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Authorized for public release by the FOMC Secretariat on 04/29/2016 Output Gaps and Inflation in DSGE Models Jonas Fisher and Alejandro Justiniano1 December 10, 2009 Summary The Philadelphia-Richmond memo “Gaps and Monetary Policy,” hereafter the “PR memo,” argues that output gaps based on Dynamic Stochastic General Equilib rium (DSGE) models cannot be taken seriously for three reasons. First, the output gaps that emerge from these models are sensitive to the underlying assumptions and it is difficult to choose among alternative assumptions. Second, fluctuations in DSGE models are typically driven in large part by shocks of indeterminate origin, hence anything derived from them is inherently suspect. Third, in practice output gaps from these models are not useful in guiding policy. Research over the past 18 months, in a collaboration between the Chicago Fed and Northwestern University, has direct bearing on these points. We describe it here. This research demonstrates that many of the problems highlighted in the PR memo stem from challenges in dealing with low and high frequency movements in hours, wages and inflation that all applied macro theories must confront. These movements can be explained with identifiable, albeit non-structural shocks. Once the low frequency trends and high frequency fluctuations are addressed head-on, then a very close association between model-based measures of the output gap and inflation emerges. The Role of Shocks in DSGE M odels Before describing this research it is instructive to return to the issues raised in the PR memo about the inclusion of shocks in DSGE models. All DSGE models have recognizable structural shocks. The more data the model attempts to explain, the more it becomes necessary to introduce disturbance terms with little or no structural interpretation. In any structural empirical macroeconomic analysis one is faced with a trade-off between parsimony and realism. The trade-off is particulary challenging in DSGE analysis. These models attempt to understand all fluctuations in a large 1Federal Reserve Bank of Chicago. We thank Spencer Krane for very helpful comments. 1 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 number of variables. The models thus need a large number of shocks in order to fit all aspects of the data and to avoid stochastic singularity.2 Ideally, we would like to have ready structural interpretations for all of these shocks. But, parsimony dic tates leaving out features of the economy's structure that cannot be modeled without introducing considerable complexity. So non-structural disturbance terms naturally take the place of the un-modeled features. There are three areas in which such unmodeled shocks are major issues for DSGE analysis. First, there are demographic trends, such as changes in rates of labor force participation, that influence the supply of labor and wage determination. Most an alysts have not attempted to model these factors because they are not necessarily crucial for understanding business cycle fluctuations. Second, there are obvious low frequency movements in inflation which are likely to have been heavily influenced by changes in monetary policy. Modeling the low frequency dynamics of policy for mation is an enormously challenging task, which is naturally set aside for the sake of parsimony. Third, wages and inflation are subject to high frequency fluctuations which one might suspect have little to do with the fundamental forces driving the real economy, and so are left unmodeled. In all these circumstances it is natural to include reduced form shocks to address the missing model structure. The research in Justiniano and Primiceri (2008) and Justiniano and Primiceri (2009) is a case in point. They specify a version of the Christiano, Eichenbaum, and Evans (2005) model which includes disturbances to neutral technology, the ef ficiency of investment, the representative agent's discount factor and labor supply, wage markups, price markups, inflation drift, the Taylor-type rule, and government (plus net export) spending.3 In line with the discussion above, we view some of these shocks as structural and others as reduced form proxies for complexities beyond the scope of the model. The labor disutility shock is designed to account for the low frequency trend in hours, the inflation drift shock accounts for the low frequency component of inflation, and the wage and price markup shocks account for the high frequency movements in wages and inflation. The government spending shock should also be viewed as a reduced form disturbance. It is included to make up the difference 2Stochastic singularity refers to the absence of at least as many shocks as observable variables used for inference, in which case at least some of the variables must be perfectly co-linear. 3For details of the model described here see Justiniano, Primiceri, and Tambalotti (2009). 