# The role of potential output in policymaking.

Often, economists equate potential output with the trend in real gross domestic product (GDP) growth. My discussion is focused on "proper" detrending of aggregate data. I will emphasize the idea that theory is needed to satisfactorily detrend data--explicit theory that encompasses simultaneously both longer-run growth and shorter-run fluctuations. The point of view I wish to explore stresses that both growth and fluctuations must be included in the same theoretical construct if data are to be properly detrended. Common atheoretic statistical methods are not acceptable. When detrending data, an economist should detrend by the theoretical growth path so as to correctly distinguish output variance in the model due to growth from the variation in the model due to cyclical fluctuations.The quest to fully integrate growth and cycle was Prescott's initial ambition; however, it is difficult to develop a model that can match the curvy, time-varying growth path often envisioned as describing an economy's long-run development. Instead, the Hodrick-Prescott (HP) filter was proposed to remove from the data a flexible time-varying trend (Hodrick and Prescott, 1980). My argument is that this procedure is unsatisfactory.

The idea in question is: How can we specify a model that will make the growth path look like the ones we see in the data? My suggestion is that, as an initial approach, we use a mainstream core growth model augmented with occasional trend breaks and learning. Learning helps the model fit the data and has important implications for policy analysis. I will discuss some applications of this idea in Real Business Cycle (RBC) and New Keynesian (NK) models from Bullard and Dully (2004) and Bullard and Eusepi (2005).

MAIN IDEAS

The equilibrium business cycle literature encompasses a wide class of models, including RBC, NK, and multisector growth models. Various frictions can be introduced in all of these approaches. Many analyses do not include any specific reference to growth, but all are based on the concept of a balanced growth path.

I will focus on a framework that is very close to the RBC model. This will provide a well-understood benchmark. However, I stress that these ideas have wide applicability in other models as well, and I will briefly discuss an NK application at the end.

Empirical studies, such as Perron (1989) and Hansen (2001), have suggested breaks in the trend growth of U.S. economic activity. One reasonable characterization of the data is to assume log-linear trends with occasional trend breaks but no discontinuous jumps in level--that is, a linear spline. This is the bottom line of Perron's econometric work. These breaks, however, suggest a degree of nonstationarity that is difficult to reconcile with available theoretical models. This is where adding learning can be helpful.

CURRENT PRACTICE

The standard approach in macroeconomics today is to analyze separately business cycles and long-term growth. The core of this analysis is the statistical trend-cycle decomposition. The standard method in the literature for trend-cycle decomposition is to use atheoretic, univariate statistical filters, that is, to conduct the decomposition series by series (see, for example, King and Rebelo, 1999). This method ignores an important dictum implied by the balanced growth path assumption: There are restrictions as to how the model's variables can grow through time and in turn, therefore, how one is allowed to detrend data. In an appalling lack of discipline, economists ignore this dictum and detrend data individually, series by series, which makes little sense in any growth theory. An acceptable theory specifies growth paths for the model's variables (i.e., consumption, investment, output); individual trends should not be taken out of the data. Still, the ad hoc practice dominates the literature.

Most of my criticisms are well known:

* Statistical filters do not remove the "trend" that the balanced growth path requires.

* Current practice does not respect the cointegration of the variables, that is, the multivariate trend that the model implies.

* Filtered trends imply changes in growth rates over time; agents would want to react to these changes and adjust their behavior.

A model without growth does not allow for this change in behavior.

* The "business cycle facts" are not independent of the statistical filter employed. The econometrics literature normally--but not always--filters the data so as to achieve stationarity for estimation and inference without regard to the underlying theory's balanced growth assumption. Even recent sophisticated models (for examples, Smets and Wouters, 2007) do not address this issue.

HOW TO IMPROVE ON THIS?

The criticisms are correct in principle. They are quantitatively important. And, these issues cannot be resolved by using alternative statistical filters, because those filters are atheoretic. Instead, theory should be used to tell us what the growth path should look like; then, this theoretical trend can be used to detrend the data.

In the model I discuss, agents are allowed to react to trend changes. The ability to react to changes in trends alters agents' behavior--how much they save, how much they consume, and so forth. Of course, this is demanding territory. I am insisting that the theorist specify both the longer-term growth and short-run business cycle aspects of a model, and then explain the model's coherence to observed data. This is the research agenda I propose.

