chris hajzler price level dispersion
TRANSCRIPT
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Price Level Dispersion versus Inflation RateDispersion: Evidence from Three Countries
David Fielding Christopher Hajzler James MacGee
Abstract
Aggregate inflation potentially affects both the dispersion of price levels across lo-
cations (relative price variability, RPV) and the dispersion of inflation rates (relative in-
flation variability, RIV). Some theory suggests that the RIV-inflation relationship could
differ markedly from the RPV-inflation relationship. However, most empirical studies
deal with RIV alone, and there is little evidence about how RIV-inflation patterns differ
from RPV-inflation patterns. Using price data from three countries, we show that the
patterns are very different. The effect of inflation on social welfare therefore depends on
the relative importance of RPV and RIV in the social welfare function.
JEL classification: E31
Keywords: Relative price variability, Inflation
This paper provides new evidence on the relationship between inflation and dispersion in
relative prices across locations within a country. The evidence is based on data from different
historical periods in Canada, Japan and Nigeria. We use this data to explore whether the
relationship depends on the measure of dispersion, focusing on two alternative measures.
The first measure, which is used more frequently in this large and growing literature, is the
variation across goods in the rate of price inflation; we term this measure relative inflation
Corresponding author. Address for correspondence: Department of Economics, University of Otago, PO
Box 56, Dunedin 9054, New Zealand. E-mail [email protected]; telephone +6434798653.Department of Economics, University of Otago.Department of Economics, University of Western Ontario.The authors are grateful for helpful comments and suggestions from Nicolas Groshenny, Martin Berka, and
Steffen Lippert, as well as seminar participants at the Southern Workshop in Macroeconomics (Auckland, 2012)
and the University of Otago, New Zealand.
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 2
variability(RIV). The second measure, which has received less attention in the literature, is
the variation in relative price levels; we term this measure relative price variability(RPV).1
The empirical focus on RIV was originally motivated by theories emphasising the impor-
tance of signal extraction problems (Lucas Jr,1973;Barro,1976). Using a signal extraction
model, it can be shown that positive or negative inflation shocks increase bothRIV and RPV
(Parks, 1978). However, other theories imply that the RIV-inflation relationship will be very
different from the RPV-inflation relationship. This is the case with menu cost models and
with several models of costly consumer search: for example, if there is a sudden increase
in inflation following a period of stable and and homogeneous inflation rates across loca-
tions, consumers may be motivated to search more intensely for lower prices. This can cause
relative prices to converge and relative inflation rates to diverge.
The number of empirical papers that investigate the effects of inflation on RPV is rel-
atively small. As noted by Parsley(1996), this is partly because the construction of RPV
figures requires detailed price level data for different products and locations. In the absence
of such detailed data, many authors use price index series instead, which limits the analy-
sis to measures of RIV.2
The few papers that have compared the impact of inflation on RIV
with its impact on RPV have reached seemingly different conclusions. Parsley(1996) and
Tommasi (1993), using US and Argentinean data, both find some evidence that RPV and
RIV are positively related to aggregate inflation. HoweverReinsdorf(1994), using monthly
prices for food in 9 US cities between 1980 and 1982, finds a negative average relationship
between RPV and unanticipated inflation. By contrast, the estimated RIV-inflation relation-
ship is V-shaped.3 AsReinsdorf(1994) admits, the differences between his results and those
1Many papers refer to RIV as relative price variability or relative price-change variability, but our terminol-
ogy follows that ofParsley (1996).2In other instances the choice appears to be motivated by the desire to compare the results with the existing
literature. This desire for comparability has also led many authors to focus on inter-marketprice dispersion
that is, dispersion across products in a particular location rather than intra-marketprice dispersion that is,
dispersion across locations for a particular product.3However, it is difficult to compare the findings ofTommasi (1993) andParsley(1996)with those of authors
such asReinsdorf (1994) who examine the separate effects of anticipated and unanticipated inflation.
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of previous authors might be driven by the short and atypical disinflation period that he con-
siders, and it remains to be seen whether his results hold over longer time horizons and in
different economic conditions.
The aim in this paper is to investigate the heterogeneity in the RIV and RPV results by
comparing RIV and RPV models within the same dataset, allowing for a variety of functional
forms in both cases. Our price dispersion measures are constructed from detailed, homoge-
nous product prices in different cities, as inReinsdorf(1994), and we compare the effects of
inflation (decomposed into anticipated and unanticipated components). Our data are drawn
from three country datasets spanning a range of historical and inflationary periods: (i) Canada
between 1922 and 1940, which includes a sustained deflationary period during 1931-33, fol-
lowed by a rapid recovery in prices,4 (ii) near-zero inflation in Japan between 2000 and 2006,
and (iii) moderate inflation in Nigeria between 2001 and 2006.5
Our results show that the RPV-inflation relationship differs significantly from the RIV-
inflation relationship in all three countries. More specifically, RPV in Canada and Japan is
monotonically decreasing in unanticipated inflation (there is no significant effect in Nigeria),
but in all three countries RIV is increasing in the absolute value of unanticipated inflation
(in other words, there is a V-shaped relationship). There is even more heterogeneity in the
effects of anticipated inflation. In Canada the RPV-inflation relationship is U-shaped, but
there is no significant effect of anticipated inflation on RIV. In Japan and Nigeria there is no
significant effect of inflation on RPV, but in Japan RIV is decreasing in anticipated inflation
while in Nigeria it is increasing. Many of these results are consistent with existing papers
that focus on a subset of the dispersion and inflation measures that we consider. What we are
able to show is that the heterogeneity in existing results is not simply a consequence of using
4Hickey and Jacks(2011)examine examine retail price dispersion in Canada using 10 of the 44 products
that we consider, and find that the infrequency of price adjustments is negatively related to intra-market price
dispersion.5The unweighted average inflation rate in Canada over the sample period is -0.14% with a standard deviation
of 1.1%. The average inflation rate in Japan is -0.08% with a standard deviation of 1.1%. For Nigeria, the
average inflation rate is 0.9% with a standard deviation of 3.0%.
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different samples in different countries: we find substantial heterogeneity between RPV and
RIV functionswithinindividual datasets.
Our empirical findings also inform a growing theoretical literature on price dispersion and
inflation. The monotonic negative relationship between RPV and inflation shocks, combined
with a V-shaped RIV-inflation relationship, is consistent with consumer search models in the
style ofReinganum(1979) andBenabou and Gertner(1993). The U-shaped relationship be-
tween anticipated inflation and RPV identified in our Canadian data is also consistent with
the dynamic search models ofvan Hoomissen(1988) andHead and Kumar(2005), as well
as with menu cost theories. We believe these theoretical perspectives are worthy of further
empirical research. If these mechanisms are the main drivers of the inflation-RPV relation-
ships observed, this implies that that a stable inflation rate close to zero offers welfare gains
by facilitating lower price dispersion and fewer market inefficiencies. It also suggests that the
efficiency costs associated with negative inflation shocks may be larger than those associated
with positive ones. More generally, our findings imply that if policymakers are primarily
concerned with RPV because it reflects market inefficiencies associated with price disparities
across homogenous goods (and less concerned about diverging rates of inflation, if this cor-
responds to price convergence), then understanding the RPV-inflation relationship will be at
least as important as understanding the RIV-inflation relationship. However, a comprehensive
assessment of the welfare effects of aggregate inflation depends on clarity about the relative
importance of RPV and RIV in the social welfare function.
1 Background
Our empirical strategy builds on three key insights from the theoretical and empirical lit-
erature. First, theory suggests that the effects of inflation on RPV and RIV need not be
the same, and which measure matters most will depend on the social welfare objectives of
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 5
the policymaker. Second, different theories imply a role for either anticipated inflation, or
unanticipated inflation, or both, and this suggests that one should estimate the effects of an-
ticipated and unanticipated inflation on price dispersion separately. Finally, different authors
have chosen to impose a variety of different functional forms on the data, and in some cases
these choices have been shown to have a substantial impact on the results: our empirical
strategy should not be overly restrictive with respect to functional form. We summarize the
salient features of this literature that inform our empirical approach.
