Intranational Price Convergence and Price Stickiness: Evidence from Denmark

AuthorChristian Heeb⊘ll, Niels Lynggård Hansen, U. Michael Bergman
Publication Date01 Oct 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
Niels Lyngg˚ard Hansen
Danmarks Nationalbank, DK-1058 Copenhagen K, Denmark
Christian Heebøll
Copenhagen Economics, DK-1411 Copenhagen, Denmark
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.
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.
The editors of The Scandinavian Journal of Economics 2017.

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