HIAS-E-114

Welfare Costs of Exchange Rate
Fluctuations:
Evidence from the 1972 Okinawa
Reversion

Kazuko Kano (a), Takashi Kano (b) (c)(c)(a) Waseda University(b)
Hitotsubashi University
Center for International Research on the Japanese Economy, The University of Tokyo

November, 2021

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
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Welfare Costs of Exchange Rate Fluctuations:
Evidence from the 1972 Okinawa Reversion
Kazuko Kano†

Takashi Kano‡† Waseda University‡ Hitotsubashi University

Center for International Research on the Japanese Economy, University of Tokyo

Current Draft: November 12, 2021
Abstract
The main tenet of the New Keynesian (NK) paradigm is that price dispersion caused by nominal price stickinessis the primary source of allocative ineﬃciency. This study empirically evaluates the welfare implications of NK
models by observing how internal and external price dispersion responds to two types of large aggregate shocks:
high inﬂation and sharp currency depreciation. For this purpose, we consider the history of US military deployment
on a small southern island in Japan called Okinawa following the Paciﬁc War. We investigate unique data variations
in micro-level retail prices surveyed in Okinawa and mainland Japan before and after the Okinawan reversion to
Japanese sovereignty in May of 1972. By considering the Okinawan experience of three currency regimes during
the high inﬂation period of the early 1970s as valid quasi-natural experiments, we identify statistically signiﬁcantdeteriorations of currency misalignment associated with the sudden exogenous large USD depreciation versus the
JPY following the Nixon Shock. Furthermore, we observe that these massive aggregate shocks left the averageabsolute size of price changes mostly unchanged, but signiﬁcantly increased the average frequency of price changes
in Okinawa. Because a calibrated small open-economy menu cost model ﬁts these empirical ﬁndings better thanthe Calvo model, the welfare costs of exchange rate ﬂuctuations may be more elusive than suggested by the openeconomy NK literature.
Key Words : Currency regime; Currency misalignment; Welfare cost; Okinawan reversion; Menu cost model
JEL Classiﬁcation Number : F31, F41, F45†

We wish to thank Naohito Abe, Martin Berka, Shin-ichi Fukuda, Masazumi Hattori, Munechika Katayama, Junko Koeda,
Ryoji Koike, Naoto Jinji, Chiaki Moriguchi, Jim Nason, Nalini Prasad, Andy Rose, Makoto Saito, Moto Shintani, Etsuro Shioji,
Masatoshi Shizume, Hajime Tomura, Kozo Ueda, and seminar and conference participants from Massey University, Waseda
University, the 2017 Fall Meetings of the Japanese Economic Association, 2019 Canadian Economics Association Meetings,
2019 European and North American Summer Meetings of the Econometrics Society, and 2019 Australasian Conference ofInternational Macroeconomics for their insightful discussion and helpful comments. Tomoya Ozeki, Masaaki Shibata, Kenji
Wada, and Haruna Yamada provided excellent research assistance. We wish to express gratitude for a grant-in-aid for scientiﬁc
research from the Japan Society for the Promotion of Science (Nos. 24330060 and 17H02542) and ﬁnancial support from the
Hitotsubashi Institute for Advanced Study. We are solely responsible for any errors and misinterpretations in this study.
‡
Contact information: Graduate School of Economics, Hitotsubashi University, Naka 2-1, Kunitachi-city, Tokyo, 186-8601,
Japan. Emails: tkano@econ.hit-u.ac.jp (T.Kano), kkano@waseda.jp (K.Kano)1. Introduction
Fifty years ago, US President Richard Nixon suddenly announced the suspension of the convertibilityof the US dollar into gold. The Nixon Shock in August of 1971 triggered a subsequent collapse of the
Bretton Woods system. Since this regime-changing historical event, the international monetary systemhas witnessed and largely suﬀered from highly volatile ﬂexible exchange rates. Our experience over the
past ﬁve decades has led to many fundamental normative questions. Should we control volatile ﬂexible
exchange rates? If so, how should we use a set of available policy tools? In particular, should our monetary
policies consider exchange rate ﬂuctuations as an explicit policy goal in addition to the conventional goalsof business cycle smoothing and price stability?
The past ﬁve decades have also provided ample evidence for the essential roles of nominal rigidities
in exchange rate ﬂuctuations. As discussed in the seminal observations of Mussa (1986), real exchange
rates change in tandem with nominal rates for most advanced currencies and the former rates are much morevolatile under ﬂexible regimes than under ﬁxed regimes. These observations are evidence against "nominal
exchange regime neutrality." As a result, open economy New Keynesian (NK) models have become thedominant framework for current exchange rate research because they emphasize the crucial roles of pricestickiness and monetary policies in exchange rate changes.
To approach the normative questions presented above through the lens of the NK paradigm, it isessential to understand how signiﬁcant real and nominal exchange rate ﬂuctuations aﬀect the welfare ofopen economies empirically. In this study, we tackle this empirical task by revisiting the US militaryhistory of deployment on a small southern island in Japan called Okinawa following the Paciﬁc War. We
investigate unique data variations in micro-level retail prices surveyed during the period around the Nixon
shock.
Our monthly dataset contains 178 goods and services retail prices from retail price surveys conducted
for the purpose of constructing consumer price indices (CPIs) for Okinawa and the other 46 prefectures inJapan. It covers the period from January of 1970 to December of 1974. Our dataset is made unique by the
post-war historical experience of Okinawa. Following the surrender of the Imperial Japanese Army in 1945,
the US military government occupied Okinawa for geopolitical reasons until the reversion of Okinawa toJapanese sovereignty in May of 1972. During the US military occupation, Okinawa suﬀered from multiple
currency conversions. In particular, the US military government introduced the US dollar as an Okinawan
legal tender in 1958. This US dollar currency regime continued until the reversion, when Okinawa mergedwith the Japanese yen currency regime. The US dollar ﬁxed-exchange-rate (USD-Fix) regime under the
Bretton Woods system occurred ﬁrst. Next, the US dollar ﬂexible-exchange-rate (USD-Flex) regime after
the Nixon Shock occurred. Finally, the Japanese yen common-currency (JPY-Com) regime resulted fromthe 1972 reversion. This currency history of Okinawa provides us with an excellent opportunity to perform ideal quasi-natural experiments to identify and estimate the eﬀects of ﬂexible exchange rates on two
dimensions of retail price dynamics, which are crucial and relevant to the normative questions regarding
exchange rate ﬂuctuations.
The ﬁrst dimension is the degree of currency misalignment between Okinawa and other mainland
prefectures in Japan. Currency misalignment, which this study identiﬁes as a deviation from the law of
one price (LOP), is relevant to the welfare of open economies because it means that an identical good
produced with identical production costs has diﬀerent regional prices in terms of a common currency
1unit. After controlling the role of transport costs, currency misalignment implies the ineﬃciency of crossregional resource allocation based on the inequality of marginal utility across regions. Based on twocountry NK models with pricing to market or local currency pricing (LCP), Engel (2011) and Corsetti etal. (2010) theoretically demonstrated that a global loss function for cooperative monetary policymakers
depends negatively on the degree of currency misalignment.
The second dimension we consider in this study is the degree of ineﬃcient price dispersion withina country or region. For example, if an identical good has diﬀerent regional prices, then the demand forthat good can vary within a country. As a result, the marginal disutility of labor for meeting demands
for goods could be divergent and lead to ineﬃcient resource allocation. Indeed, the global loss function
derived by Engel (2011) in his two-country NK model with LCP depends negatively on the degree ofinternal dispersion of four prices, namely home and foreign goods prices in home and foreign countries.
Therefore, this second dimension is relevant to our motivation of determining if exchange rate ﬂuctuations
cause ineﬃcient price dispersion in open economies.
Conventionally, NK models, which depend on the Calvo (1983) technology of price stickiness, focus
on ineﬃcient price dispersion because this nominal rigidity implies a greater degree of heterogeneity inprice adjustments across ﬁrms. Even when they face the same erosion of relative prices caused by aggregate
price inﬂation, some ﬁrms can adjust their nominal prices within a ﬁxed period, but others cannot. The
higher the inﬂation rate, the greater the nominal price dispersion and the worse the relative price distortion.
In the open-economy NK model with LCP, exchange rate ﬂuctuations aﬀect inﬂation dynamics by changing
the optimal reset price. For example, Benigno (2004) and Engel (2014a, 2019) determined that openeconomy NK Phillips curves describe the tight dependence of the inﬂation rate on the real exchange rate.
Therefore, exchange rate ﬂuctuations can have ﬁrst-order importance in terms of internal relative pricedistortions because they contribute to ineﬃcient price dispersion.
However, empirical evaluations of these two dimensions of retail price dynamics face signiﬁcantdiﬃculties. First, as discussed by Engel (2014b), we must extract the degree of ineﬃcient currency misalignment caused solely by exchange rate ﬂuctuations in collaboration with pricing to market and pricestickiness while controlling for unobservable heterogeneity in local distribution services in countries or regions. Second, the degree of ineﬃcient internal price dispersion is also diﬃcult to measure. As discussed
by Nakamura et al. (2018), we must identify internal price dispersion caused solely by price stickiness andnot by other unobservable types of product heterogeneity within a country or region.
Our dataset helps us overcome the ﬁrst empirical diﬃculty. We construct a panel dataset containing
the degrees of LOP deviation among 47 prefectural capital cities in Japan for 178 individual items reported
in retail price surveys. We then implement diﬀerence-in-diﬀerence (DID) regression by incorporatingtime-invariant city-pair-speciﬁc ﬁxed eﬀects. We expect that these ﬁxed eﬀects empirically capture thepossible roles of unobservable heterogeneity in local distribution services under our working assumptionthat the resource costs of local distribution services were not aﬀected by changes in the currency regimes
in Okinawa. Our treatment group consists of the LOP deviations between Naha, which is the capital city of
Okinawa, and each of the other 46 prefectural capital cities in mainland Japan, whereas our control group
includes those among the 46 mainland prefectural capital cities. Most importantly, we decompose the entire
sample period into three subsamples corresponding to the three currency regimes of Okinawa. Then, after
controlling for economic developments that are common across the treatment and control groups over thewhole sample period, our DID regression estimates whether the shape of the sample distribution of the2item-level LOP deviations of the treatment group change with the three currency regimes.
To tackle the second empirical diﬃculty, we follow the advice of Nakamura et al. (2018). They
argued that the average absolute sizes of price changes conditional on price revision can serve as a goodproxy for ineﬃcient internal price dispersion. Because the average absolute revision size reﬂects how long
average ﬁrms delay in revising current prices to the optimal level, there may be signiﬁcant internal pricedispersion when the average absolute revision size is large. Most importantly, this measure is robust to theeﬀects of unobservable product heterogeneity on price-level dispersion.
Furthermore, the average absolute sizes and corresponding frequencies of price changes are informative for evaluating the empirical validity of the underlying mechanisms of price stickiness in open-economy
NK models with LCP, particularly when retail price data are subject to both high inﬂation and sharp local
currency depreciation. On one hand, in the Calvo mechanism, while the frequency of price revision remains constant by construction, the average absolute size of price changes increases rapidly with inﬂationand local currency depreciation, as does ineﬃcient internal price dispersion. On the other hand, in a statedependent mechanism with menu costs, the average absolute size of price changes is roughly independentof the range of inﬂation and local currency depreciation rates. Additionally, the frequency of price changes
increases rapidly with these aggregate variables, as demonstrated by the calibration study by Flodén and
Wilander (2006). Intuitively, as discussed by Nakamura et al. (2018), prices never drift too far from theiroptimal levels in the menu cost model because ﬁrms ﬁnd it optimal to pay the menu cost before this occurs.
During a high inﬂation period, exporters will need to raise their local currency prices eventually, meaning
they pay the menu cost. Therefore, exporters have a signiﬁcant incentive to frontload and raise their local
currency prices in response to sharp exporter currency appreciation. This property signiﬁcantly limits theextent to which internal price dispersion increases with inﬂation and local currency depreciation in themenu cost model with pricing-to-market behavior. As a result, we hypothesize that the welfare loss resulting from ineﬃcient internal price dispersion caused by increasing inﬂation and depreciating local currency
will be relatively small in the open-economy menu cost model with LCP.
This study adopts the average absolute size and frequency of price changes as proxies for ineﬃcientinternal price dispersion. First, we construct a panel dataset containing the average absolute sizes andfrequencies of price revisions in the prefectural capital cities for all 178 considered goods over the threecurrency regime periods. By setting the Okinawa sample as the treatment group and the samples of theother prefectures as the control group, we then conduct DID regression exercises with city-speciﬁc ﬁxed
eﬀects to identify how a change in the currency regime impacts the average absolute sizes and frequencies
of price revisions and contributes to ineﬃcient internal price dispersion.
Following the spirit of the study by Nakamura et al. (2018), we investigate micro-level retail prices
during the high inﬂation period of the early 1970s in Japan. Table 1 reports the average annualized CPI
inﬂation rates in Okinawa and the mainland for the three currency regimes in the second and third columns.
The aggregate inﬂation rates are close to 6 % in both Okinawa and the mainland in the USD-Fix regime.
The average inﬂation rate in Okinawa increases to approximately 8% in the USD-Flex regime and morethan 24% in the JPY-Com regime. A similar surge in inﬂation can also be observed in the mainland withan average inﬂation rate of 16%. Furthermore, as shown in Figure 1, the USD sharply depreciates versus
the JPY by 14.5% from 355 JPY/USD to 304 JPY/USD within the nine months between the Nixon Shockand Okinawa reversion. This sudden sharp appreciation of the JPY versus the USD is comparable to that of
the recent large appreciation episode of the Swiss Franc versus the Euro in 2015, which was documented
3and investigated by Auer et al. (2021). Therefore, in conjunction with high inﬂation, the unexpected sharp
depreciation of the USD versus the JPY following the Nixon Shock provides an ideal environment for
distinguishing between open-economy Calvo and menu cost models as suitable theoretical frameworks forevaluating the welfare cost of exchange rate ﬂuctuations.
Our quasi-natural experiments reveal the following three ﬁndings. First, the sharp USD depreciationin the USD-Flex regime has a statistically signiﬁcant currency misalignment eﬀect relative to the USDFix regime. On average, the item-level LOP deviation deteriorates and shifts toward the Okinawan realdepreciation by 10% to 12% in the USD-Flex regime. In contrast, one can see a relatively small eﬀectof the JPY-Com regime on the item-level LOP deviation compared to the USD-Fix regime. Second, theaverage absolute size of price changes remains almost constant at approximately 8% to 10% in Okinawa andthe mainland over the three currency regimes. Third, the average frequency of price changes in Okinawa
sharply increases over the sample period, whereas there is no clear upward trend in the average frequency
in the mainland. Furthermore, the average frequency of price ups increases with inﬂation in both Okinawa
and the mainland, whereas there is no robust relationship between the average frequency of price downs
and inﬂation.
These empirical ﬁndings strongly support the implications of the menu cost model as a sticky pricegenerator. To verify this inference, we calibrate small open-economy variants of the menu cost and Calvomodels. Our stochastic simulation exercises demonstrate that the calibrated menu cost model ﬁts all of
our empirical ﬁndings regarding the external and internal price dispersion better than the Calvo model.
Therefore, it is reasonable to infer that ﬁrms could pay a relatively small ﬁxed adjustment cost and neverallow their prices to drift far from the optimal levels. If this is the case, then the observed 10% to 12%
currency misalignment reﬂects the eﬃcient response of retail prices to sharp USD depreciation and does
not necessarily imply a signiﬁcant welfare loss.
In summary, the US military history in post-war Okinawa provides no solid empirical ground for
the NK argument of ineﬃcient internal and external price dispersion caused by price stickiness. When
we adopt the inference of Nakamura et al. (2018) as a reference, we can conclude that the welfare costsof exchange rate ﬂuctuations may be more elusive than those expected by the conventional open-economy
NK model with Calvo pricing technology.
The remainder of this paper is organized as follows. Section 2 discusses related literature. Section 3 reviews the post-war history of Okinawa to provide evidence for the foundation and validity of ourquasi-natural experiments. Section 4 presents the details and results of the empirical exercises. Section 5
introduces small open-economy NK models and discusses the results of our calibration exercises. Finally,
Section 6 concludes this paper.

