Product Cycle and Consumer Price Index ∗- Very Preliminary Toshiaki Shoji†

Yuki Teranishi‡

Abstract
This paper shows that the official Consumer Price Index (CPI) is quantitatively
well affected by product entry and exit, i.e., the number of product in the entire
market. We make use of an unique environment where the Nikkei point of sale
(POS) scanner data has larger samples than the official CPI for food products anddaily necessities in Japanese supermarkets. We first estimate the representative
product entry model in Bilbiie, Ghironi, and Melitz (2007) for the Nikkei data andconfirm that the model fits to the data well and a free entry shock related to a
product entry explains about 49 percent of price variations. Then, we evaluate
whether the official CPI holds the same features as the Nikkei data or not. When
we estimate the product entry model for variants of the official CPIs, estimatedparameters are the almost same as the cases for the Nikkei data and a free entry
shock explains about 19 percent of price variations in the official CPI including
all items. Sampling for the official CPI is sufficiently precise to reflects Japanese
product market features and an effect of the number of products on prices throughan intensive margin effect though the official CPI assume a constant basket.
Our result provides several implications for economic analyses. A product entry
makes quantitatively significant effects on prices and decreases a standard deviationof the official CPI inflation rates by about 41 percent. Moreover, a product entry
contributes to make a secular deflation in the last several decades and a large
inflation rise in the last few years in Japan. It implies that a model discarding an
endogenous product entry and product number data can not evaluate these andsuffers from under and over-evaluation in estimations, variance decompositions,and impulse responses.

Keywords:

product entry; consumer price index; economic analysis∗

As of April 2024. First Draft April 2023. We thank *****.
Seikei University. E-mail: tshoji@econ.seikei.ac.jp‡
Keio University. E-mail: yukitera@fbc.keio.ac.jp

†

1

1

Introduction

Bilbiie, Ghironi, and Melitz (2007, 2012) show that a new product entry changes pricesetting behaviors in a product market by a variety effect which is described by the
number of products. Moreover, it is conventional idea in economics that a firm’s pricesetting is affected by other firms’ price settings across the entire market. A price setting
behavior changes by a degree of competition under monopoly, oligopoly, monopolisticcompetition, or perfect competition. Therefore, the number of products in a market is
an important element to change individual prices.
Recently, we can precisely observe a product cycle, i.e., a new product entry into amarket and an old product exit from a market, everyday using product-level micro data.
The number of products frequently changes in a market.1 On the other hand, the official
Consumer Price Index (CPI) excludes such frequent product entry and exit and assumes
a constant basket of products. Therefore, the index seems to ignore product entry andexit. It, however, is not necessarily discarding effects of product entry and exit.
The index naturally excludes a price effect by a change in the number of productsin the basket, i.e., an extensive margin effect. However, the index can include a priceeffect by a variable number of products in the entire market on an individual price inthe basket, i.e., an intensive margin effect. Here, we have two “if(s)” to conclude thatthe official CPI is affected by the number of products. The official CPI is affected by
the number of products if prices in the population data are affected by the number of
products, and if the official CPI well represents the population data.
For Japan, we can evaluate these two “if(s)”. We take advantage of an unique
Japanese data environment where the Nikkei point of sale (POS) scanner data has larger
samples than the official CPI as shown in Imai and Watanabe (2015) and Watanabe and1

Several empirical studies find that a frequent product entry and exit in a product market. Broda

and Weinstein (2010) show, when using product-level micro data, that the product turnover rate in the
US is about 25 percent annually. Ueda, Watanabe, and Watanabe (2019) confirm the same facts forJapan using matched samples of Nikkei point of sale scanner data and show that product turnover is
30 percent annually in Japan.

2

Watanabe (2014). The official CPI can be interpreted as a sub-sample of the Nikkei POS
scanner data. The Nikkei data is a private data and corrects sales prices and quantities
for all food products and daily necessities from Japanese supermarkets for long years
from April 1988 to present. In the end of 2022 year, the items included in data is about
170 out of the 588 items in the official CPI in Japan. However, when we restrict a sample
to these 170 items, corrected samples are much larger in Nikkei data than the official
CPI. Imai and Watanabe (2015) show that the number of products in the Nikkei datafrom 2000 to 2010 year is 462, 906. Among these samples, only 70, 966 products meet theStatistic Bureau of Japan specifications that can be sampled in the official CPI. This isbecause the Nikkei data basically includes all products in supermarkets and the official
price indexes arbitrary pick up some representative products that samplers think in eachcategory.
For the first “if”, we evaluate product entry effect on prices using the Nikkei data. In
evaluation, we focus on a mechanism behind an intensive margin effect on prices since anextensive margin effect is a simple calculation in aggregating individual prices in data.
To see an intensive margin effect, we use the representative endogenous product entry
model in Bilbiie, Ghironi, and Melitz (2007). This model is well known and commonlyused to business cycle and price analyses for a product entry. In the model, a variable
number of products in the entire market changes prices through a variety effect. For data,
based on individual prices in the Nikkei data, we construct the sales-weighted average
price across all products including temporary sales and all shops for each quarter. Thisis the Supermarket Basket Price Index (SBPI) as shown in Dong, Shoji, and Teranishi(2024). This price index allows the number of products to change over time by productentry and exit. Here, we know the real sales amount, the number of product, and SBPI,
where these are consistent each others.
We estimate the BGM model by Bayesian inference and show that the endogenous
product entry model fits to the data well. By variance decomposition, we show that a freeentry shock that is related to a product entry explains about a half of SBPI variations.
When we compare BGM model and a standard New Keynesian model to quantitatively

3evaluate a contribution of a product entry on price variations, contributions significantly
change from 40.9 percent to 56.8 percent in different specifications. These results imply
that a product entry quantitatively holds a clear effect on prices for food products anddaily necessities in Japan. This conclusion does not change even for several SBPI variants
that replicate sampling and calculation method in the official CPI. In particular, we show
two cases, using a trend component of SBPI to exclude temporary sales and a matchedproducts version of SBPI to calculate inflation rate based on individual prices. These
results are proof for the first “if”.
For the second “if”, supposing a relationship between the Nikkei data as a population
data and the official CPI as a sub-sample of the Nikkei data, we replace SBPI by theofficial CPIs and estimate models. Here, we also make use of a feature of the BGMmodel in which an individual price is the same for all products and is determined byan aggregate demand and the number of products for whole products after applying
the symmetric equilibrium assumption. Thus, if the official CPI correctly reflects the
population data, we can replace SBPI by the official CPI. We suggest a new approachfor price analyses by combining Japanese macro-level official CPI data with micro-level
Nikkei data. In the first experiment, we replace SBPI by the limited official CPI that
only includes categories of the Nikkei data. In the second experiment, we replace SBPI
by the official CPI for all items including all service prices and all goods prices. Here, weneed a strong assumption that the same endogenous entry effect holds for services andgoods that are excluded in the Nikkei data.
Estimation results show that the model is well estimated and estimated key parameters such as elasticity of substitution across goods and intertemporal elasticity of labor
substitution are the almost same as the case using Nikkei data. For a price stickiness,a price adjustment parameter is estimated larger than the case using the Nikkei data
since the official CPI excludes temporary sales and its price variations are smaller thanones of the Nikkei data. For this point, we confirm that a price adjustment parameter isestimated larger when we exclude temporary sales from SBPI. As the case of the Nikkei
data, a free entry shock explains non-trivial part of price variations in the official CPI.

4

These results show that the official CPI is affected by a product entry as the Nikkei data
though the official index itself assumes a constant basket. Thus, the official CPI is a
representative sample of population data of the Nikkei data. It implies that the second“if” is proved.
Then, we show several implications for macro-level economic analysis using the official
CPI. First, a product entry have quantitatively non-trivial effects on prices. A standard
deviation of CPI inflation rates decreases 40.9 percent by a product entry. Second, a freeentry shock that is related to a product entry explains about 19 percent of price variationsin the official CPI. Free entry shocks sometime decrease official CPI inflation rates morethan one percent and further the shock continuously contributes to a secular deflation in
Japan. Moreover, the latest inflation surge is explained by increasing number of products.
Third, a model selection failure makes a serious problem when we use the official CPI
and a model discarding a product entry and a variable number of the products. By
misidentifications, models suffer from large over- and under-evaluations in estimation,
impulse responses, and variance decompositions.
The rest of our paper is organized as follows. Section 2 describes our data anddiscuss advantage of the data. Section 3 introduces BGM model and estimate it using
Nikkei data. We show that BGM model fits to Nikkei data well. Then, we evaluatea quantitative effect of a product entry and a variable number of product on prices in
Section 4. Section 5 shows that SBPI variant data that includes sampling features of theofficial CPI gives the same result for estimations. In Section 6, we show that the official
CPI is a good sample of Nikkei data and is affected by a product entry and a variable
number of products. Section 7 discuss some implications for economic analyses. Section
8 concludes.

