KEO Discussion Paper No. 144

Benchmark 2011 Integrated Estimates of the Japan-U.S.
Price Level Index for Industry Outputs

October 2018

Koji Nomuraa), Kozo Miyagawa b), and Jon D. Samuels c)

Abstract
This paper provides new benchmark estimates of industry-level price differentials between Japanand the U.S. for 2011 based on a bilateral price accounting model anchored to the Japan-US inputoutput tables. We apply the model to translate available demand-side data on purchaser’s price PPPs for
final uses (e.g. the Eurostat-OECD PPPs) and intermediate uses (e.g. the METI survey) to unmeasured
producer’s price PPPs for industry output. These PPPs allow us to produce price level indexes at theindustry level, which we use to assess price competitiveness between Japan and the U.S. Under thenominal exchange rate of 110.6 yen per dollar as of the beginning of July 2018, we estimate that
producers in Japan have a pricing advantage in 66 of 106 industries in the manufacturing sector, and in
24 of 50 industries in the service sector. We conclude that price competitiveness of Japanese service
industries has considerably improved in the more recent time period. However, Japanese producers havea significant price disadvantage in comparison to their U.S. counterparts in electricity and gas supply,and most of the agricultural producing industries.
Keywords: Purchasing Power Parity, International Input-Output Tables, Price Level Indexes, International
CompetitivenessJEL classification: F02, C43, C67a)Professor, Keio Economic Observatory (KEO), Keio University, Tokyo, and Faculty Fellow, Research Institute of Economy,
T rade and Industry (RIETI), b) Professor, Faculty of Economics, Rissho University, T okyo. c) Research Economist, U.S. Bureau
of Economic Analysis, U.S. Department of Commerce. Nomura and Miyagawa conducted this study as a part of the project on“ Productivity Gaps and Industrial Competitiveness” (January 2018–December 2019) at RIETI. The views expressed in this paper
are solely those of the authors and not necessarily that of the RIETI, or the U.S. Bureau of Economic Analysis. The use of theunpublished data collected within the International Comparisons Program is permitted by ST D/OECD and Development
Economics/The World Bank. The authors are indebted to Hiroshi Shirane (KEO) for his research support.

1

1

Introduction
Cross country comparisons of international competitiveness at the industry-level are

inherently more difficult than aggregate comparisons. The basic issue is that comparing industries
is more data demanding than comparing aggregates in general, but this is exacerbated by the factthat price differentials are mainly measured at the level of final expenditures. 1 Price data at thelevel of final expenditures enables one to compare output across countries at the aggregate level,by estimating the PPP for GDP from the expenditure side. One of the main impediments tocomparing industries is the lack of adequate data on price differentials of domestic industry outputs
and intermediate inputs across countries. This data gap has greatly limited productivity levelcomparisons at industry level across countries and in turn, offered little insight into cross-country
supply-side efficiency measures and related policy implications (Hamadeh and AbuShanab, 2016;
Jorgenson, 2018).
The purpose of this paper is to fill this data gap for the U.S. and Japan. We employ a bilateralprice model to measure 2011 benchmark industry-level price level indices (PLIs) for outputs. The
PLI is defined as the ratio of the PPP to the market exchange rate. Our starting point is the Isardtype bilateral input-output table (BIOT), that has been developed by the Ministry of Economy,
Trade and Industry (METI), Government of Japan for the purpose of analyzing the interdependency
among Japanese and the U.S. industries since 1985. 2 METI’s Japan-US BIOTs are harmonized to
a common and detailed classification of industries 3 , and provides supplementary tables oninternational freight and insurance and tariffs by products in both countries. Although theavailability of METI’s BIOT is a major advantage in forming Japan-US comparisons (that is, dataof this nature is not available for most other countries), METI’s compilation terminated after the
publication of the 2005 BIOT (METI, 2013). In this paper, we estimate the 2011 BIOT by extending
the official 2005 BIOT.
Using the 2011 Japan-US BIOT as an anchor, we postulate an accounting model describing
the relationships among producer’s prices and purchaser’s prices for domestically-produced andimported products. The model reflects the differences in the trade structure, freight and insurance
rates, duty tax rates, wholesale and retail trade margins, and transportation costs in each product. 4
Using demand-side data of purchaser’s price differentials for final uses, e.g., the PPP estimates inEurostat-OECD (2012), and for intermediate uses, e.g., Survey on Foreign and Domestic Price
Differentials for Industrial Goods and Services in METI (2012), the producer’s price differentials
for outputs are estimated based on our Japan-US bilateral price accounting model. That is, the1

For example, the purchasing power parities (PPPs) compiled within the International Comparisons Program (ICP) in EurostatOECD (2012) and World Bank (2014).
2
T he first bilateral table between Japan and the U.S. for 1970 was developed in Japan at the Institute of Developing Economies(1978) as a joint project with Keio Economic Observatory (KEO), Keio University in 1978. The METI’s Japan-US BIOTs werecompiled for the benchmark years of Japanese benchmark IOT, i.e., 1985, 1990, 1995, 2000, and 2005.
3
T he 2005 Japan-US IOT in METI (2013) is defined as the symmetric-IOT with common classification of 173 products. This isestimated based on the Japan’s 2005 benchmark IOT and the U.S. 2005 Symmetric IOT developed at INFORUM, University of
Maryland, which was extended from the 2002 Benchmark SUT by the U.S. Bureau of Economic Analysis (BEA), Department ofCommerce.
4
T he original price model approach to determining the product PPPs between Japan and the U.S. was developed in Jorgenson,
Kuroda, and Nishimizu (1987).

2

model takes available prices on final demand and intermediate uses and converts these toconceptually appropriate industry output and intermediate input prices that are consistent with the
input-output tables. The availability of METI’s survey on PPPs for intermediate uses is a significant
advantage in the Japan-US comparison. This enables us to account for the price differentials forintermediate products like semiconductors, which do not appear in the survey on final demand
prices. It is important to note that the PPPs at purchaser’s prices are sometimes considerably
different for final and intermediate uses even within the same class of product. This could be
because the composition and quality of the products may differ between final demand andintermediate input. In our approach, we are able to identify the gap between the two, and accountfor this by constructing the PPPs for industry outputs as a composite of both.
As globalization has deepened since the early 1990s, it has become more important to consider
the impact of the differences in the import prices of the traded goods in Japan and the U.S. The
import prices allow us to parse the price of composite goods into that from domestic supply (whichfeeds into the industry output price) and that coming from imported goods. Our bilateral pricemodel has a sub model to explicitly treat the imports by product from six exogenous economies,i.e., China, Germany, Korea, Malaysia, Taiwan (Republic of China), and Thailand, to Japan andthe U.S.
Compared to the previous work in Nomura and Miyagawa (1999 and 2015), we use moreprice data than the earlier studies. This additional price data allows us to refine our estimates of theunobserved prices in our price model. The total number of price-differential data we use in thispaper is 538 at the elementary level, in which each of the price concepts (i.e., for industry orhousehold use, at producer’s or purchaser’s prices, and including imports or not) are incorporated
into the accounting model to pin down the remainder of the prices for which there is no data. For
the case that the appropriate data are not available, or their accuracy cannot be checked, the costindex approach is used. Using the cost index approach, the underlying assumption is that the output
price relative corresponds to the input price relative. In measuring costs, we include not only theprice differentials of products for intermediate uses (estimated in this paper), but also the prices oflabor and capital inputs used in production. 5 By construction, the cost index approach imposes
zero TFP differential between Japan and the U.S.
The accuracy of the estimated PPPs for industry outputs based on the price model approach
depends not only on the quality of purchaser-price PPPs of the composite products for different
uses, but also on measures of the margin rates and other related parameters that are used to translate
the available data into conceptually appropriate prices to match the input-output table. It should beof note that 2011 as the benchmark year is not necessarily ideal to observe the Japanese economy.
The first reason is that the 2011 benchmark estimates in the Japan’s system of national accounts(JSNA) depend on the 2011 Economic Census, which was conducted for the first time in the historyof Japanese economic statistics. This had the potential to improve the quality of JSNA, but on theother hand, because it was a new Census, the results had the potential to reflect changes in5

T hese are estimated in Jorgenson, Nomura, and Samuels (2018).

3

methodologies and approaches to measurement. Another reason is the impact of the East Japan
great earthquake disaster on March 11, 2011. The earthquake made it difficult to survey some areasin East Japan and to observe the economy, in general. Although it is hard to evaluate the quality of
the 2011 benchmark JSNA at present, there are some indications of measurement error in Japan’s
benchmark input-output table (IOT). Nomura and Miyagawa (2018a) pointed out that thewholesale and retail service values in the 2011 benchmark IOT were considerably underestimated.
This paper incorporates their alternative estimates of wholesale and retail margins, which are oneof the key parameters in the price model. The sensitivity to this revision is discussed the Appendix.
The remainder of this paper is organized as follows. Section 2 presents our representation of
the production systems for Japan and the U.S. that is the basis for our accounting model, and an
overview of our methodological framework. The detailed equations to describe the bilateralaccounting model are provided in the Appendix. In Section 3 we describe our data sources for theJapan-US BIOT and for the price differentials that feed into the price accounting model. The results
are presented in Section 4. Section 5 concludes.

2

Framework
We start with a basic description of our framework. Figure 1 provides the Isard-type bilateral

input-output table (BIOT). Entries of the table are in nominal values, but shown here as price times
volume to emphasize how this relates to the price accounting model that we present below. Our
BIOT separately identifies the imports from six exogenous economies: China, Germany, Korea,
Malaysia, Taiwan, and Thailand, and the rest of the world (ROW). In the Isard-type (noncompetitive import type IOT) framework (Isard, 1951), all purchases in Japan and the U.S. fromforeign countries are recorded separately from the purchases of domestically produced goods andservices. The areas surrounded by dotted squares in Figure 1 represent imports to Japan and the
U.S. The variables in the BIOT are defined in the Appendix.
The prices of domestically produced products are evaluated at producer’s prices (including
indirect taxes required for purchasers). The prices of imported products in Japan and the U.S., fromthe U.S. and Japan, respectively, are evaluated at FOB (free on board) prices (producers’ prices
plus margin and transportation costs from producers to customs). Thus, the freight and insurance
and tariff embedded in imports (in Japan-US trade) and the net indirect taxes required in imported
countries (in Japan or the U.S.) are separately recorded from the FOB-price imports. The imports
from exogenous economies are evaluated at the prices including CIF (cost, insurance, and freight),
tariff, and the net indirect taxes embedded in imports (in Japan or the U.S.).

4

Japan (J)P roducts in
the U.S. (U)Freight and insurance
for the Japan-US trade

Tarifffor the Japan-US trade

Net indirect taxes on importsof the Japan-US trade

China
(C)

Germany(G)

Korea
Import from(K)

exogenous
countries
at the price of cif,tariff, and net

Malaysia(M)

indirect taxes(E)

Taiwan(W)

Thailand
(T)

ROW
(R)

Value added
Gross output

Intermediate uses

Household consumption

Government consumption

Exports to

Gross

(N)

(H)

& Gross capital formation

exogenous

output(Z)

countris(X)(E)

Japan (J)the U.S. (U)Japan (J)the U.S. (U)Japan (J)the U.S. (U)𝑝𝑝𝑑,𝐼𝐼𝑋𝑋
𝐽𝐽,𝑖 𝐽𝐽𝐽𝐽,𝑖𝑗𝑗

𝑝𝑝𝑑,𝐼𝐼𝑋𝑋𝐽𝐽𝑈𝑈,𝑖 𝐽𝐽𝑈𝑈,𝑖𝑗𝑗

𝑒𝑒𝐽𝐽/𝑈𝑈𝑝𝑝𝑑,H
𝑋𝑋
𝐽𝐽,𝑖 𝐽𝐽𝐽𝐽,𝑖𝐻𝐻,𝐻𝐻
𝑝𝑝𝑑𝐽𝐽𝑈𝑈,𝑖𝑋𝑋𝐽𝐽𝑈𝑈,𝑖𝐻𝐻

𝑝𝑝𝑑,𝐼𝐼𝑋𝑋
𝐽𝐽,𝑖 𝐽𝐽𝐽𝐽,𝑖𝑍

𝑝𝑝𝑑,𝐼𝐼𝑋𝑋𝐽𝐽𝑈𝑈,𝑖 𝐽𝐽𝑈𝑈,𝑖𝑍

𝑝𝑝𝑑𝐽𝐽𝐸𝐸,𝑖𝑋𝑋𝐽𝐽𝐸𝐸,𝑖𝐸𝐸

𝑝𝑝𝑑𝐽𝐽,𝑖 𝑋𝑋𝐽𝐽,𝑖𝑑𝑑,𝐼𝐼
𝑝𝑝𝑈𝑈𝐽𝐽,𝑖𝑖
𝑋𝑋𝑈𝑈𝐽𝐽,𝑖𝑖𝑗𝑗

𝑑𝑑,𝐼𝐼𝑝𝑝𝑈𝑈,𝑖𝑖𝑋𝑋𝑈𝑈𝑈𝑈,𝑖𝑖𝑗𝑗

𝑑𝑑,H
𝑝𝑝𝑈𝑈𝐽𝐽,𝑖𝑖
𝑋𝑋𝑈𝑈𝐽𝐽,𝑖𝑖𝐻𝐻

𝑝𝑝𝑑𝑑,𝐻𝐻
𝑈𝑈,𝑖𝑖 𝑋𝑋𝑈𝑈𝑈𝑈,𝑖𝑖𝐻𝐻

𝑑𝑑,𝐼𝐼
𝑝𝑝𝑈𝑈𝐽𝐽,𝑖𝑖
𝑋𝑋𝑈𝑈𝐽𝐽,𝑖𝑖𝑍

𝑝𝑝𝑑𝑑,𝐼𝐼
𝑈𝑈,𝑖𝑖 𝑋𝑋𝑈𝑈𝑈𝑈,𝑖𝑖𝑍

𝑝𝑝𝑑𝑑𝑈𝑈𝑘𝑘,𝑖𝑖 𝑋𝑋𝑈𝑈𝑘𝑘,𝑖𝑖𝑘𝑘

𝑝𝑝𝑑𝑑𝑈𝑈,𝑖𝑖 𝑋𝑋𝑈𝑈,𝑖𝑖

𝑒𝑒𝐽𝐽/𝑈𝑈,𝐼𝐼𝜏𝜏𝑓𝑓𝑈𝑈𝐽𝐽 𝑝𝑝𝑓𝑓𝑓𝑓𝑓𝑓
𝑈𝑈𝐽𝐽,𝑖𝑖 𝑋𝑋𝑈𝑈𝐽𝐽,𝑖𝑖𝑗𝑗

𝑟𝑟 𝑝𝑝𝑓𝑓𝑓𝑓𝑓𝑓 ,𝐼𝐼 𝑋𝑋𝜏𝜏𝑈𝑈𝐽𝐽𝑈𝑈𝐽𝐽,𝑖𝑖𝑗𝑗
𝑈𝑈𝐽𝐽,𝑖𝑖𝑇𝑇𝑋𝑋𝐼𝐼𝑈𝑈𝐽𝐽,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝐶𝐶𝐽𝐽,𝑖 𝐶𝐶𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋𝐺𝐺𝐽𝐽,𝑖 𝐺𝐺𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋𝐾𝐾𝐽𝐽,𝑖 𝐾𝐾𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑀𝑀𝐽𝐽,𝑖 𝑀𝑀𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑊𝑊𝐽𝐽,𝑖 𝑊𝑊𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑇𝑇𝐽𝐽,𝑖 𝑇𝑇𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑅𝑅𝐽𝐽,𝑖 𝑅𝑅𝐽𝐽,𝑖𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈𝑉𝐴 𝐽𝐽,𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑑𝐽𝐽,𝑗𝑗 𝑋𝑋𝐽𝐽,𝑗𝑗
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑒𝑒𝐽𝐽/𝑈𝑈𝜏𝜏𝑓𝐽𝐽𝑈𝑈𝑝𝑝𝑓𝑜𝑜𝑏,𝐼𝐼
𝑋𝑋𝐽𝐽𝑈𝑈,𝑖𝑗𝑗
𝐽𝐽𝑈𝑈,𝑖𝑒𝑒𝐽𝐽/𝑈𝑈

