Institute for Economic Studies, Keio University
Keio-IES Discussion Paper Series

Was Inflation Observed under the First Wave of the COVID-19 Spread in Japan?
Scanner Data Evidence for Retailers in Tokyo
Masahiro Higo, Shigenori Shiratsuka
6 September, 2022
DP2022-013
https://ies.keio.ac.jp/en/publications/19062/

Institute for Economic Studies, Keio University
2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan
ies-office@adst.keio.ac.jp
6 September, 2022

Was Inflation Observed under the First Wave of the COVID-19 Spread in Japan?
Scanner Data Evidence for Retailers in Tokyo
Masahiro Higo, Shigenori Shiratsuka
Keio-IES DP2022-013
6 September, 2022
JEL Classification: C43, E31
Keywords: Consumer price index; Scanner data;Quality adjustment; Retail service
quality; Temporary sales; COVID-19

Abstract
In this paper, we examine whether inflation was observed under the first wave of the
COVID-19 spread. To address this issue, we construct high-frequency quality-adjusted
price indices by employing daily scanner data of retail stores in Tokyo. We attempt tomake explicit adjustments for not only the product characteristics but also thestructural changes in temporary sales and the retail service quality of outlet channels.
We emphasize that adjustments for the effects of temporary sales and retail service
quality are particularly important in examining the retail price dynamics under the
COVID-19 pandemic as the voluntary lockdown constrained household purchasing
behavior because of the risk of COVID-19 infection. We conclude that mild andtemporary inflation of slightly less than 1% was observed during the first wave of the
COVID-19 spread. Based on the estimation results, we decompose the differences
between the increases in the unit prices and those in the quality-adjusted price indicesinto outlet substitution effects and temporary sales effects.

Masahiro Higo
Graduate School of Economics, The University of Tokyo
7-3-1, Hongo, Bunkyo-ku, Tokyo
masahiro.higo@e.u-tokyo.ac.jp

Shigenori Shiratsuka
Faculty of Economics, Keio University
2-15-45, Mita, Minato-ku, Tokyoshigenori.shiratsuka@keio.jp

Acknowledgement : This paper is prepared for the special issue for Japan and World
Economy on “Government Statistics and Economic Performance.” INTAGE Inc.
provided the daily scanner data used in this paper under the collaborative research
project at the Center for Research and Education in Program Evaluation (CREPE), theUniversity of Tokyo. We thank Erwin Diewert, Shin’ichi Fukuda, Taisuke Nakata,
Tatsuyoshi Okimoto, Mototsugu Shintani, Nao Sudo, Jiro Yoshida, and participants of
the Japan and World Economy Symposium and seminar at the Bank of Japan as well as
an anonymous referee for their constructive comments and discussions. Shiratsuka
acknowledges the financial support from Keio University Academic Development Fund.

Was Inflation Observed under the First Waveof the COVID-19 Spread in Japan?
Scanner Data Evidence for Retailers in Tokyo *Masahiro Higo†and Shigenori Shiratsuka‡
September 6, 2022

Abstract
In this paper, we examine whether inflation was observed under the first wave of the
COVID-19 spread. To address this issue, we construct high-frequency quality-adjusted
price indices by employing daily scanner data of retail stores in Tokyo. We attempt tomake explicit adjustments for not only the product characteristics but also the structuralchanges in temporary sales and the retail service quality of outlet channels. We emphasizethat adjustments for the effects of temporary sales and retail service quality are particularly important in examining the retail price dynamics under the COVID-19 pandemic as
the voluntary lockdown constrained household purchasing behavior because of the risk of
COVID-19 infection. We conclude that mild and temporary inflation of slightly less than 1%
was observed during the first wave of the COVID-19 spread. Based on the estimation results, we decompose the differences between the increases in the unit prices and those in thequality-adjusted price indices into outlet substitution effects and temporary sales effects.

Keywords: Consumer price index, Scanner data, Quality adjustment, Retail service quality,
Temporary sales, COVID-19
JEL codes: C43, E31,

* This paper is prepared for the special issue for Japan and World Economy on “Government Statistics andEconomic Performance.” INTAGE Inc. provided the daily scanner data used in this paper under the collaborative
research project at the Center for Research and Education in Program Evaluation (CREPE), the University of Tokyo.
We thank Erwin Diewert, Shin’ichi Fukuda, Taisuke Nakata, Tatsuyoshi Okimoto, Mototsugu Shintani, Nao Sudo,
Jiro Yoshida, and participants of the Japan and World Economy Symposium and seminar at the Bank of Japan
as well as an anonymous referee for their constructive comments and discussions. Shiratsuka acknowledges thefinancial support from Keio University Academic Development Fund.
† The University of Tokyo. E-mail: masahiro.higo@e.u-tokyo.ac.jp‡ Keio University. E-mail: shigenori.shiratsuka@keio.jp

1

Introduction

In this paper, we examine whether inflation was observed under the first wave of the COVID19 spread. To address the question, we construct high-frequency quality-adjusted price indicesby employing daily scanner data at retail stores in Tokyo.
During the first wave of the COVID-19 spread in Japan in the first half of 2020, the numberof infections began to increase from mid-February and spiked through March. In response, theGovernment of Japan declared a state of emergency on April 7 in seven prefectures, including
Tokyo, and on April 16, the state of emergency was extended to the entire country. Under
these circumstances, people refrained from going out. The number of new infections peaked in
mid-April and began to decline rapidly. During the first wave of the COVID-19 spread, Japan
experienced weaker social and economic constraints under the state of emergency. Unlike thestrict lockdown in many countries, Japan implemented a voluntary lockdown, experiencing asignificant decline in economic activities.
Many previous studies have used various types of alternative data in Japan to discuss thesocial and economic issues during the COVID-19 pandemic.1 For example, Hosono (2021)
explored the low infectious cases and the large decline in consumption by extending the SIRmacro-model to incorporate Japan’s two key factors of voluntary stay-at-home and a requestbased lockdown. Using smartphone location data, Watanabe and Yabu (2021) revealed thatboth the intervention effect of government policy and the information effect of health risks
from COVID-19 infection constrain people’s behavior in response to the stay-at-home measures. Shibamoto et al. (2022) estimated a dynamic model of the interaction between infectionmobility tradeoff and mobility demand. Fujii and Nakata (2021) pointed out that the tradeoff
between output and infection in the short run does not necessarily exist in the long run basedon their simulation results with the SIR-macro-model with time-varying parameters.
Among such studies, some have employed various types of alternative data to analyze thestructural changes in household consumption expenditure and retail sales trends. These studies did not only use scanner data for retail stores but also credit card expenditure history anddata from household accounting applications. For example, Watanabe and Omori (2020) andKonishi et al. (2021) revealed that household consumption expenditure patterns changed significantly, especially from eating out to home cooking and delivery services. As a result, theretail sales trends also changed drastically, observing that supermarkets enjoyed positive impacts, whereas department stores and restaurant affiliates were negatively affected. However,
only a very limited number of studies, including the mask price analysis in Abe et al. (2020),
focused on retail price development under the COVID-19 pandemic.2
1 Japanese Economic Association has set up a webpage for information on academic papers analyzing the impact
of COVID-19 (https://covid19.jeaweb.org/scientific.html).
2 Retail scanner data research in Japan dates back to the mid-1990s when the Seiyu price index, compiled by oneof the major supermarket chains in Japan, highlighted the “price busting” phenomena in Japanese retail markets.
In the mid-1990s, Japan experienced a relatively high domestic price level. With continued low inflation under the“lost decades,” Japan’s price problem turned into a relatively low domestic price level. Scanner data research focuses on stealth inflation with product turnover and downsizing (Imai and Watanabe, 2014; Ueda et al., 2019; Ueda