We begin by defining more precisely the two measures of dispersion that we study. (This
paper focuses on measures of intra-market price dispersion, although the models described in
this paper could also be applied to inter-market price dispersion. Some notation will clarify
the distinction.)Intra-marketRPV is measured as the coefficient of variation across locations
in the price level of productiin locationj in periodt, which we denotepijt:
vit=
1
N
j
pijt
pit1
2
(1)
Here, pit is the regional or national average price. Inter-marketRPV is defined in a similar
way, by reassigning the subscripts i to products and the subscriptsj to locations.6 Denoting
the rate of change of the price of product i over periodt in location j as ijt = ln(pijt),
and average product-specific inflation as it = ln(pit), intra-market RIV is measured as
the standard deviation across locations of the rate of change of prices:
wit=
1
Nj (ijtit)2. (2)
Inter-market RIV is defined in a similar way, by again reassigning the subscripts iandj. The
6Some studies use weighted averages reflecting the relative size of locations or the relative value of trade in
individual commodities. Our analysis will use unweighted averages.
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relationship between RIV and RPV is non-linear,7 and the two measures of dispersion will
not necessarily respond in the same way to mean aggregate inflation.
The existing literature focuses mainly on RIV instead of RPV. Parks(1978) shows that
a simple log-linear signal extraction model implies a positive effect of the absolute value
of unanticipated inflation on both RIV and RPV. Using US data for 1927-1975 to exam-
ine the impact of inflation shocks on RIV, the estimated relationship is consistent with this
prediction, a finding that has been confirmed by numerous other studies from different coun-
tries using either time-series data (van Hoomissen, 1988;Lach and Tsiddon, 1992;Tommasi,
1993;Jaramillo,1999;Aarstol, 1999; Becker and Nautz, 2009,2012) or cross-sectional data
(Debelle and Lamont, 1997;Beaulieu and Mattey,1999).8 Although this theory also predicts
a V-shaped relationship for RPV, a reliance on CPI index data (instead of detailed data on
individual product prices) precludes the extension of his empirical model to RPV.
The few papers that have compared RPV and RIV models have reached a range of dif-
ferent conclusions. (seeReinsdorf, 1994;Parsley, 1996;Tommasi, 1993;Caglayan and Fil-
iztekin, 2003). One explanation for the heterogeneity in these results is that different pro-
cesses are at work in different countries and at different times. Another explanation is that
several different processes are at work in the same data. The different theories implying a re-
lationship between price dispersion and anticipated inflation make contrasting predictions, as
do the theories implying a relationship between price dispersion and unanticipated inflation,
and the patterns in the data might result from a combination of different theoretical effects.
7 More specifically, intra-market RIV for each commodity is
wit v2it+ v2it12COV (ln(pijt), ln(pijt1)).8Most empirical papers (includingParks(1978)) measure RIV as the variation in rates of inflation across
fairly broad commodity or industry groups. This is consistent with theories that emphasize the distortions caused
by shifts in relative prices across different goods when suppliers face different demand and/or supply elastici-
ties (seeHercowitz,1981;Cukierman, 1983). However, menu cost and consumer search theories suggest that
relative price changes across supplierswithinindustries are also important. Domberger(1987),van Hoomissen
(1988),Lach and Tsiddon(1992),Tommasi(1993)andParsley (1996) explore this issue using commodity-level
RIV measures for individual stores or locations.
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For example,Danziger(1987) shows that menu cost models in the style ofRotemberg(1983)
imply a U- or V-shaped relationship between anticipated inflation and RPV, but an RIV func-
tion that could be increasing, decreasing, or V-shaped depending on the inflation rate. These
predictions contrast with those of the dynamic models of consumer search proposed byvan
Hoomissen(1988) andHead and Kumar(2005), which imply that higher anticipated infla-
tion or deflation will increase both RPV and RIV.9 Among theories that predict a relationship
between price dispersion and inflation shocks,Fielding and Hajzler(2013) show that in con-
sumer search models such as Reinganum (1979) and Benabou and Gertner (1993), where
buyers search sequentially for costly price quotes from heterogenous sellers, RPV is mono-
tonically decreasing in unanticipated inflation but RIV can be a U- or V-shaped function of
unanticipated inflation, if sellers relative cost differences are persistent. These predictions
are at odds with those of signal-extraction models. The Reinganum-type search cost model
would explain the differences thatReinsdorf(1994) finds between the RIV and RPV func-
tions for unanticipated inflation, and if the effect on RPV and RIV of anticipated inflation (via
menu cost or van Hoomissen-type search cost effects) differs from that of unanticipated infla-
tion (via Reinganum-type search cost effects), it is not surprising that papers using aggregate
inflation (Parsley,1996;Tommasi, 1993) find effects that are at odds with those from papers
that decompose inflation into its anticipated and unanticipated components (Caglayan and
Filiztekin,2003). Investigating the sources of heterogeneity in the RIV and RPV results re-
quires a comparison of RIV and RPV models within the same data set, allowing for a variety
of functional forms and distinguishing between anticipated and unanticipated inflation.
Our paper builds on the work of Reinsdorf(1994) and others by adopting a modeling
9In Head and Kumar (2005), the relationship between RPV and inflation is driven by the tradeoff between the
marginal benefits of additional search due to a wider range of posted prices (primarily through a rise in prices at
the upper end of the distribution), which lowers RPV, and an increase in the opportunity cost of holding money,
which increases monopoly power and price dispersion. At higher inflation rates the latter effect dominates.
Invan Hoomissens (1988) inflation erodes the informational value of obtaining additional price quotes due
to the asynchronous price adjustments of firms, provided this inflation is persistent, resulting in higher price
dispersion.
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framework that allows for different possible functional forms. As in Reinsdorf(1994) and
Caglayan, Filiztekin, and Rauh(2008) for RPV, andLach and Tsiddon(1992),Fielding and
Mizen (2008) and Becker and Nautz (2012) for RIV, we report the effects of anticipated
and unanticipated inflation separately. Previous papers have employed a variety of different
functional forms,10 and we are mindful of the theories which suggest that some functional
form restrictions, including the assumption of symmetry between the effects of positive and
negative inflation, may bias parameter estimates. For example,Jaramillo(1999) shows that
relaxing theParks(1978) assumption of linear demand and supply curves results in a break-
down of the symmetric relationship between RIV and unanticipated inflation, andBomberger
and Makinen(1993) argue that differences in the extent of downward price stickiness across
producers results in negative inflation shocks having a more pronounced effect on RIV than
do positive shocks. Similarly,Choi and Kim(2010) argue that imposing a symmetric V-shape
function will be misleading if the true function is U-shaped with a (variable) turning point
close to the expected inflation rate. Becker and Nautz(2009,2012) also emphasize that the
search model ofHead and Kumar(2005) predicts an asymmetric relationship between aver-
age inflation and price dispersion. Our empirical model addresses these concerns by allowing
for asymmetric effects of positive and negative inflation shocks and of positive and negative
anticipated inflation. The next section describes our modeling strategy in more detail.
2 The Econometric Model
Our model is designed to identify the form of the relationship between intra-market RPV
(or RIV) and anticipated and unanticipated inflation, using the monthly data described in
the next section. The two alternative dependent variables will be the deseasonalized values
10Examples include models that are quadratic in both anticipated and unanticipated inflation ( Parks, 1978;
Aarstol, 1999; Becker and Nautz, 2009), models that are linear in both anticipated and unanticipated infla-
tion(Parsley,1996), and models that are a mixture of the two approaches ( Lach and Tsiddon, 1992).
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ofvit as defined in equation (1) and wit as defined in equation (2); these are designated
vDit andwDit respectively. Similarly, deseasonalized monthly inflation for each commodity is
designatedDit . This inflation rate is decomposed into an anticipated component (Ait ) and an
unanticipated component (Uit ), as in papers such asFielding and Mizen(2008) andBecker
and Nautz(2009). The decomposition is based on an ARCH model of aggregate inflation:
Dit =Ait +
Uit (3)
Ait =0i+1iDit1+2i
Dit2+3it (4)
Uit N
0, h2it
(5)
h2it= 0i+1i
Uit12
. (6)
Here,h2it is the conditional variance of the inflation forecast, capturing inflation uncertainty.
Note that theandparameters are specific to each itemi; in other words, the dynamics of
inflation are allowed to vary from one item to another.
