-gap path. Two instances illustrating this dependence are the early 1990s, when inflation continued to decline even though a slow recovery was underway (the so-called opportunistic disinflation), and the late 1990s, when inflation remained contained despite the very strong economic growth. These episodes are reflected in the DSGE model's output gap estimate, as this gap remains negative in the early 1990s and for much of the late 1990s. A conceptually similar output gap - - albeit one from a reduced-form model of Laubach and Williams [2003] - -shows a similar pattern over the 1990s because of the behavior of inflation. The FRB/US output gap measure is, by contrast, less closely linked to inflation: Indeed, real marginal cost, equal to the inverse of the mark-up, is the key driving variable in the model's inflation equation. The FRB/US potential output series is a production function based measure that is built up from smoothed values of multifactor productivity and production inputs. This measure saw output rising above potential through the 1990s.

I must confess that from my own perspective, the "output gap" measure thus defined as the deviation from "natural output" has some counter-intuitive aspects, including the fact that output never exceeds potential during the dot-com boom era. But the late 1990's/early 2000's were a period of low inflation, and as noted, by construction the path of the "output gap" will be driven by that phenomenon. This drawback (in my opinion) doesn't mean that one would then want to drop the entire exercise of using New Keynesian DSGE's to infer output gaps. Rather, I'd want to see how sensitive these measures are to a number of modifications; as an open economy macro guy I'd probably want to see how including the external sector matters.

Exactly because this is such a complicated issue, the Symposium on Projecting Potential Growth is particularly useful as it reviews a variety of issues encountered in estimating the output gap and potential GDP, variously defined: how definite is the distinction between the production function and time series approach, how to account for data revisions and real time data, trying to measure potential in China.

Why isn't one approach unambiguously better?

As a sort of old fashioned person, I still have an attachment to the production function approach embodied in the CBO and OECD (as well as FRB/US) measures of potential GDP. In part, this is because these measures accord better with my priors. I also understand where the differences in projections can come from (what do you assume about demographic trends, about TFP growth, capital stock depreciation, etc.); in the DSGE-based approaches, the differences can arise from any number of sources, including "deep" parameter values, nature of shocks, and so forth. Figuring out what drives the differences, then, can be a challenging (although not necessarily unrewarding) enterprise.

That being said, it is useful to keep in mind the fact that even in the production function approach, potential GDP, and hence the output gap, is estimated [4]. To illustrate this, consider the OECD different vintages of output gaps running through 2007Q4, here. The resulting graph (including the latest CBO measure) is below:

There're a lot of big revisions, particularly in the latter '90s, going from the first release to the estimates reported one year afterward. However, the corresponding revisions between initial release and 1 year afterward have been smaller since 2001. And revisions between 1 year and 3 years after initial release have been pretty small throughout, which is comforting. See Chapter 3 from the latest OECD Economic Outlook for additional discussion of revisions to potential GDP, as well as this post.

Reflecting my training in econometrics, I also find the production function approach to have some plausibility because of the findings of Basistha and Nelson. They conclude that a state space model incorporating a forward looking Phillips curve yields an implied output gap not too dissimilar to what one would obtain from the CBO's production function approach.

Two last observations

There are many different "output gaps" being estimated and reported. Understand what each one is measuring before deciding to use one or the other.

Which one is the "best" one to use depends on the question being asked, and tradeoffs regarding estimation error.

Digression: For a nifty, alternative time series approach to measuring the output gap, see James Morley and Jeremy Piger's recent work here; their most updated estimates of the output gap are here.

We cannot blame the Obama administration for failing to predict June's 9.5 percent unemployment rate. That result just shows the size of the shocks hitting the economy: Even the best forecasters can miss the unemployment rate by almost two percentage points, even when forecasting fewer than six months ahead.

That makes sense, and is in line with my previous post. But he then argues that since we’ve seen little stimulus effect so far, we should cancel the stimulus, since it'd be costly on a per-job basis (and in any case, he believes the effect on GDP to be small [1]). These are interesting assertions meriting further analysis.