𝑜𝑜 𝑝𝑝𝑓𝑜𝑜𝑏,𝐼𝐼 𝑋𝑋𝜏𝜏𝐽𝐽𝑈𝑈𝐽𝐽𝑈𝑈,𝑖𝑗𝑗
𝐽𝐽𝑈𝑈,𝑖𝑒𝑒𝐽𝐽/𝑈𝑈𝑇𝑇𝑋𝑋𝐼𝐼𝐽𝐽𝑈𝑈,𝑖𝑖𝑗𝑗

𝑝𝑝𝑚𝑚,𝐼𝐼
𝐶𝑈𝑈,𝑖𝑖 𝑋𝑋𝐶𝑈𝑈,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼
𝐺𝑈𝑈,𝑖𝑖 𝑋𝑋𝐺𝑈𝑈,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼𝐾𝑈𝑈,𝑖𝑖 𝑋𝑋𝐾𝑈𝑈,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼
𝑀𝑈𝑈,𝑖𝑖 𝑋𝑋𝑀𝑈𝑈,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼𝑊𝑊𝑈𝑈,𝑖𝑖 𝑋𝑋𝑊𝑊𝑈𝑈,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼𝑇𝑇𝑈𝑈 ,𝑖𝑖 𝑋𝑋𝑇𝑇𝑈𝑈,𝑖𝑖𝑗𝑗
𝑝𝑝𝑚𝑚,𝐼𝐼𝑅𝑅𝑈𝑈,𝑖𝑖 𝑋𝑋𝑅𝑅𝑈𝑈,𝑖𝑖𝑗𝑗

𝑒𝑒𝐽𝐽/𝑈𝑈,𝐻𝐻
𝜏𝜏𝑓𝑓𝑈𝑈𝐽𝐽 𝑝𝑝𝑓𝑓𝑓𝑓𝑓𝑓
𝑈𝑈𝐽𝐽,𝑖𝑖 𝑋𝑋𝑈𝑈𝐽𝐽,𝑖𝑖𝐻𝐻

𝑟𝑟 𝑝𝑝𝑓𝑓𝑓𝑓𝑓𝑓 ,𝐻𝐻 𝑋𝑋𝜏𝜏𝑈𝑈𝐽𝐽𝑈𝑈𝐽𝐽,𝑖𝑖𝐻𝐻
𝑈𝑈𝐽𝐽,𝑖𝑖

𝑒𝑒𝐽𝐽/𝑈𝑈𝜏𝜏𝑓𝐽𝐽𝑈𝑈𝑝𝑝𝑓𝑜𝑜𝑏,𝐻𝐻
𝑋𝑋𝐽𝐽𝑈𝑈,𝑖𝐻𝐻
𝐽𝐽𝑈𝑈,𝑖𝑒𝑒𝐽𝐽/𝑈𝑈

𝑜𝑜 𝑝𝑝𝑓𝑜𝑜𝑏,𝐻𝐻𝑋𝑋𝜏𝜏𝐽𝐽𝑈𝑈𝐽𝐽𝑈𝑈,𝑖𝐻𝐻
𝐽𝐽𝑈𝑈,𝑖𝑒𝑒𝐽𝐽 /𝑈𝑈

𝑇𝑇𝑋𝑋𝐻𝐻𝐽𝐽𝑈𝑈,𝑖𝑖𝐻𝐻

𝑇𝑇𝑋𝑋𝐻𝐻𝑈𝑈𝐽𝐽,𝑖𝑖𝐻𝐻
𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝐶𝐶𝐽𝐽,𝑖 𝐶𝐶𝐽𝐽,𝑖𝐻𝐻

𝑝𝑝𝑚𝑚,𝐻𝐻
𝐶𝑈𝑈,𝑖𝑖 𝑋𝑋𝐶𝑈𝑈,𝑖𝑖𝐻𝐻

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝐺𝐺𝐽𝐽,𝑖 𝐺𝐺𝐽𝐽,𝑖𝐻𝐻

𝑝𝑝𝑚𝑚,𝐻𝐻
𝐺𝑈𝑈,𝑖𝑖 𝑋𝑋𝐺𝑈𝑈,𝑖𝑖𝐻𝐻

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝐾𝐾𝐽𝐽,𝑖 𝐾𝐾𝐽𝐽,𝑖𝐻𝐻

𝑝𝑝𝑚𝑚,𝐻𝐻
𝐾𝑈𝑈,𝑖𝑖 𝑋𝑋𝐾𝑈𝑈,𝑖𝑖𝐻𝐻

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝑀𝑀𝐽𝐽,𝑖 𝑀𝑀𝐽𝐽,𝑖𝐻𝐻
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝑊𝑊𝐽𝐽,𝑖 𝑊𝑊𝐽𝐽,𝑖𝐻𝐻
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐻𝐻
𝑀𝑈𝑈,𝑖𝑖 𝑋𝑋𝑀𝑈𝑈,𝑖𝑖𝐻𝐻
𝑝𝑝𝑚𝑚,𝐻𝐻
𝑊𝑊𝑈𝑈,𝑖𝑖 𝑋𝑋𝑊𝑊𝑈𝑈,𝑖𝑖𝐻𝐻

𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝑇𝑇𝐽𝐽,𝑖 𝑇𝑇𝐽𝐽,𝑖𝐻𝐻

𝑝𝑝𝑚𝑚,𝐻𝐻
𝑇𝑇𝑈𝑈,𝑖𝑖 𝑋𝑋𝑇𝑇𝑈𝑈,𝑖𝑖𝐻𝐻

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐻𝐻𝑋𝑋
𝑅𝑅𝐽𝐽,𝑖 𝑅𝑅𝐽𝐽,𝑖𝐻𝐻

𝑝𝑝𝑚𝑚,𝐻𝐻
𝑅𝑅𝑈𝑈,𝑖𝑖 𝑋𝑋𝑅𝑅𝑈𝑈,𝑖𝑖𝐻𝐻

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑒𝑒𝐽𝐽/𝑈𝑈,𝐼𝐼𝜏𝜏𝑓𝑓𝑈𝑈𝐽𝐽 𝑝𝑝𝑓𝑓𝑓𝑓𝑓𝑓
𝑈𝑈𝐽𝐽,𝑖𝑖 𝑋𝑋𝑈𝑈𝐽𝐽,𝑖𝑖𝐺

𝑟𝑟 𝑝𝑝𝑓𝑓𝑓𝑓𝑓𝑓 ,𝐼𝐼 𝑋𝑋𝜏𝜏𝑈𝑈𝐽𝐽𝑈𝑈𝐽𝐽,𝑖𝑖𝑍𝑈𝑈𝐽𝐽,𝑖𝑖𝑇𝑇𝑋𝑋𝐼𝐼𝑈𝑈𝐽𝐽,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝐶𝐶𝐽𝐽,𝑖 𝐶𝐶𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋𝐺𝐺𝐽𝐽,𝑖 𝐺𝐺𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋𝐾𝐾𝐽𝐽,𝑖 𝐾𝐾𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑀𝑀𝐽𝐽,𝑖 𝑀𝑀𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑊𝑊𝐽𝐽,𝑖 𝑊𝑊𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑇𝑇𝐽𝐽,𝑖 𝑇𝑇𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑝𝑝𝑚𝑚,𝐼𝐼𝑋𝑋
𝑅𝑅𝐽𝐽,𝑖 𝑅𝑅𝐽𝐽,𝑖𝑍
𝑒𝑒𝐽𝐽/𝑈𝑈

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑒𝑒𝐽𝐽/𝑈𝑈

𝑒𝑒𝐽𝐽/𝑈𝑈𝜏𝜏𝑓𝐽𝐽𝑈𝑈𝑝𝑝𝑓𝑜𝑜𝑏,𝐼𝐼
𝑋𝑋𝐽𝐽𝑈𝑈,𝑖𝑍
𝐽𝐽𝑈𝑈,𝑖𝑒𝑒𝐽𝐽/𝑈𝑈

𝑜𝑜 𝑝𝑝𝑓𝑜𝑜𝑏,𝐼𝐼 𝑋𝑋𝜏𝜏𝐽𝐽𝑈𝑈𝐽𝐽𝑈𝑈,𝑖𝑍
𝐽𝐽𝑈𝑈,𝑖𝑒𝑒𝐽𝐽/𝑈𝑈𝑇𝑇𝑋𝑋𝐼𝐼𝐽𝐽𝑈𝑈,𝑖𝑖𝑍

𝑝𝑝𝑚𝑚,𝐼𝐼
𝐶𝑈𝑈 ,𝑖𝑖 𝑋𝑋𝐶𝑈𝑈,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼
𝐺𝑈𝑈,𝑖𝑖 𝑋𝑋𝐺𝑈𝑈,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼𝐾𝑈𝑈,𝑖𝑖 𝑋𝑋𝐾𝑈𝑈,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼
𝑀𝑈𝑈,𝑖𝑖 𝑋𝑋𝑀𝑈𝑈,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼𝑊𝑊𝑈𝑈,𝑖𝑖 𝑋𝑋𝑊𝑊𝑈𝑈,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼𝑇𝑇𝑈𝑈 ,𝑖𝑖 𝑋𝑋𝑇𝑇𝑈𝑈,𝑖𝑖𝑍
𝑝𝑝𝑚𝑚,𝐼𝐼𝑅𝑅𝑈𝑈,𝑖𝑖 𝑋𝑋𝑅𝑅𝑈𝑈,𝑖𝑖𝑍

𝑉𝐴 𝑈𝑈,𝑗𝑗

𝑝𝑝𝑑𝑑𝑈𝑈,𝑗𝑗 𝑋𝑋𝑈𝑈,𝑗𝑗

Figure 1: Japan-US Input-Output Table (the Isard-Type)
Note: See Appendix for the definition of the variables.

Based on the production system in Figure 1, we specify an accounting model describing
producer’s prices and purchaser’s prices for domestically-produced and imported products thattakes into account the trade structure, freight and insurance rates, duty tax rates, wholesale andretail trade margins, and transportation costs in each product. The details of the equations areprovided in the Appendix. Our objects of interest are the following PLIs for each product i, which
are defined as price level in Japan relative to the U.S., divided by the nominal exchange rate:
𝐏𝐏𝑖𝑖𝑑𝑑𝐏𝐏𝑖𝑖𝑑𝑑 ,𝑙𝑙𝐏𝐏𝑖𝑖𝑐𝑐 ,𝑙𝑙𝑝𝑝𝑝𝑝 ,𝑙𝑙𝐏𝐏𝑖𝑖

PLI for domestic outputs at producer’s price,
PLI for domestic outputs at producer’s price (see definition of 𝑙𝑙 below),

PLI for composite products (domestic products and imports) at producer’s price, and
PLI for composite products (domestic products and imports) at purchaser’s price,5

where l stands for the demand group. 6 We define six groups of demands, denoting:Nfor intermediate uses,Hfor household consumption (including consumption by NPISHs),G

for government consumption,F

for investment (GFCF and changes in inventories) by industries and government,Efor exports to exogenous economies, andM
for imports,
and the following three broad groups of the demands,Z

for domestic final demand excluding household consumption (Z={G, F}),I

for domestic demand by industries and government (I={N, G, F}) 7 , andD

for domestic demand (D={I,H}={N, H, G, F}).
Figure 2 illustrates the relationships among the PLIs and shows four paths used in estimation

to go from observed data to the unmeasured the PLIs of interest. The PLI surrounded by each box
indicates the observed PLI and the corresponding directional arrows indicate the estimation usedconditional on the observed data.

𝑝𝑝𝑐𝑐,𝐻𝐻

𝐏𝐏𝑖𝑖

𝐏𝐏𝑖𝑖𝑐𝑐,𝐻𝐻

𝐏𝐏𝑖𝑖𝑑𝑑,𝐻𝐻
𝐏𝐏𝑖𝑖𝑑𝑑𝑝𝑝𝑐𝑐,𝐼𝐼

𝐏𝐏𝑖𝑖

𝐏𝐏𝑖𝑖𝑐𝑐,𝐼𝐼

𝐏𝐏𝑖𝑖𝑑𝑑,𝐼𝐼

Path-1

Path-2Path-3Path-4

Figure 2: Price Deviation Paths
Path-1 starting with the box on the right shows the case where the producer-price PLI ofdomestic outputs 𝐏𝐏𝑖𝑖𝑑𝑑 is available based on surveys. In this case, the difference between 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐼𝐼 (thearrow to the lower left in Figure 2) and 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐻𝐻 (the arrow to the upper left) is due to the differencein the treatment of consumption taxes. Next, continuing to move left in the diagram, the producer-

price PLI of composite products for intermediate use 𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐼𝐼 and for household use 𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐻𝐻 are derived

by taking into account the difference in import prices for Japan and the U.S. (based on Equation

To distinguish the price level index from the prices, we use the bold as 𝐏𝐏𝑖𝑖𝑑𝑑 . T hese Japan-US PLIs are defined as Japan’s price𝑑𝑑
over the U.S. prices as in Equation (20). Although they are described as 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖 in the Appendix to identify the transactions Japan,
the U.S., and exogenous economies, the subscript “𝐽𝐽/𝑈𝑈 ” is omitted in main text.
7
Since the government consumption is defined at the actual base, the products for I={N, G, F} mainly refer the products
consumed for industries’ intermediate uses (N) and investment by industries and government (F). For simplicity, we use I to
denote demand for industry uses.
66

(21) in the Appendix). Finally, the purchaser-price PLI of the products for intermediate use 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐼𝐼and for household use 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻 are estimated by including the difference in the trade margins and thetransportation costs by product between Japan and the U.S., based on Equation (30).

Path-2 is the case where data for the purchaser-price PLI of the products for industry use 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐼𝐼and household use 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻 are available. Based on this data, 𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐼𝐼 and 𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐻𝐻 (the arrow to the rightin Figure 2) are calculated based on Equation (30). And then, 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐼𝐼 and 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐻𝐻 are estimated inaccordance with Equation (23) and 𝐏𝐏𝑖𝑖𝑑𝑑 is derived as the aggregate based on the Equation (24).
In Path-3 scenarios, only the purchaser-price PLI of the products for household use 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻 isavailable as observations (like the Eurostat-OECD PPPs). By considering the differences in trade
margins and the transportation costs, 𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐻𝐻 and 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐻𝐻 are estimated based on Equations (30) and(23), respectively. In this case, 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐼𝐼 is derived (the arrow pointing down in Figure 2) by considering

the difference in consumption taxes and 𝐏𝐏𝑖𝑖𝑑𝑑 is determined using 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐼𝐼 and 𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐻𝐻 based on Equation(24). Additionally, 𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐼𝐼 and 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐼𝐼 are estimated by taking into account the difference in importprices, the percentage of imports, the trade margins, and the transportation costs between Japanand the U.S,. In Path-4 scenarios, 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐼𝐼 is observed instead of 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻 as in the Path-3 scenario, but
the process to estimate the other PLIs is similar.

3

Data and Measurement

3.1 2011 Japan-US BIOT
In measuring the 2005 benchmark PLIs, Nomura and Miyagawa (2015) expanded the 2005
Japan-US BIOT (METI, 2013) to identify the imports from six exogenous economies; China,
Germany, Korea, Malaysia, Taiwan (Republic of China), and Thailand, and modified the table toaccount for Japan’s consumption tax. Since the introduction of the consumption tax in 1989, inthe current JSNA and Japan’s benchmark IOT, the values for intermediate uses are recorded as
the prices including not only non-deductible consumption taxes, but also deductible ones,
resulting in an inconsistency between prices recorded in the accounts and the net prices actually
paid by purchasers. In addition, consumption taxes (deductible and non-deductible) are notseparately estimated from other indirect taxes by industry. Since METI’s 2005 Japan-US BIOT
follows this price definition used in JSNA, it is difficult to compare Japan’s prices with those in
the U.S. The 2005 BIOT was revised to define output at basic prices in Nomura and Miyagawa(2015), and we follow the same approach.
Using the adjusted 2005 BIOT as the base table, this paper estimates the 2011 BIOT, byconsidering changes in production and trade from 2005 to 2011. Our adjustments are based on theofficial national accounts and trade statistics in Japan and the U.S. The international trade data ofJapan and the U.S. from the six exogenous countries and the ROW are extended in each productbased on the import data by product and by county published in the UN Comtrade Database.
To estimate the model, the trade matrix among Japan and the U.S., the six exogenous countries,
and the ROW is required as in Equation (34). In measurement of the PPPs for 2005 in Nomura andMiyagawa (2015), these matrices for industry use and household use were developed based on the7

2005 Asian International Input-Output Table published by Institute of Developing Economies(2013), which covers Japan, the U.S., China, Korea, Malaysia, Taiwan, and Thailand, and the
WIOD (World Input-Output Database) in Timmer et al. (2015), which covers Japan, the U.S.,
China, Germany, Korea, and Taiwan. In this paper, the WIOD is used to update the trade matrices
from 2005 to 2011; other trade relationships are assumed to be unchanged due to the lack of the2011 Asian International IOT.