5

2

the Nikkei POS scanner data

We use a unique data set, the Nikkei POS scanner data.2 Our data includes sales prices
and quantities for each product at each retail shop on each day from April 1988 to
December 2022. The retail shops consist of supermarkets in Japan, where typically foodproducts and daily necessities are sold. The scanner data covers 170 out of the 588 itemsin the Japanese CPI.3 At the start of our sample period, there are 29 supermarkets andthe number of shops increases to 300 at the end of the sample. Our analysis is restricted
to the 7 supermarkets that appear throughout the sample period. This sample restriction
avoids any bias caused by shop entry and exit in prices. We interpret the data from the
7 supermarkets as a random sample to observe prices, the sales amount, and the numberof products. The 7-supermarket sample has 900, 000 products in total, about 77, 000
products on average per year, and about 30, 000 products on average per retailer per
year. We use quarterly data though the original Nikkei POS scanner data is daily.4
The first advantage of our data is that we can observe product cycles. An individual
product’s life cycle can be clearly identified through its entry into and exit from theproduct market. We know an exact product number in a market. The average of thenumber of products in our Nikkei data is 52884.32 and the standard deviation of thenumber of products is 15438.89, as shown in Table 1. It is in sharp contrast withthe official CPI which changes the number of products and a variety of products only
every five years. Entry rate and exit rate in data are 0.122 and 0.115, respectively, as
shown in Table 1. These imply that all product are replaced by about nine quarters on
average. The second advantage is that we can observe individual product prices over the
product’s life cycle. Based on individual prices, we construct the sales-weighted average
price across all products including temporary sales and all shops for each quarter. Welabel this unique price index as the Supermarket Basket Price Index (SBPI) as in Dong,
2

Appendix A has detailed information about the data, including product identification by Japanese

Article Number (JAN) code, average price, entry rate, exit rate, and product varieties.
3
Our data does not include fresh food, recreational durable goods, such as computers and cell phones,
and services such as housing rent and utilities.
4
See Appendix A for a description of how we convert daily data into quarterly data.

6

Shoji, and Teranishi (2024). Naturally, this price index allows the number of products
to change over time. The third advantage is that we know the sales amount that is
consistent with the number of product and SBPI. An average nominal sales amount is
4, 354, 313, 201 yen and its one standard deviation is 750, 835, 205 yen as shown in Table
1. In real term, an average real sales amount denominated by SBPI is 6, 830, 135 andits one standard deviation is 940, 731. In the official CPI, we do not know these. Figure
1 shows SBPI inflation rate, the number of products, and the real sales amount. SBPI
inflation rate is given by year to year growth of SBPI. The number of products and thesales amount data are percentage deviations from trends calculated by HP filter. These
numbers are not multiplied by 100. The real sales amount is deflated by SBPI and wecall it as demand in following analyses. The sample covers from 1988Q2 to 2022Q4 andincludes several business cycles. Therefore, we can precisely estimate models including
product entry and exit.
Furthermore, our unique Nikkei POS data makes a new insight possible. As shown in
Imai and Watanabe (2015) and Watanabe and Watanabe (2014), the official CPI observes
the same products in Japanese supermarkets as the Nikkei data and can be interpreted asa constant sub-sample of the Nikkei data when we restrict product categories (items) as inour sample. In particular, Imai and Watanabe (2015) show that the number of productsin the Nikkei data from 2000 to 2010 year is 462, 906. Among these samples, only 70, 966
products meet the Statistic Bureau of Japan specifications that can be sampled in theofficial CPI. This is because the Nikkei data includes all products in supermarkets and theofficial price indexes arbitrary pick up some representative products that samplers thinkin each category. These official indexes keep a constant basket size without product entry
and exit and include long surviving existing products.5 Under this unique environment
in Japan, we can evaluate whether Japanese official CPI reflects a product entry effecton prices.
5

Probably, there is forced product exit and entry by a product exit from a market and adding a new

successor product to an old predecessor keeps a constant basket. We, however, can not know the details
for it.

7

3

Product Entry Effect in SBPIWhen we see Nikkei data, it is apparent that there exists a product entry and it holds
a significant effect on prices. We, however, do not know a mechanism behind the data,in particular for an intensive margin effect on prices by a product entry. Thus, throughlens of a representative endogenous product entry model in Bilbiie, Ghironi, and Melitz(2007), we quantitatively show an intensive margin effect on prices by a variety effect in
SBPI. We estimate the model with Bayesian inferences using Dynare 5.2.

3.1

Observations using Bilbiie, Ghironi, and Melitz’s Model

We use BGM model given by following five equations.

Et Nt+1 = (1 + r + ψ) Nt − (r + ρ + ψ) Ct − ψ (θ − 1) µt+ [(r + ρ + ψ) (θ − 1) + ρ] Zt − ρfE,t ,
Ct



1−ρ
1−ρ
r+ρ
=
Et Ct+1 −−Et Nt+1
1+r(1 + r) (θ − 1) 1 + r
1
1−ρ
+
Nt −
Et fE,t+1 + fE,t
θ
−
1
1
+
r


1−ρ r+ρ−(θ − 1) Et µt+1 − µt ,+1+r 1+rC
πtC = β (1 − ρ) Et πt+1
−

−

(1)

(2)

θ−1
µt
κ

1
[Nt − Nt−1 − β (1 − ρ) (Et Nt+1 − Nt )] ,
θ−1

(3)

1
1
Et Nt+1 −
Nt ,
θ−1
θ−1

(4)

C
Et Ct+1 = Ct + it − Et πt+1+

C
i = ϕπ πt+1
+ Mt ,(5)

where Nt , Ct , µt , πtC , and it are the number of products, demand, markup, CPI inflation
rate, and nominal interest rate, respectively. These are endogenous variables. As exogenous shocks, Zt , fE,t , and Mt are a productivity shock, a free entry shock, and a demand8shock, respectively. As parameters, ρ, r, θ, φ, κ, and ϕπ are separation rate, steady state
real interest rate, the symmetric elasticity of substitution across goods, intertemporalelasticity of substitution in labor supply, a price adjustment parameter, and a monetary. It notes that we assume thepolicy parameter, respectively. We define ψ = φ (r+ρ)(θ−1)+ρθ−1
CES preferences for the consumption aggregator. As mentioned in Bilbiie, Ghironi, andMelitz (2012), (1) determines the number of goods in a market according to a demand
and a productivity shock. (2) determines a markup by the number of products and a freeentry shock. (3) is a Phillips curve to determine CPI inflation rates by a markup andthe number of products. These two equations show that an endogenous product entry
holds clear effects on a price setting. (4) decides a demand according to a real interest
rate and the number of products. A forward-looking monetary policy (5) sets a nominalinterest rate as in Bilbiie, Ghironi, and Melitz (2007) and includes a demand shock.

3.2

Data and Observation Errors

We use Nikkei POS scanner data in a quarterly base over the sample from 1990Q2 to
2022Q4. The estimation uses three time series data, SBPI to πtC , the number of products
to Nt , and real demand for products to Ct . πtC is given by year to year growth of SBPI.
Nt and Ct data are percentage deviations from trends calculated by HP filter.
To include data into a model, we assume observation errors given by 10 percent
of one standard deviation to an inflation rate, i.e., 0.068/10, the number of products,
i.e., 0.04/10, and real demand, i.e., 0.2/10. Observation errors are assumed to be i.i.d.
normally distributed with zero mean.

3.3

Calibrated Parameters and Shocks

We use a conventional value for a discount factor as β = 0.99 and r = β −1 − 1 for aquarterly model. We calibrate an exit rate as ρ = 0.115 as in Table 1. This is an averageof exit rates from Nikkei data. As in Bilbiie, Ghironi, and Melitz (2007), we set ϕπ = 1.5.
We use three types of shocks, free entry shock fE,t , productivity shock Zt , and de-9mand shock Mt , as shown in the model. We assume AR1 process with i.i.d. normally
distributed disturbance as follows.

fE,t = ρf fE,t−1 + ϵft ,Zt = ρz Zt−1 + ϵzt ,Mt = ρm Mt−1 + ϵmt ,where standard deviations of ϵft , ϵzt , and ϵmt are given by σf , σz , and σm , respectively.