Stock-Flow Mismatch

We're all free to use whatever multipliers we want (although I like to look at ranges, in order to safeguard against prejudices) in making our arguments. But one thing we shouldn't do is confuse stocks and flows. Professor Mulligan writes:

"The Obama administration had said that the stimulus bill would "save or create" 3.5 million jobs while adding $787 billion to the federal budget. Admittedly, some of this money went to taxpayers and to some worthwhile public works, but it also created additional economic burdens in the process of collecting the taxes and issuing the debt to pay for it. To an order of magnitude, the promise of those 3.5 million jobs cost a quarter of a million dollars per job promised."

Note that $787 is spent over several years (a flow). 3.5 million jobs is a stock. But wouldn't we want to incorporate how long those jobs would be around? That suggests we should use job-years instead of jobs, to make the numerator and denominator comparable. The Administration estimated the number at 6.8 million [2]. That works out to a cost per job-year of $116 thousand.

From my perspective, I view the appeal to the number of jobs created and saved alone as an inadequate approach. Rather, I think the concept of focusing on output makes more sense, as it incorporates indirectly how much income goes along with that employment. And GDP incorporates the returns to land and capital, as well. Furthermore, to the extent that economic activity is above what would obtain without the stimulus, then asset prices (think houses, plant and equipment, etc.) are above what they otherwise would be. Focusing on jobs, even job-years, or even output, omits these factors. On the other side, of course, one accumulates debt, and in the absence of slack, induces crowding out. Those potential effects should also be acknowledged (and are incorporated in the simulations conducted by CBO, IMF, etc.)

Sectoral Stimulus Mismatch

I do wonder about Professor Mulligan's assertions that the effect of stimulus spending will be limited due to absence of slack resources in targeted sectors. In particular, he has argued that stimulus spending directed to health care will have little multiplier impact since unemployment in that sector is low. However, the most recent Employment Situation reveals for June 2009, unemployment in health services was 5.2 percent, compared to 3.1 percent in June 2008. As an aside, while Professor Mulligan didn't mention education services, I'll observe that a lot of spending in the stimulus bill went either directly or indirectly (via transfers to the states) in support of education. Unemployment rates in June 2009 were 9.8 percent, compared to 4.8 in June 2008...I think some slack exists even in these sectors doing relatively well.

Construction Crowding Out

By the way, Professor Mulligan argues that the presence of offsetting cycles in residential and nonresidential construction suggests that the spending now occurring in nonresidential construction will result in crowding out of residential spending. This is a quite interesting approach to the question of crowding out, although not, in my opinion, the natural way. It seems to me one would want to examine the cross correlation of private and public construction. It turns out that the Census Bureau reports these numbers here. The resulting graph is below:

A Granger causality test on first difference of each series (2 lags) fails to reject the null hypothesis that public construction does not cause private construction, at the 5% msl. On the other hand, the test rejects the null that private construction does not cause public construction at the nearly 1% msl. This is hardly a formal test, and I suspect that this conclusion could be overturned by different specifications. However, the main point is the evidence for crowding out is hardly overwhelming.

Output Multipliers

So, in my opinion, let's return to output multipliers in our discusion of fiscal policy efficacy (timing has been dealt elsewhere [2] [3], [4]). Professor Mulligan is free to use whatever multipliers he believes in. I'll rely upon a range, and here's the range the CBO uses.

The easiest thing to do is to pull down the CBO's measure (interpolated to quarterly frequency). This yields the following picture (in logs):

Two observations: (i) recessions do not necessarily coincide with negative output gaps (although they do seem to coincide with the beginning of periods of negative output gaps); and (ii) recoveries do not always coincide with positive output gaps.

This is obvious when one thinks about it, given the NBER BCDC definition of a recession as the following:

A recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. A recession begins just after the economy reaches a peak of activity and ends as the economy reaches its trough. Between trough and peak, the economy is in an expansion. Expansion is the normal state of the economy; most recessions are brief and they have been rare in recent decades.