2. Related literature
Past studies have focused on the eﬀects of currency regimes on international price dispersion (i.e.,
LOP violations) in disaggregated micro data on retail prices. Berka et al. (2018) discovered strong evidence
for the Balassa-Samuelson eﬀect in product-level real exchange rates among EU member countries adapting
ﬁxed exchange rates or common currency regimes instead of adopting ﬂexible exchange rates like othercountries. Their ﬁndings imply that a ﬁxed exchange rate or common currency regime that is immune to4volatile nominal exchange rate ﬂuctuations may yield more eﬃcient adjustments of real exchange rates tochanges in the relative prices between tradable and non-tradable goods.
Cavallo et al. (2014) claimed that a common currency regime has an empirically signiﬁcant eﬀect
on product-level real exchange rate adjustments. By exploiting online internet prices of identical goods
sold in various European countries by four large global retailers, they observed that the LOP holds in individual products among countries within the Eurozone. Simultaneously, the LOP is signiﬁcantly violated
among countries outside the Eurozone. Although Berka et al. (2012) also pointed out the same diﬀerencein the empirical relevance of the LOP in disaggregate retail prices between countries inside and outside theEurozone based on diﬀerent datasets of retail prices, Cavallo et al. (2014) revealed that the LOP is still signiﬁcantly violated among countries adopting ﬁxed exchange rate regimes. This observation is eye opening
because it suggests that the unit of currency is relevant to product-level real exchange rate adjustments.
An essential shortcoming of the past exercises described above is that they compared disaggregatedretail prices of identical goods between two countries that were either already in a common currency area
or a ﬁxed-exchange-rate regime. However, the resulting inferences may reﬂect time-invariant country-pairspeciﬁc ﬁxed eﬀects that are not necessarily related to any direct eﬀects of participating in a ﬁxed-exchangerate or common-currency regime. To make our inferences regarding currency regime eﬀects empiricallyplausible, we must conduct relevant quasi-natural experiments by constructing suitable treatment and control groups.1 To address this concern, Cavallo et al. (2015) compared the degrees of LOP deviation in retailprices of clothing goods sold by the world’s largest clothing retailer, namely ZARA, between Latvia andother Eurozone countries before and after the Latvian adoption of the Euro in 2014. They reported that the
distribution of the LOP deviation across a large number of clothing goods shrank to a mass point of zeroafter 2014. In contrast, because we investigated a much broader set of goods in our CPI construction, our
exercise should be robust to the concern that their inferences may reﬂect the speciﬁc international pricing
strategy of a single global retailer.
An important predecessor of our study is the study by Takagi et al. (2004), who investigated common currency eﬀects on real exchange rate volatilities by exploiting time series data on the aggregate CPIs
of Okinawa before and after the 1972 reversion. They scrutinized aggregate real exchange rate volatilities
under three distinct currency regimes. By using the CPI data on Japan, Okinawa, and the US, they calculated the time series variances of the Okinawan real exchange rates for both Japan and the US in each of thethree currency regimes. Interestingly, they observed that during the USD currency regime, the volatilityof the Okinawan real exchange rate was much lower in the US than in Japan. In contrast, during the JPY
currency regime, the Okinawan real exchange rate volatility was much smaller in Japan than in the US.
They interpreted their ﬁndings as solid evidence of a signiﬁcant common currency/monetary union eﬀect
on real exchange rate adjustments. Our study focuses at the micro data of retail prices, rather than aggregate
CPIs, unlike the study by Takagi et al. (2004). This diﬀerence in data is essential because we consider theintensive and extensive margins of retail price changes, which are necessary for measuring the welfare lossof price dispersion caused by price stickiness.
Few studies have scrutinized the sensitivity of price dispersion to a surge in inﬂation as a signif1

Gorodnichenko and Tesar (2009) also discussed the necessity of natural experiments for the identiﬁcation of any eﬀects
of cross-country borders on LOP deviation. Morshed (2007) conducted a DID regression exercise using historical data on
disaggregated relative prices before and after the independence of Bangladesh from Pakistan in 1971. Morshed concluded that
there are no robust border eﬀects related to the relative price structures of two countries.

5icant aggregate shock. The exception was Nakamura et al. (2018), who exploited US BLS micro databy analyzing microﬁlms dating back to the high inﬂation period of the late 1970s to identify the welfare
costs of inﬂation. They found that the frequency of price changes increases under high inﬂation, whereas
the average absolute size of price changes remains unchanged. They inferred that the welfare cost of inﬂation caused by price stickiness is elusive to the lens of the conventional NK model with Calvo pricing
technology.
Empirical literature on exchange rate pass-through focuses on the sensitivity of internal price dispersion to another well-identiﬁed aggregate shock in the form of exchange rate changes.2 For example,
Gopinath and Rigobon (2008) identiﬁed signiﬁcant price stickiness in the micro data of US import andexport prices between 1994 and 2005. In the same US import price dataset, Gopinath and Itskhoki (2010)
observed that the long-run exchange rate pass-through is positively related to the frequency of dock pricechanges, providing robust evidence for the menu cost model with variable markup. Nakamura and Zerom(2010) empirically investigated the role of menu costs in incomplete exchange rate pass-through by developing a structural oligopoly model with micro data on sales and prices in the coﬀee industry.3 Anotherbranch of pass-through research exploits large devaluation episodes as quasi-natural experiments and includes studies by Burstein et al. (2005), Alessandria et al. (2010), Gopinath and Neiman (2014), Cravino
and Levchenko (2017), and Auer et al. (2021). Our study is related to this research branch because we
scrutinize an epoch-marking post-war historical event in international ﬁnancial markets, namely the Nixon
Shock.
The main advantage of our study over previous studies is that our dataset is subject to two signiﬁcantaggregate shocks of high inﬂation and large depreciation, which are jointly used to estimate the degree ofineﬃciency of internal price dispersion and identify the underlying source of price stickiness. In particular,
as discussed by Flodén and Wilander (2006), the menu cost model with LCP implies that only under a highinﬂation environment will a large local currency depreciation yield disproportionally large price adjustments and pass-through to local retail prices.4 Therefore, our unique dataset on the Okinawa reversion in1972 has more signiﬁcant power to analyze the implications of the open-economy menu cost model withLCP.

