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Journal of Economic Interaction and Coordination

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28-10-2016 | Regular Article

Competitive moment matching of a New-Keynesian and an Old-Keynesian model

Author: Reiner Franke

Published in: Journal of Economic Interaction and Coordination | Issue 2/2018

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Abstract

The paper considers two rival models referring to the new macroeconomic consensus: a standard three-equation model of the New-Keynesian variety versus dynamic adjustments of a business and an inflation climate in an ‘Old-Keynesian’ tradition. Over the two subperiods of the Great Inflation and Great Moderation, both of them are estimated by the method of simulated moments. An innovative feature is here that the moments do not only include the autocovariances up to eight lags of quarterly output, inflation and the interest rate, but optionally also a measure of the raggedness of the three variables. In short, the performance of the Old-Keynesian model is very satisfactory and similar to the New-Keynesian model, or even better. In particular, the Old-Keynesian model is better suited to match the new moments without deteriorating the original second moments too much.

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Other macro models of that kind are Westerhoff and Hohnisch (2007), Hohnisch and Westerhoff (2008), Branch and McGough (2010), Lines and Westerhoff (2010), Anufriev et al. (2013). The two specifications of the ‘animal spirits’ are the transition probability and the discrete choice approach, for which Franke (2014) proposes a certain synthesis.

Which does not rule out that other estimation procedures have their virtues as well. Note, however, that likelihood methods become fairly complicated if, as it will be the case for us, the models contain unobservable state variables and are nonlinear.

“Effective” simulation size means that, starting from the steady state position, the models are simulated over \(200 + S\) quarters and the first 200 quarters are discarded to rule out any transient effects (which proves to be more than sufficient).

For our random variables, which are of the form \(\varepsilon _{t} \sim N(0,\sigma ^2)\), this means that in period t always the same random number \(\tilde{\varepsilon }_{t}\) is drawn from the standard normal N(0, 1) and then, depending on the specific value of \(\sigma \) under examination, \(\varepsilon _{t}\) is set equal to \(\varepsilon _{t} = \sigma \, \tilde{\varepsilon }_{t}\).

If in the course of the minimization search procedure for (1) some parameter leaves an admissible interval, it is temporarily reset to the boundary value, the loss J of the thus resulting moments is computed, and then a sufficiently strong penalty is added to J that proportionately increases with the extent of the original violation. In this way also corner solutions to (1) can be safely identified.

In detail, we apply the algorithm put forward by Corona et al. (1987); see also Goffe et al. (1994) and Goffe (1996). The most critical ‘tuning parameters’ are the reduction factor \(r_T\) and the initial temperature \(T_o\). We set \(r_T = 0.75\), a conservative value “which is suitable for a function one has little experience with” (Goffe 1996, p. 172). To obtain \(T_o\), first the median loss M of 500 widely dispersed parameter vectors is computed. Requiring that the algorithm’s (desirable) probability of accepting an increase in the loss is about 0.50, at temperature \(T_o\) and at the same step sizes that in the initial procedure have scaled the changes in the single parameter values, subsequently Boltzmann’s formula \(\exp (-M/T_o) = 0.50\) is solved for \(T_o\).

A shorter simulation horizon of \(S = 2000\) proves to be sufficient for these global investigations.

It has broader scope than gradient methods to escape from small local valleys.

An example for this can be found in Franke et al. (2015, p. 145, Table 6).

The second moments provide similar information to the impulse-response functions of the three types of shocks in the models, in which (or just one of them) many New-Keynesian studies take a greater interest.

This commitment is different from an explicit moment selection procedure as it is, for example, put to use by Karamé et al. (2008). They begin with a large set of moments, estimate their model on them, and then step by step discard the moments that the model reproduces most poorly until an over-identification test fails to reject the model any longer.

See Hall and Horowitz (1996, p. 897) and Allen et al. (2011, p. 112) for the following recentring procedure.

An application of this bootstrap approach to another New-Keynesian model is Fève et al. (2009), although they only estimate a subset of the parameters. Their moments are given by the impulse-response functions to a monetary policy shock, so that they can be analytically computed and the p value is not plagued with the sample variability from \(c = c(b)\).

The literature is sometimes rather sloppy in this respect. Cogley et al. (2010, p. 43, fn 1), for example, remarked when discussing inflation persistence that it is not always completely plain in the literature whether the focus is on raw inflation or the inflation gap.