Core Ideas

The core idea is that modelers should use "model-consistent detrending," that is, the trends that are removed from the data are the same as the trends implied by the specified model. Presumably, changes in trend are infrequent and, perhaps with some lag, are recognized by agents who then react to them. This suggests a role for learning. In addition, the cointegration of the variables or the different trends in the various variables implied by the balanced growth path is respected.

FEATURES OF THE ENVIRONMENT

As an example, I will discuss briefly the most basic equilibrium business cycle model with exogenous stochastic growth, but replace rational expectations with learning as in Evans and Honkapohja (2001). This model perhaps is appropriate when there is an unanticipated, rare break in the trend (for example, a labor productivity slowdown or acceleration). I assume agents possess a tracking algorithm and are able to anticipate the characteristics of the new balanced growth path that will prevail after the productivity slowdown occurs. If there is no trend break for a sufficient period, then there is convergence to the rational expectations equilibrium associated with that balanced growth path. Learning helps around points where there is a structural break of some type by allowing the economy to converge to the new balanced growth path following the structural break. In order for this to work, of course, the model must be expectationally stable such that the model's implied stochastic process will remain near the growth path.

Environment

The environment studied by Bullard and Duffy (2004) is a standard equilibrium business cycle model such as the one studied by Cooley and Prescott (1995) or King and Rebelo (1999). A representative household maximizes utility defined over consumption and leisure. Physical capital is the only asset. Business cycles are driven by shocks to technology. Bullard and Dully (2004) include explicit growth in the model. Growth in aggregate output is driven by exogenous improvements in technology over time and labor force growth. The growth rate is exogenous and constant, except for the rare trend breaks that are incorporated. The production technology is standard. Under these assumptions, aggregate output, consumption, investment, and capital will all grow at the same rate along a balanced growth path.

Structural Change

The idea of structural change in this setting is simply that either the growth rate of technology or of the labor force takes on a new value. In the model, changes of this type are unanticipated. This will dictate a new balanced growth path, and the agents learn this new balanced growth path.

In order to use the learning apparatus as in Evans and Honkapohja (2001), a linear approximation is needed. Using logarithmic deviations from steady state, one can define and rewrite the system appropriately, as Bullard and Duffy (2004) discuss extensively. One must be careful about this transformation because the steady-state values can be inferred from some types of linear approximations, but we really don't want to inform the agents that the steady state of the system has changed. We want the agents to be uncertain where the balanced growth path is and learn the path over time.

Recursive Learning

Bullard and Duffy (2004) study this system under a recursive learning assumption as in Evans and Honkapohja (2001). They assume agents have no specific knowledge of the economy in which they operate, but are endowed with a perceived law of motion (PLM) and are able to use this PLM--a vector autoregression--to learn the rational expectations equilibrium. The rational expectations equilibrium of the system is determinate under the given parameterizations of the model.

Should a trend break occur--say, a productivity slowdown or speedup--the change will be manifest in the coefficients associated with the rational expectations equilibrium of this system. The coefficients will change; agents will then update the coefficients in their corresponding regressions, eventually learning the correct coefficients. These will be the coefficients that correspond to the rational expectations equilibrium after the structural change has occurred.

Expectational Stability

For this to work properly the system must be expectationally stable. Agents form expectations that affect actual outcomes; these actual outcomes feed back into expectations. This process must converge so that, once a structural change occurs, we can expect the agents to locate the new balanced growth path. Expectational stability (E-stability) is determined by the stability of a corresponding matrix differential equation, as discussed extensively by Evans and Honkapohja (2001). A particular minimal state variable (MSV) solution is E-stable if the MSV fixed point of the differential equation is locally asymptotically stable at that point. Bullard and Duffy (2004) calculated E-stability conditions for this model and found that E-stability holds at baseline parameter values (including the various values of technology and labor force growth used).

WHAT THE MODEL DOES

The description above yields an entire system--one possible growth theory along with a business cycle theory laid on top of that. A simulation of the model will yield growing output and growing consumption, and so on, but at an uneven trend rate depending on when the trend shocks occur and how fast the learning guides the economy to the new balanced growth path following such a shock. The data produced by the model look closer to the raw data we obtain on the economy, and now we would like to somehow match up simulated data with actual data.