Then we fit a number of alternative RPV regression equations, each having the following
general form:
ln(vDit ) =v0i +
v1i ln(v
Dit1) +
v2i
UPit +
v3i
UNit +
v4i t +
vi
Ait
+ vi (hit) + uvit (7)
ln(wDit ) =w0i+
w1i ln(w
Dit1) +
w2i
UPit +
w3i
UNit +
w4i t +
wi
Ait
+ wi (hit) + uwit (8)
Here, theuit terms are regression residuals, thes are fixed parameters estimated separately
for each commodity, the()and ()terms stand for commodity-specific non-linear func-
tions described below, UPit = max
0, Uit
, and UNit = min
0, Uit
. The inclusion of
these two unanticipated inflation terms in the regression equations allows RPV or RIV to be
a monotonic function of unanticipated inflation (as in some theoretical search models) or a
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non-monotonic one (as in theoretical signal-extraction models). However, if the function is
non-monotonic, then the turning point is constrained to be equal to zero (as in theoretical
signal-extraction models).
Different theories suggest a wide range of functional forms for the relationship between
RPV and anticipated inflation, and this range is reflected in the variety of functional forms
in existing empirical studies: the relationship can be U-shaped or V-shaped, and the turning
point is not necessarily at A = 0. For this reason, we fit alternative versions of equations
(7)-(8) with different parameterizations of the -function. The first of these is a quadratic
function:
xi =x5i
Ait +
x6i
Ait2 , x {v, w} (9)
We will compare this quadratic parameterization with a piecewise-linear parameterization
that has been used in some other papers:
xi =x5i
APit +
x6i
ANit , x {v, w} (10)
Here,APit = max
0, Ait
andNit = min
0, , Ait
, and equation (10) allows for a V-shaped
curve with a turning point at zero. In AppendixA, we also explore the possibility of fitting
a non-parametric-function. Finally, we allow for the possibility that RPV and RIV depend
either on the standard deviation of the inflation forecast (with xi =x7i hit)or on the variance
(withxi =x7ih
2
it).
3 The Data
The model in Section2will be applied to three different datasets: one from Canada, one from
Japan and one from Nigeria. In this section we describe the construction of the RPV, RIV
and inflation variables in each dataset, and present some descriptive statistics.
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3.1 Canada
FollowingHajzler and MacGee(2012), our data are taken from monthly issues of the Canada
Labour Gazette, which are available for the period November 1922 November 1940. This
publication lists the monthly prices of a variety of grocery items in a number of Canadian
cities. These prices are averages over a number of stores in each city, reported in tenths of
cents. Not all prices are available for all cities, but the prices of 42 items are reported for
69 cities over the whole period with just a few missing observations; it is these prices that
form our data set.11 The cities and grocery items are listed in AppendixB. For each of the
42 items, we construct the variablesvit,wit and it according to the above definitions. The
corresponding deseasonalized seriesvDit ,wDit and
Dit are constructed from regressions ofvit,
witand iton a set of dummy variables for each month (February December).
3.2 Japan
The Japanese price series are taken from the dataset published by the Center for International
Price Research12 and documented byCrucini, Shintani, and Tsuruga(2010). This monthly
dataset spans the period January 2000 December 2006; the prices of 146 household grocery
items and 163 other household goods are reported for 70 cities over this period. These prices
are averages over a number of stores in each city, reported in yen. The cities and commodities
are listed in AppendixB.For each of the 309 commodities, we construct the variables vit,
wit and it in the same way as for Canada, and then deseaonalize each series using the same
method.
11
Newfoundland did not become part of Canada until 1949, so there are no Newfoundland cities in the dataset.
12These data are available at: www.vanderbilt.edu/econ/cipr/japan.html
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3.3 Nigeria
The Nigerian price series are taken from the dataset published by the Nigerian National
Bureau of Statistics (www.nigerianstat.gov.ng) and documented byFielding (2010). This
monthly dataset spans the period January 2001 December 2006; the prices of 22 house-
hold grocery items and 16 other household goods and services are reported for each of the
36 state capitals, plus the federal capital, Abuja.13 These prices are averages over a num-
ber of stores and markets in each city, reported in kobo.14 The cities and commodities are
listed in Appendix B. For each of the 38 items, we construct the variablesvit,witand itand
deseaonalize each series using the same method as for Canada.
3.4 Descriptive statistics
Our three datasets are drawn from three very different economies pre-war Canada, mod-
ern Japan, and modern Nigeria and encompass different ranges of consumer goods. The
Japanese data are the most comprehensive; the Canadian and Nigerian datasets are limited
to items that would typically be available in a wide range of small local stores (Canada) or
traditional markets (Nigeria), the typical consumer not having access to large stores or su-
permarkets on a regular basis.15 Many of the items in the datasets reflect spending patterns
that reveal the cultural idiosyncrasies of the society concerned: for example, lard in pre-
war Canada, salted fish guts in Japan, and kola nuts in Nigeria. Therefore, we should not
necessarily expect the parameters in the RPV and RIV equations to be identical across the
three datasets. Nevertheless, common patterns in the parameter values across countries could
13 These 38 items are a subset of the items included in the National Bureau of Statistics dataset. Excludedfrom our sample are (i) alcoholic beverages, the prices of which are not recorded in states with a Muslim
majority population, and (ii) a range of packaged and branded food and other household items (for example, a
tin of Andrews liver salts; a packet of 20 Benson and Hedges cigarettes; a Bic biro). These items are mostly sold
only in large stores, not in traditional markets, and for many the average value ofvit is extremely low. There is
reason to suspect that the prices of some of these items are set centrally, and are not controlled by local retailers,
so it is doubtful whether the theories discussed in Section1would be applicable to them.14 100 kobo=one nairaone US cent in 2001.15 The Nigerian dataset also includes some locally provided services, including accommodation and taxis.
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reveal some of the underlying fundamentals driving dispersion.
Some of the basic characteristics of the data are presented in Table 1 and in Figures 1-9.
Figures 1-3 illustrate average price inflation across all the items in each sample. Canadas av-
erage price inflation during the interwar period looks very similar to modern Japans average
price inflation in the early 21st century, except for a deflation and subsequent inflation be-
tween 1931 and 1934, and a spike at the beginning of World War Two. Inflation volatility in
Canada is a little higher than in Japan. Average inflation in Nigeria over 2001-2006 is a per-
centage point higher than the Canadian and Japanese averages, and exhibits higher volatility.
Figures 4-6 show that the individual inflation series Dit are not normally distributed: there is
excess kurtosis in all three countries. This means that it will be important to ascertain whether
any of our regression results is affected by outliers in the inflation distribution, and for this
reason two versions of each regression will be fitted: one with the original inflation series
(Ait ,Uit ), and another with the series trimmed at10%per month.
Means and standard deviations over time for both trimmed and untrimmed Ait and Uit
series are included in Table 1. These series are constructed by applying the GARCH model in
equations (3)-(6) to each of the D
it series in each country. It can be seen that Nigeria is again
somewhat different from the other two countries, with a standard deviation of anticipated and
unanticipated inflation (both trimmed and untrimmed) that is about twice as high as that in
Canada and Japan. The within-commodity standard deviations are also similar in Canada
and Japan, but much larger in Nigeria. This difference is not surprising: like many other
developing countries, Nigeria faces macroeconomic shocks that are larger than those typical
of developed countries in most eras.
Table 1 shows that the mean values ofln(vDit )and ln(wDit )are very similar in Canada and
Japan, and slightly lower in Nigeria. Figures 7-9 show that in all three countries the price
dispersion variables are approximately normally distributed.
Table 1 and Figures 1-9 about here
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4 Results
Equations (7)-(8) are time-series regression equations to be fitted for each commodity i. In
Canada, whereT= 217andM= 42, it is possible to fit the regression equations simultane-
ously using SUR and estimate a variance-covariance matrix for all of the parameters in all of
the commodity-specific equations. This matrix can then be used to compute standard errors
on the average values of the parameters across all of the commodities ( 1M
i
xni) using the
Delta Method. The focus of our discussion will be on these averages, which indicate the
pattern of the RPV and RIV relationships for a typical commodity. In JapanT < M, so it
is not possible to fit the regression equations simultaneously, and we assume an orthogonal
variance-covariance matrix when computing the standard errors on the average parameter
values. In NigeriaMis almost as large as T: it is possible to fit the regression equations si-
multaneously, but estimates of the individual elements of the variance-covariance matrix will
be very imprecise. Therefore, we also assume orthogonality in the Nigerian case.
