Time‐Varying Relationship between Inflation and Inflation Uncertainty
| Author | Chenghan Hou |
| DOI | http://doi.org/10.1111/obes.12327 |
| Published date | 01 February 2020 |
| Date | 01 February 2020 |
83
©2019 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 82, 1 (2020) 0305–9049
doi: 10.1111/obes.12327
Time-Varying Relationship between Inflation and
Inflation Uncertainty*
Chenghan Hou†
†Center for Economics, Finance and Management Studies, Hunan University, Hunan, China
(e-mail: chenghan.hou@hotmail.com)
Abstract
This paper investigates whether the relationship betweeninflation and inflation uncertainty
has changed and whether the change in this relationship has been gradual or abrupt. We
extend the time-varying parameter with stochastic volatility in mean model (TVP-SVM) to
include a mixture innovation disturbance in the time-varying parameter process. The pro-
posed model produces more reliable estimates and allowsus to investigate the occurrence of
breaks in the gradually evolving process of the time varying coefficients.Using data of US,
Germany, Canada, New Zealand, UK, France, Italy, Spain and Australia, we find that: (i)
the relationship between inflation and inflation uncertainty substantially varies over time;
(ii) there is strong support for the existence of abrupt changes in the US inflation–inflation
uncertainty relationship; (iii) our empirical results of Canada and New Zealand show that
the correlation between inflation and inflation uncertainty has been much weaker since
early 1990s, which coincides with the timing of the implementation of inflation targeting.
I. Introduction
The vast literature on the relationship between inflation and inflation uncertainty can be
traced back to Friedman (1977). Understanding this relationship has drawn large theoret-
ical interest as it tends to have a close link to the efficiency and cost of the inflationary
monetary policy. Ball (1992) formalizes Friedman’s idea through a repeated game between
public and the monetary authority. Ball (1992) suggests that policymakers with different
reactions to high inflation who alternate power stochastically would generate future infla-
tion uncertainty, which predicts that higher inflation results in higher inflation uncertainty.
On the other hand, Cukierman and Meltzer (1986) build a game-theoretic model in which
the central bank has an incentive to create higher inflation uncertainty so as to exploit
the trade-off between inflation and unemployment for stimulating output growth. Thus,
their model predicts that higher inflation uncertainty causes higher inflation. Evans and
JEL Classification numbers: C11, C15, C53, E31.
*I am thankful to my supervisor, Joshua C.C. Chan, for helpful comments. I am also grateful to TueGorgens, John
Stachurski and Benjamin Wongfor their valuable comments.
84 Bulletin
Wachtel (1993) highlight the importance of changes in inflation regime in future inflation
uncertainty. A few historical events have indicated that there have been several substan-
tial changes in inflation process over the last few decades. For example, many developed
countries have adopted inflation targeting policies aiming to maintain price stability after
the late 1980s, which results in a decrease in inflation volatility compared with those in the
1970s and the early 1980s. After almost a decade of low inflation volatility, the outbreak
of the Global Financial Crisis in the late 2000s brings about a large downturn in economic
activity,which in turn leads to a high inflation volatility in many economies. However, there
are few studies that provide theoretical explanations for how the changes in relationship
between inflation and inflation uncertainty in response to these changes in the inflation
process.
Empirical studies on the relationship between inflation and inflation uncertainty have
often reached different conclusions in the direction of higher inflation uncertainty causing
higher inflation. On the one hand, Holland (1995) uses survey based proxy as a measure
of inflation uncertainty and find a negative relationship between inflation and inflation
uncertainty. He suggests that policymakers who view inflation uncertainty as costly are
likely to have an incentive to control future inflation to a low level when current inflation
is high. On the other hand, Grier and Perry (1998) conducts a cross countries analysis by
using one-step ahead conditional variance from a GARCH model as a proxy for inflation
uncertainty. Their results show that a negative relationship exists in countries with more
independent central banks, whereas a positive relationship is found in countries with less
independent central banks. Subsequent research has pointed out that the dispersion of
professional economic forecast which is used as a proxyfor inflation uncer tainty byHolland
(1995) does not reflect the uncertainty of individual forecasters. Hence, this measure may
not be appropriated to be treated as a proxy for inflation uncertainty. Furthermore, using
the conditional variance estimated by GARCH as a proxy for inflation uncertainty, as in
Grier and Perry (1998), is also problematic since it does not account for the structural
instability.
