Local/import – and foreign currency prices: inflation, uncertainty and pass through endogeneity

Helmut Herwartz; Jan Roestel

doi:10.1515/snde-2016-0092

Article

Local/import – and foreign currency prices: inflation, uncertainty and pass through endogeneity

Helmut Herwartz and Jan Roestel

Published/Copyright: April 3, 2018

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From the journal Studies in Nonlinear Dynamics & Econometrics Volume 22 Issue 3

Abstract

We investigate first and second order moment interactions among import prices (IPs), local currency prices (LCPs) and producer currency prices (PCPs) for 20 (mostly) developed economies and a time period of 3 decades. We test various hypotheses on both linear and non-linear effects put forth in the literature on the endogeneity of exchange rate pass through to monetary policy. It turns out that PCP shocks give rise to IP uncertainty in a sizeable manner, while the further propagation of IP uncertainty to LCP inflation uncertainty is moderate. Moreover, LCP inflation uncertainty increases the uncertainty of IP inflation (measured in local currency). In general, both inflation and its uncertainty are diagnosed as core determinants of pass through variation. Thus, a lack of monetary credibility could serve as a catalyst for the import of foreign price pressures and uncertainty to local prices.

Keywords: Endogenous currency of price setting; exchange rate pass through; inflation uncertainty; nominal rigidities; multivariate GARCH

JEL Classification: C3; F4; E5

Funding source: Deutsche Forschungsgemeinschaft

Award Identifier / Grant number: HE 2188/3-3

Funding statement: Financial support from the Deutsche Forschungsgemeinschaft (HE 2188/3-3) is gratefully acknowledged.

A Implementation details

Estimation

For each country, we estimate the model in (1)–(4) by means of a multi step procedure. As a starting point, equations (1) to (3) are estimated without interaction terms by means of OLS and residuals ê_t are obtained. To have an initial guess for the interaction terms in (1), conditional variances are computed according to GARCH(1,1) type processes with predetermined parameter values ht∙=(1−α−β)σ^e∙2+αe^t−1∙2+βht−1∙, where • = {ip, lc}. For news response and persistence, we choose α = 0.1 and β = 0.5. Then, including interaction terms, equations (1)–(3) are estimated by means of OLS. With this initialization of parameters governing first order dynamics, we estimate a diagonal BEKK model by means of Quasi Maximum Likelihood. Then, for given diagonal BEKK parameters, we optimize the log likelihood function with respect to the first order parameters, while using the diagonal BEKK implied variances as explanatory variables in equation (1). Starting with the parameters obtained from the previous two steps, we optimize the log likelihood function with respect to VAR and diagonal BEKK parameters jointly. Taking these VAR residuals as given, we estimate the (restricted) full BEKK parameters, using the diagonal BEKK parameters from the previous step as starting values. Then, keeping BEKK parameters constant and using the associated variances for the interaction terms in (1), first order parameters are estimated. Finally, the log likelihood is maximized for VAR and BEKK parameters jointly. For the optimization of the log likelihood function, we use the gradient based fminunc procedure as implemented in Matlab 10. With respect to the parameters in (1) to (4) we explicitly check for each country that the parameter estimates imply a local minimum of the log likelihood function.

Variance impulse response functions

Below, the concept of VIRFs as introduced in Hafner and Herwartz (2006) is summarized briefly. Moreover, we propose a simulation based technique to derive MG average impulse responses that does not suffer from overly simplistic assumptions on uncorrelated shocks, or arbitrariness with respect to the necessary choice of conditional covariance scenarios.

Omitting country indices for notational convenience, the restricted BEKK(1,1) model in (4) can be written in the so called vec-form,

(7)vec(Ht)=C~+A~vec(et−1et−1′)+G~ht−1,whereC~=(C⊗C)′vec(In),A~=(A⊗A)′,G~=(G⊗G)′,

and the entries in A~ and G~ are nonlinear combinations of elements in A and G, respectively. The half vec-representation of (7) reads as:

(8)vech(Ht)=C+Avech(et−1et−1′)+Gvech(Ht−1).

Presuming that et=Ht1/2ut, with ut∼iid(0,IN), the elements in vech(H_t) can be considered as functions of innovations u_t−1, and the covariance state H_t−1. VIRFs are defined as the path of volatilities that is expected to occur in the sequel of an artificial shock ut−1∗ given history H_t−1 in comparison with a hypothetical benchmark scenario. In this benchmark scenario ut−1∗ut−1∗′ is set to its unconditional expectation, i.e. ut−1∗ut−1∗′=I. In addition, all subsequent innovations ut∗,ut+1∗,… are set to zero according to their unconditional expectation. For given H_t−1 and ut−1∗, VIRFs, labeled V_t+s, are calculated recursively as:

Vt+s(ut−1∗,Ht−1)=(A+G)s+1ADN+(Ht−11/2⊗Ht−11/2)DNvech(ut−1∗ut−1∗′−IN),s=0,1,…,36,

where D_N is a duplication matrix and DN+ denotes its Moore-Penrose inverse.

For the practical implementation of V_t+s, s = 0, 1, 2, …, i.e. the selection of ut−1∗ and H_t−1, an analyst might be led by the interest in the effect of particular MGARCH innovations in particular time instances of economic crises or financial turmoil [see Hafner and Herwartz (2006) for a variety of examples]. Any such choice, however, is arbitrary and hard to justify with regard to the cross sectional perspective adopted in this study. To cope with the issue of shock selection we generate ut−1∗ from a censored multivariate Gaussian distribution by means of Monte Carlo techniques. For the interest in the effects of a positive shock in the j-th element of u_t we only consider draws from the multivariate Gaussian distribution where u_j,t−1 > 1. Hence, any vector of standardized innovations where the shock variable exceeds unity is considered as a possible shock scenario. Let {uj,t−1∗}r=1R denote a set of R draws from u_t−1 that fulfill the criterion uj,t−1∗>1. We set R = 1000 and keep {uj,t−1∗}r=1R fixed for all experiments investigating the effects of a shock in the j-th variable. From these Monte Carlo draws an average VIRF is computed as

(9)V¯t+s(Ht−1)=1R∑r=1RVt+s(uj,t−1,r∗,Ht−1).

As provided in (9), V¯t+s(Ht−1) is well immunized against the dependence of impulse responses on the considered shock, while it is still only informative for a particular covariance state H_t−1. To overcome the dependence on the initial covariance state H_t−1 we average impulse responses over time obtaining an ‘invariant’ functional response pattern

(10)V=s=1T∑t=1TV¯t+s(Ht−1),s=0,1,…,36.

By construction, the functional pattern of V=s consists of country specific estimates. Therefore, for inferential purposes we apply again MG inference as sketched in Section 3.2.

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Published Online: 2018-4-3

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https://doi.org/10.1515/snde-2016-0092

Keywords for this article

Endogenous currency of price setting; exchange rate pass through; inflation uncertainty; nominal rigidities; multivariate GARCH