Tables 2-7 report estimates of the average parameter values in equations (7)-(8). For each
country there are two tables: one for RPV (measured asln(vDit )) and one for RIV (measured
as ln(wDit )). In each table there are four sets of parameter estimates using trimmed infla-
tion and four using untrimmed inflation; these four sets of estimates correspond to the two
alternative parameterizations of the -function and the two alternative parameterizations of
the-function described in Section2. (The parameters of the -function are statistically in-
significant, except in the case of Canadian RPV, where a higher variance of inflation shocks
reduces dispersion. The results do not vary significantly across the alternative parameter-
izations of this function.) T-ratios are reported underneath the parameter estimates, with
parameters significant at the 5% level highlighted in bold. First of all we discuss the esti-
mated effects of unanticipated inflation, as captured by the parameters on UPit andUNit ; then
we discuss the estimated effects of anticipated inflation, as captured by the parameterizations
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of the-function.
4.1 The effects of unanticipated inflation
Overall, the form of the relationship between RPV / RIV and unanticipated inflation in the
three countries can be summarized as follows:
Canada Japan Nigeria
RPV equation negative monotonic negative monotonic insignificant
RIV equation V-shaped V-shaped V-shaped
The V-shaped relationship for RIV is consistent with many of the inter-market RIV studies.
The negative monotonic relationship for RPV is consistent withReinsdorf(1994), and with
Caglayan and Filiztekins finding that the imposition of a non-monotonic functional form in
the RPV equation produces an insignificant unanticipated inflation effect. It is also consistent
with search theories of the type introduced byReinganum(1979) andBenabou and Gertner
(1993), but not with signal extraction models. If policymakers care primarily about RPV
rather than RIV, then the results imply an asymmetric optimal policy response: negative
inflation shocks raise RPV with potential welfare losses, but positive shocks do not. If on the
other hand policymakers are concerned primarily with RIV, then both positive and negative
inflation shocks are costly.
In both the Canadian and Japanese RPV results (Tables 2 and 4), the curve is significantly
steeper for negative shocks than it is for positive ones. In Canada, a one percentage point
positive inflation shocks reduces RPV (as measured byvDit )by about 0.5%; a one percentage
point negative inflation shock raises RPV by about 1%. In Japan, a one percentage point
positive inflation shocks reduces RPV by about 1%; a one percentage point negative inflation
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 16
shock raises RPV by about 1.5%. The within-commodity standard deviation of unanticipated
inflation is about two percentage points in both countries, whereas the standard deviation of
RPV is about 15%, so the order of magnitude of the RPV response to a typical shock to
inflation is in the region of 10-20% of one standard deviation of the dependent variable.
In all three countries, the absolute size of the estimated effect of inflation shocks on RIV
is greater than the absolute size of the estimated effect on RPV. In Japan this difference is
particularly large: a one percentage point inflation shock (positive or negative) raises RIV by
20-30%. The within-commodity standard deviation of RIV in Japan is just under 40%, so a
typical inflation shock (about two percentage points) raises RIV by more than one standard
deviation. In Canada and Nigeria the unanticipated inflation coefficients are much smaller: a
one percentage point inflation shock raises RIV by about 3%, or if it is a negative shock in
Nigeria, by about half this much. (Using trimmed inflation, the effect of the negative shock in
Nigeria is not quite statistically significant; this is the only substantial difference between the
trimmed and untrimmed inflation results in the tables.) Comparing Canada with Japan, very
similar RPV results do not entail very similar RIV results: the Japanese RIV coefficients are
much larger, and this difference warrants further research. Nevertheless, there is a common
pattern in the results across the countries, monotonic RPV functions contrasting with V-
shaped RIV functions.
Tables 2-7 about here
4.2 The effects of anticipated inflation
The anticipated inflation effects show more cross-country heterogeneity than the unantici-
pated inflation effects. In Canada, there is a significant coefficient on the quadratic term in the
RPV equation, with a turning-point insignificantly different from zero. The standard devia-
tion of anticipated inflation is very close to one percentage point. If anticipated inflation devi-
ates by one percentage point from its sample mean (which is very close to zero) then RPV can
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 17
be expected to rise by about 2%. This significance of the quadratic term is consistent with the
piecewise-linear regression estimates, insofar as ln
vDit
/APit > 0 > ln
vDit
/ANit ;
however, the coefficient on APit is insignificantly different from zero. The non-parametric
estimates in AppendixAsuggest that the function is indeed quadratic, with ln
vDit
/APit
increasing in APit , which may explain why the coefficient on APit is very imprecisely es-
timated. In the RIV equation there are no significant coefficients on any of the anticipated
inflation terms, although the non-parametric estimates in AppendixAdo suggest a significant
and approximately quadratic relationship, a rare case of similarity between RPV results and
RIV results.
In Japan, the results are rather different. The quadratic RPV model does not produce any
significant results, but the piecewise-linear model produces a positive coefficient on APit that
is just significant at the 5% level, so there is some weak evidence that RPV is increasing
in anticipated inflation, at least when the inflation rate is greater than zero. The standard
deviation of anticipated inflation in Japan is about 0.6 percentage points. The estimated
parameter onAPit indicates that a one standard deviation rise in anticipated inflation, when
positive, can be expected to raise RPV by around 8%. By contrast, the piecewise-linear
RIV model does not produce any significant results for anticipated inflation, whereas the
quadratic model produces a significant negative effect ofAit , though without any significant
non-linearity. A one standard deviation rise in anticipated inflation can be expected to reduce
RIV by around 30%. If RPV is increasing in anticipated inflation and RIV is decreasing in
anticipated inflation, then the choice of an optimal inflation target will certainly depend on
whether RPV or RIV matters more to policymakers.
The results for Nigeria are different again. There are no significant effects of anticipated
inflation in the RPV equation, and no significant effects in the quadratic version of the RIV
equation. However, the piecewise-linear version of the RIV equation suggests a positive
monotonic function; the effect is marginally significant at the 5% level. The standard devia-
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 18
tion of trimmed anticipated inflation in Nigeria is about 1.8 percentage points, and a standard
deviation increase inAit can be expected to raise RIV by around 9%.
The heterogeneity of the anticipated inflation effects across countries does have a the-
oretical interpretation. As shown byDanziger (1987), in a menu cost model the shape of
the RPV-inflation function will depend on the range of trend inflation, and on the shape of
a typical firms cost function, which will determine the value of the menu cost parameter.
Table 1 shows that the distribution of trend inflation in Nigeria is rather different from the
distributions in the other two countries, and there is no reason to suppose that the typical firm
in pre-war Canada faced a cost curve similar to that of a typical firm in modern Japan. But
note that again there is substantial within-country heterogeneity between the RPV effects and
the RIV effects. A significant anticipated inflation effect for one does not entail a significant
effect for the other.
4.3 A note on parameter stability
A question yet to be addressed fully (either in this paper or in the literature) is whether
the effects of inflation on RPV and RIV are stable over time.16 The Japanese and Nigerian
sample periods are quite short (2000 2006 and 2001 2006 respectively), so addressing
parameter stability issues in these two cases is not feasible. However, the Canadian dataset
encompasses a much longer sample period (1922 1940), so it is possible to investigate how
stable the parameters of equations (7)-(8) are in Canada.
In order to do this, we fit the two equations to eight-year sub-samples, the first ending
in December 1930, the second in December 1931, and so on to the last sub-sample, ending16Important exceptions to this comment are Choi(2010) andCaglayan and Filiztekin (2003). Choi (2010)
studies parameter stability in the inflation RIV relationship using CPI data for the United States (1978-2007) and
for Japan (1970-2006). He finds a positive relationship during the high-inflation periods of the 1970s and 1980s
for both countries, whereas the U-shape is prevalent during recent decades of low inflation. Using disaggregated
annual price data in Turkey, Caglayan and Filiztekin (2003) find that the effect of inflation on RPV and RIV
are significant during the relatively low-inflation 1948-1975 period, but are mainly insignificantly during the
1976-1997 rising inflation period.