Ireland (2007) and, more ambitiously, Cogley and Sbordone (2008) are two proposals of an endogenous determination of the central bank’s moving inflation target. Ireland (p. 1864), however, concludes from his estimations that still “considerable uncertainty remains about the true source of movements in the Federal Reserve’s inflation target”.

In the verbal discussions we may nevertheless omit mentioning the ‘gap’ and, for instance, simply speak of inflation.

Despite their wide acknowledgement, these stories do not perfectly meet the high and rigorous standards of New-Keynesian modelling. Two examples of well-established authors who rather characterize them as an ad hoc amendment are Fuhrer (2006, p. 50) and Rudd and Whelan (2005, p. 20f), which is the more detailed version of Rudd and Whelan (2007, p. 163, fn 7).

Contributions with positive trend inflation are Bakhshi et al. (2003), Sahuc (2006), Ascari and Ropele (2007), Ireland (2007), and Cogley and Sbordone (2008), among others. Mattesini and Nisticò (2010) incorporate positive trend growth.

Fuhrer (2006) is a study of a Phillips curve similar to that in (NK) which likewise does not require, or imply, that \(\phi _\pi \) (in the present notation) is positively bounded away from zero. In his discussion of the inflation persistence effects that strongly favours low values of \(\phi _\pi \), however, the author does not care about a rigorous structural interpretation of these situations.

To be scrupulous, one of the axioms implies that the so-called rational agents are not fully rational in the conventional sense (Branch and McGough 2009, p. 1045).

In another paper, Branch and McGough (2010), the population shares are modelled as endogenously changing over time according to a measure of evolutionary fitness, which includes a (relatively higher) cost of forming rational expectations. It is, however, another question beyond the scope of the present paper whether this conceptual progress would also yield a significantly better econometric performance.

In similar models to ours, examples of i.i.d. shocks in a hybrid Phillips curve are Lindé (2005), Cho and Moreno (2006) or Salemi (2006), while the purely forward-looking models studied by, e.g., Lubik and Schorfheide (2004), Del Negro and Schorfheide (2004), Schorfheide (2005) permit some persistence in the shock process. These references have been chosen from the discussion in Schorfheide (2008; see p. 421, Table 3).

Determinacy means that, given a sequence of the random shocks, the model has a unique rational expectations solution that remains bounded over time.

Franke (2007) discusses the ideas underlying this variable at greater length and also compares its ‘microfoundations’ with heterogenous firms to the New-Keynesian way of deriving a Phillips curve.

Complementarily, \((1 - \gamma )\) can be interpreted as measuring the inflation persistence in the Phillips curve; see Franke (2007, p. 22).

Within a one-sector world, this would be an argument of self-fulfilling expectations. It would perhaps appear less artificial in a multi-sectoral setting, when firms in one sector learn about positive demand effects in another sector, notice that these firms increase inflation for the goods they sell, and then expect some spill-over effects from there to the other sectors of the economy, including their own.

Although the model will later be compared to the New-Keynesian model, an acronym for ‘Old-Keynesian’ might be in dispute as a matter of good or bad taste.

We also know of no attempts to specify \(\phi _b\) as an endogenous, time-varying coefficient.

Appendix A3 in Franke (2012b) gives the data source from which output and the price deflators have been obtained. http://www.gwif.vwl.uni-kiel.de/en/working-papers is a URL from which our gap variables can be directly downloaded.

The Hodrick–Prescott trend itself is computed over a longer period, to avoid end-of-period effects.

Some explorations gave us no clear indication that other values of \(\alpha _b\) could distinctly improve the model’s goodness-of-fit. However, even if they did, we should give a higher priority to a reasonable order of magnitude for \(\alpha _b\).

To be more precise, there is a unique one-dimensional manifold p in the three-dimensional space towards which all (non-degenerate) trajectories converge in the sense that they move on p in the limit, although the limit motion itself may not be strictly periodic but only quasi-periodic.

Strictly speaking, the notation \(R_N(x_t) \) is slightly incorrect, but a correct one such as \(R(\{x_t\}_{t=1}^N)\) would look a bit cumbersome.

An anonymous referee has pointed out that, interestingly, this phenomenon is also often found in (calibrated or estimated) agent-based financial market models.

Apart from this, it is worth noting that the “aggregate” noise level \(\sigma _i + \sigma _y + \sigma _\pi \) in the economy is similar across the Scenarios 2b, 3a, 3b; only the distribution across the three random sources varies.

In order not to change or extend the numbering in the superscript of J, \(J^{(79)}\) may be identified with \(J^{(78)}\) for the New-Keynesian model.