1

Focusing more on the measurement issues of the consumer price index (CPI) under the
COVID-19 pandemic, Diewert and Fox (2020) pointed out the possible downward bias, notupward bias, in the CPI due to the sudden unavailability of goods and services during the
pandemic. Cavallo (2020) attempted to quantify the downward bias in the CPI due to changes
in consumer expenditure patterns by employing credit and debit transaction data. These studies mainly focused on the measurement bias of the CPI stemming from the aggregation formulawith the fixed consumption basket.
The COVID-19 pandemic may lead to mismeasurement of individual prices due to inadequate adjustments for the temporary sales effects and retail service quality. The same productis sold at different prices at different outlets as observed prices reflect the differences in thetemporary sales effects and the retail service quality across outlets. For example, prices at convenience stores are generally higher than those at other outlet channels, reflecting their convenience in terms of operating hours, location, and shopping time. The sudden and unexpectedchanges in consumer expenditure patterns induced by the COVID-19 spread are likely to produce the measurement bias in the CPI caused by individual prices without making an explicit
adjustment for the temporary sales effects and the differences in retail service quality.
Fig. 1 depicts the recent development of retail prices using a high-frequency scanner priceindex for food and beverage products and daily necessities at supermarkets.3 The T-index indicates a moderate upward trend from shortly before the first declaration of a state of emergency
in April 2020. The trend then reversed after reaching a peak under the state of emergency, revealing a downward trend toward mid-2021. During this period, two observations are noted.
First, the volatility of the T-index declined significantly, suggesting possible declines in the frequency of temporary sales and the size of price reduction. Second, the T-mode-index deviatedfrom the upward trend of the T-index significantly, although the T-index and the T-mode-index
experienced similar movements outside this period, indicating that increases in the T-index are
attributed to decreases in the frequency and the size of price reductions of temporary sales.4
Moreover, the voluntary lockdown under the state of emergency induced people to minimize
shopping frequency, travel distance, and shopping time, influencing household purchasing behavior, such as the choice of retail outlets and price sensitivity of consumption expendituredecisions. Fig. 2 depicts no significant changes in household perception of inflation during thefirst half of 2020, including the first wave of the COVID-19 spread.
et al., 2019), which tries to raise unit prices by reducing the product volume while keeping tag price unchanged.
Moreover, applications of scanner data have continued to expand by linking more broad aspects of macroeconomic
issues, such as the frequency of price changes to explore the flattened Phillips curve (Abe and Tonogi, 2010) andthe interaction of the frequency of temporary sales with macroeconomic conditions and effectiveness of monetary
policy (Sudo et al., 2018).
3 NIKKEI CPINow is the real-time daily price index computed from scanner data of supermarkets. It covers foodand beverage products and other daily necessities with a fairly long time series from 1989.
4 The T-mode-index is computed from mode prices for individual products at specific stores with daily windows
from 28 days before to 28 days after.

2

Fig. 1. Daily Retail Price Developments
Notes: The T-index aggregates product prices for each outlet at a JAN code level by applying the Törnqvist index
formula. The T-7D-MA is a seven-day backward moving average of the T-index. The T-mode-index employs mode
prices for the daily windows from 28 days before to 28 days after. The light blue areas indicate the periods under
the declaration of states of emergency in Tokyo—(i) from April 7 to May 25, 2020, (ii) from January 8 to March 21,
2021, (iii) from April 25 to June 20, 2021, and (iv) from July 12 to September 30, 2021. Year-on-year changes arecalculated as percentage changes from 364 days earlier to adjust the week-day effects. The plotted data for CPINow
are nationwide, as it does not publish the data for Tokyo metropolitan area, though it publishes other prefectural
data.
Source: Nowcast, NIKKEI CPINow.

Fig. 2. Inflation Perception by Household
Source: Bank of Japan, Opinion Survey on the General Public’s Views and Behavior.

Fig. 3 depicts that CPI inflation for the headline indicator and three core indicators, thatis, headline less perishables, headline less perishables and energy, and trimmed mean, experienced a downward trend in the first half of 2020. However, the Japanese CPI fails to reflect
the structural changes in the retail markets, probably due to its price survey method based on3the "one-specification-for-one-item" policy. The policy specifies a few popular specifications
for each item and continuously surveys their prices at specific outlets. Therefore, it is difficult
to maintain price representativeness under the rapid and significant structural changes in theretail markets.5

Fig. 3. Consumer Price Inflation in Japan
Sources: Statistics Bureau of Japan, Consumer Price Index, Bank of Japan, Measures of Underlying Inflation.

The following question arises: “Are the unit price increases observed in Fig. 1 considered
price changes on a quality-adjusted basis in terms of not only product characteristics but also
retail services at outlets, including the temporary sales effects?” We construct high-frequency
quality-adjusted price indices to address the question by making explicit adjustments to dailyscanner data on product characteristics, temporary sales effects, and retail service quality. As
the voluntary lockdown constrained household purchasing behavior, we emphasize that quality adjustments for retail services, including the temporary sales effects, are particularly important in examining the retail price dynamics during the COVID-19 pandemic. Households
responded to the voluntary lockdown by reducing shopping frequency, travel distance, andshopping time. Therefore, a quality-adjusted price index is considered to exist between the
CPINow T-index, which fully reflects the decrease in temporary sales as a price increase, andthe T-mode-index, which excludes the temporary sales effects.
Our approach is closely related to de Haan and Hendriks (2013), who applied the timeproduct dummy (TPD) method to daily web-scraping data of Dutch online stores.6 They com5 As Shiratsuka (2021) pointed out, the Japanese CPI has problems with the broadly-defined lower-level substitution bias, which corresponds to the weakened price representativeness stemming from the "one-specification-forone-item" policy of the price survey method.
6 de Haan and Hendriks (2013), de Haan and Krsinich (2014), and de Haan (2015) proposed two estimation
procedures to incorporate scanner and web-scraping data into price indices—the time dummy hedonic (TDH) index(when information on item characteristics is available) and the TPD index (when unavailable). Krsinich (2016)
examined the application of the TPD index combined with rolling estimations, called the fixed effects window
splicing (FEWS) index. She argued that the FEWS is robust to retroactive revisions from data accumulation overtime, but it is less applicable to products with rapid changes in product characteristics and consumer preferences.
Haan et al. (2021) pointed out that the TPD index is distorted toward zero due to overfitting. They argued that4

pared the TPD index with other conventional price index formulas, indicating downward biases with volatile price trends. We extend the approach of de Haan and Hendriks (2013) inthree respects. First, we extend the TPD model by taking explicit account of the difference inthe retail service quality of outlet channels (the extended TPD model). We employ the combinations of the two fixed effects, i.e. products and outlet channels, in the cross-sectional direction
as our dataset includes sales records of various store types in the same product. Second, weconstruct a high-frequency quality-adjusted price index on a weekly basis using daily scannerdata. Due to the strong weekly effects observed in the retail sales trends, we construct weekly
quality-adjusted price indices based on the estimates for weekly dummies applied to both daily
and weekly converted data. Third, we apply the extended TPD model to all food and beverage
products in a unified manner, thereby aggregating them into the overall food and beverage
product price indices.
Our conclusions are summarized as follows. We reveal that mild and temporary inflation ofslightly less than 1% (0.6−0.9%) was observed during the first wave of the COVID-19 spread.
We also decompose the differences between the increases in the unit prices and those in thequality-adjusted price indices into outlet substitution effects and temporary sales effects. In thedaily frequency estimation, the unit price increase of 1.7% is decomposed into temporary sales
effects of 0.3%, outlet substitution effects of 0.5%, and quality-adjusted price increase of 0.9%,
whereas in the weekly frequency estimation, it is 0.4%, 0.7%, and 0.6%, respectively.
The rest of this paper is as follows. Section 2 describes the extension of the TPD model
to incorporate the explicit quality adjustment for retail service quality. Section 3 explains the
INTAGE SRI (Nationwide Retail Store Panel Survey) scanner data and summarizes the retailsales trends around the first wave of the COVID-19 spread. Section 4 explains our quality adjustment strategy and constructs high-frequency quality-adjusted price indices based on thebaseline estimation results for the extended TPD model. Section 5 describes comprehensive
robustness checks on the baseline estimation results. Section 6 discusses whether inflation wasobserved under the first wave of the COVID-19 spread in Tokyo. Finally, Section 7 concludes
the paper by discussing the implications of our estimation exercises for the official CPI compilation methods.