3.4

Prior and Posterior Distributions

Table 2 shows moments for the prior distributions of structural parameters. As prior distributions, we assume calibrated parameters in Bilbiie, Ghironi, and Melitz (2007) except
shock persistences and standard deviations. For the symmetric elasticity of substitution
across goods θ, the intertemporal elasticity of substitution in labor supply φ, and a priceadjustment parameter κ, we assume Inverse Gamma Distribution since these parameters
should be positives. Regarding a shock persistence, we assume Beta distribution with
0.5 mean. For a standard deviation of shock, we assume Inverse Gamma Distribution
with 0.1 mean.
Figure 2 shows prior distributions colored by gray and estimated posterior distributions colored by black and Table 3 shows statistics for the distributions. Elasticity of
substitution across goods θ and intertemporal elasticity of labor substitution φ are estimated as 7.834 and 0.486, respectively. For elasticity of substitution across goods, theestimated number is larger than a mean of prior that is calibrated in Bilbiie, Ghironi, andMelitz (2007). It implies that a variety effect is less elastic to the number of the products.
A reason for it is that a variation of the product number is larger in our Nikkei data thanin data that Bilbiie, Ghironi, and Melitz (2007) analyze as shown in separation rates as
0.025 in the paper and 0.115 in our paper. As shown in the estimation and variancedecompositions in the next section, the product number data naturally gives fundamen-

10

tal quantitative effects for these.6 For a price stickiness, a price adjustment parameteris estimated as 41.88. This is smaller than one in Bilbiie, Ghironi, and Melitz (2007).
A reason is that the Nikkei data includes temporary sales and its price variations arelarger than the official CPI that excludes temporary sales. We clarify it in Section 5.2.
These estimation results are still reasonable numbers when comparing these to Bilbiie,
Ghironi, and Melitz (2007).7

3.5

Variance Decomposition and Impulse Responses

As shown in Table 4, a productivity shock, a free entry shock, and a demand shock
explain 38.78, 49.37, and 11.85 percent of CPI inflation rate variations, respectively. To
CPI inflation rate, a free entry shock holds the largest effect. One reason for it is thata new price by a new product is directly included in SBPI without delays since SBPI
inflation rate is calculated by year to year growth of price levels each period with sales
weights across products as shown in Appendix A. For other variables, these shocks also
play important roles.
Figure 3 shows impulse responses to a free entry shock that decreases a product entry.
As discussed in Bilbiie, Ghironi, and Melitz (2007), to the shock, new entrants decrease
and firm value increases since a relative price of investment goods increases. It makes
consumption more attractive than investment and consumption increase in an initialperiod. In the long run, however, consumption decrease due to decrease in the numberof products, i.e., extensive margin effect. CPI inflation rates decrease by negative PPI
inflation rates due to decreasing marginal cost and by a variety effect under a productnumber returning to zero from negative values. Figure 4 shows impulse responses toa productivity shock. To the productivity shock, CPI inflation rates decrease due to avariety effect. Consumption increase due to an increasing product number and negative
6
7

We show it by excluding the product number data in Appendix C for robust analyses.
In the model of Bilbiie, Ghironi, and Melitz (2007), there is no extensive margin effect on prices

since all firms set the same price each time after assuming a symmetric equilibrium. Thus, a priceadjustment parameter includes an extensive margin effect in the Nikkei data and it can further decrease
an estimated price adjustment parameter.

11real interest rate. Figure 5 shows impulse responses to a demand shock by a monetary
policy. When a nominal interest rate increases, consumption and CPI inflation rates
decrease. The number of products increases since the expected return on equity increases
by an increase in an interest rate.
These outcomes confirm that endogenous product entry well works for food products
and daily necessities in Japan and holds essential effects on prices.8

4

Quantitative Effect of Product Entry

To quantitatively evaluate effects of endogenous product entry on prices in the BGMmodel, we use a standard New Keynesian model with Rotemberg price adjustment cost.

4.1

A Standard New Keynesian Model

This model does not include product entry nor exit. Under a similar structure of consumer’s optimization problem and firm’s price setting with Rotemberg price adjustment
cost, a model is given by following two equations and the same monetary policy rule by(5).9C
πtC = βEt πt+1−

1+φθ−1(Zt − Ct ) ,φκC
Ct = Et Ct+1 − it − Et πt+1
.

(6)

(7)

The standard New Keynesian model does not include the number of products nor afree entry shock. Parameter structures also change and a price markup is constant.
8

When we use SBPI, it is reasonable to interpret products in SBPI as homogeneous since theseproducts are only food products and daily necessities in supermarkets. At the same time, we still can
pay attention for heterogeneity in food products and daily necessities. For example, estimation resultis shown for processed meats and seafoods in Appendix C for robust analysis.
9
See this model’s details in Appendix B.

12

4.2

Decomposing Price Variations by Product Entry

We quantitatively evaluate effects of endogenous product entry on prices by comparing
two models for price variations. A standard New Keynesian model extracts all effects
of product entry and exit. In impulse response analyses, we assume the same estimatedparameters and shocks for two models as shown in Table 3.
Table 5 shows simulation results for BGM model and a standard New Keynesianmodel. A standard deviation of an inflation rate sufficiently changes from a standard
New Keynesian model to BGM model. In a case of a CPI (PPI) inflation rate, a standard
deviation decreases by 40.9 (42) percent.10 Even when we exclude a free entry shock fromBGM model, a standard deviation decreases by 56.8 percent for a CPI inflation rate.
[Reason for reduction in Std] It confirms that product entry and exit hold significant
effect on inflation rates and we can not ignore these effects for economic analyses using
price data.

5

Nikkei Data and Official CPI

5.1

Unique Japanese Data Environment

Our question now is whether Japanese official CPI is affected by product entry and exit.
Moreover, if affected, is it negligible or not? Our unique Nikkei data makes a new insightpossible.
The Nikkei data is basically smaller statistic than Japanese official CPI since the
Nikkei data only includes goods prices and excludes service prices. Moreover, goods
samples are corrected in supermarkets, so the data excludes recreational durable goods,
such as computers and cell phones. Eventually, the Nikkei data covers 170 out of the
588 items in Japanese CPI. As a sales weight, Nikkei data covers 17 percent of the prices
10

To calculate PPI inflation rate πt , we use an equation below as shown in Bilbiie, Ghironi, and Melitz(2007).
πt = πtC +1(Nt − Nt−1 ) .
θ−113in the CPI. On the other hand, as shown in Imai and Watanabe (2015) and Watanabe
and Watanabe (2014), Japanese official CPI can be interpreted as a constant sub-sampleof the Nikkei POS data when we focus on these 170 items. Imai and Watanabe (2015)
show that the number of products in Nikkei POS data from 2000 to 2010 year is 462, 906.
Among these samples, only 70, 966 products meet the Statistic Bureau of Japan specifications for samples in the CPI. They show several experiments to make a similar inflation
rate as the official CPI inflation rate from the Nikkei data. They assume virtual pricecollectors to pick up samples from the Nikkei data and change frequencies of shop andproduct replacements in samplings. Their finding is that we can make a similar inflation
rate as the official CPI inflation rate from Nikkei POS data as a trend by sampling prices
through infrequent shop and product replacements in the Nikkei data. To further match
standard deviations, they show that an additional price stickiness by infrequent observation updating is necessary. Watanabe and Watanabe (2014) make another aggregate
inflation rate from the Nikkei data. This is so called S Index of Nikkei CPINow and is
updated to predict the official CPI. They show that this index can closely mimic theofficial CPI inflation rates.
These papers provide one objective evidence to show that the Nikkei data include
necessary information to make the official CPI and the official CPI is a sub-sample of
the Nikkei data.