They origin with an identification problem, which we do not discuss here. For completeness, the estimates of the other parameters in NK-a and NK-b are reported in the appendix to this paper. Incidentally, in NK-b the dynamic IS equation becomes more backward-looking than in NK-a, while the Phillips curve becomes (much) more forward-looking.

It is well-known that, under the null hypothesis that the model is true, the minimized value of the loss function represents a statistic that is asymptotically chi-square distributed—provided, it has to be added, that the weighting matrix entering the loss function is optimal (Lee and Ingram 1991, p. 204). This standard J test for overidentifying restrictions is not applicable here since the latter supposition is not satisfied.

As concerns the notation when comparing \(J^{(79)}\) for SD-2a and NK-a, footnote 36 may be taken into account for the latter. The complete parameter estimates of NK-a as well as NK-b are reported in the appendix.

To make sure, we repeat that the same random seed has then been employed for the previous estimations in Table 3.

Allen J, Gregory AW, Shimotsu K (2011) Empirical likelihood block bootstrapping. J Econom 161:110–121CrossRef

Anufriev M, Assenza T, Hommes CH, Massaro D (2013) Interest rate rules with heterogeneous expectations. Macroecon Dyn 17:1574–1604CrossRef

Ascari G, Ropele T (2007) Optimal monetary policy under low trend inflation. J Monet Econ 54:2568–2583CrossRef

Bakhshi H, Burriel-Llombart P, Khan H, Rudolf B (2003) Endogenous price stickiness, trend inflation, and the New Keynesian Phillips curve. Working paper, Bank of England and Swiss National Bank

Bernanke B, Mihov I (1998) Measuring monetary policy. Q J Econ 113:869–902CrossRef

Branch WA, McGough B (2009) A New Keynesian model with heterogeneous expectations. J Econ Dyn Control 33:1036–1051CrossRef

Branch WA, McGough B (2010) Dynamic predictor selection in a New Keynesian model with heterogeneous expectations. J Econ Dyn Control 34:1492–1508CrossRef

Cho S, Moreno A (2006) A small-sample study of the New Keynesian macro model. J Money Credit Bank 39:471–507

Christiano LJ, Eichenbaum M, Evans CL (2005) Nominal rigidities and the dynamic effects of a shock to monetary policy. J Polit Econ 113:1–45CrossRef

Cogley T, Primiceri GE, Sargent TJ (2010) Inflation-gap persistence in the US. Am Econ J: Macroecon 2(1):43–69

Cogley T, Sbordone A (2008) Trend inflation, indexation, and inflation persistence in the New Keynesian Phillips curve. Am Econ Rev 98:2101–2126CrossRef

Corona A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the ‘simulated annealing’ algorithm. ACM Trans Math Softw 13:262–280CrossRef

De Grauwe P (2010) Animal spirits and monetary policy. Econ Theory 47:423–457CrossRef

Del Negro M, Schorfheide F (2004) Priors from general equilibrium models for VARS. Int Econ Rev 45:643–673CrossRef

Fève P, Matheron J, Sahuc J-G (2009) Minimum distance estimation and testing of DSGE models from structural VARs. Banque de France, Working paper 245

Franke R (2007) A sophisticatedly simple alternative to the New-Keynesian Phillips curve. In: Aasada T, Ishikawa T (eds) Time and space in economics. Springer, Berlin, pp 3–28CrossRef

Franke R (2008) Microfounded animal spirits and Goodwinian income distribution dynamics. In: Flaschel P, Landesmann M (eds) Effective demand, income distribution and growth: research in memory of the work of Richard M. Goodwin. Routledge, London, pp 372–398

Franke R (2011) How much backward-looking is the New-Keynesian three-equations model? evidence from moment matching estimations. Working paper, University of Kiel. (http://www.gwif.vwl.uni-kiel.de/en/working-papers)

Franke R (2012a) Microfounded animal spirits in the new macroeconomic consensus. Stud Nonlin Dyn Econom 16:4, Article 4

Franke R (2012b) Competitive moment matching of a New-Keynesian and an Old-Keynesian model: extended version. Working paper, University of Kiel. (http://www.gwif.vwl.uni-kiel.de/en/working-papers)

Franke R (2014) Aggregate sentiment dynamics: a canonical modelling approach and its pleasant nonlinearities. Struct Change Econ Dyn 31:64–72CrossRef