3.2 Elementary Level PLIs
We use price-differential data obtained from Eurostat-OECD (2012), METI (2012), and manysources published by agencies and ministries of the Government of Japan and the private businesssector as our starting point. 8 The total number of price data at the elementary level used in thisstudy was 538. Since the number of products in our model based on the 2011 Japan-US BIOT is174, on average about 3 price data points are used to estimate the price of one product in our model.
In some cases, data with different price concepts at the elementary level are integrated based on
our price model, e.g., the PLIs for industry use and household use are integrated as described in
Path-2 in Figure 2. Sometimes the price data at the elementary level are highly disaggregated within
one of our 174 products of interest. For example in chemical products, the PPPs for highly
disaggregated products for intermediate uses are available in METI (2012). In this case, the productlevel PLIs are calculated as Törnqvist indices using the elementary level PLIs. If the weight for theelementary level is unavailable, the product’s PLI is calculated as a simple geometric average.
Table 1 presents the concepts of the collected data at the elementary level by broad product.
Each row corresponds to a sector of Central Product Classification Ver.2. One of the most importantdata sources is the Eurostat-OECD PPPs. At the most detailed level, the Eurostat-OECD 2011
includes price data for 206 products which are called “basic headings.” The survey observes PPPs
at purchaser’s prices of composite products purchased by households or used as investment. As
shown in Table 1, 129 price data for households and 27 price data for investment were used tocorrespond to 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐻𝐻 and 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐹𝐹, respectively . 9

For intermediate products, METI’s Survey on Foreign and Domestic Price Differentials for

Industrial Goods and Services is the main data source. 10 This survey has been conducted every
year between 1993 and 2012 and every two years since 2012. The 2011 survey (METI, 2012),
collected price data for 226 goods and 61 services for intermediate uses, and covered 6 countries
namely, Japan, the U.S., China, Germany, Korea, and Taiwan. Data in this survey is measured inpurchaser’s price PPPs. As seen in Table 1, 272 data are collected from this survey and used toestimate 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝑁𝑁 , in our framework.

8

In the context of Japan-US comparisons, a significant advantage is the availability of much richer data on price differentials
among major industrialized countries. These have been gathered by the agencies and ministries of the Government of Japan since
the late 1980s, as a response to an important policy focus on international price differentials after the Plaza Accord of 1985
resulted in the rapid appreciation of the Japanese yen.
9
In Table 1, the purchaser’s demand price for intermediate uses 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝑁𝑁 and for investments 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐹𝐹 are distinguished. Both ofthem are treated as 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐼𝐼 in the price framework explained in Section 2.
10
T he title of METI’s survey was revised in 2011 from the previous title: Survey on Foreign and Domestic Price Differentials
for Industrial Intermediate Input.

8

Table 1: Number of Data on Price Differentials at Elementary Level
Purchaser's priceHousehold consumption

Intermediate use
𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝑁𝑁

CPC code
0 Agriculture, forestry andfishery
1 Ores and minerals;
electricity, gas and water
2 Food, beverages andtobacco; textiles, appareland leather
3 Other transportable goods,
except metal products,
machinery, equipment
4 Metal products, machineryand equipment
5 Constructions andconstruction services
6 Trade; accommodation,
food and beverage serving;transport
7 Financial and related
services; real estate; rental
and leasing services
8 Business and production
services
9 Community, social andpersonal services
Total

METI Other Other Total
PPP
PPP surveys
survey surveys on unit
pricesEurostat Other Other Total-OECD
PPP surveys
PPPs surveys on unit
prices
6

10

3

13

1

76

6

7

121

1

Producer's priceInvestment

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐻𝐻

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐹𝐹

Eurostat
-OECD
PPPs

Total

13

19

1

5

19

6

1

6

59

2

5

5

123

1

8

1

174

Cost
index

6

10

3

1

5

1

47

5

52

89

14

11

1

26

3

121

20

7

7

34

18

3

𝐏𝐏𝑖𝑖𝑑𝑑Reference Total
PPP

Other
surveyson unitprices

4

4

22

28

9

1

1

11

2

15

15

5

1

1

7

2

19

19

8

5

11
297

20
129

1
31

8
272

5

14

1

3
11

11

13

1

21
171

1
27

22

2

2

41

1

3

25

5

5

38

3
43

36
538

3
21

17

Source: Our estimates.

Although these two surveys don’t cover all the products, there are rich data on international
price differentials based on the surveys implemented by a number of Japanese ministries. We use
Survey of PPPs on Consumer Goods and Services (METI, 2003), Survey of PPPs on Drugs andMedical Products (Ministry of Health, Labour and Welfare, 2003), Survey of Retail Prices of Food
Products in Tokyo and Foreign Major 6 Cities (Ministry of Agriculture, Forestry and Fisheries,2006), and others. 11 From these surveys, 14 price data for intermediate use and 31 price data forhousehold use are used to estimate 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝑁𝑁 and 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐻𝐻 respectively. 12

In addition, other surveys on unit prices are used in this study, where appropriate. For example,

the output prices of some agricultural products evaluated at producer’s price are directly observed
from Table on Value and Quantity (Butsuryo Hyo) which was compiled as a supplementary tableof the Japanese 2011 IOT and Rice Outlook, Oil Crops Outlook, or Sugar and Sweeteners Outlook
published by the U.S. Department of Agriculture. The output prices for cattle, poultry and hog inJapan and the U.S. are directly obtained from the statistical data on livestock and its products
published by the Agriculture and Livestock Industries Corporation, Japan. The output prices ofcoal, crude oil, and natural gas are obtained from Trends of the Japanese Mining Industry publishedby METI and Annual Energy Review published by the U.S. Energy Information Administration.
As a result, 22 price data are used to determine 𝐏𝐏𝑖𝑖𝑑𝑑 directly without having to appeal to the price11

In addition, Survey of PPPs on Transportation and Related Services (Ministry of Land, Infrastructure and Transport, 2007),
Survey of PPP on Information Services (Ministry for Internal Affairs and Communications, 2011) and Survey of PPPs on Major
Consumer Goods and Services (Cabinet Office, 2001) are used in our study.
12
T hese data are estimated for different years and different stages of demand. T he differences in timing of the surveys were
adjusted using the CPI and PPI in both countries. We have reconciled these data within our price model.

9model. Finally, there are surveys that provide information on unit prices paid by purchasers; these
additional surveys provide 11 price data points that are used to measure intermediate and household
purchase prices, 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝑁𝑁 and 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻, respectively .

In the process to discern the producer’s price PLIs for outputs from the purchaser’s price PLIs

based on the price model, the PLIs of wholesale and retail services have a significant role. Nomura
and Miyagawa (2018a) pointed out that the outputs of the wholesale and retail sectors in the 2011
benchmark IOT in Japan appeared to be considerably underestimated and provided alternative
estimates of wholesale and retail margins based on microdata of Census of Commerce. 13 This
paper uses these margin rate and PLI estimates for 2011. These data are counted as two data points
in “Other surveys on unit prices” in Table 1. A sensitivity analysis to our choice of margins ispresented in the Appendix.
The cost approach is also adopted for some products whose prices are difficult to directly
observe. In the cost approach, the producer-price PLIs of domestic products are estimated by the
PLIs of all intermediate products we estimated in this paper and the estimates of the PLIs for laborand capital inputs estimated in Jorgenson, Nomura, and Samuels (2018), aggregated using theweights of the cost structures obtained from the 2011 Japan-US BIOT. Figure 3 presents the PPPs
for labor and capital inputs at the aggregate level for the period 1990–2015 in Jorgenson, Nomura,and Samuels (2018). During the recent quarter of century, the PPPs for factor inputs haveconsiderably declined. In particular, the PPP for labor input declined by half. 14 Long-term declines
in PPPs for factor inputs translates to declines in PPPs for industry outputs based on the cost
approach, but obviously only for products that use the cost index approach (21 out of 538 products).
190(yen per dollar)
PPP for Capital Inputs

170

PPP for Labor Inputs

176.9

144.9

150
143.5
140.5

130

135.3

124.4

131.9
118.2

110
109.3

90
87.6
78.3

70

72.3

50
1990

1995

2000

2005

2010

2015

Figure 3: PPPs for Capital and Labor Inputs in 1990–2015
For a small set of products, we apply the reference PPP approach, in which the PPPs of the13

In Nomura and Miyagawa (2018b), the output PPP for wholesale service is estimated based on 82 goods for household use and
110 goods for industry use and the output PPP for retail service is estimated based on 87 goods for household use and 19 goods
for industry use.
14
T he quality-adjusted price of labor inputs has continued to decline in Japan for 15 years from 1997 to 2012 (Nomura andShirane, 2014).

10

similar products are applied. In this study, the cost index approach is applied for 21 elementarylevel products such as government service, education, and research (that is, we back out the relative
output prices by assuming that the gap in total factor productivity between Japan and the U.S. iszero), and the reference PPP approach is applied for 17 elementary level products.

3.3 Product Level PLIs
As shown in Table 1, many of the observed price data is based on purchaser’s demand prices.
Therefore, 𝐏𝐏𝑖𝑖𝑑𝑑 is estimated in this study by applying our price models to 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐼𝐼 and/or 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐻𝐻 fora large share of products. Table 2 presents the composition of our estimation methods. Each row

shows the Central Product Classification Ver.2, and the number in the column corresponds to thenumber of products classified in each group (the total is the number of all products, 174).
Table 2: Number of Products by Price Deviation Path
Path-1
Producer's price

CPC code
0 Agriculture, forestry and fishery
1 Ores and minerals; electricity, gas andwater
2 Food, beverages and tobacco; textiles,
apparel and leather
3 Other transportable goods, except metal
products, machinery, equipment
4 Metal products, machinery andequipment
5 Constructions and construction services
6 Trade; accommodation, food andbeverage serving; transport
7 Financial and related services; real estate;rental and leasing services
8 Business and production services
9 Community, social and personal services
Total

𝐏𝐏𝑖𝑖𝑑𝑑8

Path-2Path-3Purchaser's priceHouseholdHousehold&Industryuse
use

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐻𝐻&
𝑝𝑝𝑐𝑐,𝐼𝐼

𝐏𝐏𝑖𝑖

2

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐻𝐻

2

Path-4
Industryuse

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐼𝐼

5

1

2

6

17

6

11

4

13

4

15

5

21

(Path-4.1)(Path-4.2)(Path-4.3)
Intermediate Intermediate Investment
uses&Invest
uses
ment
𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝑁𝑁 &𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐹𝐹

3

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝑁𝑁

3

3
2
32

12
9
25

13
4

12

4
2

𝐏𝐏𝑖𝑖𝑝𝑝𝑐𝑐,𝐹𝐹

Total

34
5
4

45
4

7

3

2

2

14

4

2

1

1

7

6
4
56

1
4
38

1
3
48

1
3
35

11
13
174

4

9

Source: Our estimates. Note: The number of products (32) in Path-1 includes 9 products based on the cost approach and 7 products
based on the reference PPP approach.

According to Table 2, Path-1, which takes 𝐏𝐏𝑖𝑖𝑑𝑑 as data was applied to 32 products, which weremainly classified in Agriculture and Mining sector. Since the estimation of 𝐏𝐏𝑖𝑖𝑑𝑑 is the target of thisstudy, Path-1 based on the directly observed price data is the most preferable approach. The PLIs

for 56 products are estimated by Path-2 process, in which 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐼𝐼 and 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐻𝐻 are observed first andoutput prices are estimated via the accounting model. This is the most frequent case among four

price deviation paths and can be considered the second best path. Path-3 determines 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻 first. 38

products, most of which are final consumption goods and services, are estimated by this method.
Although Path-4, which takes as data 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐼𝐼 , is similar to Path-3, this is divided into three sub cases

depending on the kinds of the observed PLIs. In the first case, written as Path-4.1, the PLI ofpurchaser’s demand price for industries 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐼𝐼 is determined using both the PLI of the products for11𝑝𝑝𝑝𝑝 ,𝑁𝑁intermediate use and investment, 𝐏𝐏𝑖𝑖

𝑝𝑝𝑝𝑝 ,𝐹𝐹and 𝐏𝐏𝑖𝑖, respectively. Path-4.1 is applied only to 4 products
𝑝𝑝𝑝𝑝 ,𝑁𝑁

classified in Metal products, machinery, and equipment. Path-4.2 uses 𝐏𝐏𝑖𝑖

𝑝𝑝𝑝𝑝 ,𝐼𝐼

to determine 𝐏𝐏𝑖𝑖and

35 products belong to this case. The PLIs of only 9 products are estimated by Path-4.3, which uses

only 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐹𝐹 to determine 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝,𝐼𝐼 .
4

Results
Table 3 compares the PPPs for GDP developed in this paper and the Eurostat-OECD PPPs in2011. Our estimate of the PPP for GDP, which is derived from aggregating the PPPs for industryGDP at basic prices, is 109.0 yen per dollar, which closely resembles the Eurostat-OECD PPP(107.5 yen per dollar) in 2011. 15 Compared to the Eurostat-OECD PPP, our expenditure-side
estimates are somewhat lower in household consumption and building and construction (B&C) of
GFCF (gross fixed capital formation) and higher in machinery and equipment (M&E) of GFCF. 16
Table 3: Aggregated PPPs in 2011
PPP for

GDP

Householdconsumption

GFCF
B&C

M&E

Our estimates

109.0

113.4

116.6

113.7

104.0

Eurostat-OECD PPPs

107.5

116.1

110.0

114.0

99.2

Unit: yen per dollar. Source: Our estimates. Note: B&C is building and construction and M&E is machineryand equipment.

Figure 4 shows the extrapolated estimates of PPPs for GDP and household consumption from2011 to 2016, using our benchmark PPP estimates in 2011 and the price indices from the national
accounts in Japan (ESRI, Cabinet Office) and the U.S. (BEA) from 2011 to 2016, compared to theEurostat-OECD estimates. The trends are similar, but our estimate of the PPP for GDP is higher by
2–3 yen per dollar, reflecting the higher benchmark estimates. However, in the PPP estimate forhousehold consumption our benchmark estimate is slightly lower than the Eurostat-OECD PPP,
but they are quite similar in 2014–2016. In 2016, our estimates of PPPs for GDP and household
consumption are 104.1 and 107.8 yen per dollar, respectively. The current exchange rate of 110.6
yen per dollar as of the beginning of July 2018 is above our aggregate PPP estimate. As a result,both producers and consumers in Japan benefit from price advantages under the current exchange
rate. The recent depreciation of the Yen can be tied to the adoption of quantitative easing by the
Bank of Japan, followed by the election of Prime Minister Shinzo Abe in December 2012. 17

15

T he close relationship between our estimate of the aggregate PPP for household consumption and the Eurostat-OECD PPP is
expected since we used their PPP data for many consumer products at the elementary level. The relationship between our estimateof the PPP for GDP and the Eurostat-OECD measure is slightly more complicated. Conceptually, these measure the same object.
But in practice our approach to constructing the PPP for government is based on total quality-adjusted input prices including
capital and labor services and intermediate inputs, while the Eurostat-OECD approach is based on reference PPPs applied to thecomponents of gross output. See box 9.2 in Eurostat-OECD (2012).
16
In the 2005 PPPs in Nomura and Miyagawa (2015), the gaps in the estimates for M&E of GFCF were much larger as 126.1
yen per dollar of our estimates, compared to 164.0 in the Eurostat-OECD PPP. These gaps are considerably narrowed in the 2011
PPP estimates in Table 3.
17
T he historical stories on the price competitiveness and the market exchange rates are provided in Jorgenson, Nomura, andSamuels (2018).

