Modeling time-variation over the business cycle (1960–2017): an international perspective

Enrique Martínez-García

doi:10.1515/snde-2017-0101

Abstract

In this paper, I explore the changes in international business cycles with quarterly data for the eight largest advanced economies (US, UK, Germany, France, Italy, Spain, Japan, and Canada) since the 1960s. Using a time-varying parameter model with stochastic volatility for real GDP growth and inflation allows their dynamics to change over time, approximating nonlinearities in the data that otherwise would not be adequately accounted for with linear models [Granger, Clive W.J., Timo Teräsvirta, and Heather M. Anderson. 1991. “Modeling Nonlinearity over the Business Cycle.” In NBER book Business Cycles, Indicators and Forecasting (1993), edited by James H. Stock and Mark W. Watson, University of Chicago Press.; Granger, Clive W.J. 2008. “Non-Linear Models: Where Do We Go Next – Time Varying Parameter Models?” Studies in Nonlinear Dynamics and Econometrics 12 (3): 1–11.]. With that empirical model, I document a period of declining macro volatility since the 1980s, followed by increasing (and diverging) inflation volatility since the mid-1990s. I also find significant shifts in inflation persistence and cyclicality, as well as in macro synchronization and even forecastability. The 2008 global recession appears to have had an impact on some of this. I ground my empirical strategy on the reduced-form solution of the workhorse New Keynesian model and, motivated by theory, explore the relationship between greater trade openness (globalization) and the reported shifts in international business cycle. I show that globalization has sizeable (yet nonlinear) effects in the data consistent with the implications of the model – yet globalization’s contribution is not a foregone conclusion, depending crucially on more than the degree of openness of the international economy.

Keywords: great moderation; globalization; International Business Cycles; stochastic volatility; time-varying parameters

JEL Classification: E31; E32; F41; F44

Appendix A

Flattening of the Phillips Curve

An important part of the debate on globalization has to do with its potential effect on the pricing behavior of firms, on marginal costs, and on the degree of market competition (Sbordone, 2007; Martínez-García & Wynne, 2010; Benigno & Faia, 2016). A key empirical observation that has emerged as central to much of this debate is the perceived “flattening” of the short-run Phillips curve.^[16]Roberts (2006), among others, identified a flattening of the Phillips curve for the US starting around 1984 at the onset of the Great Moderation. Figure 10A illustrates the sort of estimates of the coefficient on the domestic output gap that can be found in this strand of the literature, for the eight major advanced economies.

Figure 10:

(A) Phillips curve estimated coefficient on domestic output gap.

Note: Median and interquartile range include US, UK, CA, FR, DE, JP, ES, and IT. The figure is based on OLS estimates obtained on a rolling-window basis using the previous 15 years of data and a conventional (closedeconomy) reduced-form Phillips curve specification with four lags on inflation and lagged domestic output gap. The domestic output gap is calculated with the one-sided Hodrick-Prescott filter on log real GDP index in units, expressed in percentages. Sources: Organization for Economic Cooperation and Development; author’s calculations.

(B) Slope of the Phillips curve on domestic output gap vs. import share (G8 median).

Note: Includes US, UK, CA, FR, DE, JP, ES, and IT. The OLS estimates for θ are obtained on a rolling-window basis using the previous 15 years of data and a conventional (closed-economy) reduced-form Phillips curve specification with four lags on inflation and lagged domestic output gap. The domestic output gap is calculated with the one-sided Hodrick-Prescott filter on log real GDP index in units, expressed in percentages. The import share is defined as the average over the estimation period of the ratio of real imports of goods and services in percentage over real GDP.

To construct Figure 10A, I use a reduced-form representation of the closed-economy Phillips curve that augments the univariate time series autoregressive specification with domestic output gap (slack), i.e. πt=∑j=14χjπt−j+θxt−1+ut where u_t is the estimation residual. The domestic output gap x_t is proxied with the one-sided Hodrick and Prescott (1997)-filtered domestic real GDP, while inflation π_t is derived as the annualized log-first differences of the GDP deflator (expressed in percentages). Figure 10A summarizes the slope coefficient θ obtained from OLS estimates of the reduced-form Phillips curve on a rolling-window basis using the previous 15 years of data.^[17]

In an increasingly more integrated world economy, domestic firms can charge more for their output when they face increases in world demand even if domestic slack remains invariant [a point extensively argued in Martínez-García and Wynne (2010, 2013)]. Therefore, globalization weakens the relationship between inflation and domestic slack. Consistent with that, the empirical evidence shown in Figure 10A indicates that over time inflation has become less responsive to fluctuations in the domestic output gap (θ has declined).^[18] The slope estimates appear to have bounced-back since the 2008 global recession – and even earlier for the US.