3. Natural experimental environment: economic and monetary history of the
Ryukyu Islands and Okinawa around the 1972 reversion
This section brieﬂy reviews Okinawa’s economic and monetary history following the Paciﬁc War
and discusses the relevance of the quasi-natural experimental environment exploited in this study. Our
historical review focuses on the years from the landing of the US military forces in Okinawa near theend of the Paciﬁc War in April of 1945 to the reversion of Okinawa to Japanese sovereignty in May of1972. In particular, we emphasize four historical facts. First, the Okinawan separation from and reversion
to Japanese sovereignty were the direct consequences of both the end of the Paciﬁc War and subsequent
2

Burstein and Gopinath (2014) provided an excellent literature survey of exchange rate pass-through.
Early estimation exercises using menu costs in micro retail price data under strategic complementarities can be found in thepapers by Slade (1999) and Kano (2013).
4
Relatively few past studies have investigated state-dependent pricing models in open-economy environments. Other important predecessors are the studies by Midrigan (2007) and Landry (2009, 2010).
3

6

increase in the geopolitical importance of Okinawa for the US military. Second, even under US militaryoccupation, the Okinawan economy was highly integrated into the economy of mainland Japan. Third,
the US government’s political decision to attract foreign investment for the development of the Okinawan
economy was approximately neutral in the context of the relative price structure between Okinawa andmainland Japan. Fourth, the shift from the USD ﬁxed-exchange-rate regime to the USD ﬂexible regime
as a result of the Nixon shock in August of 1971 was an unanticipated dramatic structural change in theinternational monetary system, which was a pure exogenous event for the Okinawan economy.
3.1. Economic exogeneity of Okinawan separation and reversion
The US Navy, which was the primary military body of the Allied Forces in the Paciﬁc War, landed
in Okinawa on April 1, 1945. On the same day of the landing, it issued the ﬁrst proclamation that ordered
the establishment of the US Navy Military Government in the Ryukyu Islands.5 Until the 1972 reversion,
the Ryukyu Islands and Okinawa were eﬀectively under US military occupation.
The initial goal of the US military occupation and governance over the Ryukyu Islands was to createa group of small islands to act as a bridgehead to capture the Imperial Japanese Army at the end of the
Paciﬁc War. Although Japan’s unconditional surrender accomplished the initial goal of accepting the Potsdam Declaration on August 14, 1945, the US military government continued to occupy the Ryukyu Islands.
On one hand, the Combined Chiefs of Staﬀ (CCS) ﬁrmly recognized the strategic military value and geopolitical importance of the Ryukyu Islands. Therefore, they vehemently claimed the continuation of strategic
trusteeship by the US military government. On the other hand, the US Department of State argued that the
Ryukyu Islands should return to Japanese sovereignty following demilitarization. This political conﬂict
between the CCS and US State Department deferred the oﬃcial US decision on the territorial rights andthe corresponding administrative body of the Ryukyu Islands for several years. The Bank of Ryukyu (1984)
argues that this so-called "reservation policy” delayed and threatened the restoration and development policies of Okinawa following the Paciﬁc War. It was not until May 6, 1949, when US President Harry Truman
ﬁnally approved the long-term retention of the Ryukyu Islands by the US government,6 that the reservation
policy ended and the US government began a total commitment to the restoration policy of the Okinawan
economy.
In a Joint Statement from Japanese Prime Minister Eisaku Sato and US President Lyndon Johnson on
November 15, 1967, the future possibility of the reversion of the Ryukyu Islands and Okinawa to Japanesesovereignty was oﬃcially announced in both countries. At that time, the sentiment of the Ryukyuwan
people toward the US military government, which was called the US Civil Administration of the Ryukyu
Islands (USCAR), rapidly deteriorated as a result of a military land problem known as “Gunyochi Mondai.”
The USCAR forced land expropriation to construct US military bases around the Ryukyu Islands.7 The
military land problem gave rise to an intense resistance movement acorss the Ryukyu Islands, which was
known as “Shimagurumi Toso.” Anti-US sentiment had grown not only in the Ryukyu Islands, but also
in mainland Japan based on the nationwide protest movement against the 1960 revision of the US-Japan
Security Treaty (“Anpo Toso”). To repair and improve political relationships with Japan and strengthen
5

United States Navy Military Government Ryukyu Islands Proclamation No.1.
Report by the National Security Council on Recommendation with respect to US policy toward Japan (NSC13/3), May 6,
1949.
7
CA Ordinance No.109, “Land Acquisition Procedure.”
6

7

the Security Treaty, the US Department of State insisted on more concessions to Japan’s political andeconomic requests regarding the Ryukyu Islands. However, the US military force strictly opposed any
political concession by arguing that it may damage the strategic value of the US military bases in the
Ryukyu Islands and Okinawa. Furthermore, rapidly growing geopolitical tensions in East Asia, including
the intensiﬁcation of the Vietnam War and rise in power of Communist China, increased the strategic
importance of the Ryukyu Islands. Therefore, any possibility of Okinawa’s reversion required the Japanese
government to guarantee the USCAR unconstrained operations of its bases and facilities in Okinawa.
In June of 1966, the “Special Ryukyu Island Working Group,” which consisted of members fromthe US Department of State and US Department of Defense, conducted detailed research on all Ryukyu
Island problems and resolved the sharp conﬂicts of interest between the US Department of Security andUS military force. The working group then concluded that the US military government would enable the
US military bases in Okinawa to operate under the US-Japan Security Treaty, even if the US returned theadministrative rights of the Ryukyu Islands to Japanese sovereignty. This conclusion from the working
group softened the rigid attitude of the US military force against the reversion of Okinawa signiﬁcantly.
Simultaneously, while facing the intensiﬁcation of Okinawa reversion movements and a sharp deterioration in public sentiment toward Okinawa’s problems, the Japanese government also started recognizing
Okinawa’s reversion as a top political priority.
In the Sato and Johnson Joint Statement in 1967, the two countries agreed to continuous joint reviews of the status of the Ryukyu Islands with the goal of returning administrative rights over the islands
to Japan, but postponed making a consensus on and oﬃcially announcing a speciﬁc plan for the return ofadministrative rights over Okinawa to Japan. In a Joint Statement from Japanese Prime Minister Eisaku
Sato and US President Richard Nixon on November 21, 1969, the two countries oﬃcially agreed to reversion in 1972. Under the Okinawa Reversion Agreement, which the two countries signed on June 17,
1971, the administrative rights of the Ryukyu Islands and Okinawa would return to Japanese sovereignty
on May 15, 1972.8 The 1971 reversion agreement guaranteed many beneﬁts for the US government such ascontinuing to use military bases in Okinawa, maintaining and strengthening the political alliance between
the two countries, including the US-Japan Security Treaty, and cutting down the ﬁscal burden associatedwith the administration of the Ryukyu Islands.
The Japanese government also enjoyed signiﬁcant political beneﬁts from the reversion agreement,such as regaining sovereignty over the territory separated and occupied following the Paciﬁc War, calming
down of domestic political tension and anti-US sentiment, and maintaining the US-Japan Security Treaty.
Therefore, Japan and the US had solid political incentives for the Okinawa reversion in 1972. The Bankof Ryukyu (1984) emphasizes this historical event as an essential international political event that supported the alliance of the two countries in the US-Japan Security Treaty, regardless of the political will andintention of Okinawa.
The historical fact that the territorial and economic separation of the Ryukyu Islands and Okinawa
from mainland Japan happened exogenously for the Okinawan economy is crucial for our natural experiment exercise. It was a pure outcome of the end of the Paciﬁc War and the US government’s subsequent
political and strategic decisions. Furthermore, it is also crucial to recognize that the Ryukyu Islands andOkinawa returned to Japanese sovereignty concurrently with the withdrawal of US troops from the Viet8

The Okinawa Reversion Agreement was signed oﬃcially under the “Agreement between Japan and the United States ofAmerica concerning the Ryukyu Islands and the Daito Islands.”

8

nam War under the initiative of President Nixon. The Okinawa reversion resulted from a highly politicaldecision by the US government, which fully understood the strategic and geopolitical importance of thesesmall southern islands. Therefore, the US military history in the Ryukyu Islands and Okinawa following
the Paciﬁc War supports our construction of a treatment group that is exogenous for the Okinawan relative
price structure. This fact strongly implies that inferences drawn from our natural experiments should be
immune to potential bias caused by endogeneity of the treatment group.
3.2. Economic integration of Okinawa and mainland Japan
We conﬁrm that the real sides of the Okinawan and mainland economies were integrated to a great
degree, even under US military occupation. In short, the Okinawan economy during the occupation period
is well characterized as a “military-base-dependent import-oriented economy.” At the end of the PaciﬁcWar, the Battle of Okinawa destroyed most of its production capacity. As a result, Okinawa has always
suﬀered from high inﬂation pressure stemming from severe supply shortages. In particular, the construction
boom of US military bases that emerged between 1950 and 1952 following the US decision to retain the
Ryukyu Islands in the long term and the resulting end of the reservation policy in May of 1949 worsened
the supply shortage problem around the Ryukyu Islands. Furthermore, because the USCAR needed toraise wages for workers in the military bases drastically to attract labor forces for base construction, a sharp
increase in labor wages accelerated inﬂation further.
In response to the inﬂation pressure, the USCAR decided to set a ﬁxed exchange rate for the legal
tender B-Yen to 120 B-Yen per USD by issuing Ordinance No. 6, “Military Conversion Rate of Type BYen in the Ryukyu Islands” on April 12, 1950.9 It is easy for us to understand how drastically the B-Yen
was overvalued relative to the JPY when we consider that the ﬁxed exchange rate of the JPY against the
USD was 360 JPY/USD in 1950. This policy-induced overvaluation of the B-Yen relative to the JPY andresulting cheaper import prices made it possible for the Ryukyu Islands and Okinawa to import tradable
goods from mainland Japan and resolve the supply shortage problem.10
The privatization and liberalization of international trade, which was oﬃcially allowed by Military
Government Ordinance No. 26, “Foreign Exchange and Trade Procedure in the Ryukyu Islands,” on October 20, 1950, further fortiﬁed the Okinawan import dependence on mainland Japan. As a result, theimports of the Ryukyu Islands in 1958 were seven times larger than those in 1951. The import dependencyof the Ryukyu Islands on mainland Japan was readily apparent. Its import-to-RGDP ratio was 65.5% andapproximately 72% of the total imports were from mainland Japan. Therefore, the Ryukyu Islands and Okinawa had a tight economic linkage with mainland Japan. The Bank of Ryukyu (1984, p. 1082) provides
the following statement:“[I]n other words, ... the Okinawan economy was included in the mainland economy. It is
9

The USCAR introduced B-Yen (oﬃcially called B-type military scrip) as a unique legal tender in the Ryukyu Islands
under Special Proclamation No. 29 “Conversion and Issuance of New Currency” on June 26, 1948 (i.e., the fourth currency
conversion). For a detailed investigation of the economic rationale behind the devaluation of B-Yen in 1950, see the monographby Makino (1993).
10
Because the primary exportable goods of the Ryukyu Islands were commodity goods of sugar, pineapple, and iron scrap, theRyukyu Islands had always recorded huge trade deﬁcits versus Japan. The US military budget for military bases and ﬁnancial
and economic aid from the US government through the Government and Relief in Occupied Areas Program ﬁnanced these tradedeﬁcits.

9

natural that the relative price structure of Okinawa, whose import dependency ratio was close
to 70% to 80% on imports from the mainland, was directly aﬀected by the relative price structure of the mainland. Furthermore, labor wages were determined by the supply and demandconditions of the labor market of Okinawa as a local component of the entire labor market ofthe mainland. Indeed, labor migration between Okinawa and the mainland was substantial.
The real side of the Okinawan economy was highly integrated with the mainland economy."
Furthermore, in the introduction of his analysis of aggregate price movements in Okinawa following the1972 reversion, Tanaka (1980) argued the following:“[B]efore the reversion, the Okinawan economy relied heavily on imports and exports, whichplaced enormous weight on mainland Japan. This fundamental characteristic of the Okinawan
economy did not change, even after the reversion. When investigating aggregate price movements and their fundamental drivers in Okinawa, by carefully recognizing the high dependenceof the Okinawan economy on the mainland, we can presume that there would be no signiﬁcantdiﬀerence in aggregate price dynamics between Okinawa and the mainland. The two regions
shared common factors driving aggregate prices.”
Tanaka ’s (1980) argument implies that during the sample period of our study, Okinawa and the mainland
shared a common tendency in their aggregate price movements. Figure 2 plots the CPI in Naha as a blueline and the CPI of the mainland as a red line between January of 1970 and December of 1974. In particular,
Naha’s CPI is in terms of JPY. Before the Nixon shock in August of 1971, the two lines move in tandem andare closely joined. Although Naha’s CPI begins declining following the Nixon shock as a result of a sharp
depreciation of the USD relative to the JPY, the two lines return to a common trend after the reversion in
May of 1972. Therefore, our analysis satisﬁes the common trend assumption for a valid DID regression
exercise on average retail price movements.
3.3. The USD regime following the ﬁfth currency conversion
This subsection discusses why the USD regime was established in the Ryukyu Islands and Okinawa.
We demonstrate that strategic and political decisions by the USCAR led to a ﬁfth currency conversion to
the USD regime, which was completely unrelated to the relative price structures of both the Ryukyu Islands
and mainland Japan.
The USD was adopted as the unique legal tender of the Ryukyu Islands according to the High Commissioner Ordinance No. 14 “Currency” on September 15, 1958. This ﬁfth currency conversion forced
B-yen conversion to USD at a rate of 120 B-Yen per USD. The fundamental characteristic of the fourth
currency regime with the B-yen was a currency board system that accumulated USD as an oﬃcial reserve
asset. Therefore, the supply of B-yen was backed by the USD reserve one-for-one. This currency board
system meant that when the USD reserve was accumulated (decumulated) by the current account surplus(deﬁcit), the money supply in the Ryukyu Islands and Okinawa automatically increased (decreased). In
other words, we can recognize the B-Yen currency regime as the “USD exchange standard” system. The
USD regime established on September 15, 1958 shares the same essential characteristics as the B-Yen
regime. In other words, an increase (decrease) in the USD reserve as a result of the current account surplus(deﬁcit) expanded (shrank) the money supply because the Ryukyu Islands and Okinawa had no right toissue the USD.
10