12

110

(yen per dollar)

118

PPP for GDP(yen per dollar)

PPP for household consumption

109.0
116.1

116

108

Our estimates
107.5

Eurostat-OECD

114

106.2

106

113.4

Eurostat-OECD
104

104.2

104.1

105.2

104.1

112.7

112

104.3

Our estimates
110

102

102.5

102.6

102.0

101.3

110.6

109.0

109.6
109.1

108

109.7
109.5

107.8

106.6

100

108.7

106
98

104

96

102
2011

2012

2013

2014

2015

2016

2011

2012

2013

2014

2015

2016

Figure 4: Extended PPPs for GDP and Household Consumption in 2011–2016
Table 4 presents the estimated PPP results for 2011 based on the ISIC classification. 18 The
first four columns present the price differentials in domestic outputs (the PPP excluding net indirect
taxes, including taxes, for industry use, and for household use) and the next four columns show the
PPPs for the composite of domestic and imported products (two PPPs at producer’s prices and two
at purchaser’s prices). And the last two columns indicate the price differentials between Japan andthe U.S. in their imports. 19
Our estimates show there are large differences among the PPP estimates across concepts,
implying that it is important to account for conceptual differences in price measures when making
international comparisons. For example, consider Motor vehicles. We use this example to highlight
two pertinent issues. The first issue is that observed differences in prices paid by household andindustry have important implications for measuring relative prices in domestic product, and thesecond issue that purchaser’s prices embed the margin that must be stripped out in measuring
domestic product. This becomes evident in examining the various PPPs for Motor vehicles andtrailers. For simplicity, consider as a starting point the observation that the PPP for imports ofMotor vehicles and trailers is 79.3 yen per dollar for industry use and 77.4 yen per dollar forhousehold use. While these are relatively similar, it will become evident that this similarity plays
an important role in backing out the PPP for domestic product. The next PPP to consider in thisexample is the purchase price the purchaser-price PPPs, which cover domestic products andimports. These are 83.9 and 122.8 yen per dollar for industry and household uses, respectively. The
model must reconcile these observed prices, that is: the PPP for industry use is slightly above theimport PPP, while the PPP for household use is significantly above the PPP. By stripping off themargins paid on sales to households and industry, the model estimates that the internally consistentproducer-price PPP of the Motor vehicles and trailers is estimated to be 79.9 and 95.8 yen per dollar
for industry and household use, respectively. Finally, as a composite of the products produced for18

In some products of 174 products, the unpublished data at the most detailed level (basic headings) of the Eurostat-OECD PPPs
are directly used as 𝐏𝐏𝑖𝑖𝑝𝑝𝑝𝑝 ,𝐻𝐻 . Since they are not in the public domain, we use 42 types of the broad product group for describing thedemand-side PLIs. We aggregate to the ISIC classification using T örnqvist aggregation over the 173 industries.
19
T he differences in the quality of products imported by Japan and the U.S. may be somewhat reflected in the price differentials
of imports from exogenous countries, although conceptually this should be counted in the volume differentials.

13industry and household, the PPP for output is estimated to be 87.9 yen per dollar. At the exchange
rate of 79.8 on average in 2011, using the PPP for household purchases of motor vehicles (122.8)
yields a considerably different (and conceptually inappropriate) measure of competitivenesscompared to the (conceptually appropriate) 87.9 yen per dollar.

Table 4: PPPs by Different Price Concept in 2011
Domestic products

Composite products

Imports

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑑𝑑 ∗197.7

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑑𝑑

192.8

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐼𝐼

237.5

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑑𝑑 ,𝐻𝐻
110.1

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐼𝐼
201.5

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑐𝑐 ,𝐻𝐻
104.9

𝑝𝑝𝑐𝑐 ,𝐼𝐼,
𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖

B - M ining and quarrying

236.1

223.7

214.9

251.6

154.1

---

205.2

---

110.0

---

C - M anufacture

88.6

91.9

92.8

117.4

88.1

103.4

93.0

115.8

79.9

76.8

10 - Food products

138.3

142.6

160.4

150.9

134.5

131.4

167.3

168.0

80.7

83.7

11 - Beverages

102.1

131.2

138.2

116.9

135.0

115.8

136.5

121.0

108.3

102.7

A - Agriculture, forestry and fishing205.4

𝑝𝑝𝑐𝑐 ,𝐻𝐻
𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖

133.5

𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑚𝑚 ,𝐼𝐼 𝐏𝐏𝐏𝐏𝐏𝐏𝑖𝑖𝑚𝑚 ,𝐻𝐻
97.4

73.9

12 - Tobacco products

27.1

69.9

66.7

70.1

---

69.5

---

68.9

---

66.3

13 - Textiles

104.6

105.4

107.7

89.7

104.8

---

117.9

---

115.1

68.6

14 - Wearing apparel

129.5

134.8

129.5

136.0

---

71.6

---

103.7

61.4

61.5

15 - Leather and related products

50.6

52.6

94.9

54.8

---

61.4

---

108.6

62.9

63.5

16 - Wood and wood products, except furniture

102.1

102.4

99.1

128.4

92.5

---

98.9

---

76.1

---

17 - Paper and paper products

84.2

84.6

85.4

81.0

82.4

---

94.9

---

52.5

45.3

18 - Printing and reproduction of recorded media

77.8

78.1

77.0

95.4

77.2

---

80.3

---

---

---

19 - Coke and refined petroleum products

103.5

127.8

119.0

151.8

116.2

140.3

117.1

140.8

104.3

96.3

20 - Chemicals and chemical products

77.1

77.7

86.8

43.8

81.4

44.8

87.2

82.4

66.9

52.0

21 - Pharmaceutical products

74.8

76.1

82.7

65.7

80.6

67.5

75.9

79.7

67.9

67.6

22 - Rubber and plastics products

83.1

83.5

79.6

108.2

80.3

---

79.0

---

83.6

98.2

23 - Other non-metallic mineral products

91.1

91.6

94.1

105.9

90.0

---

94.3

---

57.2

64.6

24 - Basic metals

77.7

77.7

81.2

69.3

81.9

---

81.7

---

83.9

86.0

25 - Fabricated metal products, except M &E

70.2

70.5

72.5

92.5

71.3

---

78.3

---

61.7

---

26 - Computer, electronic and optical products

90.5

91.8

94.0

111.9

88.6

102.6

92.3

91.7

84.9

93.2

27 - Electrical equipment

64.4

64.7

61.5

151.7

59.0

---

59.3

---

87.5

86.7

28 - M achinery and equipment n.e.c.

119.4

119.6

122.1

129.3

111.7

---

116.2

---

74.8

76.3

29 - M otor vehicles and trailers

87.9

88.7

85.9

104.0

79.9

95.8

83.9

122.8

79.3

77.4

30 - Other transport equipment

108.5

108.4

108.4

100.1

---

---

---

---

---

81.6

31 - Furniture

117.9

119.1

122.3

108.6

101.6

---

103.6

---

61.4

59.5

32 - Other manufacturing

126.1

128.5

103.9

208.9

97.1

127.7

114.9

105.4

83.0

87.9

33 - Repair and installation of machinery and equipment

86.6

86.8

82.8

148.6

85.6

---

87.5

---

90.0

---

D - Electricity, gas, steam and air conditioning supply

208.2

209.6

219.5

204.1

218.7

203.7

218.3

203.7

---

---

E - Water supply

92.4

93.7

92.8

95.9

92.8

95.9

92.9

96.0

---

---

F - Construction

102.2

102.1

105.5

65.3

105.5

65.3

105.5

65.3

---

---

G - Wholesale and retail trade

134.7

138.3

137.8

139.4

133.3

138.4

132.9

138.4

57.9

65.6

H - Transportation and storage

119.4

121.4

106.6

165.6

99.9

153.6

99.7

154.1

70.4

101.1

I - Accommodation and food service activities

103.9

107.5

104.0

109.0

102.6

107.8

102.5

108.0

77.3

78.8

J - Information and communication

119.7

121.6

124.5

104.9

123.1

104.3

124.7

103.7

78.0

74.2

K - Financial and insurance activities

121.6

121.2

118.7

122.1

117.1

120.4

117.4

120.4

81.1

83.9

L - Real estate activities

125.7

127.4

162.1

118.6

162.1

118.6

162.1

118.6

---

---

M - Professional, scientific and technical activities

99.0

99.2

100.6

113.2

98.7

104.8

98.7

105.4

72.5

74.4

N - Administrative and support service activities

103.8

104.5

101.0

117.4

100.6

116.8

100.6

116.9

---

78.5

O - Public administration and defense

92.4

92.4

92.4

85.9

92.4

85.9

92.4

85.9

---

---

P - Education

117.5

117.5

117.5

117.5

---

117.3

---

117.3

---

---

Q - Human health and social work activities

79.9

79.9

80.6

79.9

80.6

79.9

80.6

79.9

---

---

R - Arts, entertainment and recreation

103.3

107.0

77.6

120.3

77.5

119.5

77.5

119.6

---

80.7

S - Other service activities

124.1

128.9

106.7

140.6

103.2

138.4

105.7

138.4

86.3

76.6

----108.4
113.2
105.2
110.5
110.0
113.4
86.9
77.6
Unit: Yen per dollar (JPY/USD). Source: Our estimates. Note: Industry classification is based on the ISIC Rev.4. The market exchange rate in 2011 is 79.8 yen to the dollar
on annual average.
Total

In Agriculture, forestry and fishing, the PPP for domestic outputs was 197.7 yen per dollar in2011, indicating the Japanese producers are considerably inferior in price competitiveness ofagricultural products compared to producers in the U.S., although some gaps may be explained by

14

unobserved difference in quality. 20 This price gap in output is much larger than the purchaser-price
PPP of composite products for household use (133.5 yen per dollar), again emphasizing theimportance of accounting for the contribution of imports and margins. In summary, in order tocompare price competitiveness by industry, these cases show that it is indispensable to estimate thedifferentials in output prices, which can differ considerably from the purchaser-price PPPs ofcomposite products that are more readily available in the data. Figure 6 presents the PPPs forindustry outputs (excluding the net indirect taxes), 𝐏𝐏𝐏𝐏𝐏𝐏𝑗𝑗𝑑𝑑 ∗ , based on 173 industry classification in
2011. There are large differences across ISIC groups in Table 4. Most estimates of industry PPPs

classified in A. Agriculture, forestry and fishery (industries 1-12) are over 150 yen per dollar, withthree exceptions of 6.Other non-edible crops (76.1 yen per dollar), 10.Agricultural and forestry
services (111.0), and 12.Fishing (71.9).
In manufacturing except foods (industries 33-123), even with the highly appreciated exchange
rate (79.8 yen per dollar) in 2011, Japanese industries were still superior in price competitivenessin 25 of 91 industries. The number of industries with superior competitiveness increased to 59
under the current exchange rate (110.6 yen per dollar), indicating the importance of exchange rate
movements in determining international competitiveness. 21
In services (industries 124-173) presented in Figure 6, Japanese industries were inferior inprice competitiveness in 44 of 50 industries in 2011, most notably in 129.Gas distribution (the PPP
for output is 303.2 yen per dollar), 144.Warehousing and storage (289.1), 128.Electric power
generation and distribution (188.9), 136.Real estate (162.1), 170.Barber shops (155.3), and 142.Airtransportation (151.0). If these same relative prices held at the current nominal exchange rate (110.6
yen per dollar), 24 of 50 industries would be superior in price competitiveness. In fact, there aresome service industries in which Japan already has significant pricing advantages compared to the
U.S., like 160.Other rental and leasing (the PPP for output is 54.1 yen per dollar), 161.Motorvehicle repair (64.3), and 145.Travel arrangement services (74.9).
The declines in PPP for outputs over time in some service industries are significant. In the
PPPs for service outputs in 1990 and 2005 estimated in Nomura and Miyagawa (1999) and (2015)
respectively, Japan’s price competitiveness was evaluated to be inferior to the U.S. in 91% (43 of
47 service industries) in 1990 and in 70% (35 of 50) in 2005, using the current exchange rate (110.6
yen per dollar). Our current estimates show that 52% (26 of 50) were inferior in 2011. The PPPs
of 74% (37 of 50 service industries) declined from 2005 to 2011.
To try to relate this to industry fundamentals, Figure 5 plots the changes in the PPPs for service
outputs between 2005 and 2011 against the two-country average share of compensation of
employees (COE) in gross output for the service industries in 2011. One hypothesis is that the fallin labor prices in Japan relative to the U.S. (Figure 3) enabled relatively labor-intensive service
20

Note that the difference in the products observed at our elementary level in Section 3.2 is considered. T he purchaser’s price
PPPs for Agriculture, forestry and fishing are much higher in industry use than that in household use in Table 4. T his seems
contradict that Japan’s rice price is much higher than that in the U.S. However, this is consistent with that households are definedin Japan’s IOT to consume rice not directly from agricultural sector, but from food manufacturing sector as polished rice.
21
We do not have a full general equilibrium model that determines how prices react to changes in policy that also results inchanges to the nominal exchange rate. Therefore, our competitiveness measures reflect the joint determination of the prices andexchange rate, but we are not able to assess how prices would change if the exchange rate changes.

15

producers in Japan to charge lower prices to purchasers in 2011 than in 2005. This would manifest
as a downward sloping line between the change in the PPP level between 2011 and 2005 and the
COE share. Figure 5 shows very limited evidence of this. For example, 159. Motor vehicle rental
and leasing and 160.Other rental and leasing in Japan had a low labor share, but improved pricecompetitiveness. Furthermore, a significant share of the PPPs for services increased in 2011 and2005. Japan’s output price in 153.Veterinary service, which has labor cost of over 40% of nominal
output increased from 2005 to 2011 relative U.S. production prices. These observations suggest
two conclusions: labor costs alone cannot account for the overall decline in the PPPs for services
and using the cost approach to measuring PPPs for outputs based on input costs (for example using
the labor PPP to estimate the output PPP) likely leads to inappropriate estimates of the output PPPs.

1.6

PPP in 2011/PPP in 2005
153 Veterinary service
129 Gas distribution

155 Advertising and related services

1.4

169 Hotels and other accommodations
170 Barber shops
125 New non-residential construction
147 Telecommunications

163 Building maintenance service
152 Medical and health service

1.2

164 Legal, financial, and accounting services

134 Financial service

165 Other business services

143 Other transport services
166 Motion pictures

156 Information service

142 Air transportation

1.0

167 Other amusement and recreation services

148 Broadcasting

127 Other construction
139 Road passenger transportation

128 Electric power generationand distribution

135 Insurance

136 Real estate

173 Unclassified, etc.
150 Educational services

171 Other personal services

141 Water transportation

0.8

151 Research services

140 Road freight transportation

144 Warehousing and storage

146 Postal service

133 Retail trade
162 Other repairs

154 Other non-profit organization

138 Rail transportation

149 Government services
132 Wholesale trade
161 Motor vehicle repair

158 Commercial and industrial equipment leasing

126 Building repairing

0.6

130 Water, sewage and thermal energy supply

124 New residential construction

160 Other rental and leasing
131 Waste management
145 Travel arrangement services

159 Motor vehicles rental and leasing

157 Internet service providers and related services 168 Drinking and eating place

0.4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

COE shate in Gross Output in 2011 (two-country average)

Figure 5: Changes in PPPs for Service Outputs from 2005 to 2011

16

0

100
563.3
201.1
191.2
274.0
339.9
76.1
265.4
192.8
213.6
111.0
154.8
71.9
543.5
167.3
277.8
285.9
243.4
256.4
133.1
88.4
266.9
135.5
90.7
137.1
108.4
120.9
118.6
98.4
99.6
84.3
154.9
27.1
82.8
45.7
59.7
80.1
186.4
129.5
92.7
71.0
122.3
117.9
85.0
88.2
88.2
68.5
83.3
76.1
113.1
82.7
93.2
83.4
137.0
118.0
107.5
61.1
74.8
84.4
34.1
35.5
89.4
103.5
74.7
116.7
67.4
51.2
38.9
66.9
103.1
137.5
93.3
46.9
117.3
117.3
68.5
175.8
200.8
138.6
57.8
109.3
61.9
128.0
119.1
204.1
145.2
116.9
145.9

200

300

400

0
001 Grain farming
002 Vegetables and potatoes
003 Fruits
004 Other crop farming
005 Sugarcane and sugar beet…
006 Other non-edible crops
007 Cattle ranching, dairy cattle…
008 Poultry and egg production
009 Other animal production
010 Agricultural, forestry services
011 Forestry
012 Fishing
013 Metal ores
014 Stone, gravel and ceramic…
015 Other non-metal ores
016 Coal mining
017 Crude oil and natural gas
018 Meat and meat products
019 Dairy products
020 Seafood products
021 Grain milling
022 Bread and confectionery
023 Other processed agricultural…
024 Sugar
025 Vegetable oil
026 Seasoning and dressing…
027 Other food manufacturing
028 Liquor
029 Tea and coffee
030 Soft drinks
031 Animal food manufacturing
032 Tobacco
033 Fiber, yarn, and thread mills
034 Textile and fabric mills, fabric…
035 Knit fabric mills
036 Carpet, floor mat, and rug mills
037 Other textile product mills
038 Apparel and apparel accessories
039 Lumber and wooden chips
040 Plywood
041 Other wooden products
042 Furniture, accessories and…
043 Pulp
044 Paper
045 Paper containers
046 Other converted paper products
047 Newspaper publishers
048 Printing
049 Publishers
050 Inorganic chemical products
051 Petrochemical products
052 Organic chemical products
053 Fertilizers
054 Agricultural chemicals
055 Synthetic resin
056 Synthetic fibers
057 Pharmaceutical products
058 Soap, synthetic detergents and…
059 Cosmetics and dentifrices
060 Paints and printing ink
061 Other chemical products
062 Petroleum and coal products
063 Plastic products
064 Rubber products
065 Foot wears
066 Leather and fur products
067 Other leather products
068 Glass and glass products
069 Cement
070 Ready-mixed concrete
071 Cement products and…
072 Pottery and ceramic products
073 Carbon and graphite products
074 Miscellaneous nonmetallic…
075 Iron and steel products
076 Copper, rolled and drawn…
077 Aluminum and rolled…
078 Communication and energy…
079 Other non-ferrous metals and…
080 Metal products for…
081 Other metal products
082 Engines, turbines and boilers
083 Construction machinery and…
084 Farm machinery and equipment
085 Metal processing machinery…
086 Other general machinery for…
087 Special industrial machinery