Franke R, Jang T-S, Sacht S (2015) Moment matching versus Bayesian estimation: backward-looking behaviour in the New-Keynesian three-equations model. N Am J Econ Finance 31:126–154CrossRef

Fuhrer J (2006) Intrinsic and inherited inflation persistence. Int J Central Bank 2(3):49–86

Galí J (2008) Monetary policy, inflation, and the business cycle. Princeton University Press, Princeton

Galí J, Gertler M (1999) Inflation dynamics: a structural econometric analysis. J Monet Econ 44:195–222CrossRef

Goffe WL (1996) SIMANN: a global optimization algorithm using simulated annealing. Stud Nonlinear Dyn Econom 1(3):169–176

Goffe WL, Ferrier GD, Rogers J (1994) Global optimization of statistical functions with simulated annealing. J Econom 60:65–99CrossRef

Hall P, Horowitz JL (1996) Bootstrap critical values for tests based on generalized-method-of-moments estimators. Econometrica 64:891–916CrossRef

Hohnisch M, Westerhoff F (2008) Business cycle synchronization in a simple Keynesian macro model with socially-transmitted economic sentiment and international sentiment spill-over. Struct Change Econ Dyn 19:249–259CrossRef

Ireland PN (2007) Changes in the Federal Reserve’s inflation target: causes and consequences. J Money Credit Bank 39:1851–1882CrossRef

Karamé F, Patureau L, Sopraseuth T (2008) Limited participation and exchange rate dynamics: does theory meet the data? J Econ Dyn Control 32:1041–1087CrossRef

Lansing KJ (2002) Real-time estimation of trend output and the illusion of interest rate smoothing. Federal Reserve Bank of San Francisco. Econ Rev, pp 17–34

Lee B-S, Ingram BF (1991) Simulation estimation of time series models. J Econom 47:197–205CrossRef

Lindé J (2005) Estimating New-Keynesian Phillips curves: a full information maximum likelihood approach. J Monet Econ 52:1135–1149CrossRef

Lines M, Westerhoff F (2010) Inflation expectations and macroeconomic dynamics: the case of rational versus extrapolative expectations. J Econ Dyn Control 34:246–257CrossRef

Lubik T, Schorfheide F (2004) Testing for indeterminacy: an application to U.S. monetary policy. Am Econ Rev 94:190–217CrossRef

Mattesini F, Nisticò S (2010) Trend growth and optimal monetary policy. J Macroecon 32:797–815CrossRef

Newey WK, McFadden D (1994) Large sample estimation and hypothesis testing. In: Engle R, McFadden D (eds) Handbook of econometrics, vol 4. North Holland, Amsterdam, pp 2113–2245

Press WH et al (1986) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge

Rudd J, Whelan K (2005) Modelling inflation dynamics: a critical review of recent research. Federal Reserve Board, Washington, Finance and Economics Discussion Series, pp 2005–2066

Rudd J, Whelan K (2007) Modeling inflation dynamics: a critical review of recent research. J Money Credit Bank 39(1):155–170CrossRef

Rudebusch GD (2002) Term structure evidence on interest rate smoothing and monetary policy inertia. J Monet Econ 49:1161–1187CrossRef

Sahuc J-G (2006) Partial indexation, trend inflation, and the hybrid Phillips curve. Econ Lett 90:42–50CrossRef

Salemi MK (2006) Econometric policy evaluation and inverse control. J Money Credit Bank 38:1737–1764CrossRef

Schorfheide F (2005) Learning and monetary policy shifts. Rev Econ Dyn 8:392–419CrossRef

Schorfheide F (2008) DSGE model-based estimation of the New Keynesian Phillips curve. FRB Richmond Econ Q 94:397–433

Smets F, Wouters R (2003) An estimated dynamic stochastic general equilibrium model of the euro area. J Eur Econ Assoc 1:1123–1175CrossRef

Weidlich W, Haag G (1983) Concepts and models of a quantitative sociology: the dynamics of interacting populations. Springer, BerlinCrossRef

Westerhoff F, Hohnisch M (2007) A note on interactions-driven business cycles. J Econ Interact Coord 2:85–91CrossRef

Title: Competitive moment matching of a New-Keynesian and an Old-Keynesian model
Author: Reiner Franke
Publication date: 28-10-2016
Publisher: Springer Berlin Heidelberg
Published in: Journal of Economic Interaction and Coordination / Issue 2/2018
Print ISSN: 1860-711X
Electronic ISSN: 1860-7128
DOI: https://doi.org/10.1007/s11403-016-0181-0

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