A natural question based on these ﬁnds is why did the USCAR decide to adopt the USD regime
through a ﬁfth currency conversion, even though the two currency regimes with the B-Yen and USD shared
the same fundamental characteristics as a currency board system? The Bank of Ryukyu (1984) insisted thatthe fundamental reason behind the ﬁfth currency conversion is that the USCAR wished to liberalize the
Okinawan economy and promote regional economic development by attracting foreign direct investment
under the USD currency regime.
The USCAR attempted to manage anti-US movements by improving the economic welfare of the
Ryukyu Islands and Okinawa by promoting economic development. The Republican administration under
US President Dwight Eisenhower sought ﬁscal consolidation. This ﬁscal contraction policy and the resulting shrinkage of the military budget made it diﬃcult for the USCAR to ﬁnance economic development
policies in Okinawa. In other words, the “military-base-dependent import-oriented economy” that emergedat the beginning of the B-Yen currency regime almost failed by 1955.
In this scenario, the USCAR attempted to attract foreign direct investment as the primary source ofeconomic development by liberalizing international transactions of capital, trade, and foreign currencies in
the Ryukyu Islands. Furthermore, as an international vehicle currency with high international liquidity, theUSD had a higher practical value than the B-Yen, which was a local currency without general acceptability
in international settlements. Therefore, the USCAR considered the USD currency regime as one of thenecessary conditions for attracting foreign capital.
Therefore, the USD regime emerged from a’ highly political decision by the USCAR, which was
unrelated to the relative price structures of the Ryukyu Islands and mainland Japan.
3.4. Exogeneity of the Nixon Shock to the Okinawan economy
The Nixon Shock was a series of emergency economic policies that US President Richard Nixon
publicly announced on August 15, 1971. Under the title of “The Challenge of Peace,” President Nixon
implemented three policy measures: (i) suspending the USD’s convertibility to gold, (ii) freezing wages
and prices for 90 days, and (iii) imposing an import surcharge of 10% to ﬁx a conﬁdence problem in the
USD and reduce US unemployment and inﬂation rates. As a result, the Nixon Shock had an unprecedented
impact on international ﬁnancial markets.
The Bretton Woods system characterized the international monetary order as a “gold exchange standard” in which the USD was backed by gold at a ﬁxed conversion rate of 35 USD per ounce of gold. Allother foreign currencies were ﬁxed relative to the USD. Therefore, the suspension of backing the USD withgold allowed the conversion rate of the USD to gold to ﬂoat. The 10% import surcharge meant abandoning
a ﬁxed exchange rate system by implicitly devaluating the USD relative to all other currencies. Therefore,
the Nixon Shock ended the Bretton Woods system. Following the Nixon Shock, the major western countries temporarily closed their foreign exchange markets and began ﬂoating their exchange rates. Japan also
shifted to a managed ﬂoating system by August 28, 1971 and began revaluating JPY from the oﬃcial rateof 360 JPY/USD. On December 20, 1971, the Smithsonian Agreement revalued JPY up to an oﬃcial rate11

of 308 JPY/USD.11
The primary factors underlying the Nixon shock are summarized below. After 1958, the US balanceof payment continuously recorded a large deﬁcit as a result of the rapid economic recovery of West Germany
and Japan from the ruin following WWII and the generous amount of US oﬃcial development assistanceprograms for foreign countries to maintain the Western alliance. Furthermore, the US balance of payment
further deteriorated as a result of ﬁscal deﬁcits and the resulting high inﬂation pressure caused by a sharp
increase in military spending as a result of US military intervention in the Vietnam War in 1965.
The US balance of payment deﬁcit resulted in an excess supply of USD relative to the world economy. This excess liquidity of the USD then caused a fundamental credibility problem in the gold exchange
standard under the Bretton Woods system.12 Furthermore, in the 1970s, the US economy suﬀered fromthe “stagﬂation” problem with high inﬂation and unemployment simultaneously. Therefore, the US government prioritized macroeconomic policy autonomy for the domestic economy through the Nixon Shock,which meant abandoning international commitment to the ﬁxed-exchange-rate system.13
The Nixon Shock was the direct result of policy decisions of the US to handle the internal andexternal imbalances that the US economy suﬀered and to correct the institutional limitations imposed by
the Bretton Woods system. Therefore, it is apparent that the Nixon shock was an exogenous unanticipatedhistorical event for the small island economy of the Ryukyu Islands and Okinawa. On the day of the
Okinawa reversion on May 15, 1972, all USD circulated in the Ryukyu Islands were converted into JPY
at the oﬃcial rate of 305 JPY/USD (i.e., the sixth currency conversion). We recognize the unanticipatedexogenous transition in the currency regime in Okinawa from the USD ﬁxed regime to the USD ﬂexible
regime to the JPY common currency regime as an ideal environment for a quasi-natural experiment to
identify the eﬀects of currency regimes on ineﬃcient internal and external price dispersion.14
11

More precisely, the international monetary system returned to a ﬁxed-exchange-rate system through the Smithsonian agreement, even though it admitted intermittent devaluations of the USD. Even under the Smithsonian regime, massive speculative
attacks on the USD did not stop. As a result, advanced economies adopted ﬂoating exchange rates. After Japan began ﬂoating
JPY against major currencies in February of 1973, the Smithsonian regime ﬁnally collapsed.
12
As a result of the US balance of payment deﬁcit, other foreign countries with balance of payment surpluses accumulated a
massive amount of USD reserves. Once the USD reserves in foreign countries became much larger than the gold reserves heldby the US Fed, the USD lost its credibility because it would be impossible for all foreign USD reserves to be converted into
gold at the oﬃcial conversion rate. In contrast, if the US balance of payment had turned into a surplus, a severe shortage of the
USD as an international settlement currency would have emerged and would have stiﬂed the growth of the world economy. This
inevitable destiny of an international vehicle currency, which is well known as “Triﬃn’s dilemma” (named after Robert Triﬃn),
ﬁnally materialized in the form of the Nixon Shock.
13
According to the thesis of the “open-economy trilemma,” US policymakers allowed the USD nominal exchange rates toadjust ﬂexibly by shifting to a ﬂoating-exchange-rate regime, which regained monetary policy autonomy and maintained thefreedom of international capital ﬂow.
14
The unexpected shift to the USD ﬂexible regime and resulting sharp devaluation of the USD heavily damaged the Ryukyu
Islands economy. In particular, it caused social anxiety and uncertainty as a result of an expected decline in the amount of
currency received after the planned currency conversion from the USD to the JPY on the day of reversion. Political negotiations
between the government of the Ryukyu Islands and the Japanese government regarding the oﬃcial conversion rate applied tothe sixth currency conversion on the reversion day found it extremely diﬃcult to reach a ﬁnal agreement. On October 18, 1971,
the Japanese government oﬃcially announced the establishment of a special beneﬁt program related to currency conversion tocompensate for pecuniary losses caused by an expected revaluation of JPY from the oﬃcial conversion rate of 360 JPY/USD
under the Bretton Woods system (Tsuuka Tou Kirikae Taisaku Tokubetu Kyuhukin). Because special compensation beneﬁts
would be provided to the residents of the Ryukyu Islands following the reversion, the Government of the Ryukyu Islands, onbehalf of the Japanese government, implemented currency conﬁrmation for USD assets across the Ryukyu Islands and Okinawa

124. Empirical results
4.1. Data description and construction
In this study, we investigated monthly retail price data surveyed at selected retail stores in the capitalcities of the 47 prefectures in Japan, including Naha, which was under US military occupation. The sample
period spans ﬁve years between January of 1970 and December of 1974. The data for the 46 prefecturesin the mainland came from a retail price survey (hereafter referred to as the “mainland survey”) conductedby the statistics bureau of the oﬃce of the prime minister.15 However, the mainland survey only contains
data for Naha for the period after June of 1972. Fortunately, for the periods before May of 1972, theStatistics Agency of the Government of the Ryukyu Islands, which was the administrative body of the
USCAR, conducted a retail price survey for Naha (hereafter referred to as the “Okinawa survey”).16 Most
importantly, the Okinawa survey covered most of the same survey items as the mainland survey. This detailof the Okinawa survey makes it possible for us to conduct a DID exercise by identifying equivalent goods
and services and comparing retail prices between Okinawa and the other mainland capital cities during theentire sample period. It is noteworthy that the Okinawa survey reports retail prices in terms of the USD
before May of 1972 and in terms of the JPY after June of 1972. To measure item-level LOP deviations,
we use the JPY/USD market rate (monthly average) to convert USD prices into JPY prices in Naha before
May of 1972.17
There are three main reasons for choosing a sample period from January of 1970 to December of1974. First, the Okinawa statistical yearbook for each year before 1969 reports product categories and items
that are too coarse to make suﬃciently precise matches with mainland counterparts and construct item-level
LOP deviations precisely. Second, if we choose a more extended sample period beyond 1974, time series
variations in item-level LOP deviations most likely reﬂect the eﬀects of changes in the currency regime
and any other structural changes in the economic environment between Okinawa and mainland Japan.18
As a result, this study’s inferences regarding the JPY common currency eﬀect could have been biased or
misleading. Therefore, we limit our attention to a shorter time series sample neighboring the shifts in the
Okinawan currency regime to guarantee that other economic aspects in Okinawa and the mainland will notchange. We then empirically infer any discontinuous changes in the shapes of the cross-item distributions of
LOP deviations between Okinawa and the mainland. Finally, this sample period involves the three diﬀerent
currency regimes experienced by the Ryukyu Islands and Okinawa. Therefore, even with a relatively shortsample period, our data contain rich variations in the currency regime of Okinawa that can be used to
identify the eﬀects of exchange rate ﬂuctuations on ineﬃcient internal and external price dispersion.
This study investigates the retail prices of 178 goods and services included in both the Okinawa
and mainland surveys. The items cover a broad range of goods and services required for daily life inrepresentative households in the two regions. First, we distinguish fresh food items (31) from other items(147). Fresh food items have high price ﬂexibility. The average frequency of price changes over the three
on October 9, 1971. For the currency conﬁrmation exercise for USD assets, see the studies by Karube (2012) and Kabira (2015)
for additional details.
15“Retail Price Survey,” Bureau of Statistics, Oﬃce of the Prime Minister of Japan.
16“Retail Price Survey,” Agency of Statistics, Planning Department, Government of the Ryukyu Islands.
17
We use the monthly JPY/USD exchange rate data distributed by the FRED at the Federal Reserve Bank of St. Louis.
18
Crucial structural changes for our exercise include lowering transport costs between Okinawa and the mainland throughimprovements in transport technology.