Of course, this model is too simple to match directly with the data, but it is also a well-known benchmark model so it is possible to assess how important structural change is when determining the nature of the business cycle as well as for the performance of the model relative to the data.

One aspect of this approach is that the model provides a global theory of the whole picture of the data. The components of the data have to add up to total output. This is because in the model it adds up and one is using that fact to detrend across all of the different variables. When considering the U.S. data, then, one has to think about the pieces that are not part of the model and how those might match up to objects inside the model. Bullard and Duffy (2004) discuss this extensively.

Breaks Along the Balanced Growth Path

The slowdown in measured productivity growth in the U.S. economy beginning sometime in the late 1960s or early 1970s is well known, and econometric evidence on this question is reviewed in Hansen (2001). Perron (1989) associated the 1973 slowdown with the oil price shock. The analysis by Bai, Lumsdaine, and Stock (1998) suggests the trend break most likely occurred in 1969:Q1.

The Bullard and Duffy (2004) model says that the nature of the balanced growth path--the trend--is dictated by increases in productivity units X(t) and increases in the labor input N(t). To find break dates, instead of relying on econometric evidence alone, Bullard and Duffy (2004) designed an algorithm that uses a simulated method of moments search process (genetic algorithm) (1) to choose break dates for the growth factors and the growth rates of these factors, based on the principle that the trend in measured productivity and hours from the model should match the trend in measured productivity and hours from the data. Table 1 reports their findings. The algorithm suggests one trend break date in the early 1960s for the labor input and two break dates for productivity: one in the early 1970s and one in the 1990s.

According to Table 1, productivity grows rapidly early in the sample, then slowly from the '70s to the '90s and then somewhat faster after 1993. After each one of those breaks the agents in the model are somewhat surprised, but their tracking algorithm allows them to find the new balanced growth path that is implied by the new growth rates.

This model includes both a trend and a cycle. Looking at the simulated data from the model, what would a trend be? A trend is the economy's path if only low-frequency shocks occur. Bullard and Duffy (2004) turn off the noise on the business cycle shock and just trace out the evolution of the economy if only the low-frequency breaks in technology and labor force growth occur. Importantly, the multivariate trend defined this way is then the same one that is removed from the actual data. In this sense, the model and the data are treated symmetrically: The growth theory that is used to design the model is dictating the trends that are removed from the actual data.

Business Cycle Statistics

The reaction of the economy to changes in the balanced growth path will depend in part on what business cycle shocks occur in tandem with the growth rate changes. Bullard and Duffy (2004) average over a large number of economies to calculate business cycle statistics for artificial economies. They collect 217 quarters of data for each economy, with trends breaking as described above. They detrend the actual data using the same (multivariate) trend that is used for the model data.

The numbers in Table 2 are not the standard ones for this type of exercise. In fact, they are quite different from the ones that are typically reported for this model, both for the data and for the model relative to the data. This shows that the issues of the underlying growth theory and its implications for the trends we expect to observe are key issues in assessing theories. One simple message from Table 2 is we obtain almost twice as much volatility in this model as there would be in the standard business cycle in this economy. This is so even though the technology shock is calibrated in the standard way.

[FIGURE 1 OMITTED]

New Keynesian Application

A similar approach can be used in the NK model. This was done by Bullard and Eusepi (2005). In the NK model (with capital), a monetary authority plays an important role in the economy's equilibrium. In Bullard and Eusepi (2005), the monetary authority follows a Taylor-type policy rule. The trend breaks and the underlying growth theory are the same as in Bullard and Duffy (2004). Now, however, one can ask how the policymaker responds using the Taylor rule given a productivity slowdown that must be learned. The policymaker initially misperceives how big the output gap is and this is making policy set the interest rate too low, pushing the inflation rate up. How large is this effect? According to Bullard and Eusepi (2005), the effect is about 300 basis points on the inflation rate for a productivity slowdown of the magnitude experienced in the 1970s (Figure 1). So, this does not explain all of the inflation in the 1970s but it helps explain a big part of it.