5.2

Introducing CPI Sampling Features into SBPIIn this section, we show cases in which we introduce sampling features in the official CPI
into SBPI and confirm that such sampling natures do not change estimation results inprevious sections.
Trend for SBPI
Watanabe and Watanabe (2014) point out that the price index by the Nikkei data ismore volatile than the official CPI due to temporary sales. To mitigate its effect on
prices, they suggest to decompose the Nikkei data into a trend part and a cyclical part.
14

We replace SBPI by a trend component of SBPI. In particular, we use HP filter witha smooth parameter of 1600 as a simple method to make a trend component of SBPI.
As shown in Table 1, standard deviations of SBPI inflation rate decrease from 0.068 to
0.041 by applying HP filter. New setting for estimation is to set observation error for
CPI inflation rate as 0.041/10 and other settings do not change from Section 3.
Table 6 reports summarized statistics for posterior distributions. Elasticity of substitution across goods θ and intertemporal elasticity of labor substitution φ are estimatedas 7.212 and 0.744, respectively. Elasticity of substitution across goods does not change
from Table 3 for SBPI. Intertemporal elasticity of labor substitution slightly increases
from Table 3. For a price stickiness, a price adjustment parameter κ is estimated as
68.71. It implies that CPI inflation rates are less volatile by taking trend and a model
replicates it by a larger price adjustment parameter.
Matched-products SBPIIn the official CPI, inflation rates are calculated from individual product prices and then
are aggregated to make the index. Here, we naturally need to allow one year lag for year
to year inflation rate to include each product into the index after these products entry
into a market. We follow this procedure to make a matched-products SBPI. We show
details for a matched-products SBPI in Appendix A. A clear difference from an original
SBPI is that we aggregate all prices each period to make a price level index and thencalculate inflation rates in the SBPI. It notes that the number of products still changes
over time in this index.
As shown in Table 1, standard deviations of SBPI inflation rate decrease from 0.068
to 0.014. This decreased number is very close to ones of the official CPI inflation rate
as shown in last two rows. We replace SBPI by a matched-products SBPI. New setting
for estimation is to set observation error for CPI inflation rate as 0.014/10 and othersettings do not change from Section 3.
Table 7 reports summarized statistics for posterior distributions. Elasticity of substitution across goods θ and intertemporal elasticity of labor substitution φ are estimated15

as 7.849 and 0.679, respectively. Elasticity of substitution across goods does not change
from Table 3 for SBPI. Intertemporal elasticity of labor substitution slightly increases
from Table 3. For a price stickiness, a price adjustment parameter κ is estimated larger
as 59.71.

6

Product Entry and Official CPI: Experiments

6.1

First Experiment

We suggest a new approach for price analyses by combining Japanese macro-level official
CPI data with micro-level Nikkei data. We estimate BGM model for the limited official
CPI inflation rate that corresponds to product categories in the Nikkei data.11 Here,the official CPI is interpreted as random samples from the Nikkei data which works as
population data as shown in Imai and Watanabe (2015). For a real demand, we use
real gross domestic product (GDP) gap since it is a total demand for Japanese economy
corresponding to macro-level official CPI.12
After applying the symmetric equilibrium assumption in BGM model, an individual
price is the same for all products and is determined by aggregate demands and thenumber of products for whole products. It is a mechanism that an endogenous productentry changes an individual price setting through a variable markup. Thus, if the official
CPI correctly reflects the population data of the Nikkei data, we can use the official CPI
to πtC in a model though the official CPI has a constant basket and seems to be notaffected by product entry and exit.13 In other words, we evaluate whether the official
CPI is affected by product entry and exit or not using BGM model. A point here is not
11

See details of the official CPI that corresponds to product categories in the Nikkei data in Appendix

A.
12

A real GDP data is available in National Accounts of Japan that is published by Economic andSocial Research Institute, Cabinet Office.
13
In the model of Bilbiie, Ghironi, and Melitz (2007), there is no extensive margin effect on prices
and all prices are the same. Thus, the model is rather suitable to use the official CPI with a constantbasket and no extensive margin effect.

16

a model and is about precision in sampling for the official CPI.
In details, we apply the limited official CPI inflation rate to πtC , the number of
products to Nt from the Nikkei data, and the GDP gap to Ct . πtC is given by year
to year growth of the limited official CPI. Nt and Ct data are percentage deviations
from trends calculated by HP filter. The sample covers from 1994Q1 to 2021Q2. In an
estimation, we follow the same setting in Section 3 as shown in Table 2. For observation
errors, we assume 10 percent of one standard deviation to the limited official CPI inflation
rate, i.e., 0.015/10, the number of products, i.e., 0.035/10, and GDP gap, i.e., 0.016/10.
Table 8 and Figure 6 show estimation results. All parameters are well estimated andan endogenous product entry effect works for the official CPI. Elasticity of substitution
across goods θ and intertemporal elasticity of labor substitution φ are estimated as 10.07
and 0.644, respectively. For a price stickiness, a price adjustment parameter is estimatedas 54.13. Intertemporal elasticity of labor substitution and a price adjustment parameterare very close to the case using the trend SBPI in Table 6 and the matched-products SBPIin Table 7. It notes that the limited official CPI excludes temporary sales and its pricevariations are smaller than ones of SBPI as the trend SBPI. Elasticity of substitution
across goods is slightly larger in the case of the limited official CPI than in the cases of
SBPIs. However, this difference is negligible as shown in impulse response analysis in
the next section.
Table 9 show variance decomposition in percent contributions. A productivity shock,a free entry shock, and a demand shock explain 53.96, 20.77, and 25.27 percent of thelimited official CPI inflation rate, respectively. A free entry shock still holds a non-trivial
effect as about 20 percent on the macro-level official CPI and a product entry has a clear
effect on inflation rates. For other variables, these shocks also play important roles.
These result suggests that the limited official CPI is affected by a product entry andincluding the number of products into an estimation for macro variables works well to
explain price dynamics. Moreover, we confirm that the official CPI including limited
samples corresponding to the Nikkei data is a precise sample of population data of the
Nikkei data and at least reflects product entry and exit effects.

17

6.2

Second Experiment

In the last section, we show that the number of products holds quantitatively significant
effect on the limited official CPI that corresponds to items included in the Nikkei data.
We extend this result to all CPI items including service prices and other goods pricesthat are not included in the Nikkei data. Here, we have a strong assumption that thesame product entry effect holds for services and other goods. Estimation result, however,justifies this assumption though we need to clarify this point further.
In details, we apply the official CPI inflation rate for all goods and service to πtC , thenumber of products to Nt , and the GDP gap to Ct . πtC is given by year to year growthof the official CPI. Nt and Ct data are percentage deviations from trends calculated by
HP filter. The sample covers from 1994Q1 to 2022Q4. Figure 7 shows these three data.
We assume observation errors given by 10 percent of one standard deviation to a
CPI inflation rate, i.e., 0.0097/10, the number of products, i.e., 0.035/10, and GDP
gap, i.e., 0.016/10. Observation errors are assumed to be i.i.d. normally distributedwith zero mean. Calibrated parameters are the same as shown in Section 3.3 and priordistributions are the same as shown in Table 2.
Table 10 shows estimation results for BGM model. Elasticity of substitution acrossgoods θ, intertemporal elasticity of labor substitution φ, and a price adjustment parameter κ are estimated as 10.661, 0.669, and 59.98, respectively. These estimations arealmost the same as the limited official CPI. When we compare elasticity of substitution
across goods to the cases using the Nikkei data, the estimated number is slightly larger.
This difference, however, is too small to change impulse responses. Figures 8 shows
impulse responses to one standard deviation productivity shocks for BGM model with
official CPI data including all items. When comparing Figure 4 to Figure 8, impulse
responses are the almost same for CPI inflation rates and demands in two figures after
adjusting the size of shocks. An impulse response of the number of products is little bit
smaller in a case of Nikkei data than a case of the official CPI data. We have the similar
impulse responses for two cases even to demand shocks though we do not show figures.
As shown in Table 11, a productivity shock, a free entry shock, and a demand shock18

explain 56.79, 15.88, and 27.33 percent of CPI inflation rate variations, respectively. A
free entry shock still holds a non-trivial effect as about 15 percent on the macro-level
official CPI. For other variables, these shocks also play important roles. A product entry
has a clear effect on inflation rates even when we use the official CPI including all items.

7

Implications to Economic Analysis: Examples

Estimation and simulation results give new and strong implications for economic analysis.
Product entry and so variable number of products are fundamental elements to analyze
prices. Here, we show several implications to economic analyses.

7.1

Product Entry Effect on Official CPI

By comparing a BGM model with a standard New Keynesian model, we show quantitative implications to macro economic analysis in Japan. For it, we again use a standard
New Keynesian model as in Section 4.2. We assume the same estimated parameters andshocks for two models as shown in Table 10. It notes that a free entry shock is excluded
in a standard New Keynesian model.
Table 12 shows simulation results for BGM model and a standard New Keynesianmodel. A standard deviation of CPI inflation rates in BGM model is 40.9 percent smaller
than one in a standard New Keynesian model. For a demand, a standard deviation
increases by 24.1 percent. If we ignore a product entry effect on prices, a model andeconomic analyses quantitatively suffer from serious misidentification problems as shownin Section 7.3 below.