13

currency regimes is approximately 80%. Furthermore, most of the fresh foods in Okinawa were local
products produced and distributed only within the region, meaning they can be considered as non-tradable
goods. Therefore, the retail prices of fresh food items are not informative for identifying ineﬃcient internaland external price dispersion.
The other 147 items include processed foods, housing, furniture, household utensils, clothes, footwear,
medical care, fuel, light and water charges, transportation, communication, education, culture, recreation,and other services. These items have two notable characteristics. The ﬁrst characteristic is a high degreeof price stickiness. The average frequency of price changes over the three currency regimes is approximately 20%. Thus, these items could be the primary reason for ineﬃcient price dispersion. The second
characteristic is that 91 out of the 147 items were produced in mainland prefectures and delivered to Okinawa. The Okinawa survey reports the retail prices of these 91 items together with either brand names oflarge mainland manufacturers or simply notes of mainland products. Therefore, we identify these 91 items
as tradable goods. In contrast, the other 40 items were locally produced and delivered within Okinawa.
Because these “island” items are unlikely to be exported to the mainland, we identify these 40 items as
non-tradable goods and services. We identiﬁed the remaining 16 items as non-fresh products that were imported from the US mainland. Based on these characteristics, we mainly focus on the retail price behaviorof 147 non-fresh-food items.
Data on item-level LOP deviations were constructed as follows. Let pj,c (t) denote the natural logarithm of the retail price of item j(= 1, 2, · · · , 178) in city c(= 1, 2, · · · , 47) in period t(= 1, 2, · · · , 60) in
terms of the JPY. For Okinawa, we converted the USD prices before the reversion into JPY prices using the
JPY/USD spot rate. Let qj,c,s (t) denote the logarithm of the item-level LOP deviation of item j in period t
between distinct cities c and s(̸= c). Then, qj,c,s (t) is deﬁned as
qj,c,s (t) ≡ pj,c (t) − pj,s (t).
From each qj,c,s (t), we extract a time-invariant city pair ﬁxed eﬀect over the three currency regimes.
For this purpose, we calculate the time series average of qj,c,s (t) for city pairs (c, s) and j as q̄j,c,s ≡∑T −1 Tt=1 qj,c,s (t). Then, we subtract q̄j,c,s from qj,c,s (t) to construct our sample of item-level LOP deviations q̂j,c,s (t) ≡ qj,c,s (t) − q̄j,c,s .
For item j in city c under currency regime r(= USD-Fix, USD-Flex, JPY-Com), we construct afrequency of price changes denoted as Freqj,c (r) by dividing the number of price changes by the numberof periods within currency regime r. Similarly, we construct the average absolute size of price changes
conditional on price revision, which is denoted as avPCj,c (r), by calculating the average of the absolute
size of price changes conditional on price revision within currency regime r.
4.2. Currency misalignment: item-level LOP deviations
Tables 2(a) and 2(b) report descriptive statistics for the item-level LOP deviations q̂j,c,s (t) over all
178 items. Tables 2(a) and 2(b) correspond to city pairs including Naha as the s city (hereafter referred toas “Okinawa pairs”) and those not including Naha (hereafter referred to as “mainland pairs”), respectively,
and display the sample size, mean, and standard deviation (S.D.) for the three currency regimes. Thesetables reveal the following four facts. First, regardless of the currency regime, the mean and S.D. of the
Okinawa-pair data are more prominent in terms of absolute values than those of the mainland pair counter14

parts. Therefore, the Okinawa-pair distribution is subject to a positive ﬁxed eﬀect with heteroskedasticity.
Second, the Okinawa-pair distribution shifts its position to the right under the USD-Flex regime. Thisﬁnding is conﬁrmed by the fact that the mean and S.D. of the Okinawa-pair data are the largest and thesmallest, respectively, in the USD-Flex regime. Because we constructed the Okinawa-pair data by subtracting Okinawa prices from mainland prices, this fact also implies that on average, Okinawa’s goods andservices became cheaper during the USD-Flex regime compared to the mainland. The USD depreciatedrelative to the JPY during the USD-Flex period. This nominal depreciation led to the real depreciation of
the Okinawa currency, which is consistent with Mussa’s (1986) observations.
Third, the mean of the Okinawa-pair data under the JPY-Com regime is slightly negative. This
indicates that on average, Okinawa’s goods and services became more expensive during the JPY-Com
regime compared to the mainland. It is worth noting that this appreciation in Okinawa during the JPYCom regime did not stem from any eﬀects of the JPY common currency regime. Instead, it resulted from afaster rise in the inﬂation rate in Okinawa compared to the mainland around the end of the sample period,
as shown in Figure 1 and Table 1. Finally, as the fourth fact, contrary to the Okinawa-pair data, there areno signiﬁcant changes in the mainland-pair distribution over the three currency regimes. This guarantees
that our exercise is free from placebo eﬀects. A shift in the nominal currency regime should not matter forthe mainland distribution of the LOP deviation, which was not exposed to a currency regime change.
To reconﬁrm the second, third, and fourth facts, Figure 3 plots the kernel-smoothed densities of theitem-level LOP deviations for all items.19 In particular, Figures 3(a) and 3(b) correspond to the Okinawa
and mainland pairs, respectively. In each ﬁgure, the solid black line plots the distribution under the USDFix regime, the dashed blue line plots the distribution under the USD-Flex regime, and the dash-dotted redline plots the distribution under the JPY-Com regime.
Regarding the right shift of the distribution of the Okinawa-pair data under the USD-Flex regime,
Figure 3(a) reveals that the USD-Flex regime generates a signiﬁcant right shift of the distribution comparedto the USD-Fix regime. However, the empirical plausibility of the negative eﬀect of the JPY-Com regime
on the Okinawa-pair distribution seems unclear because the shape of the solid black line is indistinguishable
from that of the dash-dotted red line. Finally, no signiﬁcant changes in the mainland-pair distribution over
the three currency regimes are apparent in Figure 3(b).
It is important to determine the origin of the signiﬁcant right shift of the distribution of the LOP
deviation in the USD-Flex regime. If the implied deterioration of the LOP deviation stems from pricestickiness in the local currency, we should observe the same right distributional shift of the LOP deviation
for the survey items with a higher degree of price stickiness. Therefore, we split all items into fresh fooditems with high price ﬂexibility and non-fresh items with high price stickiness.20
Tables 2(c) and 2(d) report descriptive statistics for the LOP deviations of the fresh food items for
the Okinawa and mainland pairs, respectively. Similarly, Tables 2(e) and 2(f) report descriptive statistics
for the LOP deviations of the non-fresh items for the Okinawa and mainland pairs, respectively. Fromthese tables, we can derive at least two clear results. First, for both fresh and non-fresh items, there are no
signiﬁcant changes in the distribution of LOP deviations over the three currency regimes in the mainland
19

We used the Gaussian kernel for kernel smoothing.
The average frequencies of price changes of the fresh foods items over the entire sample period are 80.3% and 83.4% for
the Okinawa and mainland data, respectively, whereas those of the non-fresh items are 25.6% and 20.0%, respectively.
20

15

pairs. Second, Table 2(e) reveals that the Okinawa-pair distribution of LOP deviations shifts to the rightunder the USD-Flex regime for the non-fresh items. The mean LOP deviation has a maximum value of
0.132 in the USD-Flex regime (0.006 in the USD-Fix regime and -0.043 in the JPY-Com regime). We
can conﬁrm this ﬁnding graphically in Figures 3(a) and 3(b), which plot the kernel-smoothed densities of
the item-level LOP deviations for the non-fresh items for the Okinawa and mainland pairs, respectively.
As indicated by the dashed blue line in Figure 3(a), the Okinawa-pair distribution shifts to the right under
the USD-Flex regime. There are no changes in the shape of the mainland pair distribution over the threecurrency regimes, as shown in Figure 3(b).
In summary, based on visual comparisons of the distributions of LOP deviations, we can infer thatprice stickiness leads to currency misalignments in the form of ineﬃcient external price dispersion caused
by ﬂexible exchange rates. However, we found no robust evidence that adopting the JPY common currency
aﬀected the distribution of item-level LOP deviations. We conﬁrm these inferences by conducting formal
econometric analysis with DID regression below.
To explain the econometric model used in our DID regression analysis, we introduce several dummy
variables. Let DOkinawa
denote the dummy variable for the Okinawa-pair data such that for the 47 prefecturalc,scapital cities indexed by c and 46 prefectural capital cities (excluding Naha) indexed by s(= 1, 2, · · · , 46),
DOkinawa
takes a value of one if c = Naha and a value of zero otherwise.
c,s{
1 if c = Naha,
DOkinawa=c,s0 otherwise.
Next, we deﬁne a dummy variable for the USD-Flex regime DFlex (t) that takes a value of one when the time
subscript t indicates a period between September of 1971 and May of 1972, and value of zero otherwise.
Similarly, DCom (t) denotes the dummy variable for the JPY-Com regime, which takes a value of one when
the time subscript t indicates a period between June of 1972 and December of 1974, and a value of zerootherwise.
{
1 if t = September 1971, ..., May 1972,
DFlex (t) =0 otherwise{
1 if t = June 1972, ..., December 1974,
DCom (t) =0 otherwise
By letting αj and uj,c,s (t) denote an item-speciﬁc ﬁxed eﬀect and an i.i.d. disturbance, respectively, weconstruct the following econometric model of the item-level LOP deviation q̂j,c,s (t):+ β1 DFlex (t) + β2 DCom (t)q̂j,c,s (t) = αj + β0 DOkinawac,s+ γ0 DOkinawa∗ DFlex (t) + γ1 DOkinawa∗ DCom (t) + uj,c,s (t). (1)c,sc,sIn the DID regression above (1), we intend for the coeﬃcients γ0 and γ1 to capture the average treatmenteﬀects of adopting the USD-Flex and JPY-Com regimes, respectively, on the item-level LOP deviation in
the Okinawa pair data relative to the USD-Fix regime. Our review of the post-war Okinawan history in
Section 3 provides narrative evidence that serves as a valid instrument. There are unlikely endogeneity
problems that cause correlations between the dummy variables DFlex (t) or DCom (t) and the disturbance16