100

200

300

400

114.7
90.1
173.3
91.9
110.2
109.4
70.2
44.3
117.1
86.4
72.3
81.2
106.0
96.9
100.4
154.8
39.8
116.3
50.2
97.5
82.5
112.9
105.9
111.1
60.9
89.5
166.6
105.0
62.1
287.7
95.6
242.4
90.1
228.9
83.3
128.1
85.4
81.2
104.2
149.1
188.9
303.2
92.8
92.0
133.5
136.3
136.2
96.2
162.1
106.1
132.9
144.9
84.2
122.0
151.0
116.9
289.1
74.9
132.3
134.8
100.0
92.4
117.5
91.8
79.7
111.2
114.1
117.6
111.8
78.5
79.6
113.8
54.1
64.3
97.9
136.6
129.0
93.4
147.7
103.3
103.7
105.1
155.3
125.1
86.2
94.7

Figure 6: PPPs for Industry Outputs in 201117088 Semiconductor machinery
089 Other general machinery
090 Vending, commercial and…
091 Audio and video equipment
092 Household electrical appliances
093 Electronic computer
094 Computer peripheral equipment
095 Wired telecommunication…
096 Other telecommunication…
097 Applied electronic equipment
098 Watch, clock, and measuring…
099 Semiconductor and related…
100 Electron tubes
101 Magnetic tape and flexible disk
102 Rotating electric machinery
103 Electric bulbs
104 Other electronic component
105 Batteries
106 Other electric equipment
107 Motor vehicles
108 Motor vehicle body and parts
109 Motorcycle and bicycle
110 Ship building and repairing
111 Railroad rolling stock and…
112 Aircraft and repairing
113 Other transportation equipment
114 Photographic and…
115 Surgical, medical and dental…
116 Other precision instruments
117 Toys and sporting goods
118 Musical instruments
119 Audio and video media…
120 Writing instruments and…
121 Small personal adornments
122 Ordnance
123 Other miscellaneous…
124 New residential construction
125 New non-residential construction
126 Building repairing
127 Other construction
128 Electric power generation and…
129 Gas distribution
130 Water, sewage and thermal…
131 Waste management
132 Wholesale trade
133 Retail trade
134 Financial service
135 Insurance
136 Real estate
137 Lessors of dwellings…
138 Rail transportation
139 Road passenger transportation
140 Road freight transportation
141 Water transportation
142 Air transportation
143 Other transport services
144 Warehousing and storage
145 Travel arrangement services
146 Postal service
147 Telecommunications
148 Broadcasting
149 Government services
150 Educational services
151 Research services
152 Medical and health service
153 Veterinary service
154 Other non-profit organization
155 Advertising and related services
156 Information service
157 Internet service providers and…
158 Commercial and industrial…
159 Motor vehicles rental and leasing
160 Other rental and leasing
161 Motor vehicle repair
162 Other repairs
163 Building maintenance service
164 Legal, financial, and…
165 Other business services
166 Motion pictures
167 Other amusement and…
168 Drinking and eating place
169 Hotels and other accommodations
170 Barber shops
171 Other personal services
172 Scrap, used and secondhand…
173 Unclassified, etc.

5Conclusion
This paper provides new benchmark estimates of Japan-US industry-level price differentials

for 2011, based on a price accounting model that links prices between the U.S. and Japan and maps
available price data to model consistent industry prices. Price comparisons among countries at theindustry level is a challenging task, but constructing measures that are conceptually appropriate is
indispensable for evaluating efficiency in production systems and international competitiveness on
world markets.
We find that the PPP for GDP, derived from aggregating our estimates of the PPPs forindustry-GDP at basic prices, is 109.0 yen per dollar in 2011. In 2011, the Yen appreciated to ahistoric high of 79.8 yen per dollar. Under the current exchange rate of 110.6 yen per dollar as of the

beginning of July 2018, we estimate that Japanese industries are superior in price competitivenessin 59 of 91 industries in the manufacturing sector except foods and in 26 of 50 industries in service
sector in comparison to U.S. producers. Some Japanese producers are considerably inferior in pricecompetitiveness in comparison to the U.S; in particular, the energy industries providing electricity,gas, and heat, and industries producing most agricultural products.
The accuracy of the estimated PPPs for industry outputs depends critically on the quality ofthe data on margin rates and the other related parameters. In addition, our analysis of the PPPs ofservice outputs and their relation to labor inputs indicates that the cost approach to measuring PPPs
for outputs likely leads to inaccurate estimates. Employing simplifying assumptions on therelationship between prices likely leads to significant biases and incorrect measures of international
competitive position. This indicates that improving the measurement of price differentials and therelated parameters at the detailed product level is the best path forward in building conceptuallyconsistent and precise price competitiveness measures across industries and countries.
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Appendix: Bilateral Price Model
1

Producer’s Prices

To construct the price model describing the production system in Figure 1, we use thefollowing notation for product i:
𝑝𝑝𝑘𝑘𝑑𝑑,𝑖𝑖
Prices of products produced in country k at producer’s prices in currency of country k,

𝑑𝑑
𝑝𝑝𝑘𝑘𝑘𝑘,𝑖𝑖

Prices of products produced in country k, purchased by exogenous economies at

producer’s prices (excluding net indirect taxes on products and consumption tax) incurrency of country k,

𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖

Prices of products produced in country k, purchased by industries (I) or household (H) in
country k at producers’ prices in currency of country k, (If l = I, the product is purchasedby industries for intermediate uses or investment, and the price includes net indirect taxes
on products. If l = H, the product is purchased by household for final consumption, andthe price includes net indirect taxes on products and consumption tax.),

𝑑𝑑,𝑙𝑙
𝑝𝑝𝑘𝑘𝑘𝑘′,𝑖𝑖

Prices of products produced in country k, purchased by industries (I) or household (H) in
country k’ at producers’ prices in currency of country k, (If l = I, the product is purchasedby industries. If l = H, the product is purchased by household. The both prices exclude
net indirect taxes on products.),

𝑚𝑚,𝑙𝑙
𝑝𝑝𝑘𝑘𝑘𝑘′,𝑖𝑖

Prices of imports from country k, purchased by industries (I) or household (H) in k’country at the CIF prices plus tariff and net indirect taxes on imports in currency ofcountry k’, (If l = I, the product is purchased by industries and the price excludes
consumption tax. If l = H, the product is purchased by household and the price includes
consumption tax.),

𝑓𝑓𝑓𝑓𝑓𝑓 ,𝑙𝑙
𝑝𝑝𝑘𝑘𝑘𝑘′ ,𝑖𝑖

Prices of imports from country k, purchased by industries (I) or household (H) in countryk’ at the FOB prices in currency of country k, (If l = I, the product is purchased byindustries. If l = H, the product is purchased by household.)

𝑝𝑝𝑘𝑘𝑐𝑐,𝑙𝑙,𝑖𝑖

Prices of composite products (domestic products plus imports), purchased by industries(I) or household (H) in country k at producers’ prices in currency of country k, (If l = I,
the product is purchased by industries and the price includes net indirect taxes on products.
If l = H, the product is purchased by household and the price includes net indirect taxes
on products and consumption tax.),

𝑋𝑋𝑘𝑘𝑘𝑘′ ,𝑖𝑖𝑖𝑖

Volumes of products produced in country k and purchased by sector j in country k’,

𝑋𝑋𝑘𝑘 ,𝑖𝑖

Volumes of products produced in country k,
Rates of freight and insurance for imports from country k, purchased in country k’,
Rates of tariff for imports from country k, purchased in country k’,𝑙𝑙𝜏𝜏𝑘𝑘,𝑖𝑖

Rates of net indirect taxes on products in country k for industries (I) or household (H),𝑓𝑓𝜏𝜏𝑘𝑘𝑘𝑘′,𝑖𝑖𝑟𝑟𝜏𝜏𝑘𝑘𝑘𝑘′,𝑖𝑖20

(If l = I, the rate is for industries and excludes consumption tax. 22 If l = H, the rate is forhouseholds and includes consumption tax.),𝑑𝑑𝜏𝜏𝑘𝑘,𝑖𝑖

The effective rates of indirect taxes in country k,

𝑇𝑇𝑇𝑇𝑘𝑘𝑑𝑑,𝑖𝑖

The amount of indirect taxes of domestic products in country k

𝑒𝑒𝑘𝑘/𝑘𝑘′

Exchange rate of currency of country k against the currency of country k’, (e.g. Japan’s
exchange rate to the U.S. dollar is 𝑒𝑒𝐽𝐽/𝑈𝑈 )𝑒𝑒,𝑙𝑙𝑇𝑇𝑘𝑘,𝑖𝑖

Transportation service input for one unit of exports in country k, (If l = I, the service isinput for industries. If l = H, the service is input for households.),

𝑊𝑊𝑘𝑘𝑒𝑒,𝑖𝑖,𝑙𝑙Trade service input for one unit of exports in country k, (If l = I, the service is input for

𝑚𝑚𝑇𝑇𝑘𝑘,𝑖𝑖,𝑒𝑒,𝑙𝑙,𝑒𝑒,𝑙𝑙𝑚𝑚𝑊𝑊
𝑘𝑘,𝑖𝑖

industries. If l = H, the service is input for households.),
Rates of transportation cost (T) of products in country k for exported products, (If l = I,
the rate is for industries. If l = H, the rate is for households.),
Rates of trade margin (W) of products in country k for exported products, (If l = I, therate is for industries. If l = H, the rate is for households.).
We begin with clarifying the treatment of indirect taxes in our model. In Japan’s transactionsof Figure 1, only households pay the consumption tax. Therefore, we distinguish between the
producer’s prices of the domestically produced outputs, 𝑝𝑝𝐽𝐽𝑑𝑑,𝐼𝐼(for industry) and 𝑝𝑝𝐽𝐽𝑑𝑑,𝐻𝐻
(for
,𝑖𝑖
,𝑖𝑖

household). 23 The rates of net indirect taxes on products for industries and households are also𝐼𝐼
𝐻𝐻
distinguished as 𝜏𝜏𝐽𝐽,𝑖𝑖
and 𝜏𝜏𝐽𝐽,𝑖𝑖, respectively. As for the prices of exports, since both the consumption
𝑑𝑑,𝐻𝐻
tax and other indirect taxes on products are deductible, Japan’s export prices to the U.S. (𝑝𝑝𝐽𝐽𝐽𝐽,𝑖𝑖 and

𝑑𝑑,𝐼𝐼
𝑝𝑝𝐽𝐽𝐽𝐽,𝑖𝑖 ) are formulated as:

𝑑𝑑,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑙𝑙
�
𝑝𝑝𝐽𝐽𝐽𝐽(𝑘𝑘 = 𝐽𝐽, 𝑈𝑈 and 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).
(1)
,𝑖𝑖 = 𝑝𝑝𝐽𝐽,𝑖𝑖 (1 + 𝜏𝜏𝐽𝐽,𝑖𝑖 )On the other hand, the Japanese producer’s price 𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 is defined as a composite of the

producer’s prices across all types of demand. The total of the domestic indirect taxes (excluding
indirect tax for imported products) of product i is described as:(2)

𝑇𝑇𝑇𝑇𝐽𝐽𝑑𝑑,𝑖𝑖 = �𝜏𝜏 𝐼𝐼𝐽𝐽,𝑖𝑖∑𝑗𝑗∈𝐼𝐼 𝑋𝑋𝐽𝐽𝐽𝐽,𝑖𝑖𝑖𝑖 + �� 𝑝𝑝𝐽𝐽𝑑𝑑,𝐼𝐼,𝑖𝑖

1+𝜏𝜏 𝐼𝐼𝐽𝐽,𝑖𝑖

𝜏𝜏 𝐻𝐻
𝐽𝐽,𝑖𝑖

� 𝑝𝑝𝐽𝐽𝑑𝑑,𝐻𝐻,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 .

1+𝜏𝜏 𝐻𝐻
𝐽𝐽,𝑖𝑖

The first term on the right-hand side represents the amount of other indirect tax paid by industries(I) and the second term is the amount of the consumption tax and other indirect tax paid byhouseholds (H). Based on 𝑇𝑇𝑇𝑇𝐽𝐽𝑑𝑑,𝑖𝑖 , the effective rate of indirect taxes for domestic product i in Japanis defined as:
(3)

𝑑𝑑
𝑑𝑑
𝜏𝜏𝐽𝐽,𝑖𝑖= 𝑇𝑇𝑇𝑇𝐽𝐽𝑑𝑑,𝑖𝑖 �(𝑝𝑝𝐽𝐽,𝑖𝑖
𝑋𝑋𝐽𝐽,𝑖𝑖 − 𝑇𝑇𝑇𝑇𝐽𝐽𝑑𝑑,𝑖𝑖 ),𝑑𝑑
where 𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 𝑋𝑋𝐽𝐽 ,𝑖𝑖 is gross output in Japan. Using 𝜏𝜏𝐽𝐽,𝑖𝑖, Japan’s export price to the exogenous

economies is formulated as:

22

T he consumption tax on the products purchased by the producers who produce consumption tax exempt products (e.g. medicalcare) are non-deductible. We describe that the consumption tax is excluded from 𝜏𝜏𝐼𝐼𝑘𝑘 ,𝑖𝑖 in the description of our price model for
simplicity, but some non-deductible consumption taxes in domestic final demand excluding household consumption (Z) areconsidered in our actual estimation.
23
In addition to the differences in indirect taxes for industry and household uses, our price model permits differences in the basic
prices for industry and household uses, reflecting the observed price differentials in different demand types of the product which
are classified to the same group. T hese may indicate that the types or qualities of the same product at the more detail level aredifferent, but we treat them as if they were additive for simplicity of our price model.

21

(4)

𝑑𝑑
𝑑𝑑
𝑑𝑑
𝑝𝑝𝐽𝐽𝐽𝐽,𝑖𝑖 = 𝑝𝑝𝐽𝐽 ,𝑖𝑖 �(1 + 𝜏𝜏𝐽𝐽,𝑖𝑖 ) .

In the case of exports to exogenous economies, that is Equation (4), we do not distinguish between
exports to industry and households due to data constraints, unlike the bilateral trade prices between
Japan and the U.S. which do account for price differences between households and industry.
Analogous Equations (1) to (4) also hold for the U.S.
The IOT in Figure 1 imposes that the value of output is balanced across uses:(5)𝑑𝑑,𝐼𝐼 ∑
𝑑𝑑,𝐻𝐻
𝑑𝑑,𝐻𝐻
𝑑𝑑
∑𝑗𝑗∈𝐼𝐼 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽
𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 𝑋𝑋𝐽𝐽 ,𝑖𝑖 = 𝑝𝑝𝐽𝐽𝑑𝑑,𝐼𝐼,𝑖𝑖,𝑖𝑖 𝑗𝑗∈𝐼𝐼 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽 ,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖

The first term on the right-hand side represents industry uses (intermediate uses and investment)
in Japan, the second term is the imports by the U.S. industries for the intermediate uses, the third
term is the household uses in Japan, the fourth term is the imports by the U.S. households, and thefinal term accounts for exports to exogenous economies.
Corresponding to the Isard-type BIOT in Figure 1, we define the Chenery-Moses-type IOT(the competitive import type IOT) for both Japan and the U.S. (Chenery, 1953; Moses, 1955).
Figure A1 represents this table for Japan (the table for the U.S. is defined analogously).