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in November 1940. Each of sub-sample has 96 observations except the first one (missing
January 1923) and the last one (missing December 1940), which have 95 observations. These
first and last subsamples both exclude the trough of the Great Depression (1931-1932); other
subsamples include the trough. If the Depression affects the relationship between RPV and
inflation, this should be apparent in differences in parameter estimates across subsamples.
The charts in Figure 10 illustrate the A andU parameter estimates in equation (4) the
RPV model using untrimmed inflation and quadratic forms for the- and-functions. The
sub-sample results in this figure correspond to the whole-sample results in the first column
in Table 2. The stylized facts discussed here also apply to the parameter estimates in the
other versions of equation (7), which are not shown. The charts in Figure 11 illustrate the
equivalent estimates for equation (8) the RIV model. The sub-sample results in this figure
correspond to the whole-sample results in the first column in Table 3. In both figures, the
parameter estimates are indicated by the black lines, with the 95% confidence interval in gray.
In each chart, the horizontal axis indicates the last year in the sub-sample corresponding to
the parameter estimate measured on the vertical axis.
Overall, there does seem to be some change in the relationship between RPV and antici-
pated inflation, as shown in Figure 10. The(A)2 parameter is significantly greater than zero
in subsamples ending in 1935 or earlier, but its value falls over time, and is insignificantly dif-
ferent from zero in later subsamples. By the final subsample, neither the meanA parameter
nor the mean(A)2 parameter is significantly different from zero. The relationship between
RPV and unanticipated inflation is somewhat more stable. The UP andUN parameter es-
timates are significantly below zero in all subsamples, with little change in the value of the
parameters over time. Also, Figure 11 shows that there is very little change in any of the RIV
parameter values over time. Estimates of the A parameters remain insignificantly different
from zero throughout the sample period. TheUP parameter estimate is significantly greater
than zero for the whole sample period, and theUN parameter estimate significantly less than
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 20
zero, as in Table 3.
The contrast between the stability and significance of the U parameters here with the
insignificance or instability of theA parameters reinforces the impression that there is more
potential for heterogeneity in the effects of anticipated inflation than there is in the effects of
unanticipated inflation. RPV can be expected to be lower with large positive inflation shocks,
and higher with large negative shocks; RIV can be expected to be higher with large positive
or negative shocks. The effects of trend inflation, however, seem to vary somewhat across
countries and over time.
Figures 10-11 about here
5 Summary and Conclusion
Economic theory suggests the possibility of a wide range of different relationships between
the dispersion of commodity- or region-specific relative price levels and the aggregate infla-
tion rate (either anticipated or unanticipated). The same is true of the dispersion of inflation
rates. Existing evidence has produced an equally wide range of different results, although
methodological heterogeneity limits the extent to which different sets of results can be com-
pared. One key question that needs to be answered is whether the impact of aggregate infla-
tion on price level dispersion resembles its impact on inflation rate dispersion. This matters
if, for example, monetary policymakers care about dispersion of a particular kind, or indeed
of both kinds.
In this paper, we fit the same set of models to datasets from three different countries
(Canada, Japan and Nigeria) in order to establish the form of the relationship between price
level dispersion and aggregate inflation, and measure the extent to which it resembles the
relationship between inflation rate dispersion and aggregate inflation. With regard to the
effects of unanticipated inflation, we find similar results across all three countries. Large
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 21
negative inflation shocks tend to increase both price level and inflation rate dispersion, if they
have any affect at all; large positive inflation shocks tend to increase inflation rate dispersion
but reduce price level dispersion. These effects are consistent with some of the relevant
economic theory based on search costs; they mean that a monetary policy maker who cares
about price level dispersion might respond very differently to an aggregate inflation shock
than one who cares about inflation rate dispersion.
With regard to the effects of anticipated inflation, there is evidence of substantial hetero-
geneity across the two measures of dispersion, across countries, and (when the sample period
is long enough to test this) over time. This heterogeneity is consistent with some of the rele-
vant theory based on menu costs. It means that any generalisations about the effect of trend
inflation on dispersion are likely to be highly misleading.
It follows that if we wish to assign a welfare level to each aggregate inflation rate, then
we need to know exactly how much to value reductions in price level dispersion relative to
reductions in inflation rate dispersion. Such an exercise will require the modeling of the
sources of welfare loss associated with dispersion, both insofar as an increase in dispersion
represents a loss of economic efficiency and insofar as it represents an increase in inequality
between regions. This will be the subject of future research.
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Appendices
A A Semi-parametric Model of RPV and RIV
As noted in the literature review, there is some diversity in the way that existing papers
parameterize the relationship between RPV/RIV and anticipated inflation, and the quadratic
and piecewise-linear functions in equations (9)-(10) do not encompass all of them. (For
example, these equations do not allow for a V-shaped function with a turning point at a
positive inflation rate.) However, we can also fit a semi-parametric model similar to the ones
used byFielding and Mizen(2008) andChoi(2010). In this model, the parameterizations of
the -function in equations (9)-(10) are replaced by a non-parametric estimate of the function,
using the method described byRobinson(1988) andHardle(1992, Chapter 9.1). Here, we
present estimates of a semi-parametric model applied to the Canadian data which are relevant
to the discussion in the main text; results for the other countries are available on request.
Robust estimation of a semi-parametric model requires a large number of observations,
so now the data are pooled across all grocery items, and the following regression equation is
fitted to the panel:
ln
xDit
=0+1ln
xDit1
+2UPit +3
UNit +4t+
Ait
+5hit (A1)
+1ln
xDi0
+2UPi +3
UNi +4
Ai + 5hi+uit
wherex {v, w}. The second row of the equation contains a term in the initial value of price
dispersion, and terms in the mean values of the different regressors: yi = 1T
tyit. These
terms are included to control for unobserved heterogeneity across the different grocery items.
The first step in fitting equation (A1) to the data is to create transformed regressors that
are orthogonal to Ait . This is achieved by fitting a non-parametric regression equation for
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 26
each of the regressors other thanAit :
yit= y Ait+ yit (A2)
Here, yit is a regression residual. The non-parametric functiony()is fitted in the same
way as the function()which is described below. Theand parameters in equation (A1)
are then estimated using the following regression equation:
ln
xDit
=0+1ln
xDit1
+2 UPit +3
UNit +4t+5
hit (A3)
+1ln
xD
0
+2 UP
i +3 UN
i + eta4 A
i +5hi+it.
Here,it is a regression residual. Finally, the shape of()is estimated using the following
non-parametric regression equation:
it=
Ait
+uit (A4)
There are several different kernel density estimators that could be used to estimate the shape
of(). The results reported below are based on one particular kernel density function, but re-
sults using other kernel density functions that are robust to outliers (such as the Epanechnikov
Kernel) produce similar results.17 First, we choose specific values of anticipated inflation at
which the derivative of() is to be estimated. These values are equidistant points within
the observed range ofAit . (The estimate at each point is independent of the others; enough
points are chosen for the shape of()to be clear.) At any particular point0, the derivative
0 is estimated by fitting a linear regression equation using Weighted Least Squares. The
regression equation is:
it= 0+0Ait + uit (A5)
17 The kernel density function here is used for example in Deaton and Paxson (1998). SeeFan (1992, 1993)
for a discussion of the properties of alternative kernel density functions.
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 27
and the weightsWitare as follows:
Wit=15
161 0it
4z
2
2
if |0it|
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 28
in the RPV equation for the different values of z, along with the corresponding t-ratios.
Other parameter estimates are available on request. The parameter estimates are not very
sensitive to the choice ofz; they have the same sign as the estimates reported in Table 2 of
the main text (implying a negative monotonic function), and are significantly different from
zero. Their absolute value is somewhat smaller than in Table 2, and in the case of3 this
difference is statistically significant. However, the overall conclusions regarding the effect of
unanticipated inflation on RPV are unchanged.