2

Empirical Framework

We extend the TPD model in the studies by de Haan and Hendriks (2013) and de Haan andKrsinich (2014) by explicitly considering the difference in the retail service quality of outlet
channels (extended TPD model). Assuming that N different products are sold during the sample period from 0 to T, the period 0 is the base period, and the periods from 1 to T are thecomparison periods. pi,t denotes the price of a product i at period t (t = 0, 1, ..., T). By using
log-transformed prices as a dependent variable, the log-linear time-dummy hedonic (TDH)
the TDH method makes robust and explicit quality adjustments based on quality characteristics, whereas the TPD
method has problems with making implicit quality adjustments.

5

model is stated as follows:
T

K

t =1

k =1

lnpi,t = α + ∑ λt TDi,t + ∑ β k zk,i + ei,t ,(1)

where TDi,t is the time dummy variable, which takes the value of 1 if the observation is theperiod t and 0 otherwise. zk,i is the indicators of product characteristics k for a product i, andβ k is the corresponding estimated parameter. ei,t is the error term. The price index from period
0 to t is computed by taking the exponential of the estimated parameter for the time dummyλt .
Similarly, the log-linear TPD model is defined as follows:
T

N −1

t =1

i =1

lnpi,t = α + ∑ λt TDi,t + ∑ γi PDi + ei,t ,(2)where PDi is the product dummy variable, which takes the value of 1 if the observation relates
to a product i and 0 otherwise, and the dummy for an arbitrary product N is excluded in theestimation specification to identify the model. The estimated parameters λt andγi are fixed
effects for time and product, respectively. As with the TPD model, the price index from period
0 to t is computed by taking the exponential of the estimated parameter for the time dummyλt .
We extend the log-linear TPD model by making an explicit quality adjustment for retailservices by introducing an additional cross-sectional control variable for stores as follows:
T

N −1

S −1

t =1

i =1

s =1

lnpi,t = α + ∑ λt TDi,t + ∑ γi PDi + ∑ δs STs,i + ei,t ,(3)where STs,i is the store dummy variable, which takes the value of 1 if a product i is sold at astore s and 0 otherwise, and the dummy for an arbitrary store S is excluded in the estimation
specification to identify the model.
As discussed by Krsinich (2016), in theory, the price indices based on the TDH model andthe TPD model are the same because the fixed effect for a product i corresponds to the net
effect of the characteristics for a product i. However, in practice, the TPD model is less efficientthan the TDH model if sufficient information on the characteristics is available. The numberof relevant characteristics can be narrowed down considerably by applying the TDH model.7
However, the TDH model is often difficult to apply to analyses with scanner data because, inmany cases, it is hard to link scanner data to a dataset of the characteristics of a wide range of
products.
Thus, choosing either the TDH or TPD model is a practical issue based on data availability.
We consider the TPD model a realistic option in this paper because it needs to handle scanner
data covering a wide variety of product categories in a unified manner.
7 For example, see the study by Shiratsuka (1995) for the selection of explanatory variables in the THD model.
He applied the TDH model to automobiles in Japan by selecting three key performance characteristics—max power,
wheelbase, and interior space—out of 11 characteristics.

6

3

Data

In this section, we explain the INTAGE SRI scanner data and then summarize the retail sales
trends under the first wave of the COVID-19 spread.

3.1

INTAGE scanner data

We employ daily scanner data of food and beverage products, SRI (Nationwide Retail Store
Panel Survey) provided by INTAGE Inc. The dataset contains the daily sales, size, and quantity information of nationwide retail stores in Japan at a barcode level from January 2019 to June
2020. The sales records cover sales of food and beverage products with JAN codes, recorded
as a stock keeping unit (SKU) in the dataset. Food and beverage products cover about 20% of
the consumption expenditure basket for the CPI. The outlets are classified into seven types−(i)general merchandise stores (GMS), having a sales floor of 3,000 or more square meters and morethan 50 employees, (ii) supermarkets (SM), having 500 square meters or above, (iii) mini supermarkets (M-SM), (iv) convenience stores (CVS), (v) home centers and discount stores (HC/DS),(vi) large drug stores (Drug/L), and (vii) discount liquor stores (Liquor/DS).8
We focus on the data for retail stores in Tokyo from January to June 2020 to analyze theeffects of the first wave of the COVID-19 spread in Tokyo. Table 1 summarizes information on
the dataset from the product side on the upper panel and the store side on the lower panel.
The upper panel reveals that the total number of SKUs is just over 76,000, categorized into 151
items, such as rice and bread. The items are further classified into eight categories, including
staple foods. The lower panel presents the daily average data on retail trends. GMS has thelargest number of price observations (products) and attracts many customers, registering large
sales amounts in a relatively small number of stores. SM has the largest total sales amounts anda relatively large number of price observations and customers. In contrast, CVS and Drug/L
have a limited number of price observations and relatively low total sales amounts in a relatively large number of stores.
8 INTAGE data divide SM into large and small sizes by floor size, but we merge them as similar retail sales trends

are observed in the two outlet types. We also drop outlets classified as small drug stores (Drug/S) and small liquor
shops (Liquor/S) because of the small outlet samples and fewer SKUs. INTAGE scanner data expand its coverageof stores from January to March 2019, especially in HC/DS.

7

Table 1
Summary Statistics(1) Items and SKUs
Category
Staple foods
Seasonings
Processed foods
Sweets / Snacks
Milk beverages
Coffee / Tea
Soft drinks
Alcoholic beverages
Total

Numberof items
17
36
45
19
4
8
16
6
151

Numberof SKUs
10,58011,89020,22016,270
789
2,049
5,074
9,058
75,930

Mean
622
330
449
856
197
256
317
1,510
503

SKUs per item
Maximum Minimum
3,204
30
1,696
11
2,117
22
2,695
10
441
55
706
61
724
73
2,744
491
3,204
22

(2) Retail Sales Trend (Daily Average)

Outlet type

Sales amount(million yen)

Number ofstores

GMS
SM
M-SM
CVS
HC/DS
Drug/L
Liquor/DS
Total

71.8
126.0
13.6
7.3
12.9
12.9
4.7
249.2

15.1
60.9
17.6
51.4
14.6
85.6
9.7
254.9

Per outlet
Number of
Number ofpricecustomers
observations
4,641.0
6,505.7
2,927.8
2,639.8
1,469.5
1,297.8
473.7
728.1
909.7
2,510.3
380.3
704.0
406.5
335.2
1,366.4
1,645.5

Per customer
Sales amount
(yen)
743.8
783.9
586.3
204.1
335.9
193.6
1,413.0
450.7

Notes: Figures in the table include SKUs sold from January 6, 2020, to June 28, 2020.