Intermediate
inputsValue added
Gross output

Intermediate inputs(N)

Householdconsumption(C)

Government
consumption& Gross capitalformation(Z)

𝑝𝑝𝐽𝐽𝑐𝑐,𝑖𝑖,𝐼𝐼𝑋𝑋𝐽𝐽,𝑖𝑖𝑗𝑗

𝑐𝑐,𝐻𝐻
𝑝𝑝𝐽𝐽,𝑖𝑖
𝑋𝑋𝐽𝐽,𝑖𝑖𝐻𝐻

𝑐𝑐,𝐼𝐼
𝑝𝑝𝐽𝐽,𝑖𝑖𝑋𝑋𝐽𝐽𝐽𝐽,𝑖𝑖𝑍

Exports (E)

𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐻𝐻
� 𝑝𝑝𝐽𝐽𝑈𝑈,𝑖𝑖
𝑋𝑋𝐽𝐽𝑈𝑈,𝑖𝑖𝑗𝑗 + 𝑝𝑝𝐽𝐽𝑈𝑈,𝑖𝑖
𝑋𝑋𝐽𝐽𝑈𝑈,𝑖𝑖𝐻𝐻𝑗𝑗∈𝐼𝐼+ 𝑝𝑝𝑑𝐽𝐽𝐸𝐸,𝑖𝑋𝑋𝐽𝐽𝐸𝐸,𝑖𝐸𝐸(–)Imports (M)Gross output (X)𝑚𝑚,𝐻𝐻� (�𝑝𝑝𝑚𝑚,𝐼𝐼
𝑘𝑘𝐽𝐽,𝑖𝑖𝑋𝑋𝑘𝑘𝐽𝐽,𝑖𝑖𝑗𝑗 + 𝑝𝑝𝑘𝑘𝐽𝐽,𝑖𝑖 𝑋𝑋𝑘𝑘𝐽𝐽,𝑖𝑖𝐻𝐻)

𝑑𝑑 𝑋𝑋
𝑝𝑝𝐽𝐽,𝑖𝑖
𝐽𝐽,𝑖𝑖

𝑘𝑘=𝑈𝑈,𝑘𝑘 𝑗𝑗∈𝐼𝐼

𝑉𝐴𝐽𝐽,𝑗𝑗

𝑑𝑑
𝑝𝑝𝐽𝐽,𝑗𝑗
𝑋𝑋𝐽𝐽,𝑗𝑗

Figure A1: Japanese Input-Output Table (the Chenery-Moses-Type)
Based on the Chenery-Moses-type input-output framework in Figure A1, the output balance
including Japan’s uses of imports at current prices is described as:
(6)

𝑐𝑐,𝐻𝐻
𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐻𝐻
𝑑𝑑
�∑𝑗𝑗∈𝐼𝐼 𝑝𝑝𝐽𝐽𝐽𝐽
�
𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 𝑋𝑋𝐽𝐽 ,𝑖𝑖 = ∑𝑗𝑗 ∈𝐼𝐼 𝑝𝑝𝐽𝐽𝑐𝑐,𝐼𝐼,𝑖𝑖 𝑋𝑋𝐽𝐽,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽 ,𝑖𝑖 𝑋𝑋𝐽𝐽 ,𝑖𝑖𝑖𝑖 +,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖
𝑚𝑚,𝐼𝐼
𝑚𝑚,𝐻𝐻
�
− ∑𝑘𝑘 =𝑈𝑈,𝐸𝐸�∑𝑗𝑗∈𝐼𝐼 𝑝𝑝𝑘𝑘𝑘𝑘,𝑖𝑖 𝑋𝑋𝑘𝑘𝑘𝑘,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝑘𝑘𝑘𝑘 ,𝑖𝑖 𝑋𝑋𝑘𝑘𝑘𝑘 ,𝑖𝑖𝑖𝑖 ,where 𝑋𝑋𝐽𝐽,𝑖𝑖𝑖𝑖 is the domestic demand of product i by sector j in Japan including both domestic

products and imports, and 𝑝𝑝𝐽𝐽𝑐𝑐,𝐼𝐼,𝑖𝑖 stands for the corresponding prices of the composite products (ofdomestically produced products plus imports). These demand prices are embedded in theaccounting identity as:
(7)

𝑑𝑑,𝑙𝑙
𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
𝑝𝑝𝐽𝐽𝑐𝑐,𝑙𝑙,𝑖𝑖 𝑋𝑋𝐽𝐽 ,𝑖𝑖𝑖𝑖 = 𝑝𝑝𝐽𝐽,𝑖𝑖
𝑋𝑋𝐽𝐽𝐽𝐽,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖
𝑋𝑋𝑈𝑈𝑈𝑈,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖
𝑋𝑋𝐸𝐸𝐸𝐸 ,𝑖𝑖𝑖𝑖( 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) .

The outputs at constant prices are assumed to be additive among the different demand types;(8)

𝑋𝑋𝐽𝐽 ,𝑖𝑖 = ∑𝑗𝑗∈𝐷𝐷 𝑋𝑋𝐽𝐽𝐽𝐽,𝑖𝑖𝑖𝑖 + ∑𝑗𝑗∈𝐷𝐷 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖= ∑𝑗𝑗∈𝐷𝐷 𝑋𝑋𝐽𝐽,𝑖𝑖𝑖𝑖 + ∑𝑗𝑗∈𝐷𝐷 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 + 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖 − ∑𝑗𝑗∈𝐷𝐷 𝑋𝑋𝑈𝑈𝑈𝑈 ,𝑖𝑖𝑖𝑖 − ∑𝑗𝑗∈𝐷𝐷 𝑋𝑋𝐸𝐸𝐸𝐸 ,𝑖𝑖𝑖𝑖 .

The former equation corresponds with the nominal balance of Equation (5) and the lattercorresponds to Equation (6). We also assume additivity among domestic inputs and imports:(9)

𝑋𝑋𝐽𝐽 ,𝑖𝑖𝑖𝑖 = 𝑋𝑋𝐽𝐽𝐽𝐽,𝑖𝑖𝑖𝑖 + 𝑋𝑋𝑈𝑈𝑈𝑈,𝑖𝑖𝑖𝑖 + 𝑋𝑋𝐸𝐸𝐸𝐸,𝑖𝑖𝑖𝑖(𝑗𝑗 ∈ 𝐷𝐷) .
22

We define the output share at constant prices:(10) 𝑤𝑤𝐽𝐽𝐽𝐽𝑑𝑑,𝑙𝑙,𝑖𝑖 = ∑𝑗𝑗∈𝑙𝑙 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖𝑖𝑖 ⁄ 𝑋𝑋𝐽𝐽 ,𝑖𝑖 (𝑘𝑘 = 𝐽𝐽, 𝑈𝑈, 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) and 𝑤𝑤𝐽𝐽𝐽𝐽𝑑𝑑 ,𝑖𝑖 = 𝑋𝑋𝐽𝐽𝐽𝐽 ,𝑖𝑖 ⁄ 𝑋𝑋𝐽𝐽 ,𝑖𝑖 ,
𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐻𝐻
𝑑𝑑,𝐻𝐻
𝑑𝑑
where 𝑤𝑤𝐽𝐽𝐽𝐽𝑑𝑑,𝐼𝐼,𝑖𝑖 + 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖 + 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖 + 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 + 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 = 1 . Based on Equations (5) to (10), Japan’s output
price of product i is described as:
(11)

𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐻𝐻 𝑑𝑑,𝐻𝐻
𝑑𝑑,𝐻𝐻 𝑑𝑑,𝐻𝐻
𝑑𝑑
𝑑𝑑
𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 = 𝑝𝑝𝐽𝐽𝑑𝑑,𝐼𝐼,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 + 𝑝𝑝𝐽𝐽 ,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 + 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 .

By substituting Equations (1) and (4) into Equation (11), we obtain:
𝑑𝑑,𝐼𝐼

𝑑𝑑,𝐻𝐻

𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖

𝑤𝑤𝑑𝑑

𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖

𝑑𝑑,𝐼𝐼
𝑑𝑑,𝐻𝐻
� 𝑤𝑤𝐽𝐽𝐽𝐽𝑑𝑑,𝐼𝐼,𝑖𝑖 +� + 𝑝𝑝𝐽𝐽𝑑𝑑,𝐻𝐻
� 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖�� � �1 − 𝐽𝐽𝐽𝐽,𝑖𝑖
�.
+(12) 𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 = � 𝑝𝑝𝐽𝐽,𝑖𝑖,𝑖𝑖
1+𝜏𝜏 𝑙𝑙1+𝜏𝜏 𝑙𝑙1+𝜏𝜏 𝑑𝑑Thus Japan’s output price,

𝐽𝐽,𝑖𝑖

𝑝𝑝𝐽𝐽𝑑𝑑,𝑖𝑖 , is measured using

𝑝𝑝𝐽𝐽𝑑𝑑,𝐼𝐼
,𝑖𝑖

𝐽𝐽,𝑖𝑖

and

𝐽𝐽,𝑖𝑖

𝑝𝑝𝐽𝐽𝑑𝑑,𝐻𝐻,𝑖𝑖 , the output shares, and the rates

of indirect taxes.
𝑑𝑑,𝑙𝑙
On the other hand, in order to clarify the relationship between the U.S. producer’s price 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖

𝑚𝑚,𝑙𝑙
for sales to Japan, and Japan’s import prices from the U.S., 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 , we describe the U.S. FOB priceas:𝑓𝑓𝑓𝑓𝑓𝑓 ,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑒𝑒
𝑒𝑒
(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻),
(13) 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 = 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 + 𝑝𝑝𝑈𝑈𝑈𝑈,𝑇𝑇 𝑇𝑇𝑈𝑈,𝑖𝑖 + 𝑝𝑝𝑈𝑈𝑈𝑈 ,𝑊𝑊 𝑊𝑊𝑈𝑈,𝑖𝑖
𝑑𝑑,𝑙𝑙
𝑑𝑑,𝑙𝑙
where 𝑝𝑝𝑈𝑈𝑈𝑈 ,𝑇𝑇 and 𝑝𝑝𝑈𝑈𝑈𝑈,𝑊𝑊 are the prices of U.S. transportation and trade sectors for the exports to𝑒𝑒,𝑙𝑙Japan, respectively, and 𝑇𝑇𝑈𝑈,𝑖𝑖
and 𝑊𝑊𝑈𝑈𝑒𝑒,𝑖𝑖,𝑙𝑙 are the volumes of transportation and trade services for

one unit of exports of product i required in the U.S. We define the rate of transportation cost 𝑚𝑚𝑇𝑇,𝐸𝐸,𝑙𝑙
𝑈𝑈,𝑖𝑖,𝑒𝑒,𝑙𝑙and the rate of trade margin 𝑚𝑚𝑊𝑊
for exported products as,
𝑈𝑈,𝑖𝑖𝑓𝑓𝑓𝑓𝑓𝑓,𝑙𝑙
,𝑙𝑙
𝑑𝑑,𝑙𝑙
,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑒𝑒 � 𝑓𝑓𝑓𝑓𝑓𝑓 ,𝑙𝑙
and 𝑚𝑚𝑊𝑊,𝑒𝑒= 𝑝𝑝𝑈𝑈𝑈𝑈,𝑊𝑊𝑊𝑊𝑈𝑈𝑒𝑒,𝑖𝑖 �𝑝𝑝𝑈𝑈𝑈𝑈 ,𝑖𝑖(14) 𝑚𝑚𝑇𝑇,𝑒𝑒
𝑈𝑈,𝑖𝑖 = 𝑝𝑝𝑈𝑈𝑈𝑈,𝑇𝑇 𝑇𝑇𝑈𝑈,𝑖𝑖 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖
𝑈𝑈,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) ,respectively. From Equation (13) and (14), the FOB prices for households and industries are
represented as:
𝑓𝑓𝑓𝑓𝑓𝑓 ,𝑙𝑙

𝑑𝑑,𝑙𝑙
,𝑙𝑙
𝑊𝑊,𝑒𝑒 ,𝑙𝑙� (1 − 𝑚𝑚𝑇𝑇,𝑒𝑒(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).
(15) 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 = 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖
𝑈𝑈,𝑖𝑖 − 𝑚𝑚𝑈𝑈,𝑖𝑖 )
𝑚𝑚,𝐼𝐼
𝑚𝑚,𝐻𝐻
The prices of imports for industry and household uses, 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 and 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 , are calculated by adding

the custom duty and indirect taxes on products to the CIF price as:
𝑓𝑓

𝑓𝑓𝑓𝑓𝑓𝑓 ,𝑙𝑙

𝑚𝑚,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑙𝑙 ��
𝑟𝑟 ��
𝑙𝑙
(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻 ) ,= 𝑒𝑒𝐽𝐽/𝑈𝑈 �1 + 𝜏𝜏𝐽𝐽,𝑖𝑖
1 + 𝜏𝜏𝑈𝑈𝑈𝑈,𝑖𝑖
1 + 𝜏𝜏𝑈𝑈𝑈𝑈,𝑖𝑖 �𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖 = 𝑒𝑒𝐽𝐽/𝑈𝑈 𝜔𝜔𝑈𝑈𝑈𝑈,𝑖𝑖
𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖(16) 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖
𝑓𝑓
𝑟𝑟and 𝜏𝜏𝑈𝑈𝑈𝑈,𝑖𝑖
are
where 𝑒𝑒𝐽𝐽/𝑈𝑈 is the exchange rate of the Japanese yen against the U.S. dollar, 𝜏𝜏𝑈𝑈𝑈𝑈,𝑖𝑖

the rates of the international freight and insurance and the tariff for one unit of product i imported
𝑓𝑓
𝑙𝑙
𝑙𝑙 ��
𝑟𝑟
is defined as �1 + 𝜏𝜏𝑘𝑘′,𝑖𝑖
1 + 𝜏𝜏𝑘𝑘𝑘𝑘′
from the U.S. to Japan, respectively, and 𝜔𝜔𝑘𝑘𝑘𝑘′,𝑖𝑖,𝑖𝑖 ��1 + 𝜏𝜏𝑘𝑘𝑘𝑘′ ,𝑖𝑖 �/𝑊𝑊 ,𝑒𝑒,𝑙𝑙
24(1 − 𝑚𝑚𝑇𝑇,𝑒𝑒,𝑙𝑙𝑈𝑈,𝑖𝑖 − 𝑚𝑚𝑈𝑈 ,𝑖𝑖 ) for 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻 for notational simplicity.

Meanwhile, the volume share of demand of domestic product and imported product is defined

as:
𝑐𝑐,𝑙𝑙
= ∑𝑗𝑗∈𝑙𝑙 𝑋𝑋𝑘𝑘𝑘𝑘 ,𝑖𝑖𝑖𝑖 ⁄∑𝑗𝑗∈𝑙𝑙 𝑋𝑋𝐽𝐽 ,𝑖𝑖𝑖𝑖(𝑘𝑘 = 𝐽𝐽, 𝑈𝑈, 𝐸𝐸 and 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻),
(17) 𝑤𝑤𝑘𝑘𝑘𝑘,𝑖𝑖
𝑐𝑐,𝑙𝑙
𝑐𝑐,𝑙𝑙
𝑐𝑐,𝑙𝑙
where 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 + 𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖 + 𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖 = 1 for 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻 . By assigning Equations (16) and (17) to Equation (7),

we obtain:

𝑐𝑐,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑐𝑐,𝑙𝑙
𝑚𝑚,𝑙𝑙 𝑐𝑐,𝑙𝑙𝑙𝑙(18) 𝑝𝑝𝐽𝐽𝑐𝑐,𝑙𝑙,𝑖𝑖 = 𝑝𝑝𝐽𝐽𝑑𝑑,𝑙𝑙,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 + 𝑒𝑒𝐽𝐽/𝑈𝑈 𝜔𝜔𝑈𝑈𝑈𝑈,𝑖𝑖 𝑝𝑝𝑈𝑈𝑈𝑈 ,𝑖𝑖 𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖 + 𝑝𝑝𝐸𝐸𝐸𝐸 ,𝑖𝑖 𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖

Similarly, the demand prices in the U.S. are shown as:

𝑐𝑐,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑐𝑐,𝑙𝑙
𝑚𝑚,𝑙𝑙
𝑐𝑐,𝑙𝑙
𝑙𝑙
+ 𝜔𝜔𝐽𝐽𝐽𝐽(19) 𝑝𝑝𝑈𝑈𝑐𝑐,𝑙𝑙,𝑖𝑖 = 𝑝𝑝𝑈𝑈𝑑𝑑,𝑙𝑙,𝑖𝑖 𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖,𝑖𝑖 𝑝𝑝𝐽𝐽𝐽𝐽 ,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽 ,𝑖𝑖 �𝑒𝑒𝐽𝐽 /𝑈𝑈 + 𝑝𝑝𝐸𝐸𝑈𝑈 ,𝑖𝑖 𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).

(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) .

Equations (18) and (19) describe the price relationship between the producer’s prices of Japan and𝑓𝑓𝑟𝑟
T he data 𝜏𝜏𝑈𝑈𝑈𝑈,𝑖𝑖
is based on our extended 2011 Japan-US BIOT and the data 𝜏𝜏𝑈𝑈𝑈𝑈,𝑖𝑖
is assumed to be identical with the estimatesin the 2005 Japan-US BIOT by METI.