term uj,c,s (t).
Table 3 summarizes the results of our DID analysis. We estimated the econometric model (1) using OLS. To consider the apparent heteroskedasticity in the Okinawa pair data, we calculated White’sheteroskedasticity-robust standard errors. The point estimates and standard errors reported below are provided in percentage terms for expositional purposes.
The second column, which is labelled as "Pooled," represents the point estimates and standard errorsof the coeﬃcients in Eq. (1) for all items. The estimated average treatment eﬀect of the USD-Flex regimeis 9.943%, which has statistical signiﬁcance. Therefore, the average size of the currency misalignment
caused by the sudden, sharp depreciation of the USD following the Nixon shock is approximately 10%
over the pooled sample period. The estimated average treatment eﬀect of the JPY-Com regime is -7.104%,
which has statistical signiﬁcance, which suggests that the JPY-Com regime worsens the LOP deviations
relative to the USD-Fix regime. An important caveat is that the negative average treatment eﬀect of the
JPY-Com regime does not necessarily reﬂect ineﬃcient currency misalignment caused by price stickiness.
The third column, which is labelled as "Fresh Foods," corresponds to the results for the fresh food itemswith high price ﬂexibility. The estimated average treatment eﬀect of the JPY-Com regime is more negativeat -18.646%. Therefore, the price stickiness in local currency cannot be a primary reason for the 7% realappreciation of the Okinawa currency in the JPY-Com regime observed in the pooled sample period.
Next, we investigate if currency misalignment caused by the USD-Flex regime reﬂects ineﬃcient
external price dispersion caused by price stickiness. The fourth column, which is labelled as “Non-fresh,”presents the results for the non-fresh items, which have high degrees of price stickiness in local currency, toresolve this fundamental issue. The estimated average treatment eﬀect of the USD-Flex regime signiﬁcantly
increases to 12.457% in this subsample. Therefore, it is plausible to infer that the observed currency
misalignments under the USD-Flex regime stem from ineﬃcient local currency price stickiness.
Table 3 further breaks down the non-fresh items into two informative categories. The ﬁrst is nonfresh items produced in the mainland and is labelled as “Mainland.” The crucial property of this category isthat most items were produced by large mainland ﬁrms and exported to Okinawa. Therefore, this subsample provides an ideal empirical basis for evaluating open-economy NK models in which monopolisticallycompetitive ﬁrms export their products to foreign countries following sticky local currency pricing withthe menu cost or Calvo technology.
The second category, which is labelled as “Okinawa,” includes non-fresh items produced in Okinawa
for the Naha samples. Because the Okinawa local producers only distributed their products to the Okinawa
market, the three currency regimes are irrelevant to the retail prices of these island items in the local
currency. This characteristic of the second category of non-fresh items leads to two hypotheses. First, theaverage LOP deviation in the second category is worse than that in the ﬁrst category under the USD-Flex
regime because we expect little pass-through of exchange rate ﬂuctuations into local currency retail prices.
Second, the degrees of the LOP deviations of the items in the second category are identical under the
USD-Fix and JPY-Com regimes with no exchange rate ﬂuctuation.
The sixth and seventh columns in Table 3 correspond to these subsamples. The Mainland subsample
yields approximately the same results as the non-fresh subsample, where the estimated average treatmenteﬀects of the USD-Flex and JPY-Com regimes are 11.200% and -5.705%, respectively. In contrast, the Okinawa subsample exhibits a more signiﬁcant average treatment eﬀect of the USD-Flex regime of 15.236%,
17but no signiﬁcant average treatment eﬀect of the JPY-Com regime (0.361%). Therefore, the Okinawa subsample indicates the empirical plausibility of the two hypotheses presented above.
Our DID analysis indicates that the USD depreciation relative to the JPY following the Nixon Shockgenerated an approximately 12% deterioration of the ineﬃcient external price dispersion caused by pricestickiness. However, we found no clear evidence that the JPY common currency improved ineﬃcient
external price dispersion.
4.3. Ineﬃcient internal price dispersion
Table 4 summarizes the descriptive statistics of the average absolute sizes of price changes conditional on price revisions. Tables 4(a) and 4(b) report the sample numbers, mean, and S.D. values of theaverage absolute sizes of price changes for the Okinawa and mainland data for all items. Tables 4(c) and4(d) report the same values for the Okinawa and mainland data for the fresh food items. Tables 4(e) and 4(f)report the same values for the Okinawa and mainland data for the non-fresh items. These descriptive statistics reveal that the average absolute sizes of price changes are approximately ﬂat across the three currency
regimes. For example, for the pooled sample of the Okinawa data in Table 4(a), the cross-sectional meansof the average absolute sizes of price changes are 16.9%, 14.4%, and 12.1% for the USD-Fix, USD-Flex,
and JPY-Com regimes, respectively, and the diﬀerences between them are negligible. The SDs also do notappear to exhibit any particular correlation patterns with the currency regimes.
It is noteworthy that as shown in Table 4(e), the cross-sectional means of the average absolute sizes of
price changes in the mainland non-fresh items exhibit values of approximately 8% across all three currency
regimes. Most importantly, these values are very close to the estimate of 8% for the US sample between
1978 and 2014 reported by Nakamura et al. (2018).21 This ﬁnding indicates that the argument of theelusive cost of inﬂation by Nakamura et al. (2018) could also apply to the Japanese mainland data fromthe early 1970s. Even with high inﬂation, there is no solid evidence for crucial ineﬃcient internal pricedispersion in mainland Japan. With this inference regarding the welfare cost of inﬂation robustly drawn
for two countries as the reference, we can econometrically infer how signiﬁcantly the diﬀerent currency
regimes aﬀected ineﬃcient internal price dispersion in Okinawa by conducting DID regression analysis.
Formal econometric analysis using DID regression can conﬁrm this inference. To explain the econometric model in our DID regression analysis, we introduce several dummy variables as follows. Let DOkinawacdenote the dummy variable for the Okinawa data such that for the 47 prefectural capital cities indexed byc, DOkinawa
takes a value of one if c = Naha and a value of zero otherwise.
c{
1 if c = Naha,
DOkinawa=c0 otherwise
Next, we deﬁne the dummy variable for the USD-Flex regime DFlex (r) such that for the three currency
regimes, it takes a value of one when the regime subscript r indicates the USD-Flex regime and a value ofzero otherwise. Similarly, DCom (r) denotes the dummy variable for the JPY-Com regime, which takes a21

Gopinath and Itskhoki (2010) also reported a median absolute size of price changes ranging from 6% to 7% in US importprice data between 1994 and 2005.

18

value of one when the regime subscript r indicates the JPY-Com regime and a value of zero otherwise.
{{
1 if r = USD-Flex,
1 if r = JPY-Com,
DFlex (r) =and DCom (r) =0 otherwise
0 otherwise.
By letting αj and uj,c (r) denote an item-speciﬁc ﬁxed eﬀect and an i.i.d. disturbance, respectively, we canconstruct the following econometric model of the average absolute size of price changes avPCj,c (r):avPCj,c (r) = αj + β0 DOkinawa+ β1 DFlex (r) + β2 DCom (r)c∗ DCom (r) + uj,c (r). (2)∗ DFlex (r) + γ1 DOkinawa+ γ0 DOkinawacc
We estimate the value of Eq. (2) using OLS with item-speciﬁc ﬁxed eﬀects. To consider item- andprefectural-speciﬁc heteroskedasticity, we calculate White’s heteroskedasticity-robust standard errors.
Table 5 reports the results of DID regression analysis for the average absolute size of prices changes.
It is noteworthy that except for two estimates, all estimates of the average treatment eﬀects are not statistically signiﬁcant at any conventional signiﬁcance levels. The ﬁrst and second exceptions are in the averagetreatment eﬀects of the USD-Flex regime on the Non-fresh and Mainland items. Their point estimates areboth 0.025 with standard errors of 0.011 and 0.013, respectively. Therefore, we can infer that the sudden
sharp USD depreciation relative to the JPY following the Nixon Shock slightly increased the ineﬃcientinternal price dispersion by at most 2.5% relative to the USD-Fix regime. As reported in the last column
in Table 5, we can infer no signiﬁcant eﬀects of currency regime changes on the ineﬃcient internal pricedispersion of locally produced Okinawa items, even with a high degree of price stickiness.
Nakamura et al. (2018) pointed out that the frequency of price changes is a compensatory factor. If
inﬂation rises, but the size of the price changes does not, then the price change frequency must be adjusted.
Similarly, if the exchange rate ﬂuctuates, but the pass-through size does not, then the frequency of pricechanges in the local currency must change. Importantly, our unique dataset from the large USD depreciation
episode during the Great Inﬂation period has signiﬁcant power for distinguishing between open-economy
NK models with diﬀerent price-setting mechanisms.
Table 6 presents descriptive statistics of the average frequency of price changes in the local currency.
Tables 6(a) and 6(b) report the sample numbers, mean, and S.D. values of the average price change frequencies for the Okinawa and mainland data for all items. Tables 6(c) and 6(d) list the same values for
the Okinawa and mainland data for the fresh food items. Table 6(e) and 6(f) list the same values for the
Okinawa and mainland data for the non-fresh items. The most outstanding observation from these tables
is that the cross-sectional mean of Okinawa’s average price change frequency increases over the sample
period from the USD-Fix to the JPY-Com regime in all item categories. However, we identiﬁed no clear
trends in the average price change frequency in the mainland sample.
Our formal DID analysis conﬁrmed the observations discussed above. We constructed the following
econometric model of the average price change frequency Freqj,c (r):Freqj,c (r) = αj + β0 DOkinawa+ β1 DFlex (r) + β2 DCom (r)c+ γ0 DOkinawa∗ DFlex (r) + γ1 DOkinawa∗ DCom (r) + uj,c (r), (3)cc19where αj and uj,c (r) denote item-speciﬁc ﬁxed eﬀects and i.i.d. disturbances, respectively. We estimate
the value of Eq. (3) using OLS with consideration for item-speciﬁc ﬁxed eﬀects. To consider item- andprefectural-speciﬁc heteroskedasticity, we calculate White’s heteroskedasticity-robust standard errors.
Table 7 presents the results of DID regression analysis for the average price change frequency. It
is noteworthy that except for the fresh-foods items, all coeﬃcients for the average treatment eﬀects of the
USD-Flex and JPY-Com regimes are positive with high statistical signiﬁcance. For example, the USD-Flex
and JPY-Com regimes increase the average price change frequency of Okinawa’s non-fresh items by 16.5%
and 14.0%, respectively, relative to the USD-Fix regime. Particularly for Okinawa’s Mainland items, the
USD-Flex regime sharply increases the average price change frequency by 21.6% relative to the USD-Fix
regime.
The empirical ﬁndings discussed above regarding the average price change frequency support statedependent pricing technology with menu costs as the underlying mechanism of price stickiness in an openeconomy environment. High inﬂation quickly erodes the relative price of a good. Therefore, according
to the menu cost model, high inﬂation increases the incentives for producers to revise retail prices to the
optimal level frequently, even if they must pay ﬁxed adjustment costs. Furthermore, under high inﬂation,
mainland exporters expect to sooner or later increase their local currency prices in Okinawa eventuallyto compensate for menu costs. Therefore, exporters have a solid incentive to revise and increase their
Okinawa local currency prices in response to sharp JPY appreciation. This implication of the menu costmodel consistently explains why we observe a signiﬁcantly large average treatment eﬀect of the USD-Flex
regime on the price change frequency of Mainland items in Okinawa.
Table 8 separates the average frequency of price ups and average frequency of price downs. Specifically, the third and fourth columns report the mean and S.D. values of the frequency of price ups, andthe ﬁfth and sixth columns report the same values for the frequency of price downs. Interestingly, Table 8
conﬁrms the observation by Nakamura et al. (2018) that the average frequency of price ups increases withinﬂation both in Okinawa and the mainland, whereas there is no robust relationship between the averagefrequency of price downs and inﬂation. This asymmetry of the price change frequency is consistent with
the implications of the open-economy menu cost model discussed by in Flodén and Wilander (2006), whereretail prices tend to bunch toward the bottom of the inaction (S,s) band under high inﬂation with rapid local
currency depreciation.
All the results for the average absolute size and average frequency of price changes seem to support
the implications of the open-economy menu cost model. In the next section, we present simulations of acalibrated small open-economy menu cost model to evaluate how closely the proposed model replicatesthe empirical ﬁndings discussed in this section compared to the conventional Calvo counterpart.