7.2

Quantitative Role of Free Entry Shock on Historical Inflation

Figure 9 shows a historical variance decomposition using estimated BGM model in Section 6.2. We confirm that a free entry shock significantly contributes to inflation and19deflation in Japan. In some periods, the free entry shock changes inflation rates morethan one percent positively and negatively. This is impossible finding in a model that
discards product entry and exit.
As shown in an impulse response to a free entry shock in Figure 10, CPI inflation
rates decrease as the number of products decreases. In details, when we see period from
20 to 50 in Figure 6, lowered product numbers make negative effects on inflation rate andinduce chronic deflation in the historical decomposition given by Figure 9. Moreover, alarge drop of the product number from 60 to 70 induces a deep deflation. On the other
hand, an inflation rate surges with increasing number of products around the end of
the sample period. In Japan, non-negligible part of inflation rates can be explained byproduct entry.

7.3

Model Selection Failure in Price Analysis

An endogenous product entry makes quantitatively significant effects on price and demand. A standard New Keynesian model, however, discards an endogenous productentry. We estimate a standard New Keynesian model using our Nikkei data and show
outcomes by a misidentification due to gaps between the model and data. In particular,
we evaluate effects of two misidentifications in an estimation. The first one is that a pricesetting does not depend on an endogenous product entry. In a standard New Keynesianmodel, a price markup is constant and is not related to the number of products. The
second one is that there is no extensive margin effect in product supply and demand. Ina standard New Keynesian model, a variety of the product is one and constant.
An estimation procedure is basically the same as in Section 3. Differences are touses two time series data, SBPI to πtC and real demand for products to Ct , and toassume two types of shocks, productivity shock Zt and demand shock Mt . Figure 11
shows prior and posterior distributions and these summarized statistics are reported inTable 13. Elasticity of substitution across goods θ and intertemporal elasticity of labor
substitution φ are estimated as 8.536 and 1.793, respectively. For a price stickiness, aprice adjustment parameter κ is estimated as 75.198. However, when we see prior and20

posterior distributions in Figure 11, distributions for φ and κ seems to well overlap. It
implies that estimation does not work well due to inconsistency between a model anddata.14
By misidentifications, estimated parameters are not well estimated and could be
biased. A price adjustment parameter are estimated larger to reduce price variations ina standard New Keynesian model than in BGM model. This is because price variations
are constrained by a variable price markup due to an endogenous product entry in BGMmodel. Regarding shocks, a standard deviation of productivity shock becomes double toreplicate economic variations since a standard New Keynesian model can not include afree entry shock.
Impulse responses quantitatively show effects of misidentifications for economic dynamics. Figure 12 show impulse responses to a productivity shock for a standard New
Keynesian model. CPI inflation rates are more elastic to the shock in comparing to thosefor BGM model. On the other hand, a demand is less elastic to the shock. About ademand shock, two models show the similar size of impulse responses for an initial period
though impulse response persistences are longer, almost two times, in BGM model asshown in Figure 13. These outcomes imply that misidentifications make quantitatively
significant errors in economic analysis when we apply a model discarding an endogenous
product entry to data showing relationships among product entry, price, and demand.
We can apply a model selection failure problem to the official CPI for all items and
GDP gap since behind these data, there exists a product entry and the number of products change over time. Table 14 shows summarized statistics for posterior distributions
for a standard New Keynesian model. In estimation, we use the official CPI inflation
rate for all goods and services to πtC and the GDP gap to Ct , and other settings are
the same as in Section 3. Figure 14 shows impulse responses to one standard deviation
productivity shock. When we compare Figures 8 and 14, CPI inflation rates are less14

To check robustness, we estimate one of these three parameters separately under given jointly

estimated other two parameters and we confirm that our conclusion here does not change. Please see
details in Appendix C.

21

elastic to the shock in a standard New Keynesian model than in BGM model.

8Concluding Remark

In this paper, we evaluate whether the official CPI is affected by a product entry andthe number of products in a market. We make use of Japanese unique data environment
where the Nikkei data including larger samples than the official CPI is available foranalysis. Our conclusion is that a product entry holds quantitatively significant effecton the official CPI as on the Nikkei data through an intensive margin effect though theofficial CPI has a constant basket and seems to exclude a product entry effect. The
official CPI is a precise sample to correctly reflect a product entry effect in Japanese
product market.
The outcome that the official CPI is affected by the number of products gives several
questions. Among those, we need to ask whether a model discarding a product entry andassuming a constant price basket suffers from misidentification for economic analysis.
Our result shows that this misidentification is quantitatively large and makes serious
misunderstandings for estimation, variance decomposition, and impulse responses.
Our future works include evaluations on a product entry effect in the official CPI by
using another types of models such as an oligopoly model for pricing. Evaluations on a
product entry effect by rich general equilibrium models including a variety of frictions
are necessary for robust analyses. Extending analysis to other countries is mandatory
since we observe product entry and exit every day in supermarkets. Moreover, we canfocus on service prices since new services come into a market and old services exit froma market.

22

References[1] Bilbiie, Florin, Fabio Ghironi, and Marc Melitz, 2007. “Monetary Policy and Business Cycles with Endogenous Entry and Product Variety,” NBER Macroeconomics
Annual 22, pp. 299-353.
[2] Bilbiie, Florin, Fabio Ghironi, and Marc Melitz, 2012. “Endogenous Entry, Product
Variety, and Business Cycles,” Journal of Political Economy 120(2), pp. 304-345.
[3] Broda, Christian, and David E. Weinstein, 2010. “Product Creation and Destruction: Evidence and Price Implications,” American Economic Review 100(3), pp.
691-723.
[4] Dong, Mei, Toshiaki Shoji, and Yuki Teranishi, 2024. “Product Cycles and Phillips
Curve: Theory and Evidence,” Mimeo.
[5] Imai, Satoshi and Tsutomu Watanabe, 2015. “Replicating Japan’s CPI Using Scanner Data,” UTokyo Price Project Working Paper Series No. 054.
[6] Watanabe, Kota and Tsutomu Watanabe, 2014. “Estimating Daily Inflation Using
Scanner Data: A Progress Report,” CARF Working Paper F-342.
[7] Ueda, Kozo, Kota Watanabe, and Tsutomu Watanabe, 2019. “Product Turnover
and the Cost-of-Living Index: Quality versus Fashion Effects,” American Economic
Journal: Macroeconomics 11(2), pp. 310-347.

23

PIC_obs

0.4
0.2
0
-0.2
20

40

60

80

100

120

80

100

120

80

100

120

ND_obs

0.2

0

-0.2
20

40

60

CD_obs

0.2

0

-0.2
20

40

60

Figure 1: Inflation Rate, Number of Product, and Demand
Note: PIC obs: SBPI inflation rate, ND obs: Number of products, CD obs: Demand.

24

SE_E_PS

SE_E_FS

SE_E_MP

15

150

10

100

10

5

50

0
0.05 0.1 0.15 0.2 0.25

0

30
20

0.1 0.2 0.3 0.4 0.5

phi

kappa
0.4

0.4

10

0.2

0.2

1

2

3

4

5

0

5

rhops

10

10

15

0

40

rhofs

60

80

100

rhomp
6

10

4

5

0

0.05 0.1 0.15 0.2 0.25

theta

20

0

0

5

0.2

0.4

0.6

0.8

0

2
0.2

0.4

0.6

0.8

0

0.2 0.4 0.6 0.8

Figure 2: Posterior Distributions
Note: SE E PS, SE E FS, and SE E MP denote σz , σf , and σm , respectively. phi, theta,
and kappa denote φ, θ, and κ, respectively. rhops, rhofe, and rhomp denote ρz , ρf , andρm , respectively. Prior distribution is colored by gray and estimated posterior distribution
is colored by black.

25

PIC

0.02

CD

0.02

0

0

-0.02

-0.02

-0.04

-0.04
5

10

15

20

5

ND

0

10

15

20

15

20

15

20

MU

0.2
0.1

-0.1
0
-0.2

-0.1
5
-3

5

10

15

20

5

ID

×10

10

FS

0.4

0
-5

0.2

-10
-15

0
5

10

15

20

5

10

Figure 3: Impulse Response to Free Entry Shock
Note: PIC: SBPI inflation rate, ND: Number of products, CD: Demand, ID: Nominalinterest rate, and FS: Free entry shock. Impulse responses to one standard free entry
shock with AR1 persistence as shown in Table 3.