3.2

Unit price and effective quantity indicesWe employ unit prices as the dependent variables in estimating high-frequency quality-adjusted
price indices at an elementary aggregation level. Prior to our analysis, we examine how the
relationship between unit prices and quantity changed across retail channels during the firstwave of the COVID-19 spread.
The sales amounts are calculated by multiplying the price (P) and the quantity (Q) of anindividual product and summing them up over all products. The price is decomposed into the
product of the unit price (UP) and unit size (US). The unit size multiplied by the quantity is defined as the effective quantity (EQ). Thus, the sales amounts can be redefined as the summationof the product of the unit price and effective quantity of all products, as follows:
SAk,t = ∑ Pi,k,t × Qi,k,t = ∑ UPi,k,t × USi,k,t × Qi,k,t = ∑ UPi,k,t × EQi,k,t ,
i

i

(4)

i

where subscript i, k, and t indicate a product, store, and time, respectively.
Based on the decomposition of Eq. (4), we construct the unit price index (UPI) and effective
8

quantity index (EQI) using the real-time weight of the daily sales amounts as shown by Eqs.
(5) and (6) below:
UPIt = ∑ ∑ swi,k,t UPIi,k,t ,(5)

EQIt = ∑ ∑ swi,k,t EQIi,k,t ,

(6)

i

i

k

k

where sw denotes weight for a product i at store k at time t. The indices are constructed using
the first week of January 2020 as the base period.
Fig. 4 depicts the computed results for the UPI and EQI across store types. Three points
should be noted. First, the sharp increase in the UPIs for GMS, SM, M-SM, and HC/DS shortly
before the first declaration of the state of emergency corresponds to the spike in the EQIs.
The UPI for Drug/L increased slightly in early March. The UPIs for other store types did notexperience such significant increases, especially those for CVS experienced a very flat trend
over time, even under the first declaration of the state of emergency. Second, the EQIs for moststore types, except for CVS and Liquor/DS, experienced two spikes in the early and end of
March, suggesting a stock-piling behavior at many households in preparation for the stay-athome request under the state of emergency. Third, the UPIs for GMS, SM, and M-SM, which
increased shortly before the first declaration of the state of emergency, started declining after
lifting the state of emergency.
Based on the first and second points, the increases in the UPIs are associated with the increases in the EQIs, suggesting that all the increases in the UPIs should not be considered as
price hikes on a quality-adjusted basis. During the first wave of the COVID-19 spread, due
to the increased risk for COVID-19 infection, households decided to purchase at higher prices
than usual to reduce shopping frequency, travel distance to stores, and shopping time.9
9 As can be seen from Fig. 4, the effective sales value remained flat at a high level during the first declarationof the state of emergency. Although not depicted in the figure, the number of customers visiting stores decreased
during this period, whereas the sales amounts per customer increased. This observation also suggests that households tried to minimize shopping frequency by making bulk purchases in a single shopping trip to control the riskof COVID-19 infection.

9

(1) Unit Price Indices(2) Effective Quantity IndicesFig. 4. Unit Price Indices and Effective Quantity Indices by Outlet Types
Notes: The plotted figures are backward seven-day moving averages, starting from the date on the horizontal axis.
The light blue areas indicate the period of the first declaration of a state of emergency in Tokyo.

3.3

Temporary sales

We now examine the effects of temporary sales. We define temporary sales as a day that theobserved price of a product at a store is at least two yen lower than the mode price for the pastseven days, including the current day, following the study of Abe and Tonogi (2010). We also
define a price reduction as the deviation of the observed price at a temporary sale from themode price. We aggregate the frequency and size of price reductions over items by computing
simple mean and weighted mean with sales amounts.
Fig. 5 depicts the frequency of temporary sales and the size of price reductions at temporary
sales over time.10 These figures reveal that temporary sales declined rapidly from early March
10 Sudo et al. (2018) examine the effects of temporary sales on the macroeconomic implication by focusing on
the households’ allocation of time for work, leisure, and bargain hunting. They compute various measures forthe frequency of temporary sales based on two types of sales filters: mode price during a certain window length(Eichenbaum et al., 2011, and Kehoe and Midrigan, 2015) and filtered V-shaped price fluctuations as a temporary
sale (Nakamura and Steinsson, 2008). Their estimates for the closest definition to ours, mode price for a seven-day
widow, are around 0.2 in the 2010s and slightly higher than our estimates in early 2020. In this respect, our estimates
for the frequency of temporary sales become slightly higher, around 0.2, when limiting data only for GMS and SM,
which seems consistent with the estimates in Sudo et al. (2018).

10

(1) Frequency of temporary sales(2) Size of Price Reductions

Fig. 5. Frequency and Price Discount of Temporary Sales
Notes: The bold lines are backward seven-day moving averages starting from the date on the horizontal axis. The
light blue areas indicate the period of the first declaration of a state of emergency in Tokyo.

toward the first declaration of the state of emergency, as indicated by the significant divergence
between the T-index and the T-mode-index of CPINow in Fig. 1. Before March, the differences
between the simple and weighted means remained almost constant, but they started narrowing
in early March. These observations confirm that both the frequency of temporary sales and thesize of price reductions declined during this period. This suggests the importance of considering the temporary sales effects on the retail sales trends when computing the high-frequency
quality-adjusted price indices.
To confirm the structural changes in temporary sales under the first wave of the COVID19 spread, we perform a statistical test for structural changes with an unknown break point.
Fig. 6 plots the sup-Wald statistics for structural changes in the differences between simple andweighted means for the share of temporary sales and the size of price reductions, respectively.
The sup-Wald statistics are computed from January 6 to June 28 in 2020, with 15% trimming fordetecting an unknown break point. The sup-Wald statistics start increasing from mid-February
and reach their peaks around the end of March. The detected breakpoints for the share of
temporary sales and the size of price reductions are March 28 and 24, 2020, respectively.
It should be noted that declines in the frequency of temporary sales and the size of price reduction influence how to measure the central tendency of the unit price distributions over time.
11

Fig. 6. Test for Structural Changes with an Unknown Breakpoint
Notes: The plotted figures are the sup-Wald statistics for detecting an unknown break point for the differences
between the simple and weighted means for sales share and price reductions. The bold horizontal line indicates thecritical value for 1% with 15% trimming for detecting an unknown break point. The breakpoints for sales share andprice reductions are March 28 and 24, 2020, respectively.

Fig. 7 plots three statistical measures for the central tendency of the unit price distributions overtime—mean, median, and mode of weekly windows for a product at a store—aggregated by
the time-varying sales amount weights. The three measures are indexed at 100 with the mode
values for the first week of January 2020.

Fig. 7. Summary Statistics for Central Tendency of Unit Price Distributions
Notes: The light blue area indicates the period for the first declaration of a state of emergency in Tokyo.

The order of the three statistics remains unchanged over time: mode, median, and meanfrom top to bottom, indicating that the unit price distributions are skewed toward the left.
However, the mean moves closer to the mode, reflecting a decrease in the temporary sales
effects from the end of February, and the leftward-skewness of the unit price distributions
also declined. This implies that inflation trends are estimated differently, depending on themeasures for the central tendency of the unit price distributions used. The mean values forunit prices are most influenced by the declines in temporary sales under the first wave of the
COVID-19 spread, and the mode values are the least influenced.
However, the unit size of products purchased by households did not change significantly

12during the first wave of the COVID-19 spread. Fig. 8 plots quantiles of the unit size distributions for products purchased by households on a weekly basis. The plotted figures arenormalized using the mean and standard deviation for the first week of January 2020. The distributions remain almost unchanged, slightly shifting toward a larger direction. In response to
the declined temporal sales, households continued to purchase products with approximately
the same unit size, suggesting that, due to the increased risk for COVID-19 infection, households chose to purchase at higher prices to reduce travel distance to stores and shopping time.

Fig. 8. Unit Size Distributions
Notes: The light blue area indicates the period of the first declaration of a state of emergency in Tokyo.

4High-frequency Quality-adjusted Price Index

In this section, we explain our quality adjustment strategy and construct high-frequency qualityadjusted price indices based on the baseline estimation results for the extended TPD model.