2 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 between observed consumption plus investment, and output. The interpretation of discount factor shocks is less clear. However, there is a long tradition in real business cycle analysis of considering these shocks.4 The Role of Shocks in Explaining O utput Gaps and Inflation It is possible to decompose the endogenous variables in the model into components accounted for by each of the disturbances. In what follows we focus on a decomposi tion of inflation across different categories of shocks.5 Figure 1 displays quarterly GDP deflator inflation (solid, grey line) along with the component of inflation driven solely by the inflation drift term (dashed, black line) that we call “trend.” The role of this shock in picking up low frequency vari ation in inflation is clear. Figure 2 displays model-detrended inflation (solid, grey line), that is inflation less trend inflation from Figure 1. It also shows what Jus tiniano and Primiceri (2009) call fundamental inflation (dashed, black line).6 Table 1 summarizes this definition of inflation as well as other concepts discussed below. Fundamental inflation corresponds to the component of inflation driven by shocks to neutral technology, the efficiency of investment, the representative agent's discount factor and labor supply, the Taylor-type rule, and government spending. Put another way, fundamental inflation is model-detrended inflation after removing the influence of the wage and price markup shocks. The difference between the solid and dashed lines thus indicates the role played by the markup shocks in explaining high frequency fluctuations in inflation. Figure 3 displays fundamental inflation (dashed, black line) along with the modelbased output gap (solid, grey line).7 The output gap is defined as the difference between actual observed GDP and the model-based estimate of potential output. Potential output is defined as the level of output obtained at the estimated model parameters after eliminating the nominal rigidities, the markup shocks, the inflation drift term and the Taylor-type rule shock. That is, the level of output in an economy driven entirely by real disturbances and with complete price flexibility. 4Two examples include Eichenbaum and Singleton (1986) and Fisher and Hornstein (2000). 5The model is estimated on the sample 1962q1 to 2009q2. Similar results are obtained using the post-1984 sample. 6Means also have been removed from the variables before plotting them. 7Means again have been removed from the variables before plotting them. 3 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 The high degree of co-movement between the output gap and fundamental infla tion in Figure 3 is striking (the correlation is 0.86).8 The co-movement between the gap and fundamental inflation seems to be better before the mid-1990s than after. Still, in the recent period there is also a high degree of co-movement. So, while this measure of the output gap is clearly not a sufficient statistic for fundamental infla tion, Figure 3 suggests that it could be a valuable summary indicator of inflationary pressures. Even if this output gap co-moves strongly with a suitably filtered measure of inflation, one may still be skeptical of its use depending on what ends up explaining this co-movement. Table 2 addresses this question. This table shows fractions of business cycle variation (fluctuations of period 6 to 32 quarters) of various endogenous variables attributable to markup shocks (column A), the inflation drift shock (column B) , shocks to the Taylor-type rule, labor supply and government spending (column C) , and shocks to neutral technology, the efficiency of investment, and the discount factor (column D). The main real variables, output and hours, are driven almost entirely (80 percent) by shocks to neutral technology, investment efficiency and the discount factor. The first two account for 67 and 65 percent of output and hours fluctuations on their own (not shown). Shocks to the Taylor-type rule, government spending and labor supply account for less than 10 percent of fluctuations in these variables. Combined, these results stand in contrast to the findings in Chari, Kehoe, and McGrattan (2009) who argue that the bulk of business cycle fluctuations in output and hours are driven by shocks to markups, labor supply, government spending, and the discount factor. A large fraction of inflation, even at business cycle frequencies, is driven by markup shocks, which highlights the need to understand these disturbances. Nonetheless the fraction of inflation fluctuations at business cycle frequencies that is driven by shocks to neutral, investment efficiency and the discount factor exceeds 20 percent. And, by definition, all of fundamental inflation is driven by shocks other than to markups or the inflation drift. As seen in the bottom panel of Table 2, the model-based output gap at business 8Obviously these are two endogenous variables so this correlation does not reflect causation. We address causation below by decomposing the variability in these series across the model's shocks. 4 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 cycle frequencies is mostly driven by shocks other than to markups or the inflation drift. This means that an alternative version of this gap that excludes the influence of the markup and inflation drift shocks (to put the gap on a comparable basis to fundamental inflation) strongly resembles the one plotted in Figure 3 and thus still tracks fundamental inflation closely (the correlation is 0.90). Furthermore, the output gap is strongly correlated with model-based and empirical measures of marginal cost.9 This is reflected in Table 2 where we see that modelbased marginal cost is 62 percent driven by shocks other than to the markup and the inflation drift. Given that the New-Keynesian Phillips curve equation is sitting inside the model and marginal cost is a key term in this equation, then the correlation between the model-based output gap and marginal cost should not be surprising. Finally, the model-based output gap bears some resemblance to simple statistical output gaps. This is demonstrated in Figure 4 which displays the model-based output gap along with linearly detrended GDP (the correlation is 0.44).10 Conclusion Overall, these results build confidence