26

PIC

0

CD

0.06

-0.01

0.04

-0.02

0.02

-0.03

0
5

10

15

20

5

ND

0.15

0.01

0.05

0

0

15

20

15

20

15

20

MU

0.02

0.1

10

-0.01
5

10

15

20

5

ID

0

PS

0.1

-0.02

10

0.05

-0.04

0
5

10

15

20

5

10

Figure 4: Impulse Response to Productivity Shock
Note: PIC: SBPI inflation rate, ND: Number of products, CD: Demand, ID: Nominalinterest rate, and PS: Productivity shock. Impulse responses to one standard productivity
shock with AR1 persistence as shown in Table 3.

27

PIC

0

CD

0.05

-0.0050-0.01-0.015

-0.05
5

10

15

20

5

ND

0.06

10

15

20

15

20

15

20

MU

0.04

0.04
0.02
0.02
0

0
5
-3

15

10

15

20

5

ID

×10

10

MP

0.04

10
5

0.02

0
-5

0
5

10

15

20

5

10

Figure 5: Impulse Response to Demand Shock
Note: PIC: SBPI inflation rate, ND: Number of products, CD: Demand, ID: Nominalinterest rate, and MS: Demand shock. Impulse responses to one standard demand shockwith AR1 persistence as shown in Table 3.

28

SE_E_PS

SE_E_FS

150

800
40

100
50

20

0

0

600
400
200

0.05 0.1 0.15 0.2 0.25

0.05 0.1 0.15 0.2 0.25

phi

theta

0

0.05 0.1 0.15 0.2 0.25

kappa

0.1

0.4

4

0.05

0.2

2
0

SE_E_MP

1

2

3

4

5

0

rhops
6
4

5

10

15

0

40

rhofs

60

80

100

rhomp

10

10

5

5

2
0

0.2 0.4 0.6 0.8

0

0.2 0.4 0.6 0.8

00

0.2 0.4 0.6 0.8

Figure 6: Posterior Distributions for BGM Model with Limited Official CPI
Note: SE E PS, SE E FS, and SE E MP denote σz , σf , and σm , respectively. phi, theta,
and kappa denote φ, θ, and κ, respectively. rhops, rhofe, and rhomp denote ρz , ρf , andρm , respectively. Prior distribution is colored by gray and estimated posterior distribution
is colored by black.

29

PIC_obs

0.05

0

-0.05
10

20

30

40

50

60

70

80

90

100

110

70

80

90

100

110

70

80

90

100

110

ND_obs

0.1
0
-0.1
-0.2
10

20

30

40

50

60

CD_obs

0.05
0
-0.05
-0.1
10

20

30

40

50

60

Figure 7: Official CPI Inflation Rate, Number of Product, and GDP Gap
Note: PIC obs: Official CPI inflation rate, ND obs: Number of products, CD obs: GDP
Gap. The sample covers from 1994Q1 to 2022Q4.

30

PIC

0

CD

0.015
0.01

-0.005
0.005
-0.01

0
5

10

15

20

5

ND

0.06

4

0.04

2

0.02

0

0

×10-3

10

15

20

15

20

15

20

MU

-2
5

10

15

20

5

ID

0

10

PS

0.03
0.02

-0.005
0.01
-0.01

0
5

10

15

20

5

10

Figure 8: Impulse Response to Productivity Shock for BGM Model with Official CPI
Note: PIC: Official CPI inflation rate, ND: Number of products, CD: GDP Gap, ID:
Nominal interest rate, and PS: Productivity shock. Impulse responses to one standard
productivity shock with AR1 persistence as shown in Table 10.

31

0.04

0.03
E_PS

0.02

E_FS

0.01

0

E_MP
-0.01

-0.02
Initial values

-0.03
0

20

40

60

80

100

Figure 9: Historical Decomposition for Official CPI using BGM Model
Note: E PS, E FS, and E MP denotes productivity shock, free entry shock, and demand
shock. Initial values denotes an effect by initial condition.

32

5

×10-3

PIC

5

×10-3

CD

0
0
-5
-10

-5
5

10

15

20

5

ND

0

10

15

20

15

20

15

20

MU

0.02
0.01

-0.02
0
-0.04

-0.01
5
-4

5

10

15

20

5

ID

×10

FS

0.08

0

0.06

-5

0.04

-10

0.02

-15

10

0
5

10

15

20

5

10

Figure 10: Impulse Response to Free Entry Shock for BGM Model with Official CPI
Note: Note: PIC: Official CPI inflation rate, ND: Number of products, CD: GDP Gap,
ID: Nominal interest rate, and FS: Free entry shock. Impulse responses to one standard
productivity shock with AR1 persistence as shown in Table 10.

33

SE_E_PS

SE_E_MP

15
100

10
5

50

0

0

0.6
0.4
0.2

0

0.2

0.4

0.6

theta

0.4

0.05 0.1 0.15 0.2 0.25

0.2

10

0

20

0

2

4

6

8

rhops
10
5

0.02

0

0

kappa
0.04

0

phi
0.8

40 60 80 100120140

0

0.2

0.4

0.6

0.8

rhomp

6
4
2
0

0

0.2 0.4 0.6 0.8

Figure 11: Posterior Distributions for New Keynesian Model with SBPI
Note: SE E PS and SE E MP denote σz and σm , respectively. phi, theta, and kappa
denote φ, θ, and κ, respectively. rhops and rhomp denote ρz and ρm , respectively. Prior
distribution is colored by gray and estimated posterior distribution is colored by black.

34

PIC

0

CD

0.04

-0.01
0.03
-0.02
0.02

-0.03
-0.04

0.01
-0.05
-0.06

0
5

10

15

20

5

ID

0

0.2

-0.02

0.15

-0.03

0.1

-0.04

0.05

-0.05

15

20

15

20

PS

0.25

-0.01

10

0
5

10

15

20

5

10

Figure 12: Impulse Response to Productivity Shock for New Keynesian Model with SBPI
Note: PIC: Limited Official CPI inflation rate, ND: Number of products, CD: Demand,
ID: Nominal interest rate, and PS: Productivity shock. Impulse responses to one standard
productivity shock with AR1 persistence as shown in Table 3.

35

PIC

0

CD

0

-0.002-0.01-0.004-0.02-0.006-0.03-0.008-0.04-0.01-0.012

-0.05
5

10

15

20

5

ID

0.03

10

15

20

15

20

MP

0.04

0.025
0.03
0.02
0.02

0.015
0.01

0.01
0.005
0

0
5

10

15

20

5

10

Figure 13: Impulse Response to Demand Shock for New Keynesian Model with SBPI
Note: PIC: SBPI CPI inflation rate, ND: Number of products, CD: Demand, ID: Nominalinterest rate, and MS: Demand shock. Impulse responses to one standard demand shockwith AR1 persistence as shown in Table 3.

36

0

×10-3

PIC

6

×10-3

CD

5
-2
4
-4

3
2

-6
1
-8

0
5

0

×10-3

10

15

20

5

ID

0.06

-4

0.04

-6

0.02

-8

15

20

15

20

PS

0.08

-2

10

0
5

10

15

20

5

10

Figure 14: Impulse Response to Productivity Shock for New Keynesian Model with
Official CPI
Note: PIC: Official CPI inflation rate, ND: Number of products, CD: GDP gap, ID:
Nominal interest rate, and PS: Productivity shock. Impulse responses to one standard
productivity shock with AR1 persistence as shown in Table 14.

37

Table 1: Basic Statistics

Number of products
Entry rate
Exit rate
Nominal sales amountReal sales amount
SBPI inflation
Trend SBPI inflation
Matched-products SBPI inflation
Limited official CPI inflation
Official CPI inflation

Average
52884.32
0.122
0.115
4354313201
68301350.024
0.024-0.0060.004
0.002

Standard deviation
15438.89
0.018
0.01750835205
940731
0.068
0.041
0.014
0.016
0.011

Note: Quarterly base. A sample period for the number of products is from 1988Q2 to
2022Q4. A sample period for entry rate is from 1988Q3 to 2022Q4. A sample period forexit rate is from 1988Q2 to 2022Q3. A sample period for matched-products SBPI priceinflation, trend SBPI price inflation, SBPI price inflation, limited official CPI inflation,
sales amount, and real sales amount is from 1990Q2 to 2022Q4. A sample period for
official CPI is from 1994Q1 to 2022Q4.

38

Table 2: Prior Distributions

Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm

Description
Elasticity of substitution across goods
Intertemporal elasticity of labor substitution
Price adjustment parameter
Persistence of free entry shock
Persistence of productivity shock
Persistence of demand shock
S.D. of free entry shock
S.D. of productivity shock
S.D. of demand shock

Note: S.D. denotes a standard deviation.