CONCLUSION

The approach outlined above provides some microfoundations for the largely atheoretical practices that are currently used in the literature. Structural change is not a small matter, and structural breaks likely account for a large fraction of the observed variability of output. One way to think of structural change is as a series of piecewise balanced growth paths. Learning is a glue that can hold together these piecewise paths.

I think this is an interesting approach and I would like to encourage more research that goes in this direction. It doesn't have to be a simple RBC-type model; one could instead use a more elaborate model that incorporates more empirically realistic ideas about what is driving growth and what is driving the business cycle. The approach I have outlined forces the researcher to lay out a growth theory, which is a tough and rather intensive task, but also leads to a more satisfactory detrending method and a model that is congruent with the macroeconomic data in a broad way.

REFERENCES

Bai, Jushan; Lumsdaine, Robin L. and Stock, James H. "Testing for and Dating Common Breaks in Multivariate Time Series." Review of Economic Studies, July 1998, 65(3), pp. 395-432.

Bullard, James and Dully, John. "Learning and Structural Change in Macroeconomic Data." Working Paper No. 2004-016A, Federal Reserve Bank of St. Louis, August 2004; http://research.stlouisfed.org/wp/2004/2004-016.pdf.

Bullard, James and Eusepi, Stefano. "Did the Great Inflation Occur Despite Policymaker Commitment to a Taylor Rule?" Review of Economic Dynamics, April 2005, 8(2), pp. 324-59.

Cooley, Thomas F. and Prescott, Edward C. "Economic Growth and Business Cycles," in T.F. Cooley, ed., Frontiers of Business Cycle Research. Princeton, NJ: Princeton University Press, 1995, pp. 1-38.

Evans, George W. and Honkapohja, Seppo. Learning and Expectations in Macroeconomics. Princeton, NJ: Princeton University Press, 2001.

Hansen, Bruce E. "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity." Journal of Economic Perspectives, Fall 2001, 15(4), pp. 117-28.

Hodrick, Robert J. and Prescott, Edward C. "Postwar U.S. Business Cycles: An Empirical Investigation." Discussion Paper 451, Carnegie-Mellon University, May 1980.

King, Robert G. and Rebelo, Sergio T. "Resuscitating Real Business Cycles," in J.B. Taylor and M. Woodford, eds., Handbook of Macroeconomics. Volume 1C. Chap. 14. Amseterdam: Elsevier, 1999, pp. 927-1007.

Orphanides, Athanasios and Williams, John C. "The Decline of Activist Stabilization Policy: Natural Rate Misperceptions, Learning and Expectations." Journal of Economic Dynamics and Control, November 2005, 29(11), pp. 1927-50.

Perron, Pierre. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, November 1989, 57(6), pp. 1361-401.

Smets, Frank and Wouters, Rafael. "Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach." CEPR Discussion Paper No. 6112, Centre for Economic Policy Research, February 2007; www.cepr.org/pubs/dps/DP6112.asp.

* This discussion is based on the panel discussion, "The Role of Potential Output in Policymaking," available at http://research.stlouisfed.org/econ/bullard/FallPolicyConference Bullard16oct2008.pdf and on Bullard and Duffy (2004).

(1) See Appendix B in Bullard and Duffy (2004).

James Bullard is president of the Federal Reserve Bank of St. Louis.

Table 1 Optimal Trend Breaks N(t) X(t) Initial annual growth rate (percent) 1.20 2.47 Break date 1961:Q2 1973:Q3 Mid-sample annual growth rate (percent) 1.91 1.21 Break date -- 1993:Q3 Ending annual growth rate (percent) 1.91 1.86 Table 2 Business Cycle Statistics, Model-Consistent Detrending Volatility Relative volatility Contemporaneous correlations Data Model Data Model Data Model Output 3.25 3.50 1.00 1.00 1.00 1.00 Consumption 3.40 2.16 1.05 0.62 0.60 0.75 Investment 14.80 8.86 4.57 2.53 0.65 0.92 Hours 2.62 1.54 0.81 0.44 0.65 0.80 Productivity 2.52 2.44 0.77 0.70 0.61 0.92

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Title Annotation: | Panel Discussion |
---|---|

Author: | Bullard, James |

Publication: | Federal Reserve Bank of St. Louis Review |

Article Type: | Column |

Geographic Code: | 1USA |

Date: | Jul 1, 2009 |

Words: | 3306 |

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