in the usefulness of the model-based output gap as an indicator of underlying inflationary pressures. The underlying determinants of inflation are the model's shocks; but, the output-gap itself appears to be a useful summary statistic for these shocks. Obviously, results depend on the assumptions. All economic analysis involves assumptions. What matters is how compelling the assumptions are. We think the arguments supporting the modeling choices driving the results here are compelling. They are driven by reasonable considerations of empirical exigency and model par simony. This suggests that the issues raised in the PR memo are more about poor model specification than a fundamental flaw in the DSGE methodology. We do not wish to suggest this is the end of the story. Justiniano and Primiceri have not concluded their research. It is unclear at this stage what optimal policy looks like. And, there are many parts of the current generation of DSGE models that can be improved on. In particular, the treatment of wage and price setting, financial 9For example, real unit labor costs in the non-farm business sector as published by the BLS. 10This might be surprising in light of the results in Gali and Gertler (1999). 5 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 markets, and commodity prices needs work. However, until there is a viable alterna tive, the research described in this memo suggests that there is useful information for policymakers in state-of-the-art DSGE models. References Chari, V. V., P. Kehoe, and E. McGrattan (2009). New keynesian models: Not ready for policy analysis. American Economic Journal: Macroeconomics 1 (1), 242-266. Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005). Nominal rigidities and the dynamic effects of a shock to monetary policy. Journal of Political Economy 113 (1), 149-158. Eichenbaum, M. and K. Singleton (1986). Do equilibrium real business cycle theories explain postwar U. S. business cycles? NBER Macroeconomics Annual 1, 91-135. Fisher, J. D. and A. Hornstein (2000). (S, s) inventory policies in general equilibrium. Review of Economic Studies 67(1), 117-146. Gali, J. and M. Gertler (1999). Inflation dynamics: A structural econometric analysis. Journal of Monetary Economics 44 (2), 195-222. Justiniano, A. and G. E. Primiceri (2008). Potential and natural output. Northwestern University Manuscript. Justiniano, A. and G. E. Primiceri (2009). DSGE-based output gaps and inflation determination. Chicago Fed Presentation. Justiniano, A., G. E. Primiceri, and A. Tambalotti (2009). Investment shocks and business cycles. New York Fed Staff Report 322. 6 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 Table 1: Definitions of Potential Output and Fundamental Inflation Exogenous l Shocks Included ExogenousShocksIncluded ExogenousShocksIncludedExogenusShckIld Nominal Rigidities Included All remaining disturbances1Sefotn1.][ Markups Series Monetary Policy: Yes shocks to Taylor-type rule and drifting No average inflation Output2[Sefotn2.] Yes Yes Yes Potential Output3[Sefotn3.] No No Inflation4efotn4.][S Yes Yes Yes Yes Fundamental Inflation5Sefotn5.][ Yes No No drifting average inflation Yes Yes Notes to table 1: 1[Fotne1. Shocks to neutral technology, investment efficiency, discount factor, government and labor supply.dfotne1.]E 2[Fotne2.Output corresponds to real GDP per-capita.Endfote2.] 3[Fotne3.Potential output is the model-based level of output that would prevail in an economy without nominal rigidities, and, with constant markups in prices and wages.Endfote3.] 4[Fotnoe4.Inflation corresponds to the 400 times the quarterly log-difference in the GDP deflator.Endfote4.] 5[Fotnoe5.Fundamental inflation is the model-based measure of inflation explained by all shocks except for the markup shocks in prices and wages and the shock to drifting average inflation.Endfote5.] 7 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 T a b le 2 : M o d e l- b a s e d V a r ia n c e D e c o m p o s itio n o v e r th e B u s in e s s C y c le 1[Sefotn1.] Percentage of variation explained by exogenous shocks 2]2.eotnfS[ Column A B C D Neutral Taylor-type Technology, rule, Investment Government Efficiency and and Labor Discount Supply 3 [Sefotn3.] Factor3 Markups Drifting Average Inflation Output 7 2 9 82 Hours 7 2 9 81 Inflation 56 18 3 23 Nominal Interest 10 5 29 55 Output Gap 13 4 29 55 Marginal Cost 37 1 2 60 Shocks Actual Data 4[Sefotn4.] Model-Generated Data 5 efotn5.][S Notes to table 2: 1[Footnote 1. Defined as cycles of between 6 and 32 quarters. End footnote 1.] 2[Fotnote2.May not add up to 100 due to rounding.Endfote2.] 3[fotnote3.T his presents a more disaggregated taxonomy of shocks than in table 1.ndfote3.]E [Fotne4.Corresponds to the level of GDP per-capita (although the model is estimated using the first difference of this series), hours per-capita, quarterly inflation in the GDP deflator and the effective Federal Funds rate.Endfote4.] 5[Fotne5. The model-based output gap is defined as the difference between observed output and potential output, where the latter is described in table 1. Marginal cost is in real terms.dfotne5.]E 8 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 Figure 1: Observed Inflation and Model-Based Trend Inflation Figure 2: Model-Based Detrended and Fundamental Inflation 9 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 Figure 3: Model-Based Output Gap and Fundamental Inflation 10 of 11 Authorized for public release by the FOMC Secretariat on 04/29/2016 Figure 4: Model-Based Output Gap and Observed Output Deviations from a Linear Trend 11 of 11
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