4.1

Quality adjustment strategy

Given the observations about the significant structural changes in the retail sales trends under
the first wave of COVID-19 in the previous section, we point out the importance of the quality
adjustments in two respects, in addition to the standard quality adjustments for product characteristics. First, we need to pay careful attention to accounting for the structural changes in
the frequency and size of price reductions of temporary sales. Due to the significant structuralchanges in the relative relationship between the regular and discount prices of temporary sales,
the treatment of discount prices significantly influences the estimated price index. It should be
noted that both supply- and demand-side factors induce such structural changes in the retailsales trends. On the one hand, retailers try to raise prices in real terms by reducing the frequency and size of price reductions of temporary sales to cover the increased costs of infection
prevention measures. On the other hand, consumers are more likely to purchase at higherthan-normal prices to minimize the risk of COVID-19 infection under voluntary lockdown.
13Second, we also need to consider outlet substitution bias. This bias is induced by the structural change in retail markets, as observed by the shift in shopping sites across the outlet types.
The shifts in nearby outlets indicate possible changes in consumers’ preference due to the stayat-home request under the voluntary lockdown and the risk of COVID-19 infection. Under
such circumstances, households are likely to alter their shopping behavior to minimize shopping frequency, travel distance, and shopping time. Such changes in consumers’ behavior indicate that, on a quality-adjusted basis, they perceive that the prices for the same products soldat supermarkets nearby are less expensive than before.11
To deal with the temporary sales effects and the retail service quality differences, we employ
four baseline specifications in Table 2—D-ROL_SK+ST, D-ROL_SK+TY, W-MO_SK+ST, and WMO_SK+TY.
Table 2
Specification for Baseline Estimations
Abbreviation

Frequency

Sample Period

Conversion
D-ROL_SK+ST

None

D-ROL_SK+TY
W-MO_SK+ST
W-MO_SK+TY

Weekly Mode

Fixed Effects

SKU

Store

Two-week staggeredrolling sample period!

!

Whole sample
period!

!
!

Store Type!
!
!

The four specifications are a combination of strategies to deal with the two factors—the temporary sales effects and the retail service quality differences. The first part of the abbreviations,
D-ROL or W-MO, corresponds to the strategy to deal with the effects of structural changes in
temporary sales. D-ROL employs two-week staggered rolling estimations for daily frequency
data with weekly time dummies. Rolling estimations are expected to absorb item-wide structural changes, including the frequency and price discount of temporary sales, by changes inconstant terms over time. W-MO converts daily frequency data to weekly frequency data using the weekly mode of unit prices. The weekly mode conversion is a direct adjustment for
temporary sales effects on unit prices, as discussed in the previous section.
The second part of the abbreviations, SK+ST or SK+TY, represents the fixed effects for across-sectional direction to control differences in the product quality and the retail service quality across the outlet channels. SK+ST employs two fixed effects for SKU code and store identity(ID) separately, thereby controlling the retail service quality differences at an individual store
level. SK+TY employs SKU code and store type dummies for GMS, SM, M-SM, CVS, HC/DS,
11 Shiratsuka (1999) pointed out that the CPI failed to reflect consumers’ shift from retail shops and department

stores to discount stores in the mid-1990s due to the limited coverage of discount stores in price surveys. Suchstructural changes in retail markets are called “price busting.” It was induced by the massive expansion of largescale shopping sites, such as general merchandise stores and large discount stores. After the sharp appreciation of
the Japanese yen after the Plaza accord in 1985, it is often pointed out that the inefficiency of retail markets in Japanis the cause of price level differences between Japan and other advanced economies.

14

Drug/L, and Liquor/DS separately, thus, controlling the retail service quality differences at theoutlet channel level. Comparing the estimation results for the two types of fixed effects enables
us to confirm whether differences in retail service quality matter at a store or an outlet channel
level. In addition, the second type of fixed effects also has the advantage that the estimates of
fixed effects provide convenience premiums or discounts across outlet channels.

4.2

Estimation procedure

We construct the high-frequency quality-adjusted price indices in two steps. The first step isto estimate the extended TPD model for all 151 items, thereby computing elementary priceindices for all items. The second step aggregates elementary indices to an overall index using
sales amounts as weights.
As the first step for computing high-frequency quality-adjusted price indices, we estimate
the extended TPD model for all 151 items based on the four baseline specifications, as shownin Table 2. The specifications for the daily frequency estimation of D-ROL_SK+ST and DROL_SK+TY are given by Eqs. (7) and (8), respectively.
w
lnUPi,k,t = λw D_WK i,k,t+ γi + δk + ei,k,t ,(7)w
lnUPi,k,t = λw D_WK i,k,t+ γi + µ j + ei,k,t ,(8)w
D_WKi,k,t=1t belongs to the week w

0otherwise,

w represent unit price and week dummy of second-week observawhere UPi,k,t and D_WKi,k,ttions in the rolling subsample period for SKU code i at store ID k and time t, respectively. γi ,δk , and µ j are fixed effects for a product with SKU code i, a store with store ID k, and store
type j, respectively. The fixed effect for product γi controls all the product characteristics, including the unit size, tracing a shadow price for the quality of a product i. The fixed effects
for store δk and store type µ j control all the quality differences related to retail services at store
and store type levels, respectively. Here store ID k is included in store type j, i.e., GMS, SM,
M-SM, CVS, HC/DS, Drug/L, and Liquor/DS. The estimated coefficient for week dummies(λw ) corresponds to the quality-adjusted price index using week one as the base period.
The specifications for the weekly frequency estimation of W-MO_SK+ST and W-MO_SK+TY
are given by Eqs. (9) and (10) below:
WMOv
lnUPi,k,w= ∑ λv D_WKi,k,w+ γi + δk + ei,k,w ,

(9)

v =2
W

MO
v
lnUPi,k,w= ∑ λv D_WKi,k,w+ γi + µ j + ei,k,w ,
w =2

15

(10)

v
D_WKi,k,t=1t belongs to the week v

0otherwise,

MO and D_WK v
where UPi,k,w
i,k,t indicate the weekly mode of unit price and week dummies for

SKU code i, at store ID k, and week v, respectively. γi , δk , and µ j indicate the fixed effects fora product with SKU code i, a store with store ID k, and store type j, which are the same as thedaily frequency estimation specifications.
Table 3 summarizes the estimation results for W-MO_SK+ST and W-MO_SK+TY on thethree selected items—sweetened buns with the largest number of SKUs, honey with the median number of SKUs, and skimmed milk with the smallest number of SKUs. We find two important points about the estimation results in the table. First, the adjusted R-squared for all theestimations is generally high, indicating that the two types of fixed effects for a cross-sectional
direction—SKU and store as well as SKU and store type—effectively control the time-invariant
factors for product characteristics and retail service quality. Second, the estimated qualityadjusted price indices differ from product to product, even with generally high precision in
the estimation results. The price indices for honey reveal statistically significant increases fromthe first week of January 2020 during most of the sample period, whereas those for skimmed
milk remain almost unchanged, as seen in the statistically insignificant estimates for most of
the weeks, and those for sweetened buns exhibit statistically significant decreases during thesecond half of the sample period.
We repeat the full sample estimation of the extended TPD model of Eqs. (9) and (10) for
all the 151 items for the weekly frequency estimations. For the daily frequency estimation, we
first conduct the two-week staggered rolling regressions on the extended TPD model of Eqs.
(7) and (8) 24 times over the sample period of 25 weeks and then repeat that process for all the
151 items. This is the first step of computing the elementary price indices of the items.
In the second step, we aggregate elementary price indices to the overall price index byusing sales amounts as weights. In the daily frequency estimation for the two-week subsample periods, the estimated coefficients for week dummies correspond to quality-adjusted pricechanges from the previous week. The cumulative quality-adjusted price changes are computedby linking the estimated week-on-week price changes from the base week. In the weekly frequency estimation for the full sample period, the estimated coefficients for week dummies
correspond to the cumulative quality-adjusted price changes from the base week. Thus, thehigh-frequency quality-adjusted price indices for the week w in the daily and weekly frequency
estimations—HFQAPIwD− ROL and HFQAPIwW − MO —are computed as follows:w

I

HFQAPIwD− ROL = ∑ ∑ swi λv,i ,(11)

v =2 i =1
I

HFQAPIwW − MO = ∑ swi λw,i ,
i =1

16

(12)