5. Small open-economy NK models
This section introduces sticky price models for item-level real exchange rates between Okinawa andmainland Japan under the three distinct currency regimes. Our targets are the sample moments of theretail prices of non-fresh items in Okinawa and mainland Japan reported in the previous section because
these items are characterized by high degrees of price stickiness, which is the source of ineﬃcient internaland external price dispersion. The considered models are small open-economy variants of those proposed20

by Nakamura et al. (2018). There is a continuum of ﬁnal goods indexed by z in the unit interval [0, 1]
produced by monopolistically competitive producers facing idiosyncratic technology shocks At (z). We
split the unit interval into two subintervals by z̄. If z is in the ﬁrst subinterval [0, z̄], then a monopolisticallycompetitive mainland ﬁrm z produces and delivers its product to both the mainland and Okinawa markets.
When delivering products to the mainland market, the ﬁrm incurs no transport costs. When exporting
products to the Okinawa market, the ﬁrm must pay product-speciﬁc iceberg-type transport costs τ (z). The
ﬁrm employs labor from the competitive mainland labor market for goods production and must hire laborfrom the competitive Okinawa labor market for product delivery in Okinawa.
If z is in the second subinterval (z̄, 1], then the item z is internationally non-deliverable, meaning themainland ﬁrm z delivers its products only to the mainland market and the Okinawa local ﬁrm z delivers its
products only to the Okinawa local market. In particular, the Okinawa ﬁrm employs labor from the Okinawa
labor market and uses intermediate goods imported from the competitive mainland intermediate goods
market. These production and delivery structures make the Okinawa market’s marginal costs dependent
on real exchange rate ﬂuctuations,as indicated in the menu cost model proposed by Gopinath and Itskhoki
Po S(2010). Here, Qt ≡ Pt t t denotes the real exchange rate accompanied by the JPY/USD nominal exchange
rate St , where Pt and Pot are the aggregate consumer price levels prevailing in the mainland and Okinawa,
respectively, in period t.
All ﬁrms set their monopoly prices in terms of local currency with price stickiness. When exporting
products to the Okinawa market, the mainland ﬁrm z ∈ [0, z̄] adopts the LCP strategy by setting themonopoly price in terms of the Okinawa local currency, which is the USD for r = USD-Fix/USD-Flex
and JPY for r = JPY-Com. We will investigate menu cost and Calvo mechanisms as generators of pricestickiness. Furthermore, we assume that all ﬁrms must pay variable adjustment costs when choosing torevise their current prices, as discussed by Slade (1998).
Mainland households consume only domestically produced goods. The mainland consumption basket is represented by a Dixit-Stiglitz aggregator deﬁned over a continuum of domestic products ct (z) forz ∈ [0, 1] with a constant elasticity of substitution θ. The households in Okinawa consume mainland
products z ∈ [0, z̄] and Okinawa local products z ∈ (z̄, 1]. The corresponding consumption basket isrepresented by a Dixit-Stiglitz aggregator deﬁned over the product interval with the constant elasticity of
substitution θo . The aggregate price levels in the mainland and Okinawa during period t, Pt and Pot , aredeﬁned as
1
] 1−θ

[∫ 1
Pt =

pt (z)

1−θ

dz

[∫ z̄
,

and

Pot =

0

0

o
p∗t (z)1−θ dz +∫ 1opot (z)1−θ dz

1
] 1−θ
o

,

(4)

z̄

where pt (z) and p∗t (z) denote the local currency retail prices of item z in the mainland and Okinawa markets
that the mainland ﬁrm z produces and delivers. pot (z) denotes the local currency retail price of item z in
the Okinawa market that Okinawa ﬁrm z produces and delivers.
The mainland ﬁrm z ∈ [0, 1] faces a downward-sloping demand curve in the mainland market ct (z) =(pt (z)/Pt )−θ C, where ct (z) is the quantity demanded for item z in the mainland market during period t
and C is the time-invariant consumption basket in the mainland. If z is within [0, z̄], then themainlando∗∗o −θﬁrm z faces a downward-sloping demand curve in the Okinawa market ct (z) = (pt (z)/Pt ) C o , wherec∗t (z) is the quantity demanded for the deliverable item z in the Okinawa market during period t and C o is21the time-invariant consumption basket in Okinawa. For z ∈ (z̄, 1], the Okinawa ﬁrm z faces a downwardo
sloping demand curve with a constant price elasticity θo in the Okinawa market cot (z) = (pot (z)/Pot )−θ C o ,where cot (z) is the quantity demanded for the non-deliverable item z in the Okinawa market during periodt.
The mainland ﬁrm z ∈ [0, 1] is equipped with a linear production function when delivering products
to the mainland market.
yt (z) = At (z)Lt (z),where yt (z) is the quantity produced during period t, At (z) is the level of labor productivity during periodt, and Lt (z) is the amount of labor input during period t. The ﬁrm hires labor from a competitive mainlandtlabor market with a competitive real wage W. When delivering products to the Okinawa market, thePtmainland ﬁrm z ∈ [0, z̄] must use a local distribution service in Okinawa. For simpliﬁcation, we assume
that the mainland ﬁrm has the following Cobb-Douglas production function for the Okinawa market:yt∗ (z) = aAt (z)Lt (z)η L∗t (z)1−η ,η ∈ (0, 1),

where yt∗ (z) is the quantity produced for the Okinawa market, L∗t (z) is the labor input of the Okinawa local
distribution service, and a is an adjustment constant. The cost minimization problem solved by the ﬁrm() ( )η ()1−η
Qt WtoWto
1
Wt
provides the real marginal cost of delivering products to Okinawa At (z)
,
where
is
o
Pt
Pt
Pot
the real wage in Okinawa. The mainland ﬁrm must pay an iceberg-type transport cost τ (z) when shipping
good z from the mainland to the Okinawa market.
For a product z ∈ (z̄, 1], the Okinawa ﬁrm z produces a non-deliverable island item using the Okinawa labor input and mainland intermediate good with the Cobb-Douglas production function
yto (z) = ao Aot (z)Lot (z)ν Mt (z)1−ν ,ν ∈ (0, 1),

where yto (z) is the output of the Okinawa product, Aot (z) is the level of Okinawa labor productivity during
period t, Lot (z) is the amount of labor input from the Okinawa labor market during period t, and Mt (z) is theamount of the mainland intermediate good during period t. Mainland intermediate goods are produced in
the competitive intermediate goods market with a linear production function for the mainland labor input.
t. The cost minimizaThe real marginal cost of an intermediate good is equal to the mainland real wage W
Pt( 1−ν) ( o )ν (
)1−ν
Wt
Wt
tion problem solved by the Okinawa ﬁrm provides the real marginal cost τA(z)o (z)
.
o
Pt
Qt Pt
t
We assume that the Okinawa ﬁrm muts pay the same iceberg-type transport cost τ (z) when importingintermediate goods from the mainland.
In this partial-equilibrium small open-economy model, we assume that At (z), Aot (z), Pt , P∗t , and St
follow exogenous stochastic processes. First, the labor productivity levels in the mainland and Okinawa,
which are denoted as At (z) and Aot (z), respectively, follow idiosyncratic logarithmic AR(1) processes asfollows:
ln At (z) = ρ ln At−1 (z) + ϵt (z),ln Aot (z) = ρ ln Aot−1 (z) + ϵot (z),ϵt (z) ∼ N (0, σA ),ϵot (z) ∼ N (0, σA ),(5)where ρ ∈ (0, 1) and σA are the common AR roots and standard deviation of the productivity shocks.
22For simplicity, we assume that the stochastic processes of productivity levels are independent of the currency regime r. Second, the stochastic processes of the aggregate price levels of the mainland and Okinawa, which are denoted as Pt and Pot , respectively, are characterized by the following currency-regimedependent inﬂation rate processes:∆ ln Pt = µ(r) + ηt ,∆ ln Pot = µo (r) + ηto ,ηt ∼ N (0, σπ (r)),ηto ∼ N (0, σπo (r)).

(6)

In particular, we allow the parameters µ(r), µo (r), σπ (r), and σπo (r) to depend on the currency regime stater to reﬂect rapid changes in the inﬂation rates in mainland Japan and Okinawa over our sample period.
Finally, to replicate the historical path of the JPY/USD nominal exchange rate during our sample
period, we adopt the following stochastic logarithmic process for St :{0,
if r = USD-Fix or JPY-Com,
ln St =,
(7)2
ln St−1 + ω + λt , λt ∼ N (0, σλ ),if r = USD-Flex
where ω is the mean depreciation rate during the USD-Flex regime. The stochastic processes of the inﬂation
rate and nominal exchange rate, which are deﬁned in Eqs. (6) and (7), respectively, imply that the realexchange rate Qt follows
ln Qt = ln Qt−1 + ζ(r) + υt (r),where ζ(r) is the currency-regime-dependent mean of the real depreciation rate, where{µo (r) − µ(r),if r = USD-Fix or JPY-Com
ζ(r) =,oµ (r) − µ(r) + ω,
if r = USD-Flexand{ηto − ηt ,
υt (r) =ηto − ηt + λt ,if r = USD-Fix or JPY-Com
if r = USD-Flex

is the currency-regime dependent shock to the real depreciation rate.
5.2. Flexible price equilibrium
We characterize the ﬂexible price equilibrium as a benchmark without variable adjustment costs.
The mainland ﬁrm z ∈ [0, 1] maximizes the static proﬁt function for the mainland market with respect tothe local currency price pt (z) during each period. If z ∈ [0, z̄], then the ﬁrm maximizes the static proﬁtfunction with respect to the local currency price p∗t (z) during each period. The optimal ﬂexible prices areθWtpt (z) =θ − 1 At (z)andp∗t (z) =

θo
τ (z)
o
θ − 1 Qt At (z)

(

Wt
Pt

)η (

Qt Wto
Pot

)1−η
Pot .

Similarly, the Okinawa local ﬁrm z ∈ (z̄, 1] maximizes the static proﬁt function with respect to the local

23

currency price pot (z) during each period. The optimal ﬂexible price ispot (z) =θo τ (z)1−ν
θo − 1 Aot (z)

(

Wto
Pot

)ν (

Wt
Q t Pt)1−νPot .

These optimal ﬂexible prices deﬁne markups over the nominal marginal costs.
Given the optimal ﬂexible price for the mainland market pt (z), the mainland aggregate price Pt in
θ Wt
Eq. (4) becomes Pt = θ−1, where Af is the aggregate labor productivity. Because the logarithm ofAflabor productivity ln At (z) follows the ergodic stochastic process in Eq. (5), the aggregate productivity
Af converges to a constant value that is approximately equal to one (Af ≈ 1). Therefore, the equilibriumtcompetitive real wage W
is equal to θ−1. For simplicity, we assume that this competitive mainland realPtθwage under the benchmark ﬂexible price equilibrium always holds throughout our exercise below. Additionally, as suggested by our historical review of the Okinawan economy, the labor market in Okinawa
was integrated with the mainland labor market to a great degree, even during the U.S. military occupation
period, so it iso a reasonable approximation that the equilibrium real wage in Okinawa is equal to that in theWtmainland ( Pot = W
= θ−1
).
Pt
θ
t

The item-level real exchange rate in the benchmark ﬂexible price equilibrium for item z ∈ [0, z̄] is( o )()
θ
p∗t (z)Stθ−1=
qt (z) ≡τ (z)Qt1−η .
opt (z)θ −1θTherefore, if z ∈ [0, z̄], then the item-level real exchange rate in the ﬂexible price equilibrium can be
decomposed into three factors. The ﬁrst factor originates from the transport cost τ (z). The Okinawa priceis likely to be higher than the mainland price as a result of the transport cost. The second factor is thediﬀerence in the (degreemarkupbetween the mainland and Okinawa markets based on the pricing-to) (of)θ−1θo. The third factor is the real exchange rate Qt , which originates from the realmarket behavior θo −1θmarginal cost of the local distribution service on Okinawa.
The item-level real exchange rate in the benchmark ﬂexible price equilibrium for a non-deliverable
product z ∈ (z̄, 1] is( o )()()θθ−1
At (z)pot (z)Sto=τ (z)1−ν Q1−ν.
qt (z) ≡tpt (z)
θo − 1θAot (z)In this case, the item-level real exchange rate at the ﬂexible price equilibrium is decomposed into four
factors. The ﬁrst three factors are the same as those mentioned above. The fourth factor is the productivity
diﬀerential between the mainland and Okinawa AAot (z)induced by the real marginal cost diﬀerential.
(z)t

5.3. Menu cost model
Price stickiness in this model stems from ﬁxed adjustment costs combined with variable adjustment
costs. In each period, a ﬁrm z ∈ [0, 1] in the mainland determines the current price pt (z) in the mainland24

market. The static real proﬁt of this ﬁrm is[(
π(pt (z); pt−1 (z), At (z), Pt ) =pt (z)
Pt

)