Next we discuss the anticipated inflation effects in the RIV function shown in Figures A5-
A7. Figure A5 shows that with z= 1% there is a smooth and approximately quadratic function
with a significantly negative slope for inflation rates below 0.25% and a significantly positive
slope for inflation rates above 0.75%. Generally, the curve for RIV with z = 1% is quite
similar to the curve for RPV with z= 1%; both indicate that the minimal level of dispersion
is reached when inflation is positive. Recall that the parametric models in Table 3 of the main
text do not produce any significant anticipated inflation effect. One possible explanation for
this difference is that the parametric results are confounded by extreme values of inflation
(whenA
it is outside the range shown in the figures) at which the quadratic relationship fails
to hold. This suspicion is reinforced by the observation that the slope of the ()function is
insignificantly different from zero at all levels of anticipated inflation when we setz2%,
as shown in Figure A7.
Table A2 reports estimated values of2 and 3 (the unanticipated inflation parameters)
in the RIV equation for the different values ofz, along with the corresponding t-ratios. The
parameter estimates are again not very sensitive to the choice ofz; they have the same sign
as the estimates reported in Table 3 of the main text (implying a V-shaped function), and
are significantly different from zero. Their absolute value is again somewhat smaller than
in Table 3, and for both parameters this difference is statistically significant. However, the
overall conclusions regarding the effect of unanticipated inflation on RPV are unchanged.
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PRICE LEVEL D ISPERSION VSINFLATIONR ATE DISPERSION 29
Appendix Tables A1-A2 and Figures A1-A7 about here.
B Lists of Cities and Items Included in the Three Samples
Appendix Tables A3-A8 about here.
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i
TABLE 1
DESCRIPTIVE STATISTICS FOR THE THREE DIFFERENT SAMPLES
Canada Japan Nigeria
meanwithin-
commodity
std. dev.
meanwithin-
commodity
std. dev.
meanwithin-
commodity
std. dev.
ln Ditv -2.210 0.187 -1.944 0.138 -2.678 0.531
ln Ditw -2.869 0.245 -3.152 0.388 -3.844 1.440
A
it -0.001 0.010 -0.001 0.006 0.007 0.018
U
it 0.000 0.025 0.000 0.026 0.000 0.061
A
it (trimmed) -0.001 0.010 -0.001 0.006 0.001 0.018
U
it (trimmed) 0.000 0.022 0.000 0.016 0.000 0.049
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ii
TABLE 2
AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditv IN CANADA
T-ratios are reported in italics.
A B C D
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
1ln Ditv 0.757 0.758 0.756 0.757 0.758 0.758 0.756 0.757110.5 111.1 110.4 110.7 110.8 110.9 110.3 110.7
A
it -0.332 -0.272 -0.324 -0.293
-0.793 -0.649 -0.776 -0.701
2)(100 A
it 2.119 2.150 2.035 2.033
2.964 3.005 2.848 2.845
AP
it 0.127 0.080 0.016 0.076
0.307 0.193 0.037 0.182
AN
it
-2.090 -2.068 -2.018 -2.052-6.852 -6.754 -6.516 -6.629
UP
it -0.505 -0.564 -0.513 -0.568 -0.513 -0.568 -0.514 -0.564-5.581 -6.003 -5.688 -6.069 -5.659 -6.035 -5.694 -6.026
UN
it
-0.922 -0.933 -0.924 -0.925 -0.911 -0.931 -0.915 -0.924-9.922 -9.901 -9.982 -9.851 -9.788 -9.874 -9.890 -9.842
100 (hit)2
-3.896 -3.681 -2.679 -2.788-4.686 -4.892 -4.686 -4.400
100 hit -0.125 -0.113 -0.083 -0.091-3.484 -3.200 -4.087 -2.418
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iii
TABLE 3
AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditw IN CANADA
T-ratios are reported in italics.
A B C D
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
1ln Ditw 0.476 0.477 0.474 0.474 0.476 0.476 0.473 0.47351.31 51.30 50.72 50.74 51.15 51.17 50.543 50.64
A
it -0.799 -0.820 -0.757 -0.830
-1.134 -1.161 -1.076 -1.178
2)(100 A
it -1.951 -2.011 -2.025 -2.105
-1.343 -1.384 -1.407 -1.463
AP
it -9.425 -9.500 -9.608 -9.562
-1.480 -1.484 -1.507 -1.492
AN
it
-0.404 -0.384 -0.351 -0.380-0.567 -0.537 -0.489 -0.528
UP
it 2.674 2.884 2.671 2.900 2.657 2.868 2.661 2.88313.07 13.71 13.08 13.81 12.97 13.62 13.02 13.74
UN
it
-2.708 -2.797 -2.721 -2.814 -2.688 -2.784 -2.697 -2.799-12.56 -12.81 -12.64 -12.90 -12.46 -12.76 -12.54 -12.84
100 (hit)2 0.771 -0.617 1.148 0.582
0.346 -0.239 0.694 0.285
100 hit 3.847 -8.449 1.629 -1.7030.385 -0.734 0.236 -0.180
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TABLE 4
AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditv IN JAPAN
T-ratios are reported in italics.
A B C D
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
1ln Ditv 0.738 0.736 0.740 0.737 0.738 0.736 0.739 0.737168.9 167.9 170.1 169.2 168.9 167.9 170.4 169.4
A
it -2.089 -1.966 -1.998 -1.875
-1.799 -1.676 -1.725 -1.602
2)(100 A
it -5.472 -5.431 -5.687 -5.652
-0.946 -0.939 -0.979 -0.973
AP
it 12.59 12.57 13.32 13.30
2.175 2.171 2.255 2.251
AN
it
2.000 1.587 1.991 1.5761.323 1.023 1.321 1.018
UP
it -1.044 -1.093 -1.044 -1.093 -1.044 -1.093 -1.043 -1.091-10.65 -10.91 -10.71 -10.96 -10.61 -10.86 -10.66 -10.90
UN
it
-1.506 -1.495 -1.514 -1.502 -1.500 -1.489 -1.511 -1.499-15.71 -15.45 -15.95 -15.67 -15.58 -15.32 -15.88 -15.60
100 (hit)2 3.715 3.714 2.959 2.967
1.309 1.308 1.098 1.101
100 hit 2.195 2.218 1.542 1.6760.482 0.487 0.342 0.371
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TABLE 5
AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditw IN JAPAN
T-ratios are reported in italics.
A B C D
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
1ln Ditw 0.198 0.196 0.201 0.200 0.198 0.197 0.201 0.20030.64 30.46 31.19 31.10 30.65 30.47 31.24 31.12
A
it -47.31 -47.34 -46.48 -46.51
-2.445 -2.447 -2.400 -2.403
2)(100 A
it -32.69 -32.75 -28.54 -28.80
-0.182 -0.182 -0.157 -0.159
AP
it 52.66 51.61 53.57 52.72
0.940 0.922 0.960 0.945
AN
it
40.79 37.75 40.55 37.681.526 1.414 1.519 1.412
UP
it 23.70 24.63 23.36 24.29 23.72 24.65 23.39 24.3216.00 16.59 15.63 16.23 15.93 16.53 15.64 16.24
UN
it
-30.33 -30.95 -30.05 -30.69 -30.36 -31.00 -30.13 -30.76-19.97 -20.35 -19.80 -20.19 -19.95 -20.34 -19.84 -20.23
100 (hit)2 69.32 69.32 80.51 80.52
1.148 1.148 1.378 1.378
100 hit 117.1 117.1 124.9 125.01.136 1.136 1.221 1.222
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TABLE 6
AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditv INNIGERIA
T-ratios are reported in italics.
A B C D
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
1ln Ditv 0.616 0.608 0.617 0.609 0.614 0.608 0.617 0.60939.12 38.28 39.30 38.23 39.10 38.28 39.22 38.25
A
it 1.148 0.357 1.298 0.369
0.417 0.453 0.472 0.469
2)(100 A
it 0.142 0.302 0.045 0.286
0.105 0.794 0.033 0.754
AP
it 1.369 -0.026 1.236 -0.144
1.283 -0.033 1.151 -0.179
AN
it
-2.094 -1.276 -2.421 -1.481-1.042 -0.732 -1.201 -0.846
UP
it 0.110 0.426 0.028 0.346 0.136 0.397 0.039 0.3420.433 1.276 0.112 1.041 0.538 1.193 0.153 1.027
UN
it
-0.034 -0.448 -0.028 -0.444 -0.049 -0.420 -0.035 -0.438-0.137 -1.298 -0.111 -1.277 -0.198 -1.218 -0.140 -1.259
100 (hit)2 2.628 -1.828 1.137 -1.371
0.786 -0.455 0.420 -0.326
100 hit 50.38 -28.71 24.15 -19.721.085 -0.507 0.626 -0.334
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TABLE 7
AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditw INNIGERIA
T-ratios are reported in italics.