24

23

the U.S. through bilateral trade.
Based on the definitions of our prices, we define several price level indices (PLI) between Japanand the U.S. as,𝑑𝑑=(20) 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
𝑒𝑒

𝑝𝑝 𝑑𝑑
𝐽𝐽,𝑖𝑖

𝑑𝑑
𝐽𝐽/𝑈𝑈 𝑝𝑝 𝑈𝑈,𝑖𝑖

𝑑𝑑 ,𝑙𝑙, 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
=

𝑑𝑑,𝑙𝑙

𝑝𝑝 𝐽𝐽,𝑖𝑖

𝑑𝑑,𝑙𝑙
𝑒𝑒𝐽𝐽/𝑈𝑈 𝑝𝑝 𝑈𝑈,𝑖𝑖

𝑐𝑐 ,𝑙𝑙, 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
=

𝑐𝑐,𝑙𝑙

𝑝𝑝 𝐽𝐽,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻),

𝑐𝑐,𝑙𝑙

𝑒𝑒𝐽𝐽/𝑈𝑈 𝑝𝑝 𝑈𝑈,𝑖𝑖

where 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖 is the PLI of output at producer’s price of product i between Japan and the U.S. The

second equation describes the definition of the PLIs of output at producer’s price for households,𝐻𝐻,𝐼𝐼and 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖, respectively. The third equation describes the PLIs of demandand for industries, 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖,𝐻𝐻,𝐼𝐼
prices at producer’s price, 𝐏𝐏𝐽𝐽𝑐𝑐/𝑈𝑈,𝑖𝑖
and 𝐏𝐏𝐽𝐽𝑐𝑐/𝑈𝑈,𝑖𝑖, respectively. By substituting Equations (18) and (19),

into (20), the Japan-US PLI of domestic demand prices for households and industries are obtained
as follows:(21)

𝑐𝑐 ,𝑙𝑙
𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
=

𝑑𝑑,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝑚𝑚,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖+𝜔𝜔𝑙𝑙𝑈𝑈𝑈𝑈,𝑖𝑖𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖 �(1+𝜏𝜏 𝑙𝑙𝑈𝑈,𝑖𝑖)+𝐏𝐏𝐸𝐸𝐽𝐽/𝑈𝑈,𝑖𝑖𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).

𝑐𝑐,𝑙𝑙
𝑑𝑑,𝑙𝑙
𝑐𝑐 ,𝑙𝑙𝑚𝑚,𝑙𝑙𝑐𝑐,𝑙𝑙
𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖+𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖𝜔𝜔𝑙𝑙𝐽𝐽𝐽𝐽,𝑖𝑖𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖 �(1+𝜏𝜏 𝑙𝑙𝐽𝐽,𝑖𝑖)+𝐏𝐏𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖

𝑚𝑚 ,𝑙𝑙𝐏𝐏𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖
is the PLI of the imports from exogenous economies to Japan or the U.S., relative to thedomestic producer’s prices in the U.S. These imports PLIs are defined as:(22)

𝑚𝑚 ,𝑙𝑙𝐏𝐏𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖
=

𝑚𝑚,𝑙𝑙

𝑝𝑝 𝐸𝐸𝐸𝐸,𝑖𝑖

𝑑𝑑,𝑙𝑙
𝑒𝑒𝐽𝐽/𝑈𝑈 𝑝𝑝 𝑈𝑈,𝑖𝑖

𝑚𝑚,𝑙𝑙and 𝐏𝐏𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖=

𝑝𝑝 𝑚𝑚,𝑙𝑙
𝐸𝐸𝐸𝐸,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).

𝑑𝑑,𝑙𝑙

𝑝𝑝 𝑈𝑈,𝑖𝑖

𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
The import price indices for Japan and the U.S., 𝑝𝑝𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖
and 𝑝𝑝𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖 respectively , are endogenous

in the model and determined by the sub model, as presented in the subsequent section. From
Equation (21), we obtain:
𝑑𝑑 ,𝑙𝑙=(23) 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖

𝑐𝑐,𝑙𝑙

𝑚𝑚,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝑚𝑚,𝑙𝑙

𝑐𝑐,𝑙𝑙

𝜔𝜔𝑙𝑙𝑈𝑈𝑈𝑈,𝑖𝑖𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖�(1+𝜏𝜏 𝑙𝑙𝑈𝑈,𝑖𝑖)+𝐏𝐏𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖−𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖�𝑤𝑤𝑈𝑈𝑈𝑈,𝑖𝑖+𝐏𝐏𝐸𝐸𝐸𝐸/𝑈𝑈,𝑖𝑖𝑤𝑤𝐸𝐸𝐸𝐸,𝑖𝑖�
𝑐𝑐,𝑙𝑙
𝑐𝑐,𝑙𝑙
𝑐𝑐,𝑙𝑙
𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖𝜔𝜔𝑙𝑙𝐽𝐽𝐽𝐽,𝑖𝑖𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖�(1+𝜏𝜏 𝑙𝑙𝐽𝐽,𝑖𝑖)−𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).

If the PLIs of the demand prices and the imports from exogenous economies are available as data,
the PLI of output at producer’s price are measured by this equation.
,𝐼𝐼,𝐻𝐻
When the PLIs for 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖
and 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖(price level indexes for industry and household) areavailable in the data, we can measure the PLI of domestic outputs, 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖 , based on Equation (12)
as:

,𝐼𝐼
𝑑𝑑
�
= � 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖(24) 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖

𝑑𝑑,𝐼𝐼

𝑑𝑑,𝐼𝐼

𝑝𝑝 𝑈𝑈,𝑖𝑖𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖
𝑝𝑝 𝑑𝑑
𝑈𝑈,𝑖𝑖

+

𝑑𝑑,𝐼𝐼 𝑑𝑑,𝐼𝐼

𝑝𝑝 𝑈𝑈,𝑖𝑖𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖

𝑑𝑑 ,𝐻𝐻𝑑𝑑 � + 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖 �(1+𝜏𝜏 𝐼𝐼𝐽𝐽,𝑖𝑖)𝑝𝑝 𝑈𝑈,𝑖𝑖

𝑑𝑑,𝐻𝐻 𝑑𝑑 ,𝐻𝐻

𝑝𝑝 𝑈𝑈,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖
𝑝𝑝 𝑑𝑑
𝑈𝑈,𝑖𝑖

+�

𝑑𝑑,𝐻𝐻 𝑑𝑑,𝐻𝐻

𝑝𝑝 𝑈𝑈,𝑖𝑖 𝑤𝑤𝐽𝐽𝐽𝐽,𝑖𝑖

𝑑𝑑 �� � �1 −1+𝜏𝜏 𝐻𝐻
𝐽𝐽,𝑖𝑖� 𝑝𝑝 𝑈𝑈,𝑖𝑖

𝑤𝑤𝑑𝑑
𝐽𝐽𝐽𝐽,𝑖𝑖�.

1+𝜏𝜏 𝑑𝑑
𝐽𝐽,𝑖𝑖

𝑑𝑑
is defined including the indirect taxes. Since our framework is based on
In this equation, 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
𝑑𝑑
METI’s symmetric BIOT, this product-PLI is identical to the industry-PLI (𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖 = 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑗𝑗). To

enable us to compare the prices and volumes of outputs, the PLI of j-industry outputs at basic prices
𝑑𝑑 ∗𝐏𝐏𝐽𝐽/𝑈𝑈,𝑗𝑗
as:
(25)

𝑑𝑑 ∗
𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖= 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖

1+𝜏𝜏 𝑑𝑑
𝑈𝑈,𝑖𝑖
1+𝜏𝜏 𝑑𝑑
𝐽𝐽,𝑖𝑖.

In our study, only the Japan-US differences in the indirect taxes on the consumption of liquor,
tobacco, and gasoline are taken into account.

24

2

Purchaser’s Prices
The first section of the Appendix described the price model based on producer’s prices.

However, the PPP data in the main data sources are measured at purchaser’s prices. In this section,
we describe the relationship between the producer’s prices and purchaser’s prices. Some additional
notation is required:𝑝𝑝𝑝𝑝,𝑙𝑙

𝑝𝑝𝑘𝑘 ,𝑖𝑖

Prices of products in country k, purchased by industries (I) or household (H) in country
k at purchasers’ prices in currency of country k, (If l = I, the product is purchased byindustries for intermediate uses or investment. If l = H, the product is purchased byhousehold for final consumption.),𝑝𝑝𝑝𝑝,𝑙𝑙
𝑝𝑝𝑘𝑘𝑘𝑘′ ,𝑖𝑖

Prices of products produced in country k, purchased by industries (I) or household (H) in
country k’ at purchasers’ prices in currency of country k, (If l = I, the product is purchasedby industries. If l = H, the product is purchased by household.),

𝑝𝑝𝑝𝑝,𝑙𝑙
𝑝𝑝𝑘𝑘𝑘𝑘′ ,𝑖𝑖

𝑇𝑇𝑘𝑘𝑙𝑙 ,𝑖𝑖

Prices of imports from country k, purchased by industries (I) or household (H) in countryk’ at purchasers’ prices in currency of country k’, (If l = I, the product is purchased byindustries. If l = H, the product is purchased by household.),
Transportation service input for one unit of imported and domestic products in country k,(If l = I, the service is input for industries. If l = H, the service is input for households.),
Trade service input for one unit of domestic products in country k, (If l = I, the service is

𝑊𝑊𝑘𝑘𝑑𝑑,𝑖𝑖,𝑙𝑙𝑊𝑊𝑘𝑘𝑚𝑚,𝑖𝑖 ,𝑙𝑙
𝑚𝑚𝑇𝑇𝑘𝑘,𝑖𝑖,𝑙𝑙

input for industries. If l = H, the service is input for households.),
Trade service input for one unit of imports in country k, (If l = I, the service is input forindustries. If l = H, the service is input for households.),
Rates of transportation cost (T) of products in country k for imported and domestic
products, (If l = I, the rate is for industries. If l = H, the rate is for households.)
Rates of trade margin (W) of products in k-country for imported and domestic products,

,𝑙𝑙
𝑚𝑚𝑊𝑊
𝑘𝑘,𝑖𝑖

,𝑑𝑑,𝑙𝑙𝑚𝑚𝑊𝑊
𝑘𝑘,𝑖𝑖,𝑚𝑚,𝑙𝑙
𝑚𝑚𝑊𝑊
𝑘𝑘,𝑖𝑖(If l = I, the rate is for industries. If l = H, the rate is for households.)
Rates of trade margin (W) of products in country k for domestic products, (If l = I, therate is for industries. If l = H, the rate is for households.)
Rates of trade margin (W) of products in country k for imported products, (If l = I, therate is for industries. If l = H, the rate is for households.)
The purchaser’s price paid by industries and households is defined as the sum of the producer-

price value, the transportation cost, and the trade margin as:
𝑝𝑝𝑝𝑝,𝑙𝑙

𝑑𝑑,𝑙𝑙 𝑙𝑙𝑑𝑑,𝑙𝑙
𝑑𝑑 ,𝑙𝑙(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻),
(26) 𝑝𝑝𝐽𝐽 ,𝑖𝑖 = 𝑝𝑝𝐽𝐽𝑑𝑑,𝑙𝑙,𝑖𝑖 + 𝑝𝑝𝐽𝐽 ,𝑇𝑇 𝑇𝑇𝐽𝐽,𝑖𝑖 + 𝑝𝑝𝐽𝐽,𝑊𝑊 𝑊𝑊𝐽𝐽 ,𝑖𝑖
𝑑𝑑,𝑙𝑙
𝑑𝑑,𝑙𝑙
where 𝑝𝑝𝐽𝐽 ,𝑇𝑇 and 𝑝𝑝𝐽𝐽 ,𝑊𝑊 are the output prices of the transportation and trade services in Japan and

𝑇𝑇𝐽𝐽𝑙𝑙,𝑖𝑖 and 𝑊𝑊𝐽𝐽 𝑑𝑑,𝑖𝑖 ,𝑙𝑙 are the transportation and the trade services required for one unit of product i. In ourmodel, since the trade margin rates are distinguished for domestic products and imports, thesuperscript “d” is added for the trade margin. The rates of transportation cost and trade margin to
the purchaser’s prices of domestic products are defined as:(27)

𝑝𝑝𝑝𝑝,𝑙𝑙𝑇𝑇,𝑙𝑙𝑑𝑑,𝑙𝑙 𝑙𝑙
𝑚𝑚𝐽𝐽,𝑖𝑖= 𝑝𝑝𝐽𝐽,𝑇𝑇
𝑇𝑇𝐽𝐽,𝑖𝑖 �𝑝𝑝𝐽𝐽,𝑖𝑖

𝑝𝑝𝑝𝑝,𝑙𝑙

𝑊𝑊 ,𝑑𝑑,𝑙𝑙
𝑑𝑑 ,𝑙𝑙� 𝑝𝑝𝐽𝐽 ,𝑖𝑖
and 𝑚𝑚𝐽𝐽,𝑖𝑖= 𝑝𝑝𝐽𝐽𝑑𝑑,𝑙𝑙,𝑊𝑊 𝑊𝑊𝐽𝐽 ,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻),

respectively, for each of industry or household use. Based on Equations (26) and (27), the25

relationship between producer’s prices and purchaser’s prices is given by:(28)

𝑝𝑝𝑝𝑝,𝑙𝑙𝑇𝑇,𝑙𝑙
𝑊𝑊 ,𝑑𝑑,𝑙𝑙
�1 − 𝑚𝑚𝐽𝐽,𝑖𝑖
�
𝑝𝑝𝐽𝐽𝑑𝑑,𝑙𝑙− 𝑚𝑚𝐽𝐽,𝑖𝑖,𝑖𝑖 = 𝑝𝑝𝐽𝐽 ,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻 ).

Analogous equations exist for the U.S. The PLI in purchaser’s prices for domestic products is
described as:(29)𝑝𝑝𝑝𝑝,𝑙𝑙

𝑊𝑊 ,𝑑𝑑,𝑙𝑙
�1−𝑚𝑚𝑇𝑇,𝑙𝑙
𝑝𝑝 𝐽𝐽,𝑖𝑖
𝑈𝑈,𝑖𝑖−𝑚𝑚𝑈𝑈,𝑖𝑖 �𝑝𝑝𝑝𝑝 ,𝑙𝑙
𝑑𝑑 ,𝑙𝑙
𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖 =
𝑝𝑝𝑝𝑝,𝑙𝑙 = 𝐏𝐏𝐽𝐽 /𝑈𝑈,𝑖𝑖 �𝑇𝑇,𝑙𝑙𝑊𝑊,𝑑𝑑,𝑙𝑙
1−𝑚𝑚𝐽𝐽,𝑖𝑖 −𝑚𝑚𝐽𝐽,𝑖𝑖 �𝑒𝑒𝐽𝐽/𝑈𝑈 𝑝𝑝 𝑈𝑈,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) .

This equation gives the relationship between the producer-price PLI and the purchaser-price PLIof domestic products.
The PLI for composite demand, which reflects the prices of both imports and its domestic
counterpart, is represented as:(30)

𝑝𝑝𝑝𝑝 ,𝑙𝑙

𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖 =

𝑝𝑝𝑝𝑝,𝑙𝑙

𝑝𝑝 𝐽𝐽,𝑖𝑖

𝑊𝑊 ,𝑙𝑙�1−𝑚𝑚𝑇𝑇,𝑙𝑙
𝑈𝑈,𝑖𝑖−𝑚𝑚𝑈𝑈,𝑖𝑖 �

𝑐𝑐 ,𝑙𝑙𝑝𝑝𝑝𝑝,𝑙𝑙 = 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖 �

𝑇𝑇,𝑙𝑙

𝑊𝑊,𝑙𝑙

1−𝑚𝑚𝐽𝐽,𝑖𝑖 −𝑚𝑚𝐽𝐽,𝑖𝑖 �𝑒𝑒𝐽𝐽/𝑈𝑈 𝑝𝑝 𝑈𝑈,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻).