39

Mean
3.8
2
77
0.5
0.5
0.5
0.1
0.1
0.1

S.D.
5
1
10
0.15
0.15
0.15
0.05
0.05
0.05

Distribution
Inv. Gamma
Inv. Gamma
Inv. Gamma
Beta
Beta
Beta
Inv. Gamma
Inv. Gamma
Inv. GammaTable 3: Posterior Distributions
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
7.834
0.486
41.88
0.691
0.641
0.443
0.319
0.099
0.03
470.998

Note: MDD denotes marginal data density.

40

90 percent interval[6.358, 9.221][0.452, 0.525][40.24, 43.85][0.636, 0.744][0.579, 0.72][0.347, 0.534][0.269, 0.372][0.082, 0.212][0.026, 0.034]

Table 4: Variance Decomposition in Percent
Variable
πtC
Ct
Nt
µt

Productivity Free entry
38.78
49.37
58.08
30.01
41.58
54.65
4.17
89.22

Demand
11.85
11.91
3.77
6.61

Note: Productivity, Free entry, and Demand denote productivity shock, free entry shock,and demand shock, respectively.

41

Table 5: Product Entry Effect on CPI/PPIModel
BGM model
BGM model + no fE,t
NK modelS.D. of inflation rate
S.D. of demand
CPI 0.052 [-40.9 %] 0.12 [46.3 %]PPI 0.051 [-42 %]CPI 0.038 [-56.8 %] 0.1 [22 %]CPI & PPI 0.088
0.082

Note: S.D. denotes a standard deviation. [ ] denotes percent change from NK model.

42

Table 6: Posterior Distributions for Trend SBPI
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
7.212
0.744
68.71
0.97
0.854
0.593
0.088
0.055
0.026
791.733

Note: MDD denotes marginal data density.

43

90 percent interval[6.352, 8.164][0.569, 0.906][58.3, 78.78][0.955, 0.985][0.816, 0.892][0.526, 0.658][0.075, 0.102][0.049, 0.062][0.023, 0.029]

Table 7: Posterior Distributions for Matched-products SBPI
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
7.849
0.679
59.71
0.832
0.872
0.248
0.088
0.057
0.029
815.092

Note: MDD denotes marginal data density.

44

90 percent interval[6.814, 8.792][0.541, 0.812][51.86, 67.92][0.781, 0.89][0.84, 0.907][0.162, 0.345][0.074, 0.102][0.051, 0.063][0.025, 0.034]

Table 8: Posterior Distributions for BGM Model with Limited Official CPI
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
10.07
0.644
54.13
0.794
0.651
0.103
0.073
0.028
0.023
831.302

Note: MDD denotes marginal data density.

45

90 percent interval[8.503, 11.46][0.523, 0.769][47.2, 61.17][0.732, 0.849][0.55, 0.737][0.05, 0.168][0.061, 0.084][0.024, 0.032][0.023, 0.024]

Table 9: Variance Decomposition in Percent for BGM Model with limited Official CPI
Variable
πtC
Ct
Nt
µt

Productivity Free entry
53.96
20.77
50.14
15.41
48.41
45.87
8.11
41.08

Demand
25.27
34.44
5.72
50.8

Note: Productivity, Free entry, and Demand denote productivity shock, free entry shock,and demand shock, respectively.

46

Table 10: Posterior Distributions for BGM Model with Official CPI
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
90 percent interval
10.689 [9.195, 12.304]
0.657[0.525, 0.787]
58.79[51.01, 66.6]
0.76[0.686, 0.838]
0.62[0.488, 0.755]
0.091[0.038, 0.144]
0.064[0.053, 0.075]
0.026[0.023, 0.028]
0.023[0.023, 0.024]
861.229

Note: MDD denotes marginal data density.

47

Table 11: Variance Decomposition in Percent for BGM Model with Official CPI
Variable
πtC
Ct
Nt
µt

Productivity Free entry
52.91
18.51
45.51
12.14
53.79
38.6
7.52
37.56

Demand
28.59
42.34
7.61
54.93

Note: Productivity, Free entry, and Demand denote productivity shock, free entry shock,and demand shock, respectively.

48

Table 12: Product Entry Effect on Official CPI
Model
BGM model
NK modelS.D. of CPI inflation rate
0.013 [-40.9 %]0.022

S.D. of demand
0.036 [24.1 %]0.029

Note: S.D. denotes a standard deviation. [ ] denotes percent change from NK model.

49

Table 13: Posterior Distributions for New Keynesian Model with SBPI
Parameters
θ
φ
κ
ρz
ρm
σz
σm
MDD

Mean
90 percent interval
8.536[3.369, 13.627]
1.793[0.847, 2.806]
75.198 [61.171, 89.882]
0.517[0.458, 0.58]
0.298[0.192, 0.417]
0.213[0.095, 0.394]
0.034[0.029, 0.039]
402.703

Note: MDD denotes marginal data density.

50

Table 14: Posterior Distributions for New Keynesian Model with Official CPI
Parameters
θ
φ
κ
ρz
ρm
σz
σm
MDD

Mean
2.972
1.983
77.38
0.632
0.132
0.07
0.024
679.068

Note: MDD denotes marginal data density.

51

90 percent interval[1.937, 4.078][0.942, 3.225][60.9, 91.6][0.567, 0.692][0.075, 0.195][0.037, 0.099][0.023, 0.025]

Appendix
A

Details of Nikkei Data

A.1

Product Identification

A barcode including the Japanese Article Number (JAN) code is printed on all products
and products are distinguished by fairly detailed classifications in Nikkei POS scannerdata. In the JAN code, the first seven digits indicate the company code and the lastsix digits indicate the individual product. When JAN codes are different for the same
type of products by the same company, these products are different in terms of packaging, ingredients, etc. In addition, the barcodes provide information about the productcategory (such as butter, yogurt, or shampoo) and the producer of each product.

A.2

Price

The Nikkei data contains the sales values and quantities sold for each product in eachshop on a daily basis. By dividing the sales values by the quantities sold, we calculate thedaily price for each product. Based on these individual prices, we calculate an average
price for all products. We use sales values as weights to calculate average prices.
To calculate the average prices, we use price levels. The first reason is that this is
the average price that Japanese consumers face in shops to decide on purchases. The
second reason is that price dispersion is not large because prices in the Nikkei data arefor products in supermarkets where food products and daily necessities are sold. Figure
A1 shows the price distribution for all prices in our 7 supermarket sample, where one
price is defined as a yearly modal price of a product sold at a shop. The figure showsthat about 70 percent of prices are between 100 yen and 999 yen. The median price andmean price are 284 yen and 622.3 yen, respectively. The minimum price and maximum
price are one yen and 80, 290 yen, respectively.
In details, an average price is calculated in a following equation. We call this price52

index as SBPI.
P

i∈I,s∈S priceist weightist

SBP It =Pi∈I,s∈S weightist,

where priceist is a price of product i sold at shop s in a quarter t and weightist is salesof product i at shop s in a quarter t. Note that our original data frequency is daily andwe make a quarterly price (sales) by using these daily prices (sales). We have similar
equations for an average price for new products.
Figure A2 show growth rates of price indexes, such as SBPI, trend component of
SBPI, matched-products version of SBPI, the limited official CPI that includes items in
the Nikkei data, and the official CPI.

A.3

Entry Rate and Exit Rate

In calculating the entry (exit) rate, we define a new (discontinued) product as one forwhich a transaction is firstly (finally) recorded in a given period. Then, we obtain thenumber of new (discontinued) products in a given period, which is divided by the total
number of products in a given period to calculate entry (exit) rates. Note that these
rates are not weighted by sales. We interpret that a new product enters into the market
when we observe the new product in at least one shop. We interpret that an existingproduct exits from the market when no shops sell the existing product. Thus, entry(exit) rates are at the product level. Equations for the entry (exit) rate are given by

Entry Rate at T ime t =Exit Rate at T ime t =N umber of N ew P roducts at T ime t,
T otal N umber of P roducts at T ime t

N umber of Discontinued P roducts at T ime t.
T otal N umber of P roducts at T ime t

53

A.4

Product Categories

We show average prices, sales shares, and the number of individual products for 17
product categories in our 7 supermarket sample in Table A1. The average price for acategory is obtained by the average of yearly modal prices of products in a category
across shops for the sample period 1989-2022. A sales share is the sales amount ofeach category divided by the total sales amount for the sample period. Note that thesales amount includes sales with temporary promotion prices. The number of products
denotes the total number of products sold in each category in the sample period.