A B C D
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
untrimmedinflation
trimmedinflation
1ln Ditw 0.125 0.121 0.124 0.121 0.124 0.121 0.123 0.1217.715 7.563 7.661 7.575 7.621 7.563 7.612 7.566
A
it -7.868 -5.147 -7.468 -5.084
-1.041 -0.925 -0.989 -0.914
2)(100 A
it 4.365 1.065 1.065 1.065
1.065 1.124 1.023 1.112
AP
it 5.525 4.300 5.331 4.271
1.978 1.997 1.898 1.979
AN
it
14.69 5.889 13.95 5.6502.597 1.786 2.462 1.703
UP
it 3.315 3.420 3.172 3.402 3.313 3.396 3.181 3.3855.034 4.044 4.829 4.040 5.055 4.017 4.858 4.021
UN
it
-1.416 -0.899 -1.408 -1.019 -1.412 -0.886 -1.425 -1.009-2.036 -1.035 -2.033 -1.171 -2.032 -1.020 -2.059 -1.160
100 (hit)2 2.440 10.25 4.927 10.28
0.426 1.561 1.060 1.458
100 hit 33.74 143.6 65.38 142.90.424 1.576 0.995 1.475
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APPENDIX TABLE A1
UNANTICIPATED INFLATION COEFFICIENTS IN THE SEMI-PARAMETRIC MODEL OF ln( Dit
v )
T-ratios are in italics.
z= 1.0 z= 1.5 z= 2.0
UP
it -0.361 -0.314 -0.300
-6.311 -6.035 -6.044
UN
it
-0.503 -0.601 -0.616-7.684 -10.086 -10.841
APPENDIX TABLE A2
UNANTICIPATED INFLATION COEFFICIENTS IN THE SEMI-PARAMETRIC MODEL OF ln( Dit
w )
T-ratios are in italics.
z= 1.0 z= 1.5 z= 2.0
UP
it 1.522 1.558 1.573
13.671 14.567 14.975
UN
it
-0.768 -0.852 -0.850-6.012 -6.943 -7.059
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APPENDIX TABLE A3
ITEMS INCLUDED IN THE CANADIAN DATASET
Fresh food Dr y & packaged food
Bacon (unsliced) Coffee
Bacon (sliced) Corn (canned)
Butter (creamery) Corn syrup
Butter solids Currants
Cheese Flour
Eggs (cooking) Peaches (canned)
Eggs (fresh) Peas (canned)
Finnan haddie Prunes
Ham (sliced) Raisins
Lard Rice
Leg of lamb Rolled oats
Milk Salmon (canned)
Mutton leg roast Sugar (granulated)
Onions Sugar (yellow)
Potatoes (15lb bag) TapiocaPotatoes (100lb bag) Tea
Rib roast Tomatoes (canned)
Round steak
Salt cod
Salt mess pork
Shoulder roast
Sirloin steak
Soda biscuits
Stewing beef
Veal shoulder
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APPENDIX TABLE A4
CITIES INCLUDED IN THE CANADIAN DATASET
City Province City Province
Amherst Nova Scotia Stratford OntarioHalifax Nova Scotia Sudbury Ontario
New Glasgow Nova Scotia Timmins Ontario
Sydney Nova Scotia Toronto Ontario
Truro Nova Scotia Windsor Ontario
Windsor Nova Scotia Woodstock Ontario
Charlottetown Prince Edward Island Hull Quebec
Bathurst New Brunswick Montreal Quebec
Fredericton New Brunswick Quebec Quebec
Moncton New Brunswick Saint Hyacinthe Quebec
Saint John New Brunswick Saint Johns Quebec
Belleville Ontario Sherbrooke Quebec
Brantford Ontario Sorel Quebec
Brockville Ontario Thetford Mines Quebec
Chatham Ontario Trois-Rivires Quebec
Cobalt Ontario Brandon Manitoba
Fort William Ontario Winnipeg Manitoba
Galt Ontario Moose Jaw Saskatchewan
Guelph Ontario Prince Albert Saskatchewan
Hamilton Ontario Regina Saskatchewan
Kingston Ontario Saskatoon Saskatchewan
Kitchener Ontario Calgary Alberta
London Ontario Drumheller Alberta
Niagara Falls Ontario Edmonton Alberta
North Bay Ontario Lethbridge Alberta
Orillia Ontario Medicine Hat Alberta
Oshawa Ontario Fernie British Columbia
Ottawa Ontario Nanaimo British Columbia
Owen Sound Ontario Nelson British ColumbiaPeterborough Ontario New Westminster British Columbia
Port Arthur Ontario Prince Rupert British Columbia
Saint Catharines Ontario Trail British Columbia
Saint Thomas Ontario Vancouver British Columbia
Sarnia Ontario Victoria British Columbia
Sault Sainte Marie Ontario
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APPENDIX TABLE A5
ITEMS INCLUDED IN THE JAPANESE DATASET
(i): Food for the HomeAsparagus Clams in soy sauce Furikake seasonings Oranges Sausages
Bacon Cooked curry Grapefruit Peanuts Scallops
Baked fish bars Cream puffs Green peppers Pickled cabbage Sea bream
Bananas Croquettes Gyoza Pickled plums Shiitake mushrooms
Bean curd Cucumbers Hens eggs Pickled radishes Shimeji mushrooms
Bean sprouts Cuttlefish Horse mackerel Pork cutlets Soy sauce
Bean jam buns Deep fried chicken Ice cream Pork loin Soybean paste
Bean jam cakes Devil's tongue jelly Imported beef Pork shoulder Spaghetti
Beef loin Dried bonito fillets Imported cheese Potato chips Spinach
Beef shoulder Dried horse mackerel Instant curry Powdered milk Steamed fish cakes
Biscuits Dried laver Jam Prawns Sugar
Boiled beans Dried sardines Jelly Pudding Sweet bean jelly
Boiled noodles Dried mushrooms Kasutera cakes Pumpkins Sweet potatoes
Boxed lunches Dried small sardines Kidney beans Radishes Tangle in soy sauce
Broccoli Dried tangle Kimuchi Red beans Taros
Broiled eels Dried young sardines Kiwi fruits Rice (not koshihikari) Tomatoes
Burdock Edible oil Lemons Rice (koshihikari) Tuna fish
Butter Eggplants Lettuce Rice balls Uncooked noodles
Cabbage Enokidake mushrooms Liquid seasonings Rice cakes Veg in soy sauce
Cakes Fermented soybeans Liver Rice crackers Vinegar
Candies Fish in soybean paste Lotus roots Roast ham Wakame seaweed
Canned oranges Flavor seasonings Mackerel Salad Welsh onions
Canned peaches Flounder Margarine Salmon Wheat crackers
Capelin Fresh milk (bottled) Mayonnaise Salted cod roe Wheat flour
Carrots Fresh milk (cartons) Mazegohan no moto Salted fish guts White bread
Cheese Fried bean curd Mochi rice-cakes Salted salmon White potatoes
Chicken Fried fish patties Nagaimo Sandwiches Worcester sauce
Chinese cabbage Frozen croquettes Octopus Sardines Yellowtail
Chocolate Frozen pilaf Onions Saury Yogurt
Clams
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(ii): Other I tems
Dr ink Household items Room air conditioner Mini disk player Toothbrushes
100% fruit drinks Alarm clock Rush floor covering Notebook Toothpaste
Black tea Bathtub Scrubbing brush Pants for exercise
Calpis Bed Sealed kitchen ware Pencil cases Apparel
Canned coffee Boards Sewing machine Pencils Adults' canvas shoes
Coffee beans Carpet Sheets Personal computer Baby clothes
Foaming liquors Chests of drawers Sitting table Roses Baseball cap
Green tea (Bancha) Curtains Telephone set Soccer ball Belt
Green tea (Sencha) Dining set Toilet seat Swimming suit Boy's short pants
Imported beer Dishes Towel Toy car Child's canvas shoes
Imported whisky Electric iron Vacuum cleaner TV set (CRT) Child's shoes
Imported wine Electric pot Wardrobes Child's undershirt
Instant coffee Electric rice cooker Washing machine Pharmacy items Handkerchief
Local beer Fabric softener Water purifier Chinese medicine Imported handbag
Local whisky (40%+) Facial tissue Wine glass Cold medicine Imported necktie
Local whisky (43%+) Fluorescent fittings Contact lens cleaner Imported watch
Mineral water Fluorescent lamp Sports / leisur e goods Dermal medicine Local handbag
Sake (grade A) Food wrap Baseball gloves Disposable diapers Local necktie
