Intranational Price Convergence and Price Stickiness: Evidence from Denmark

• DOI: http://doi.org/10.1111/sjoe.12259
• Author: Christian Heeb⊘ll,Niels Lynggård Hansen,U. Michael Bergman
• Date: 01 October 2018
• Published date: 01 October 2018

Scand. J. of Economics 120(4), 1229–1259, 2018

DOI: 10.1111/sjoe.12259

Intranational Price Convergence and Price

Stickiness: Evidence from Denmark*

U. Michael Bergman

University of Copenhagen, DK-1353 Copenhagen K, Denmark

michael.bergman@econ.ku.dk

Niels Lyngg˚ard Hansen

Danmarks Nationalbank, DK-1058 Copenhagen K, Denmark

nlh@nationalbanken.dk

Christian Heebøll

Copenhagen Economics, DK-1411 Copenhagen, Denmark

chh@copenhageneconomics.com

Abstract

We showthat estimates of the half-life of deviations from the law of one price are biased when

their precision is not taken into account when aggregating data for differenttypes of goods. Using

a comprehensive dataset with monthly price data for 124 homogeneous products across regions

in Denmark overthe period 1997–2010, we f‌ind a large positive aggregation bias. On average, we

f‌ind that the half-life is 8.4 months when taking the bias into account, compared with 28.7 months

when applying thestandard method. The heterogeneity in the estimated half-life can be explained

by price stickiness, distance between regions, and whether the good is traded or non-traded.

Keywords: Aggregation bias; goods prices; law of one price; price convergence; price stickiness

JEL classif‌ication:C23; F31; F41

I. Introduction

Most economists believe in some variant of the purchasing power parity

(PPP) as an anchor of long-run real exchange rates. However, the empirical

support for this theory is not very solid (see, for example, the surveys by

Rogoff, 1996; Taylor, 2006). Real exchange rates appear to be, if not non-

stationary, then at least very persistent, and deviations from PPP disappear

very slowly with a half-life in the range of three to f‌ive years (Rogoff,

*Wethank twoanonymous referees, Heino Bohn Nielsen, and Anders Rahbek for useful comments

and suggestions. Financial support from EPRN is gratefully acknowledged. The points of view

and conclusions stated are the responsibility of the individual contributors, and do not necessarily

ref‌lect the views of Danmarks Nationalbank.

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The editors of The Scandinavian Journal of Economics 2017.

1230 Intranational price convergence and price stickiness

1996).1At the same time, this empirical observation seems inconsistent

with, on the one hand, the very large short-term volatility of real exchange

rates, and, on the other hand, recent studies of individual retail prices in

the US suggesting fast price adjustments across a wide range of goods and

services (Bils and Klenow, 2004; Klenow and Kryvtsov, 2008; Nakamura

and Steinsson, 2008) with the duration of price changes in the range of

7–11 months. Similar results also hold for Japanese (Crucini et al., 2010a)

and Danish (Hansen and Hansen, 2007) micro-data. Both Andrade and

Zachariadis (2016) and Bergin et al. (2013) use semi-annual data from the

Economists Intelligence Unit and they f‌ind that the observed persistence

in real exchange rates stems from global or aggregate shocks. The implied

half-life, conditional on idiosyncratic or local shocks, is around one year.

Hence, both from theoretical and empirical points of view, the slow price

convergence constitutes a puzzle.

In this paper, we provide new measures of the half-life of deviations

from the law of one price (LOOP). Using a comprehensive set of micro-

data collected by Statistics Denmark over the period January 1997 until

May 2010, we construct price series on 124 different types of goods

in 13 regions of Denmark. The goods are quite heterogeneous, covering

13 different categories (according to the Classif‌ication of Individual

Consumption According to Purpose, COICOP, f‌ive-digit code): food;

fruit and vegetables; confectionery and non-alcoholic beverages; alcoholic

beverages; clothing and footwear; furnishings; household equipment and

maintenance; transport; audio-visual equipment; recreation and culture;

personal services and care; jewelry, clocks and watches; and other goods

and services.

As is standard in the body of literature, we estimate the half-life of each

item for each region separately and then we aggregate over all regions (or

relative prices) to obtain a measure of the half-life for each good. However,

we suggest that this standard method, used by, for example, Gadea and

Mayoral (2009) and Imbs et al. (2005), introduces an aggregation bias

stemming from the fact that the aggregation does not take into account

the precision of the estimated half-life of each item across regions. The

standard method entails taking the average of the estimated half-life across

all relative prices for each good, implicitly assuming identical standard

errors of these estimated half-lives. We show that this aggregation bias

can be substantial if standard errors on the estimated half-lives are not

identical. This holds both when aggregating estimated half-lives for specif‌ic

goods across regions or when aggregating across goods. To take this bias

1The half-life is def‌ined as the time required for a unit shock to the real exchange rate to dissipate

by one half.

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The editors of The Scandinavian Journal of Economics 2017.