B

Derivation of New Keynesian ModelWe briefly show a derivation for a standard New Keynesian Model with a adjustment
cost by Rotemberg (1978). We follow BGM model as possible as we can for structures,parameters, and notations. However, we simplify an unnecessary part of a model. A
representative household only holds bond. The model only includes the CPI and keeps
the number of product as one.

B.1

Aggregator

The household consumes the basket of goods Ct as
Z 1
θ−1
θ−1
θ
Ct =
ct (i) θ di,0

where θ is the symmetric elasticity of substitution across goods. A corresponding priceaggregator is given by
Pt1−θ =Z 1

pt (i)1−θ di.

0Then, the household’s demand for an individual good i is
ct (i) =pt (i)
Pt

54

−θ
Ct .

B.2

Firm

We assume a continuum of monopolistically competitive firms and each firm i produce
one differentiated good i. To produce a good yt (i), a firm uses a labor lt (i) and so wehave yt (i) = Zt lt (i), where Zt is a productivity shock. Productivity shock is exogenous
and follows an AR(1) process.
Firms face nominal rigidity in the form of a quadratic cost function, which is measured
in terms of goods, to adjust prices following Rotemberg (1982) as2κ pt (i)pt (i)
pact (i) =−1yt (i).
2 pt−1 (i)Pt
The firm maximizes following discounted profit.
"
#
2

∞
X
pt (i)
pt (i)
κ pt (i)Λt,t+sEt−1
yt (i)wt lt (i) −yt (i) ,
P
2
p
(i)
P
t
t−1
t
s=t
where Λt,t+s = βs−t CCst is the discount factor. Here, all the firms set the price andproduce the same output. Thus, we have pt (i) = pt = Pt , pact (i) = pact , lt (i) = Lt ,and yt (i) = yt = Yt . This is symmetric assumption for equilibrium. Thus, the aggregate
resource constraint is given by
Yt = Ct + pact = Zt Lt .
Then, the first order condition with respect to the demand function is given by



Ct
Yt+1
wt
1 − κ (πt + 1) πt + κβEt
(πt+1 + 1) πt+1
= θ(1 − ),
Ct+1
Yt
Zt

(8)

t
where πt = PPt−1− 1 and a demand function for yt (i) is given byyt (i) =pt (i)
Pt

−θ
Yt ,

where a model assumes the same goods allocation for a price adjustment cost as consumption.

55

B.3

HouseholdA representative household maximizes the following an utility function,


1
1+ φ
∞
X
Ls 
Et
βs−t lnCs + χ,
1 + φ1s=t
subject to a budget constraint,
Bt+1 + Pt Ct = (1 + it−1 )Bt + Wt Lt + Tt + Dt ,where where Ct is consumption, it is the nominal interest rate, Bt is nominal bondholdings, Wt is the nominal wage rate, Lt is the labor supply, Tt are lump sum taxes,
and Dt is nominal dividends. χ is the Frisch elasticity of labor supply to wage and φ isthe intertemporal elasticity of substitution in labor supply. Then, we have the following
first order conditions.
1= β(1 + it )Et
Ct



Pt 1
Pt+1 Ct+1


,

1
Wt
= wt = χCt Ltφ .
Pt

B.4

(9)
(10)

Closed System and Linearization

From (B.2), (B.2), (B.2), and (B.2), we have a closed system of economy for Ct , πt , andit . By log-linaerizing these equations, we have a New Keynesian model.

C

Robust Analysis

C.1

Estimation using two data

We show an estimation result for a case where we only use two data, SBPI and a demand,and include the product number data. In estimation, we follow the setting in Section 3.
Table A2 shows the estimation result. Estimated results are significant different from
Table 3 that use three data. Table A3 shows variance decomposition in percents. Free
entry shock less contribute to inflartion rate in Table A3 than in Table 4.
56

C.2

Estimation for Food Products and Daily Necessities

We show an estimation result for processed meats and seafoods from Table A1. Processedmeats and seafoods category has 7 percent share in sales base in SBPI. An average
number of products in the category is 33275 and average price is 348.6 yen.
In estimation, we follow the setting in Section 3 except several points. We newly
assume observation errors given by 10 percent of one standard deviation to a inflation
rate for processed meats and seafoods category, i.e., 0.032/10, the number of products,
i.e., 0.064/10, and a real demand, i.e., 0.048/10. We set a separation rate as 0.127
from Nikkei data. Table A4 show estimation result for these parameters. Estimatedparameters slightly change to reflect product heterogeneity from Table 3.15

C.3

Separate Estimation for New Keynesian Model

To check robustness for estimation for new Keynesian model using Nikkei data, weestimate parameters, φ, θ, and κ, separately. For example, when we estimate φ, wecalibrate other two parameters given as in Table 13.
Table A5 shows estimation result for these parameters. Estimated parameters do notchange a lot from Table 13.

15

Basically, estimation results change by categories in Table A1. However, our conclusion that a

product entry has significant effects on prices does not change. Furthermore, even when we use moredetailed data, such as only processed meats, we have the same conclusion. These estimation results areavailable upon a request.

57

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
0

1

2

3

Figure A1: Price Distribution
Note: A horizontal axis is Log 10 price.

58

4

0.4

0.3

SBPI

Trend SBPI

Limited CPI

CPI

Match SBPI

0.2

0.1

0

-0.1

1994Q1
1995Q1
1996Q1
1997Q1
1998Q1
1999Q1
2000Q1
2001Q1
2002Q1
2003Q1
2004Q1
2005Q1
2006Q1
2007Q1
2008Q1
2009Q1
2010Q1
2011Q1
2012Q1
2013Q1
2014Q1
2015Q1
2016Q1
2017Q1
2018Q1
2019Q1
2020Q12021Q12022Q1-0.2

Figure A2: Price Indexes
Note: All indexes are yest to year growth rate. SBPI denotes an original SBPI. Trend
SBPI denotes a trend component of SBPI. Match SBPI denotes a matched-products SBPI.
Limited CPI denotes the official CPI including only items in the Nikkei data. CPI denotes
the official CPI including all items.

59

Table A1: Product Categories: Average Price, Sales Share, and the Number of Productsin Each Category
Categories

PricesShares

Product Numbers

Processed meats and seafoods

348.6

0.07

33275

Dairy products and milks

264.4

0.083

33929

Beverages

426.3

0.08

42907

Seasonings

273.3

0.057

21310

Instant and frozen foods

218

0.089

55529

Canned foods

249.9

0.012

6722

Breads and cakes

208.4

0.055

60505

Confectioneries

250.6

0.084

155077

Alcoholic beverages

1146.4

0.066

37893

Other foods

322.8

0.085

58347

Body/Oral care products

671.3

0.025

35675

Detergents and cosmetics

1411.60.077

130677

Stationeries

335

0.007

58255

Pet foods and sanitary products

403.2

0.008

17941

Other daily necessities

712.5

0.071

77659

Other agricultural products

247.7

0.06

27747

Baby foods, cereals, and eggs

1966.8

0.072

41092

Note: Price is Japanese Yen.

60

Table A2: Posterior Distributions When Using Two Data for BGM Model
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
15.74
3.28
70.11
0.339
0.363
0.631
0.103
0.066
0.033
381.216

Note: MDD denotes marginal data density.

61

90 percent interval[13.41, 17.95][1.73, 4.85][57.07, 82.18][0.103, 0.559][0.16, 0.568][0.549, 0.702][0.053, 0.149][0.047, 0.087][0.029, 0.037]

Table A3: Variance Decomposition When Use Two Data for BGM Model
Variable
πtC
Ct
Nt
µt

Productivity
34.41
38.78
39.34
16.78

Free entry
10.15
14.39
18.36
38.83

Demand
55.44
46.83
42.3
44.38

Note: Productivity, Free entry, and Demand denote productivity shock, free entry shock,and demand shock, respectively.

62

Table A4: Posterior Distributions for BGM Model with Processed Meats and Seafoods
Category
Parameters
θ
φ
κ
ρf
ρz
ρm
σf
σz
σm
MDD

Mean
90 percent interval
12.671 [11.322, 14.413]
0.562[0.467, 0.646]
54.67[48.02, 61.08]
0.685[0.608, 0.767]
0.764[0.687, 0.844]
0.21[0.107, 0.309]
0.185[0.15, 0.218]
0.053[0.047, 0.059]
0.038[0.032, 0.043]
587.109

Note: MDD denotes marginal data density.

63

Table A5: Posterior Distributions by Separate Estimations
Parameters Mean 90 percent interval
θ
3.97[2.497, 5.469]
φ
1.989 [0.911, 3.024]
κ
78.59 [63.42, 93.34]
Note: We estimate θ, φ, and κ separately.

64