The rate of transportation cost for the component of imports is the same as that for the domestic
𝑇𝑇,𝑙𝑙products. Thus the same rates of 𝑚𝑚𝐽𝐽,𝑖𝑖
and 𝑚𝑚𝑇𝑇,𝑙𝑙
𝑈𝑈,𝑖𝑖 are applied in Equations (29) and (30). On the,𝑚𝑚,𝑙𝑙other hand, the rate of domestic trade margin for imports 𝑚𝑚𝑊𝑊
is different from that for domestic
𝑘𝑘,𝑖𝑖,𝑑𝑑,𝑙𝑙,𝑙𝑙
products 𝑚𝑚𝑊𝑊
in our model. Therefore, equation (30) is described using, 𝑚𝑚𝐽𝐽𝑊𝑊,𝑖𝑖,𝑙𝑙 and 𝑚𝑚𝑊𝑊
𝑘𝑘,𝑖𝑖
𝑈𝑈,𝑖𝑖 ,

which are the rates of trade margin for composite products measured as:(31)

𝑝𝑝𝑝𝑝,𝑙𝑙𝑝𝑝𝑝𝑝,𝑙𝑙𝑝𝑝𝑝𝑝,𝑙𝑙,𝑙𝑙
𝑊𝑊 ,𝑚𝑚,𝑙𝑙 ∑∑𝑚𝑚𝑊𝑊
𝑗𝑗∈𝑙𝑙 �𝑝𝑝𝑘𝑘′ 𝑘𝑘,𝑖𝑖 𝑋𝑋 𝑘𝑘′ 𝑘𝑘,𝑖𝑖𝑖𝑖 + 𝑝𝑝𝐸𝐸𝐸𝐸 ,𝑖𝑖 𝑋𝑋𝐸𝐸𝐸𝐸,𝑖𝑖𝑖𝑖 �� 𝑗𝑗∈𝑙𝑙 𝑝𝑝𝑘𝑘,𝑖𝑖 𝑋𝑋𝑘𝑘,𝑖𝑖𝑖𝑖
𝑘𝑘,𝑖𝑖 = 𝑚𝑚𝑘𝑘,𝑖𝑖
𝑝𝑝𝑝𝑝,𝑙𝑙𝑝𝑝𝑝𝑝,𝑙𝑙,𝑑𝑑,𝑙𝑙 ∑+𝑚𝑚𝑊𝑊∙ 𝑗𝑗∈𝑙𝑙 𝑝𝑝𝑘𝑘𝑘𝑘,𝑖𝑖 𝑋𝑋𝑘𝑘𝑘𝑘,𝑖𝑖𝑖𝑖 �∑𝑗𝑗∈𝑙𝑙 𝑝𝑝𝑘𝑘 ,𝑖𝑖 𝑋𝑋𝑘𝑘 ,𝑖𝑖𝑖𝑖
𝑘𝑘,𝑖𝑖(𝑘𝑘𝑘𝑘 ′ = 𝐽𝐽𝐽𝐽 𝑜𝑜𝑜𝑜 𝑈𝑈𝑈𝑈 and 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) .

Equation (31) indicates that the rate of trade margin for composite products 𝑚𝑚𝑊𝑊,𝑙𝑙𝑘𝑘,𝑖𝑖 is measured as,𝑚𝑚,𝑙𝑙,𝑙𝑙
a weighted average of 𝑚𝑚𝑊𝑊
and 𝑚𝑚𝑊𝑊,𝑑𝑑, with weights reflecting the nominal value shares
𝑘𝑘,𝑖𝑖
𝑘𝑘,𝑖𝑖

evaluated at the purchaser’s prices. This study uses the trade margin rates in Nomura and Miyagawa(2018a).
,𝐼𝐼
𝑝𝑝𝑝𝑝,𝐻𝐻
The PLIs, 𝐏𝐏𝐽𝐽𝑝𝑝𝑝𝑝/𝑈𝑈,𝑖𝑖
and 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
in Equation (30), reflect the Japan-US relative price differences

for demand prices evaluated by purchaser’s prices for industry and household uses, respectively.
By isolating the PLI of the products for household use, we are able to define the Japan-US
Purchasing Power Parity (PPP) for household consumption by product as:
𝑝𝑝𝑝𝑝,𝐻𝐻

𝐻𝐻= 𝑒𝑒𝐽𝐽 /𝑈𝑈 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖 .
(32) 𝐏𝐏𝐏𝐏𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
𝑝𝑝𝑝𝑝,𝐻𝐻
𝐻𝐻
If the PPP data, 𝐏𝐏𝐏𝐏𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖, or the purchaser-price PLI, 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖, on household consumption between

𝑐𝑐 ,𝐻𝐻,Japan and the U.S. are available, we can measure the producer-price PLI of demand prices, 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖,𝐻𝐻
from Equation (30), and then the PLI of domestic products, 𝐏𝐏𝐽𝐽𝑑𝑑/𝑈𝑈,𝑖𝑖, can be measured from Equation

(23).

3

Import Prices from Exogenous Economies
We next describe the role of import prices from exogenous economies (E) to Japan (J) and the
𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
U.S. (U). The estimates of these prices, 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖
and 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖 , respectively, are used to infer the

𝑑𝑑 ,𝑙𝑙producer-price PLI of domestic products 𝐏𝐏𝐽𝐽/𝑈𝑈,𝑖𝑖
in Equation (23). Some intuition of this is asfollows: suppose we observe the price of paper exported from China into Japan, and we observe26the final demand price paid for paper in Japan. In our accounting framework, the gap between thetwo prices reflects the (unmeasured) production price in Japan (after accounting for trade margins
𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
and taxes). We define 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖
and 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖 as the combined import prices from exogenous economies:(33)

where the

𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
𝑙𝑙
𝑝𝑝𝐸𝐸𝑚𝑚,𝑙𝑙= ∑𝑘𝑘 𝑝𝑝𝑘𝑘𝑚𝑚,𝑙𝑙
𝑣𝑣 𝑚𝑚,𝑙𝑙 = ∑𝑘𝑘≠𝑅𝑅 𝑒𝑒𝑘𝑘′ /𝑘𝑘 𝜔𝜔𝑘𝑘𝑘𝑘′,𝑖𝑖
𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 𝑣𝑣𝑘𝑘𝑘𝑘′,𝑖𝑖 + 𝑝𝑝𝑅𝑅𝑅𝑅′ ,𝑖𝑖 𝑣𝑣𝑅𝑅𝑅𝑅′,𝑖𝑖 ,𝑘𝑘′ ,𝑖𝑖𝑘𝑘′ ,𝑖𝑖 𝑘𝑘𝑘𝑘′ ,𝑖𝑖
𝑚𝑚,𝑙𝑙
𝑣𝑣𝑘𝑘𝑘𝑘′ ,𝑖𝑖(𝑙𝑙 = 𝐼𝐼, 𝐻𝐻, 𝑘𝑘 = 𝐶𝐶, 𝐺𝐺, 𝐾𝐾, 𝑀𝑀, 𝑊𝑊, 𝑇𝑇, 𝑅𝑅, and 𝑘𝑘′ = 𝐽𝐽 𝑜𝑜𝑜𝑜 𝑈𝑈) ,stands for the import shares at current prices from country k (the exogenous

𝑚𝑚,𝑙𝑙
economies) to country k’ (Japan and the U.S.). The sum of the import shares ∑𝑘𝑘 𝑣𝑣𝑘𝑘𝑘𝑘′ ,𝑖𝑖 is one.
𝑚𝑚,𝑙𝑙𝑙𝑙
𝑝𝑝𝑅𝑅𝑅𝑅′,𝑖𝑖
is the average price of imported goods from the rest of the world (ROW). 𝜔𝜔𝑘𝑘𝑘𝑘′,𝑖𝑖, which isdefined in Equation (16), is the combined coefficient to transform the output prices in country k to

the import prices in country k’ from country k. Since it is difficult to obtain the output prices incountry k (𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 ) directly from statistical data, we construct the following sub model to determine
𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 in six exogenous economies (k) excluding the ROW. 25

We describe the demand price (of the composite products) in country k as:

(34)

𝑐𝑐,𝑙𝑙
𝑙𝑙
𝑑𝑑,𝑙𝑙 𝑐𝑐,𝑙𝑙
𝑑𝑑,𝑙𝑙 𝑐𝑐,𝑙𝑙𝑙𝑙∑
𝑝𝑝𝑘𝑘𝑐𝑐,𝑙𝑙,𝑖𝑖 = 𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 𝑣𝑣𝑘𝑘𝑘𝑘,𝑖𝑖 + 𝑘𝑘≠𝑘𝑘′ 𝑒𝑒𝑘𝑘/𝑘𝑘′ 𝜔𝜔𝑘𝑘′ 𝑘𝑘,𝑖𝑖 𝑝𝑝𝑘𝑘′ ,𝑖𝑖 𝑣𝑣𝑘𝑘′ 𝑘𝑘,𝑖𝑖 + 𝑒𝑒𝑘𝑘/𝐽𝐽 𝜔𝜔𝐽𝐽𝐽𝐽,𝑖𝑖 𝑝𝑝𝐽𝐽 ,𝑖𝑖 𝑣𝑣𝐽𝐽𝐽𝐽,𝑖𝑖
𝑐𝑐,𝑙𝑙
𝑙𝑙
𝑐𝑐𝑐𝑐
+𝑒𝑒𝑘𝑘/𝑈𝑈 𝜔𝜔𝑈𝑈𝑈𝑈,𝑖𝑖
𝑝𝑝𝑈𝑈𝑑𝑑,𝑙𝑙,𝑖𝑖 𝑣𝑣𝑈𝑈𝑈𝑈,𝑖𝑖+ 𝑝𝑝𝑅𝑅𝑚𝑚,𝑙𝑙
𝑅𝑅,𝑖𝑖 𝑣𝑣𝑅𝑅𝑅𝑅′ ,𝑖𝑖 ,(𝑘𝑘 = 𝐶𝐶, 𝐺𝐺, 𝐾𝐾, 𝑀𝑀, 𝑊𝑊, 𝑇𝑇, 𝑘𝑘′ = 𝐶𝐶, 𝐺𝐺, 𝐾𝐾, 𝑀𝑀, 𝑊𝑊, 𝑇𝑇, and 𝑙𝑙 = 𝐼𝐼, 𝐻𝐻) .
𝑐𝑐,𝑙𝑙
where 𝑣𝑣𝑘𝑘𝑘𝑘′ ,𝑖𝑖 is the demand share of the domestic product and the imported product at current

𝑐𝑐,𝑙𝑙
prices from country k to country k’. The sum of the demand shares ∑𝑘𝑘 𝑣𝑣𝑘𝑘𝑘𝑘′ ,𝑖𝑖 is one. In this equation,

𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 in the first and second terms of the right hand are the prices to be determined endogenously inthe sub model. The third and fourth terms are the import prices from Japan and the U.S.,
𝑑𝑑,𝑙𝑙
𝑑𝑑,𝑙𝑙
and 𝑝𝑝𝑈𝑈𝑈𝑈,𝑖𝑖, are pre-determined in the main model and arerespectively, whose output prices, 𝑝𝑝𝐽𝐽𝐽𝐽,𝑖𝑖
𝑚𝑚,𝑙𝑙
treated as exogenous variables in the sub model. And the final term, 𝑝𝑝𝑅𝑅𝑅𝑅,𝑖𝑖 , is the exogenous prices

of imports from the ROW.
In the left-hand side of Equation (34), the demand-price PPPs in country k, 𝑝𝑝𝑘𝑘𝑐𝑐,𝑙𝑙,𝑖𝑖 , are observedin Eurostat-OECD (2012), METI (2012), or other PPP surveys. The third and fourth terms of theright-hand side of Equation (34), i.e., the output prices in Japan and the U.S., are pre-determinedin our main model, as described in the Appendices 1 and 2. The fifth term, i.e., the exogenous
prices of imports from the ROW, is also usually unobserved. In this paper, the purchaser’s price ofimports from the ROW in country k is assumed to be identical with the purchaser’s price of thecomposite product of domestic product in country k and imported products from Japan, the U.S.,
and other five exogenous countries. 26 For each product i, Equation (34) is defined for the six
countries that we consider. Six endogenous variables of domestic output prices in country k, 𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 ,are determined simultaneously by solving these six linear equations in each product i.

Some iterations are required between the main model and the sub model. By substituting theoutput prices (𝑝𝑝𝑘𝑘𝑑𝑑,𝑙𝑙,𝑖𝑖 ) estimated in the sub model for six countries and the exogenous prices of imports
25

In the sub model, indirect taxes are not considered for simplicity.
T he estimates of PPP for outputs are sensitive to the assumption on import prices, in the process to parse the observed price ofcomposite goods into that from domestic supply and that coming from imported goods. In measuring PPPs for 1990 in Nomura
and Miyagawa (1999), the similar assumption was applied only for the total of six exogenous economies and the ROW. This
induced unreasonable estimates in some products. The explicit treatment of six exogenous economies contributes to reduce these
events to be happened. However, in some exceptional cases when the estimated results are unreasonable, the import prices fromthe ROW are adjusted.

26

27

𝑚𝑚,𝑙𝑙from the ROW ( 𝑝𝑝𝑅𝑅𝑅𝑅,𝑖𝑖 ) in to Equation (33), the import prices from exogenous economies to Japan

𝑚𝑚,𝑙𝑙
𝑚𝑚,𝑙𝑙
and the U.S., 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖
and 𝑝𝑝𝐸𝐸𝐸𝐸,𝑖𝑖 , are affected. These then require the further adjustment in the𝑑𝑑,𝑙𝑙estimates of 𝑝𝑝𝐽𝐽𝑑𝑑,𝑙𝑙,𝑖𝑖 and 𝑝𝑝𝑈𝑈 ,𝑖𝑖 in Equation (23) of the main model, which impacts the third and fourthterms of the right-hand side of Equation (34) in the sub model. Through a few reiterations between
the main model and the sub model, we obtain the final results of all types of PLIs between Japanand the U.S.

4

Sensitivity to Margin Rates
In this section, we evaluate the sensitivity of the PPPs for industry outputs to our choice ofmargin rates. Our baseline PPP estimates depend on the margin rates of wholesale and retailservices estimated in Nomura and Miyagawa (2018a). They examined the accuracy of the estimatesof the trade margin values in the 2011 benchmark IOT in Japan and found the total margin value
was underestimated by about 40% due to estimation methods used in the 2011 Economic Census.
If lower margin rates are used in the measurement of PPPs via the price model, they induce higher
PPPs for industry outputs (Paths-2, -3, and -4 defined in Figure 2). Figure A2 presents the impact
on the PPPs for outputs when the margin values were reduced by 40% (on the y-axis) from ourbaseline estimates (on the x-axis). This low-margin case reduces the price competitivenessmeasures by more than 50% in 15 industries and by more than 20% in 44 industries. 27 The PPPs
based on the (official) low margin case imply significantly lower productivity levels in Japanesemanufacturing than those based on the adjusted margins. These low productivity levels in
manufacturing are implausible in comparison to earlier studies of Japan-U.S. productivity gaps. 28

27

For example, the PPP for industry output of 170.Motor vehicles is revised to 120.0 yen per dollar in low-margin case, comparedto 97.5 in baseline estimates. T he PPP for domestic output estimated in low-margin case seems to be unrealistically high as anevaluation of price competitiveness of the Japanese motor vehicle industry.
28
Kuroda and Nomura (1999), and Jorgenson and Nomura (2007), as well as Jorgenson, Nomura and Samuels (2016).

28

Estimates in low-margin case350

(yen per dollar)

+20%

+50%
003 Fruits

0%

121 Small personal
adornments

037 Other textile product mills
002 Vegetables and potatoes
084 Farm machinery and equipment

300

123 Other miscellaneous manufacturing
105 Batteries

021 Grain milling

025 Vegetable oil

250

114 Photographic andphotocopying equipment

023 Other processed
agricultural food products

090 Vending, commercial
and office machinery

118 Musical instruments
200

020 Seafood products

096 Other telecommunication machinery
074 Miscellaneous nonmetallic mineral products

065 Foot wears
150

092 Household electrical appliances

035 Knit fabric mills
036 Carpet, floor mat, and rug mills
034 Textile and fabricmills, fabric dyeing

091 Audio and video equipment

066 Leather
and fur
products

006 Other non-edible crops

107 Motor vehicles

100

046 Other converted paper products
098 Watch, clock, and measuring devices

50

116 Other precision instruments
059 Cosmetics and dentifrices

067 Other leather products(yen per dollar)

032 Tobacco

0
0

50

100

150

200

250

300

350

Baseline estimates

Figure A2: PPPs for Goods Based on the Low Margin Scenario versus the Baseline
At the aggregate level, the low-margin case leads to and increase the PPP for GDP to 111.8
yen per dollar, from 109.0 in the baseline scenario, expanding the gap with the expenditure-side
PPP for GDP in the Eurostat-OECD (107.5 yen per dollar). However, the impact of the low-margincase at the aggregate level is small compared to the impacts at the industry level presented in Figure
A2. This is because higher PPPs for GDP in the manufacturing industries are compensated by therevised lower PPPs for GDP of the wholesale and retail industries. The low-margin case has asignificant impact on the PPP for wholesale service (95.3 yen per dollar from 133.5 in the baseline
estimate) and the PPP for retail service (119.7 from 136.3). These estimates based on the lower
margin rates seem to be inconsistent with previous studies, providing additional evidence that those
based on the official Japan Census data appear implausible.

29