Asymmetric Quantile Persistence and Predictability: the Case of US Inflation
| Author | Sebastiano Manzan,Dawit Zerom |
| Published date | 01 April 2015 |
| Date | 01 April 2015 |
| DOI | http://doi.org/10.1111/obes.12065 |
297
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 0305–9049
doi: 10.1111/obes.12065
Asymmetric Quantile Persistence and Predictability:
the Case of US Inflation*
Sebastiano Manzan† and Dawit Zerom‡
†Bert Wasserman Department of Economics and Finance, Baruch College, CUNY (e-mail:
sebastiano.manzan@baruch.cuny.edu)
‡California State University-Fullerton (e-mail: dzerom@fullerton.edu),
Abstract
This article investigates the evidence of time-variationand asymmetr y in the persistence of
US inflation. We compare the out-of-sample performance of different forecasting models
and find that quantile forecasts from an Auto-Regressive(AR) model with level-dependent
volatility are at least as accurate as the forecasts of the Quantile Auto-Regressivemodel, in
particular for the core inflation measures. Our results indicate that the persistence of core
inflation has been relatively constant and high, but it declined for the headline inflation
measures. We also find that the asymmetric persistence of inflation shocks can be mostly
attributed to the positive relation between inflation level and its volatility.
I. Introduction
There is a vast literature that investigates the, possibly changing, time series persistence
of inflation with unsettled conclusions. Fuhrer (2010) is a recent overview that discusses
the empirical and theoretical aspects of inflation persistence. On the empirical side, Fuhrer
suggests that the evidence seems to point to the conclusion that US inflation persistence
has declined starting from the second half of the 1980s, in particular when considering
the Consumer Price Index (CPI) and the Personal Consumption Expenditure (PCE) price
index, although there is less convincingevidence when analyzing the GDP deflator and core
measures of inflation. A standard approach to evaluate the persistence of inflation are unit
root tests that typically conclude that inflation is non-stationarity when using samples up to
1984, but stationary when only the post-1984 period is considered. The decline in inflation
persistence after the mid-1980s has been established also by Cogley and Sargent (2002)
using a Bayesian VAR model with time-varying parameters. They show that persistence
was high during the 1970s and the first half of the 1980s and low in the 1960s and since
the mid-1980s, which also suggests the existence of a relationship between the persistence
and the level of inflation. On the other hand, Stock (2002) and Pivetta and Reis (2007)
*Wewould like to thank the Editor and two referees for many insightful comments. Financial support by the PSC-
CUNY Research Award Program and the Bert W. Wassermanfund is g ratefullyacknowledged. The usual disclaimers
apply.
JEL Classification numbers: C22, C53, E31, E52.
298 Bulletin
argue that inflation persistence has been mostly high and constant overtime and conjecture
that findings of its decline might be the spurious result of neglecting to account for the
fall in volatility that occurred after the mid-1980s. In addition, Tsong and Lee (2011) and
Tillmann and Wolters (2012) apply the Quantile Auto-Regressive (QAR) model proposed
by Koenker and Xiao (2004, 2006) to US and international inflation rates at the quarterly
frequency.They interpret the evidence of asymmetric persistence as suggesting that positive
shocks (high conditional quantiles) to inflation have a permanent effect on inflation while
negative ones (low conditional quantiles) have a quick mean-reverting effect. They also
find that their results are, to a large extent, robust to considering breaks in the series which
might spuriously lead to the conclusion that persistence varies over time.
In this article, we aim at re-examining the evidence on US inflation persistence, in
particular its variation over time and the notion that it might be asymmetric across the in-
flation distribution. A possible explanation for the contradictory results in the literature is
that inflation persistence and volatility seem to be positively related to the level of inflation
so that misspecification in the dynamics of one component leads to the conclusion of time
variation in the other component. In order to distinguish between these alternative expla-
nations, we perform an out-of-sample test of the predictive accuracy of a semi-parametric
specification, the QAR model, to that of an Auto-Regressive (AR) time series model with
constant persistence and conditional standard deviation of the errors depending on the level
of inflation (see Evans, 1991 and Brunner and Hess, 1996, among others). This approach
can be interpreted as an out-of-sample specification test in which the performance of a
parametric model is compared to that of a non-parametric one, with the performance being
measured by their forecast accuracy. In particular, we compare forecasts of quantiles, rather
than the conditional mean, given our interest in evaluatingthe persistence of inflation along
its distribution, and in explaining its determinants. We thus interpret findings of equal or
higher accuracy of the parametric forecasts (relative to the QAR forecasts) as supporting
the heteroskedastic AR model for inflation dynamics. On the other hand, if the parametric
forecasts are less accurate compared to the QAR ones, we conclude that the former is
inadequate, either because of misspecification of the volatility equation or because per-
sistence might be time-varying and/or asymmetric. In addition, we also consider a QAR
specification in which we impose a unit root at all quantiles and we refer to this model
as Quantile Unit Root (QUR). Comparing the accuracy of the QUR quantile forecasts to
those of the QAR and heteroskedastic AR models provides an evaluation of the loss of
(out-of-sample) predictability that derives from assuming non-stationarity at specific parts
of the inflation distribution.
We forecast core and headline CPI and PCE inflation at the monthly frequency from
January 1985 until June 2011. The evidence from the out-of-sample comparison indicates
that the quantile forecasts of the heteroskedastic AR model are equally or more accurate
relativeto those from the QAR which confirms its validity as a model for inflation dynamics.
The rolling estimates of inflation persistence in the heteroskedastic AR model are found
to be fairly stable around 0.9 in the out-of-sample period for core CPI and PCE, which
agrees with the findings of Stock (2002) and Pivetta and Reis (2007) that accounting for
the volatility of inflation leads to persistence estimates that are high and relativelyconstant.
However, for the headline measures we find that inflation persistence experiences a decline
to 0.2–0.3 in the mid-2000s which can be attributed to the effect of excluding the high-
©2014 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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