chris hajzler price level dispersion

8/12/2019 Chris Hajzler Price Level Dispersion

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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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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
http://www.vanderbilt.edu/econ/cipr/japan.htmlhttp://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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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


17/53


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-


18/53


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.


19/53


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


20/53


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


21/53


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


26/53


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.


27/53


and the weightsWitare as follows:

Wit=15

161 0it

4z

2

2

if |0it|


28/53


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.


29/53


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.


30/53

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


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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iv

TABLE 4

AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditv IN JAPAN


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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v

TABLE 5

AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditw IN JAPAN


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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vi

TABLE 6

AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditv INNIGERIA


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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vii

TABLE 7

AVERAGE PARAMETER VALUES IN THE MODELS OF ln Ditw INNIGERIA


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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viii

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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ix

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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x

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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xi

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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xii

(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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xiii

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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xiv

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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xv

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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xvi

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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xvii

-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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xviii

-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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xix

-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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xx

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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xxi

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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xxii

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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xxiii

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

chris hajzler price level dispersion

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