17

Coef
SE
−0.003 *** (0.001)
0.001(0.001)0.002 *
(0.001)0.000(0.001)−0.001(0.001)0.001(0.001)0.002 **
(0.001)−0.002 **(0.001)−0.001(0.001)−0.003 **(0.001)0.005 *** (0.001)−0.001(0.001)0.001(0.001)−0.001(0.001)−0.002(0.001)−0.005 *** (0.001)−0.009 *** (0.001)−0.004 *** (0.001)−0.002(0.001)−0.004 *** (0.001)−0.010 *** (0.001)−0.007 *** (0.001)−0.006 *** (0.001)−0.006 *** (0.001)
4.744 *** (0.001)
449,013
0.882
SKU & Store

Coef
SE−0.003*** (0.001)
0.001(0.001)0.002*(0.001)0.000(0.001)−0.001(0.001)0.001(0.001)0.002*(0.001)−0.003**(0.001)−0.002(0.001)−0.003*** (0.001)
0.004*** (0.001)−0.001(0.001)0.000(0.001)−0.002(0.001)−0.002**(0.001)−0.005*** (0.001)−0.009*** (0.001)−0.005*** (0.001)−0.002(0.001)−0.005*** (0.001)−0.010*** (0.001)−0.007*** (0.001)−0.006*** (0.001)−0.006*** (0.001)
4.744*** (0.001)
449,0130.870
SKU & Store Type

Notes: Robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

2wk_id3wk_id4wk_id5wk_id6wk_id7wk_id8wk_id9wk_id10wk_id
11wk_id
12wk_id
13wk_id
14wk_id
15wk_id
16wk_id
17wk_id
18wk_id
19wk_id
20wk_id
21wk_id
22wk_id
23wk_id
24wk_id
25wk_id
Constant
Observations
Adj. R-squared
Fixed effects

Sweetened Buns
(Largest number of SKUs)
CoefSE
0.005*(0.003)−0.010*** (0.003)
0.001(0.003)0.010*** (0.003)−0.013*** (0.003)
0.009*** (0.003)
0.007*** (0.003)
0.011*** (0.003)
0.015*** (0.003)
0.001(0.003)0.014*** (0.003)
0.013*** (0.003)
0.018*** (0.003)
0.017*** (0.003)
0.011*** (0.003)
0.016*** (0.003)
0.018*** (0.002)
0.016*** (0.003)
0.014*** (0.003)
0.015*** (0.003)
0.011*** (0.003)
0.012*** (0.003)
0.014*** (0.003)
0.013*** (0.003)
0.737*** (0.002)
36,414
0.988
SKU & Store

Coef
SE
0.004
(0.003)−0.010*** (0.003)
0.002(0.003)0.010*** (0.003)−0.013*** (0.003)
0.010*** (0.003)
0.008*** (0.003)
0.011*** (0.003)
0.015*** (0.003)
0.001(0.003)0.013*** (0.003)
0.012*** (0.003)
0.017*** (0.003)
0.016*** (0.003)
0.012*** (0.003)
0.017*** (0.003)
0.018*** (0.003)
0.017*** (0.003)
0.014*** (0.003)
0.015*** (0.003)
0.011*** (0.003)
0.013*** (0.003)
0.015*** (0.003)
0.013*** (0.003)
0.737*** (0.002)
36,414
0.986
SKU & Store Type

Honey
(Median number of SKUs)

Table 3
Representative Estimation Results for Weekly Frequency Estimations

Coef
SE
0.000
(0.004)−0.009*(0.005)−0.003(0.004)−0.003(0.005)−0.002(0.005)0.000(0.004)0.001(0.004)−0.001(0.004)−0.006(0.006)−0.008(0.006)−0.004(0.005)−0.007(0.005)−0.001(0.004)−0.003(0.005)−0.002(0.005)0.000(0.004)0.001(0.004)0.001(0.003)0.000(0.004)−0.001(0.004)−0.003(0.004)−0.002(0.004)−0.001(0.004)−0.002(0.004)0.728*** (0.003)
4,111
0.965
SKU & Store

Coef
SE−0.001(0.006)−0.009(0.007)−0.002(0.006)−0.004(0.007)−0.004(0.007)0.000(0.006)0.001(0.006)−0.001(0.007)−0.002(0.008)−0.007(0.007)−0.002(0.007)−0.004(0.007)0.002(0.007)0.002(0.007)0.000(0.007)0.003(0.006)0.006(0.006)0.007(0.006)0.003(0.006)−0.003(0.006)−0.007(0.008)−0.002(0.006)0.001(0.006)−0.002(0.006)0.727*** (0.004)
4,111
0.931
SKU & Store Type

Skimmed Milk
(Smallest number of SKUs)

where swi is the sales amounts weight for item i, and I is the number of SKUs of the item. We
use the fixed weight in this paper because of the two reasons. First, using the fixed or timevarying weights in the daily frequency estimations produces similar results over time. Second,
the weekly frequency estimations with full sample data do not fit well with the time-varying
weights aggregation.

4.3

Baseline estimation results

Fig. 9 summarizes the estimated HFQAPIs based on the baseline estimation results for DROL_SK+ST, D-ROL_SK+TY, W-MO_SK+ST, and W-MO_SK+TY. The plotted figures are thecumulative price changes on a quality-adjusted basis, using the week starting on January 6,
2020, as the base period. The figure also includes the UPI for reference. The light blue shaded
area in the figures indicates the period of the first declaration of a state of emergency in Tokyo.

Fig. 9. Baseline Estimation Results
Notes: The light blue area indicates the period for the first declaration of a state of emergency in Tokyo.

The figure depicts three points regarding the inflation developments for food and beverage
products during the first half of 2020. First, all the indicators, including UPI, reveal very similar
trends until the end of February. Second, UPI and other quality-adjusted price indices reveal
different trends since then because of the heightened concern over the wide and rapid spreadof COVID-19 in Tokyo. Third, again, all the indicators reveal a similar downward trend fromthe end of the first declaration of a state of emergency.
The cumulative inflation from the beginning of January to the peak is estimated at 0.9% in
the daily frequency estimations and 0.6% in the weekly frequency estimations. The estimates
are slightly different but stay between UPI and zero inflation. In addition, the estimates for the
daily and weekly specifications are not influenced by the two types of fixed effects in a crosssectional direction, SKU and store as well as SKU and store type. This suggests that the retailservice quality differences are well controlled at the store type level.
Fig. 10 plots the aggregated fixed effects of store types, δ, over all items using sales amount18

share as weights. The base store type is GMS, and the plotted figures indicate the convenience
premiums or discounts of the store type against GMS. The estimates reveal very stable movements over time for all store types. This suggests that convenience premium or discount for
store types remained unchanged under the first wave of the COVID-19 spread. CVS has thelargest premium, reflecting its high retail service quality in terms of operating hours, location,and shopping time. SM and M-SM have smaller but positive premiums. HC/DS, Drug/L,and Liquor/DS give discounts, which is consistent with the sales strategy of lowering prices
by reducing retail services. Discounts for Liquor/DS started shrinking slightly from March,reflecting the growing demand for home drinking under a voluntary lockdown.

Fig. 10. Estimates for Store Type Fixed EffectNotes: GMS is used as the base of the fixed effect on the store type, and the plotted figures indicate the convenience
premiums or discounts of the store type against GMS. The light blue area indicates the period for the first declarationof a state of emergency in Tokyo.

The results of the baseline estimations seem consistent with Fig. 1, which indicates that the
inflation of UPI (CPINow T-index) accelerated, whereas there was no acceleration in the mode
UPI (CPINow T-mode-index). The T-index fully reflects the decrease in temporary sales as a
price increase, whereas the T-mode-index does not account for changes in temporary sales. The
quality-adjusted price indices, in terms of both product characteristics and retail service quality,
are somewhere between the two CPINow indicators because households try to minimize therisk of COVID-19 infection by reducing travel distance to outlets and shopping time. In thenext section, we examine the appropriateness of the estimated quality-adjusted price index
with various robustness checks.