Toavoid these problems, Grier and Perry (2000) adopt a GARCH in mean (GARCH-M)
model in which the time varying volatility and its impact on inflation are jointly estimated
and find no evidence that higher inflation uncertainty raises inflation rate. In contrast, Beru-
ment,Yalcin andYildirim (2009) investigate the inflation–inflation uncertainty relationship
using stochastic volatility in mean (SVM) model and find evidence supporting the view of
Cukierman and Meltzer (1986) that higher inflation uncertainty increases inflation.
As many recent studies have pointed out the widespread nature of structural instability
in many macroeconomic time series (Stock and Watson, 1996, 2007; Cogley and Sargent,
2001; Kim, Nelson and Piger, 2004), Chan (2017) extends the SVM model of Koopmanand
Hol Uspensky (2002) to allow for time-varying parameters and re-examinethe relationship
between inflation and inflation uncertainty. By allowing the coefficient associated with the
volatility in the conditional mean to be changing over time, Chan (2017) finds substantial
time-variation in this relationship using data from the US, the UK and Germany. He suggests
that models with constant coefficients are likely to average out the potential time-varying
effects which give misleading results. However, the TVP-SVM model proposed by Chan
(2017) shares the common drawback of most conventionaltime-varying parameter models
– the changes in the parameters are restricted in magnitude and do not accommodate the
©2019 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
Inflation and inflation uncertainty 85
occurrence of drastic changes immediately (Koop and Potter, 2007). Instead, a large level
shift in the parameters can only be gradually captured by a sequence of small changes after
the change-point, which may lead to bias estimates and result in unreliable inference.
The main goal of this paper is to investigate the time-varying relationship between
inflation and inflation uncertainty. To this end, we extend the TVP-SVM model of Chan
(2017) so as to allow the gradually evolving parameters to have potential drastic changes.
For this purpose, we draw on the mixture innovation approach (McCulloch and Tsay,
1993; Gerlach, Carter and Kohn, 2000; Giordani and Kohn, 2008) and focus on modelling
the time-varying coefficients associated with the volatility in the conditional mean. To
be specific, the time-varying parameters are assumed to evolve as a random walk with
a two-component Gaussian mixture innovation. Conventional mixture innovation model
usually assumes the mixture probabilities to be time-invariant. However we find that this
setting might not be appropriate in identifying in-sample breaks. This problem can be
surmounted by assuming the mixture probabilities to be time-varying. To be specific, we
impose assumption that breaks in the sample do not directly learn from each other. We
conduct a simulation study to shed light on this issue in Section 3. In our empirical study,
the sensitivity analysis also shows that the proposed model produces more reliable esti-
mates for detecting in-sample breaks. More details will be discussed in section ‘sensitivity
analysis’.
Weuse the proposed model to investigate the inflation–inflation uncertainty relationship
for the US, Germany, Canada and New Zealand. Our empirical results show that the
relationship between inflation and inflation uncertainty is substantially changing overtime,
which is consistent with the findings in Chan (2017). Another important finding is that the
inflation–inflation uncertainty relationship is unlikely to be gradually evolving over the last
few decades for the US and the Germany. We find a large downward shift, from positive to
negative, in this relationship in the US and Germany during the Global Financial Crisis in
the late 2000s. Our empirical results suggest that ignoring the potential drastic changes in
this relationship may lead to biased estimates. Lastly we find that the correlation between
inflation and inflation uncertainty has been much weaker since late 1990s for Canada and
New Zealand which coincides the timing of the implementation of inflation targeting.
The rest of the paper is organized as follows. Section II presents the new model for
investigating the inflation–inflation uncertainty relationship. Section III conducts a sim-
ulation study. Section IV discusses the posterior sampler for fitting the proposed model.
Section V first discusses the data, priors, empirical results and then conducts a sensitivity
analysis.
II. TVP-SVM with time varying mixture innovation model
In this section, we discuss the model used to investigate the relationship between inflation
and inflation uncertainty. We extend the time-varying parameter stochastic volatility in
mean model (TVP-SVM) of Chan (2017) by allowing the time varying coefficients asso-
ciated with the volatility in the conditional mean to have a Gaussian mixture innovation
(TVP-SVM-TVMI). To be specific, we consider
yt=t+teht+y
t,y
t∼N(0, eht), (1)
©2019 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
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