That is a recession is the description of the first derivative of output taking on a negative value, while an output gap is a description of output relative to the output level consistent with the "normal" utilization of factors of production (also "full-employment"). For details of how CBO calculates potential GDP, see this document.

Looking at the last ten years provides another insight.

The US economy only barely made it close to full-employment in the expansion of 2001-2007/8/?, and is now declining again. I think I had realized this (especially in the course of various past debates over the surge in tax receipts, which I think has now been resolved -- see [1], [2] for a recollection.)

As I noted in the beginning of this post, I was finding it difficult to discern the most appropriate measure, so I will share the other measures I have investigated as indicators of potential (or "trend") GDP (which can then be used to calculate corresponding measures of the output gap): (1) the Hodrick-Prescott filter; (2) the Band Pass filter; and the quadratic time trend.

The Hodrick-Prescott filter is a ubiquitous two-sided filter used in time series macroeconometrics and elsewhere (I've even seen it used in the analysis of temperature data! [3]). Essentially, the HP filter calculates a trend that minimizes the weighted sum of squared deviations from trend, and squared changes in the the growth rate of the trend. This weighting is controlled by a parameter which is usually set at 1600 for quarterly data. As a public service, I'll note there are serious hazards associated with this filter, especially when trying to correlate various macro series that have been put through the same filter [4].

There is an additional problem (which is often ignored), namely that the HP filter is two-sided, so that running the filter up to the end point of data will tend to result in the trend being too close to the last data point (in our case, the output gap will be pulled to zero).

There are several band pass filters; the one most commonly used in the macroeconometric literature is the Baxter-King version.

Band pass filters are called this because (in the frequency domain) they pass through any cyclical components within a particular frequency band, and elimates the others. In the time domain, this means fluctuations that are shorter or longer than a specific length are ignored. In the business cycle area, then, in order to use this filter, one would have to have a prior on how long a "typical" business cycle is. More on both the HP and BP filters can be found in Tim Cogley's entry for the New Palgrave Dictionary of Economics [5].

The final means of identifying the output gap is to the simplest (at least in implementation) -- take the deviation from an estimated quadratic trend in time. This is not an uncommon procedure, but if you are pretty confident there is a unit root in log GDP, you might feel a little queasy about doing this [6]. But for completeness' sake, I'll show what happens when you do this as well.

Note that in order to circumvent the two-sided filter aspect of the HP filter, I have done a standard fix, which is to use an ARIMA(1,1,1) on log GDP over the 1980-08q1 period to dynamically forecast out 12 quarters, and then apply the HP filter to this "extended" series. I could have done a similar procedure for the BP filter, but opted to use the Christiano and Fitzgerald (2003) one-sided asymmetric version of the band pass filter to estimate the trend series.

First, the good news. Using the band pass filter, one finds that the output gap is still positive, at less than one percentage point of GDP in 2008q1. The HP filter indicates an essentially zero output gap. The quadratic trend indicates something similar to what the CBO indicates -- something close to a 2 percentage point negative output gap in 2008q1, versus 1.5 percentage points for CBO.

I don't want to say that there is one best version. Variations in the sample period, and the parameters used in each filter, will change the results. And of course, data revisions will mean the real-time output gaps will differ from the final revised output gaps we estimate today using either mechanical or judgmental approaches. For a pessimistic view regarding real time use, see Orphanides and van Norden (2004) [pdf].

Nonetheless, the distinction between the rate of change in economic output, and where output levels will gravitate to (and at what pace) is a useful one. And I think it will become of greater usefulness as the slowdown ends, if and when growth resumes. In particular, I'm thinking of whether the pattern of smaller -- but more persistent -- ups and downs continues (the half life of a deviation from potential has risen from 8 quarters in the 1970-90q1 period to 11.6 quarters in the 1990q2-2008q1 period).

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