5

Robustness Checks

We now carry out the robustness checks from the following five perspectives: (1) alternative
fixed effect for product-store combination, (2) whole sample estimation using daily frequency
data, (3) alternative summary statistics for weekly conversion (mean and median), (4) inclusion19

of temporary sales dummy as an explanatory variable for the daily frequency estimation, and(5) extension of subsample period to three weeks in the staggered rolling regression. Table 4summarizes the five robustness checks.
Table 4
Robustness Checks
Abbreviations(1)

Details on Robustness Checks

D-ROL_SKxST
W-MO_SKxST(2)

D-WHL_SK+ST
D-WHL_SK+TY

Alternative fixed effect for product-store combination(SKxST)
Whole sample estimation using daily frequency data
(WHL)

W-MN_SK+ST(3)

W-MN_SK+TY
W-MD_SK+ST

Alternative summary statistics for weekly conversion:mean (MN) and median (MD)

W-MD_SK+TY
D-ROL_SK+ST_TS(4)

D-ROL_SK+TY_TS

Inclusion of temporary sales dummy as an explanatory
variable for daily frequency estimation (TS)D-ROL_SKxST_TS(5)

D-ROL3_ST+TY_1
D-ROL3_ST+TY_2

5.1

Extension of subsample period to three weeks in staggeredrolling regression with different linking methods

Robustness check 1: Fixed effect for the product−store combination

The first robustness check examines the impacts of alternative fixed effects for the product-store
combination as the cross term of SKU code and store ID. In this case, the same products sold at
different stores are considered different goods. The estimation specifications of D-ROL_SKxST
and W-MO_SKxST are given by Eqs. (13) and (14) for the daily and weekly frequency estimations, respectively:w
lnUPi,k,t = λw D_WK i,k,t+ ηi,k + ei,k,t ,

(13)

W

MO
v
lnUPi,k,w= ∑ λv D_WKi,k,w+ ηi,k + ei,k,w ,

(14)

v =2

where ηi,k is a fixed effect for the product−store combination for SKU code i and store ID k.
Fig. 11 plots D-ROL_SKxST and W-MO_SKxST along with the baseline specifications of DROL_SK+ST and W-MO_SK+ST as well as the UPI. Conducting the estimations with the crossterm of SKU and store as a fixed effect for a cross-sectional direction produces lower estimates
for the quality-adjusted price indices in both the daily and weekly frequency estimations. The
downward revision is larger in the daily frequency estimation. This estimation results suggest
20

the possibility of the overadjustments of SKU-store specific price increases when using thecross term of SKU and store as a fixed effect. This tendency is further amplified by the twoweek staggered rolling estimations for daily frequency data through the time-varying constantterms.

Fig. 11. Robustness Check 1: Fixed Effect for the Product-Store Combination
Notes: The light blue area indicates the period of the first declaration of a state of emergency in Tokyo.

5.2

Robustness check 2: Daily estimation for the full sample period

The second robustness check focuses on the effects of structural changes in temporary sales inthe daily frequency estimations by comparing the results of the daily estimation for the fullsample period data with those of the baseline two-week staggered rolling estimations. The
staggered rolling estimations are expected to absorb item-wide structural changes, including
the frequency and price discount of temporary sales, by changes in constant terms over time.
The estimation specifications of D-WHL_SK+ST and D-WHL_SK+ST are given by Eqs. (15)and (16) for the two types of fixed effects, respectively:
Ww
lnUPi,k,t = ∑ λw D_WK i,k,t+ γi + δk + ei,k,t ,

(15)

w =2
W

w
lnUPi,k,t = ∑ λw D_WK i,k,t+ γi + µ j + ei,k,t ,

(16)

w =2

Fig. 12 depicts the estimation results for D-WHL_SK+ST and D-WHL_SK+TY, along withthe baseline estimation results for D-ROL_SK+ST and D-ROL_SK+TY as well as the UPI. The
cumulative inflation for D-WHL_SK+ST and D-WHL_SK+TY are both estimated at 1.2%, which
is higher than the baseline estimation results. However, the estimates are not influenced by thetwo types of fixed effects in a cross-sectional direction for SKU and store as well as SKU andstore type.

21

Fig. 12. Robustness Check 2: Daily Estimation for the Full Sample Period
Notes: The light blue area indicates the period of the first declaration of a state of emergency in Tokyo.

The differences between D-ROL and D-WHL are estimated at 0.3%. The differences comefrom the time-varying constant terms in the two-week staggered rolling estimations. The timevarying constant terms are deemed effective in absorbing item-wide structural changes, including the frequency and price discount of temporary sales. Thus, we regard the differences as theeffects of reduced frequency and price reduction of temporary sales in the daily frequency estimations. In addition, the differences between UPI and D-WHL of around 0.5% are regarded
as outlet substitution effects stemming from the households’ behavior to purchase from a store
nearby at slightly higher prices because of the risk of COVID-19 infection.

5.3

Robustness check 3: Weekly data conversion measures

The third robustness check focuses on the effects of structural changes in temporary sales in
the weekly frequency estimations by comparing the estimation results using two alternative
summary statistics for data conversion on a weekly basis—mean (MN) and median (MD). The
estimation specifications of W-MN_SKxST, W-MN_SKxST, W-MN_SKxST, and W-MN_SKxST
are given by Eqs. (17), (18), (19), and (20) for the two types of fixed effects, respectively:
W

MN
v
lnUPi,k,w= ∑ λv D_WKi,k,w+ γi + δk + ei,k,w ,

(17)

v =2
W

MN
v
lnUPi,k,w= ∑ λv D_WKi,k,w+ γi + µ j + ei,k,w ,

(18)

w =2
W

MD
v
lnUPi,k,w= ∑ λv D_WKi,k,w+ γi + δk + ei,k,w ,

(19)

v =2
W

MD
v
lnUPi,k,w= ∑ λv D_WKi,k,w+ γi + µ j + ei,k,w .
w =2

22

(20)

The estimation results in Fig. 13 are ordered from highest to lowest as follows: W-MN,
W-MD, and W-MO, with almost identical estimates for the two types of fixed effects in a crosssectional direction. The results suggest that W-MN is mostly influenced by declines in thefrequency and size of price reductions of temporary sales. This is consistent with the observation in Fig. 7 that compares the inflation trend with the three statistical measures for thecentral tendency of unit price distributions, revealing that the mean is the highest, followed by
the mean and median. Thus, it is likely that W-MN and W-MD make overadjustments of thetemporary sales effects.

Fig. 13. Robustness Check 3: Weekly Data Conversion Measures
Notes: The light blue area indicates the period of the first declaration of a state of emergency in Tokyo.

As in the previous robustness check for the daily full sample estimations, the differences
between W-MN and W-MO (0.4%) and those between UPI and W-MN (0.7%) are regarded as
the effects of temporary sales and outlet substitution, respectively. The differences between
W-MN and W-MO solely come from the summary statistics measures in weekly frequency
conversion, that is, the mean or mode of unit prices in a week, which corresponds to the effects
of temporary sales in terms of reduced frequency and price reduction.