However, Martínez-García and Wynne (2010) and Martínez-García (2017) as well as the theory laid out in this paper also suggest that one should not expect the flattening of the New Keynesian Phillips curve to be linearly related to measures of increased openness. Interestingly, consistent with the predictions of New Keynesian theory, I find that the estimated slope on the domestic output gap tends to decline with the import share – at least until the data for the post-2008 period gets factored in (as can be seen in Figure 10B).

Inferences based on a reduced-form specification – while often used in practice – are neither very precise nor structural per se and should be taken with a grain of salt. First, data mismeasurement and misspecification problems matter when exploring the relationship between inflation and the output gap [see, e.g. Martínez-García and Wynne (2010) on the impact of filtering output, Ihrig et al. (2010) on trend inflation, Kabukçuoglu and Martínez-García (2016, 2018) on the reliability of global slack indicators, Borio, Disyatat, and Juselius (2017a) on unmodeled shifts in potential, etc.].

For example, using the Hodrick and Prescott (1997) filter on real GDP to compute the output gap – as conventionally done (including for Figure 10A and B) – implicitly imposes a local-linear trend specification on potential and assumes the output gap to be purely transitory white noise.^[19] However, those assumptions are inconsistent with the analytic reduced-form solution of the New Keynesian model derived in Section 2. Hence, estimating the flattening of the slope of the Phillips curve poses in practice a joint hypothesis testing problem since it cannot be separated from other modeling assumptions (like those imposed on the unobservable output potential).

Second, there is a body of evidence supportive of the global slack hypothesis both in reduced-form and in more structural settings whereby the relevant trade-off arises between domestic inflation and the global output gap [see, e.g. Borio and Filardo (2007), Binyamini and Razin (2007), Martínez-García and Wynne (2010), Eickmeier and Pijnenburg (2013), Bianchi and Civelli (2015), and Duncan and Martínez-García (2015, 2018) , and Kabukçuoglu and Martínez-García (2016, 2018)]. Hence, to the extent that globalization is a significant force influencing the dynamics of inflation, Phillips-curve-based specifications relying on the domestic output gap alone might be subject to omitted variable biases. Not too surprisingly, Atkeson and Ohanian (2001) and more recently Kabukçuoglu and Martínez-García (2016) and Duncan and Martínez-García (2018) show that backward-looking Phillips curve forecasts of domestic inflation based on domestic output gaps are often found to be inferior against a naïve or univariate time series forecasting benchmark across many different countries – notably during the Great Moderation period.

Third, a number of empirical studies from very early on have challenged the notion that the flattening of the Phillips curve is much related to globalization – reporting mixed results on the relationship between openness and the sensitivity of inflation to the domestic (and even global) output gap over different time periods and across countries [see, e.g. IMF (2006) and IMF (2013), Ball (2006), Pain, Koske, and Sollie (2006), Ihrig et al. (2010), and Milani (2010, 2012)]. Figure 10B illustrates this same point suggesting that the inverse comovement between the import share and the slope of the Phillips curve on domestic slack implied by theory has leveled off or even reversed since 2008.

A more structural approach is warranted because the relationship between the observed variables does not map directly into the slope of the Phillips curve. For instance, the theory laid out in Section 2 suggests a reversal in the correlation between inflation and the output gap can result from a shift towards cost-push shocks (and away from other structural shocks). To conclude, while greater openness can diminish the slope of the Phillips curve on domestic slack as predicted by theory, the nonlinear relationship found in the data is suggestive of other economic forces at play, including possibly shifts in the contribution of the different shocks and even shifts in monetary policy.

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I dedicate this work to my father, Valentín Martínez Mira, whose inspiration and unwavering support made it all possible. This document has greatly benefited from the outstanding research assistance of Valerie Grossman, from my ongoing work with María Teresa Martínez García, and from many comments/feedback provided by Nathan S. Balke, Christiane Baumeister, Claudio Borio, William A. Brock, Celso Brunetti, Menzie D. Chinn, Mario J. Crucini, Michael B. Devereux, Charles Engel, Andrew Filardo, Marc P. Giannoni, Joseph H. Haslag, Likka Korhonen, Jae Won Lee, Aaron Mehrotra, Jamel Saadaoui, Chiara Scotti, John B. Taylor, Timo Teräsvirta, Fatih Tuluk, Víctor Valcárcel, and Kenneth D. West. I would also like to thank participants at the 3^rd International Workshop on Financial Markets and Nonlinear Dynamics (2017), 2018 Spring Midwest Macro Meetings, and 93^rd Western Economic Association International annual conference (2018) for helpful suggestions. I acknowledge the support of the Federal Reserve Bank of Dallas. All remaining errors are mine alone. The views expressed in this paper are those of the author and do not necessarily reflect the views of the Federal Reserve Bank of Dallas or the Federal Reserve System.

Published Online: 2018-11-22

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