Sake (grade B) Fragrance Bicycle Eyewashes Local watch
Sports drinks Gas cooking table Building blocks Face cream Men's briefs
Vegetable juice Gasoline Camera Face lotion Men's business shirt
Glasses Carnations Foundation Men's shoes
Restaurant food Hot water equipment Chrysanthemums Stomach medicine Men's suit materials
Chicken & rice Imported pan Computer game Hair dye Men's umbrella
Chinese noodles Insecticide Copy paper Hair liquid Men's undershirt
Coffee Kitchen cabinet Doll Hair rinse Panty hose
Curry & rice Kitchen detergent Dry electric battery Health drinks Slips
Gyudon beef on rice Laundry detergent Film Imported shaver Suitcase
Hamburger steaks Local pan Fishing rod Lipstick Women's blue jeans
Hamburgers Microwave oven Gardening soil Local shavers Women's sandals
Hand rolled sushi Moth balls Golf clubs Plasters Women's shoes
Japanese noodles Quilt Imported tennis racket Sanitary napkins Women's socks
Shrimp & rice Refrigerator Local tennis racket Shampoo Women's zori sandals
Sushi rolled in laver Rice bowl Marking pens Spectacles Woollen yarn
Rolled toilet paper Mini disk media Toilet soap
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APPENDIX TABLE A6
CITIES INCLUDED IN THE JAPANESE DATASET
Akita Kobe Otsu
Aomori Kochi Saga
Asahikawa Kofu Saitama
Atsugi Koriyama Sakura
Chiba Kumamoto Sapporo
Fuchu Kyoto Sasebo
Fukui Maebashi Sendai
Fukuoka Matsue Shizuoka
Fukushima Matsumoto Tachikawa
Fukuyama Matsuyama Takamatsu
Gifu Mito Tokorozawa
Hakodate Miyazaki Tokushima
Hamamatsu Morioka Tokyo
Higashi-Osaka Nagano Tottori
Himeji Nagaoka Toyama
Hirakata Nagasaki Tsu
Hiroshima Nagoya Ube
Itami Naha Utsunomiya
Kagoshima Nara Wakayama
Kanazawa Niigata Yamagata
Kasugai Nishinomiya Yamaguchi
Kawaguchi Oita Yokohama
Kawasaki Okayama Yokosuka
Kitakyushu Osaka
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APPENDIX TABLE A7
ITEMS INCLUDED IN THENIGERIAN DATASET
Fresh food Apparel
Bananas Embroidery lace (per metre)
Beans (brown) Guinea brocade (per metre)
Beans (white) Khaki drill (per metre)
Beef Mattress
Carrots Mens shoes
Chicken (agricultural) Pillow
Chicken (locally produced) Poplin (per metre)Gari (white) Singlet
Gari (yellow) Womens shoes
Guinea corn
Irish potatoes Services
Kola nuts Blood test
Maize (white) Rent for a flat
Maize (yellow) Rent for a bungalow
Okra Rent for a room with parlour
Onions Rent for a room
Oranges Room in a hotel
Rice (locally produced) Taxi fare (per kilometre)
Salt
Sweet potatoes
Tomatoes
Yams
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APPENDIX TABLE A8
CITIES INCLUDED IN THENIGERIAN DATASET
City State City State
Abakaliki Ebonyi Jalingo Taraba
Abeokuta Ogun Jos Plateau
Abuja Federal Capital Territory Kaduna Kaduna
Ado-Ekiti Ekiti Kano Kano
Akure Ondo Katsina Katsina
Asaba Delta Lafia Nasarawa
Awka Anambra Lokoja KogiBauchi Bauchi Maiduguri Borno
Benin City Edo Makurdi Benue
Birnin Kebbi Kebbi Minna Niger
Calabar Cross River Oshogbo Osun
Damaturu Yobe Owerri Imo
Dutse Jigawa Port Harcourt Rivers
Enugu Enugu Sokoto Sokoto
Gombe Gombe Umuahia Abia
Gusau Zamfara Uyo Akwa Ibom
Ibadan Oyo Yenagoa Bayelsa
Ikeja Lagos Yola Adamawa
Kano Kano
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FIG. 1. Time series of aggregate average inflation (t
) in Canada.
FIG. 2. Time series of aggregate average inflation ( t ) in Japan.
FIG. 3. Time series of aggregate average inflation (t
) in Nigeria.
1925 1930 1935 1940-0.04-0.020.000.020.040.06 t
2001 2002 2003 2004 2005 2006-0.010-0.0050.0000.0050.010 t
2002 2003 2004 2005 2006-0.10-0.050.000.05
t
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-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
200
400
600
800
000
200
requencyf
FIG. 4. Distribution of inflation (it) in Canada trimmed at 10%.
-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
1000
2000
3000
4000
5000
6000
7000 frequency
FIG. 5. Distribution of inflation (it) in Japan trimmed at 10%.
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-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10
50
100
150
200
frequency
FIG. 6. Distribution of inflation (it) in Nigeria trimmed at 10%.
-3.5 -3.0 -2.5 -2.0 -1.5 -1.0
100
200
300
400
500
600
requencyf
FIG. 7. Distribution of relative price variability (ln(vit)) in Canada.
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-4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0
500
1000
1500
2000
requencyf
FIG. 8. Distribution of relative price variability (ln(vit)) in Japan.
-6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5
50
100
150
200
250
requencyf
FIG. 9. Distribution of relative price variability (ln(vit)) in Nigeria.
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FIG. 10. Recursive estimates of the Canadian RPV-inflation parameters two standard errors.
FIG. 11. Recursive estimates of the Canadian RIV-inflation parameters two standard errors.
1930 1935 1940-2-1012A arameter
1930 1935 1940-202468
(A)2 arameter
1930 1935 1940
-0.75-0.50-0.250.00
UP arameter
1930 1935 1940
-1.25-1.00-0.75
U arameter
1930 1935 1940-4-3-2-101
23 A arameter
1930 1935 1940-10
-505
1015 (A)2 arameter
1930 1935 19402.02.53.03.54.04.5
UP arameter
1930 1935 1940-4.0-3.5-3.0-2.5-2.0-1.5 U arameter
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FIG. A1. Values of d ln dD Ait it v with a 95% confidence interval (semi-parametric model,z = 1%).
FIG. A2. Values of d ln dD Ait it v with a 95% confidence interval (semi-parametric model,z = 1.5%).
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-9-8-7-6-5-4-3-2-10123456 dln(vD
it)/ dit
it
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
-5-4-3-2-10123 dln(vD
it )/ dit
it
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FIG. A3. Values of d ln dD Ait it v with a 95% confidence interval (semi-parametric model,z = 2%).
FIG. A4. Values of d ln dD Ait it v with a 95% confidence interval (quadratic model).
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5
-3
-2
-1
0
1 dln(vDit)/ dit
it
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-16-14-12-10
-8-6-4-20246810
12141618 dln(vDi )/ dit
it
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FIG. A5 Values of d ln dD Ait it w with a 95% confidence interval (semi-parametric model,z = 1%).
FIG. A6. Values of d ln dD Ait it w with a 95% confidence interval (semi-parametric model,z = 1.5%).
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-8-6-4-202468 dln(wDit )/ dit
it
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-4-3-2-1012345 dln(wDit )/ dit
it
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FIG. A7. Values of d ln dD Ait it w with a 95% confidence interval (semi-parametric model,z = 2%)
-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5-2
-1
0
1
2dln(wD
it )/ dit
it