5.4

Robustness check 4: Estimation with the temporary sales dummy

The fourth robustness check introduces the temporary sales dummy as an additional explanatory variable in the two-week staggered rolling estimations with daily data. This robustness
check examines the existence of additional temporary sales effects, which are not detected in
the baseline estimation specifications for the daily frequency estimations. As explained in Section 3, temporary sales are defined as a day when the observed price for a product at a store is
at least two yen lower than the mode price for the past seven days, including the current day,following Abe and Tonogi (2010).
The estimation specifications of D-ROL_SK+ST_TS, D-ROL_SK+TY_TS, and D-ROL_SKxST_TS
are given by Eqs. (21), (22), and (23).
23

w
lnUPi,k,t = λw D_WKi,k,t+ κD_TSi,k,t + γi + δk + ei,k,t ,(21)

w
lnUPi,k,t = λw D_WKi,k,t+ κD_TSi,k,t + γi + µ j + ei,k,t ,(22)

w
lnUPi,k,t = λw D_WKi,k,t+ κD_TSi,k,t + ηi,k + ei,k,t ,(23)

D_TSi,k,t =1

temporary sales for SKU code i, store id k, at time t

0otherwise

where D_TSi,k,t indicate the temporary sales dummy for SKU code i at store ID k and time t. κ
is the estimated coefficient for the temporary sales dummy.
Fig. 14 depicts the estimation results. Surprisingly, all the three specifications with the temporary sales dummy—D-ROL_SK+ST_TS, D-ROL_SK+TY_TS, and D-ROL_SKxST_TS—exhibit
almost identical fluctuations over time, suggesting that the inclusion of the temporary sales
dummy eliminates the temporary price fluctuation at the individual price observation level.
However, the result is consistent with the no acceleration in the year-on-year changes in the
CPINow T-mode-index, as depicted in Fig. 1. The above observations suggest that introducing
the temporary sales dummy as an additional explanatory variable leads to overadjustments ofthe temporary sales effects by eliminating all the temporary price reductions.

Fig. 14. Robustness Check 4: Estimation with Temporary Sales Dummies
Notes: The light blue area indicates the period of the first declaration of a state of emergency in Tokyo.

5.5

Robustness check 5: three-week staggered rolling regression

We perform the final robustness check by extending the subsample periods for the staggeredrolling regression from two to three weeks, as given by Eq. (24).
24

w
w +1
lnUPi,k,t = λw D_WK i,k,t+ λw+1 D_WK i,k,t+ γi + µ j + ei,k,t .

(24)

We construct two types of quality-adjusted price indices based on the estimation results using the estimated coefficients for the second- and third-week dummies, denoted as D-ROL3+SK+TY_1
and D-ROL3+SK+TY_2, respectively. The first linking method, D-ROL3+SK+TY_1, links themost recent period movement to the previous estimates. The second linking method, D-ROL3+SK+TY_2,
links the whole period movement to the previous estimates.
As depicted in Fig. 15, D-ROL3+SK+TY_1 and D-ROL3+SK+TY_2 move almost identicallyand very close to D-ROL_SK+TY. This confirms that extending the subsample period to three
weeks does not significantly influence the estimation results.

Fig. 15. Robustness Check 5: Three-Week Staggered Rolling Estimations
Notes: The light blue area indicates the period for the first declaration of the state of emergency in Tokyo.

6

Inflation Trend Under the First Wave of the COVID-19 Spread

Table 5 decomposes changes in UPI into three components—temporary sales effects, outlet
substitution effects, and changes in quality-adjusted price indices. In the daily frequency estimation, the increase in UPI of 1.7% is decomposed into the temporary sales effects of 0.3%,
the outlet substitution effects of 0.5%, and the increase in the quality-adjusted price index of
0.9%, whereas in the weekly frequency estimation, it is 0.4%, 0.7%, and 0.6%, respectively. The
observed increases in UPI overestimate the quality-adjusted price increases caused by the inappropriate adjustments of the outlet substitution effects and the temporary sales effects.
The cumulative increases in quality-adjusted price indices reached their peaks at 0.9% in
the daily frequency estimation and 0.6% in the weekly frequency estimation in early April,remaining around those levels until late May and then started declining. Due to the possibilityof different assessments of the temporary sales effects from person to person, inflation is 1.2%
in the daily frequency estimation and 1.1% in the weekly frequency estimation by counting the25Table 5
Decomposition of Unit Price Changes
Daily Estimation
Unit Price Index

Weekly Estimation

1.7% (= UPI)

Outlet Substitution
Effects

0.5%(= UPI − D-WHL)

0.7%(= UPI − W-MN)

Temporary Sales
Effects

0.3%(= D-WHL − D-ROL)

0.4%(= W-MN − W-MO)

Quality-adjusted
Price Index

0.9%(= D-ROL)

0.6%(= W-MO)

temporary sales effects as inflation.
Our answer to the question of this paper, “Was inflation observed under the first wave of
the COVID-19 spread?” is yes, but it was fairly mild and temporary.

7

Conclusions

We examined whether inflation was observed under the first wave of the COVID-19 spread inJapan. To address this question, we constructed high-frequency quality-adjusted price indicesby employing daily scanner data of retail stores in Tokyo. We made explicit adjustments for not
only the product characteristics but also the structural changes in temporary sales and the retailservice quality of outlet channels. We assumed that adjustments for the effects of temporary
sales and retail service quality are particularly important in examining the retail price dynamics
under the COVID-19 pandemic as the voluntary lockdown constrained household purchasing
behavior.
We concluded that mild and temporary inflation of slightly less than 1% (0.6%-0.9%) was
observed during the first wave of the COVID-19 spread based on the overall assessment of
the baseline estimations and the five robustness checks. We also decomposed the differences
between the increases in the unit prices and those in the quality-adjusted price indices into
outlet substitution effects and temporary sales effects. In the daily frequency estimations, theincrease in UPI of 1.7% was decomposed into the temporary sales effects of 0.3%, the outlet
substitution effects of 0.5%, and the increases in the quality-adjusted price indices of 0.9%. In
the weekly frequency estimations, it was 0.4%, 0.7%, and 0.6%, respectively.
Our empirical results revealed that the construction of quality-adjusted price indices becomes very difficult when faced with large-scale structural changes in the retail markets, including the frequency of temporary sales and the size of price reductions. As discussed in
Section 1, the widening deviations between the two types of daily price indices—the T-index
and the T-mode-index—indicate the possibility of structural changes in the retail markets. Fig.
16 plots the long time series of the deviations from 1990. As depicted in the figure, the pe26

riod of our focus, January to June 2020, experienced the largest positive deviations between thetwo indices, suggesting that structural changes in retail markets were unprecedentedly large,
although for a short period.12

Fig. 16. Spreads between T-index and T-mode-index
Notes: The figure plots the divergence between year-on-year changes in T-index and T-mode-index. The light blue
area indicates the first half of 2020, that is, the period under primary analysis in this paper.
Source: Nowcast, CPINow.

However, it should be noted that the mid-1990s to the early 2000s also experienced significant and continued deviations between the two indices in a negative direction. This period
corresponds to observing the “price busting” phenomenon when large-scale structural changes
in the retail markets, symbolized by the expansion of large-scale retail stores, were advanced.
As Shiratsuka (1999) has pointed out, the outlet substitution bias severely affected the Japanese
CPI during that period.
We stress that the CPI needs to consider how to deal with possible large-scale structuralchanges in the retail markets as it is hard to anticipate such changes in advance. It is also
important to respond flexibly to such structural changes in the retail markets once it occurs.
However, the current price survey method based on a “one-specification-for-one-item” policy
is unable to deal with that issue, as the method specifies a few most popular specifications
for each item and continuously surveys their prices at specific outlets.13 The most promisingalternative price information is the use of scanner data, as considered in this paper. Althoughscanner data cover about 20% of the CPI basket, these products represent a significant portionof the Retail Price Survey, which is the primary data source for the CPI. It is a future challenge
to explore an estimation framework to produce stable results while flexibly incorporating theeffects of structural changes with longer-term scanner data.
12 Another major divergence was observed immediately after the Great East Japan Earthquake in March 2011.
13 Shiratsuka (2021) examined the lower-level substitution bias using the micro-data for the Retail Price Survey,

which is the primary source data for the Japanese CPI. He revealed that the lower-level substitution bias stemmingfrom the elementary aggregation formula is very limited but volatile in both positive and negative directions.

27

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