(
−

θ−1
θAt (z))] (pt (z)
Pt

)−θ

(
−γ

)2
pt (z)−1 ,pt−1 (z)where γ is the coeﬃcient of variable adjustment costs. If the ﬁrm chooses to revise the price in the mainlandmarket, then it sets the current price pt (z) to the desired level pt (z) by paying real ﬁxed adjustment costs
θ−1
K and quadratic adjustment costs γ (pt (z)/pt−1 (z) − 1)2 . If the ﬁrm chooses not to revise the price,θthen it maintains the current price pt (z) at the one-period past level pt−1 (z). Similarly, if z is in the interval[0, z̄], then the mainland ﬁrm z delivers its product to the Okinawa local market engaging in the LCP
strategy. The static real proﬁt from this product delivery isπ ∗ (p∗t (z); p∗t−1 (z), At (z), Pot , Qt ) =[ ( ∗ )()] ( ∗ )−θo( ∗)2pt (z)
θ−1
pt (z)
pt (z)1−ηQt− τ (z)
Qt
−γ
−1 .
Pot
θAt (z)Potp∗t−1 (z)If the ﬁrm chooses to revise the current price p∗t (z) in the Okinawa market, then z sets p∗t (z) to the desired
Qt K o and quadratic adjustment costs
level p∗t (z) and pays menu costs adjusted by the real exchange rate θ−1
θ
)
( ∗
2
γ pt (z)/p∗t−1 (z) − 1 .22 If the current price is not revised, then the ﬁrm sets p∗t (z) to the one-period pastlevel p∗t−1 (z).
If z is in the interval (z̄, 1], then the Okinawa local ﬁrm z ∈ (z̄, 1] delivers products to the local
Okinawa market. The static real proﬁt of the Okinawa ﬁrm is
π o (pot (z); pot−1 (z), Aot (z), Pot , Qt ) =
[(
)2
) (
)1−ν ()] ( o )−θo
( o
τ (z)
θ−1
pt (z)
pt (z)pot (z)
−1 .
−
−γ
Pot
Qt
θAot (z)Pot
pot−1 (z)In this case, the ﬁrm sets the current price pot (z) to the desired level pot (z) and pays menu costs θ−1
K o andθ)( o2quadratic adjustment costs γ pt (z)/pot−1 (z) − 1 . If the current price is not revised, the ﬁrm keeps thecurrent price at the one-period past level pot−1 (z).
All ﬁrms in the mainland and Okinawa maximize the expected present discounted values of future real proﬁts based on the subjective discount factor β ∈ (0, 1). Because the corresponding Bellman
equations for ﬁrm problems are standard, we provide the details in an online appendix. For the sake ofcomparison, we also solve a variant of the small open-economy model with Calvo pricing technology witha price non-resetting probability α. The online appendix provides details regarding the construction of the
Calvo model.
5.4. Calibration
We calibrate the menu cost and Calvo models based on the information provided by Nakamura et
We assume that the menu costs K o for price changes in Okinawa are paid to the households in Okinawa in terms of theconsumption basket of Okinawa.
22

25

al. (2018), and Gopinath and Itskhoki (2010). The time unit of the models was one month. We set the1
subjective discount factor β to 0.96 2 . We calibrate the mainland elasticity of substitution θ to four based thebenchmark value set by Nakamura et al. (2018), but we slightly adjust the Okinawa elasticity of substitution
θo to a lower value of three. Because the availability of alternative goods was limited in the Okinawa
market, the price elasticity of demand was low in the Okinawa market relative to the mainland market.
We also borrow calibrated values for the stochastic processes of the idiosyncratic labor productivity shockin Eq. (5), where ρ = 0.7 and σA = 0.037. We derive menu cost parameters K and K o to match themean frequency of price changes of 11.4% per month and mean absolute size of price changes of 6.5%
in the mainland data during the USD-Fix regime. This moment-matching exercise resulted in 80% of thecalibrated level of menu cost with K = K o = 0.8 × 0.019. For the Calvo model, we conduct the same
moment matching exercise and obtained 120% of the calibrated Calvo probability with α = 1.2 × 0.087.
We set the iceberg transport cost τ (z) to 1.05, which is common across all goods z ∈ [0, 1]. With allother factors being equal, the Okinawa price is 5% higher than the mainland price as a result of shipping
costs. We set the factor share of the Okinawa local distribution service in the production function for the
mainland ﬁrm z ∈ [0, z̄] to 20% by setting η to 0.8. This value is close to 0.75, which was selected by
Gopinath and Itskhoki (2010). Similarly, we also set the factor share of the mainland intermediate goods inthe production function of the Okinawa local ﬁrm z ∈ (z̄, 1] to 30% by setting ν to 0.7. This calibration ofν reﬂects the high dependence of the Okinawa local production structure on the mainland economy, evenduring the US military occupation, as suggested by our historical review in Section 3. We set the variableadjustment cost parameter γ to 0.5 to reﬂect Slade’s (1998) point estimate of 0.68 based on retail pricedata.
To calibrate the stochastic processes of the inﬂation rates in Okinawa and the mainland for the threecurrency regimes, we ﬁt Eq. (6) to the sample means and standard deviations of the monthly CPI inﬂation
rates of the mainland and Naha: {µ(r), µo (r)} = {0.0047, 0.0048} and {σπ (r), σπo (r)} = {0.0067, 0.0108}
for r = USD-Fix; {µ(r), µo (r)} = {0.0047, 0.0063} and {σπ (r), σπo (r)} = {0.0087, 0.0127} for r = USDFlex; and {µ(r), µo (r)} = {0.0124, 0.0185} and {σπ (r), σπo (r)} = {0.0108, 0.0258} for r = JPY-Com.
As shown in Figure 1, in the USD-Flex regime, the JPY appreciates sharply relative to the USD.
Between August of 1971 and May of 1972, the mean monthly appreciation rate is -0.021 with a mean
standard deviation of 0.0137. We ﬁt the parameters ω and σλ for the stochastic process of the nominal
currency return in Eq. (7) to the monthly sample estimates.
We numerically solve the calibrated Bellman equations for the menu cost and Calvo models using
the value function iteration method implemented by Nakamura et al. (2018). We then simulated 30,000
repetitions of the synthetic data on retail prices from the resulting policy functions with the same sample
lengths as in the real data for each currency regime. In particular, we construct Okinawa’s non-fresh sample
by merging the synthetic time series generated from the local mainland and Okinawa ﬁrms. The simulation
results reported in the next subsection are based on the simulated 30,000 target moments of item-level LOP
deviations, average absolute size of price changes, and average price change frequencies.
5.5. Simulation results
Table 9 summarizes the results of our calibration exercises. First, Tables 9(a) and 9(b) report themeans of the average LOP deviations estimated by the menu cost and Calvo models in the third and fourthcolumns for the Okinawa and mainland pairs, which are accompanied by the non-fresh data counterparts26

in the second column.23 Both the menu cost and Calvo models replicate the mean of the average item-level
LOP deviations in the data reasonably well. For example, for the Okinawa pairs, the menu cost model
implies average LOP deviations of 0.000, 0.103, and -0.046 for the USD-Fix, USD-Flex, and JPY-Com
regimes, which are reasonably close to the data counterparts of 0.006, 0.132, and -0.046. We also found asimilar ﬁt of the Calvo model to the average LOP deviation over the three currency regimes. Additionally,both models can reproduce the zero mean of the average LOP deviation in the mainland pairs as observedin the real data.
The most signiﬁcant diﬀerence in statistical dimensions between the two models is the distributional
shape. Figures 5(a) and 5(b) plot the kernel-smoothed densities of the average LOP deviation for the
Okinawa and mainland pairs simulated by the menu cost model, respectively. Similarly, Figures 6(a) and6(b) display the same kernel-smoothed densities estimated by the Calvo model. These ﬁgures replicate theshifts in the distribution of item-level LOP deviations over the three currency regimes observed in the real
data in Figures 3 and 4. In particular, both models capture the right shift of the distribution of Okinawa
pairs under the USD-Flex regime, which is caused by the sharp depreciation of the USD. However, theCalvo model distributions plotted in Figures 6(a) and 6(b) are more heavily tailed than those of the menu
cost model plotted in Figures 5(a) and 5(b). It is worth recalling that we performed identical calibrationon the primitives for both models, except for price stickiness. Therefore, these distributional diﬀerences
clearly indicate that the Calvo model predicts worse ineﬃciency in external price dispersion than the menu
cost model as a result of the random nature of the timing of price adjustments.
This previously unidentiﬁed implication of the Calvo model regarding ineﬃcient external price dispersion stems from its large time series variability in LOP deviations. To highlight this factor, we present
time series plots of the means (solid blue line) and 68% probability intervals (dashed blue lines) of the
LOP deviations predicted by the menu cost and Calvo models in Figures 7 and 8, respectively. Each ﬁgure
also plots the real exchange rate Qt between Okinawa and the mainland as a solid black line.24 As shownin Figure 7, on average, the menu cost model closely traces the real exchange rate with small simulation
variability until the ﬁrst half of 1973. However, Figure 8 reveals that the Calvo model fails to track thereal exchange rate based on large simulation variability throughout the sample period. This result conﬁrms
that the Calvo model yields excess time series variability of the LOP deviations as a result of random priceadjustments.
Second, the menu cost model has better implications for the average absolute size of price changes
compared to the Calvo model. Tables 9(c) and 9(d) present the ensemble means of the average absolute
sizes of price changes for the Okinawa and mainland simulations. The menu cost model predicts an almost
ﬂat proﬁle around 8% of the average absolute size of price changes over the three currency regimes for
the Okinawa and mainland data, as observed in the real data. In contrast, the Calvo model yields muchlarger values for this statistical moment, particularly for the Okinawa data, which yield a value of 13%. In
particular, the Calvo model’s average absolute size of price changes jumps up to 19.8% under the USD-Flex
regime, which is almost twice the real value of 10.9%. Therefore, the Calvo model produces excessively
large adjustments of retail prices to the desired levels in response to the sharp depreciation of the USD
23

For each simulation, we ﬁrst calculate the time series average of the LOP deviations for each currency regime. We thencalculate the mean value of the average LOP deviations over 30,000 repetitions. This construction of the average LOP deviation
reﬂects no item-speciﬁc heterogeneity that should be included in the actual data.
24
We constructed the real exchange rate plots using the average CPIs of Naha and the mainland.

27under the calibrated high-inﬂation environment, which is inconsistent with the real retail price behavior.
Finally, Tables 9(e) and 9(f) report the ensemble means of the average price change frequencies for
the Okinawa and mainland samples. Again, the menu cost model successfully generates an upward trend
in the average price change frequency over time, as observed in the real data. In contrast, based on its
construction, the Calvo model derives no meaningful implications regarding this statistical moment. The
average price change frequency of the Calvo model is almost independent of inﬂation and exchange rates.
Therefore, as suggested by Flodén and Wilander (2006), the extensive margin of price changes by ﬁrms
should be state dependent on inﬂation and exchange rates.
The results of our calibration exercises presented in this section strongly favor the menu cost modelover the Calvo model. To understand retail price behavior in Okinawa and the mainland in the early 1970s,
it is highly plausible to infer that ﬁrms had the option to pay a relatively small ﬁxed adjustment cost andnever allowed their prices to drift far from the optimal levels, as indicated by the menu cost model.

6. Conclusions
Our ﬁndings in this study seem to support Friedman’s (1953) case for ﬂexible exchange rates in the
LCP environment. In our data, the ﬁrms were likely to adjust the degree of price stickiness ﬂexibly inresponse to the large USD depreciation relative to the JPY following the Nixon Shock, as predicted by themenu cost model. Therefore, the ineﬃciency of domestic and international price dispersion caused by local
currency price stickiness should be more subtle than expected under ﬂexible exchange rates according to
the conventional Calvo model.
This study’s solid empirical micro foundation required us to evaluate recent conclusions in the literature regarding the optimality of ﬁxed exchange rate or common currency regimes drawn from the openeconomy Calvo model. It is certainly possible that ﬂexible exchange rates and high inﬂation have otheressential costs. Therefore, the argument for the optimality of ﬁxed exchange rates or common currency
regimes must depend on these other costs outweighing the beneﬁts of ﬂexible exchange rates.
The unique US military history of deployment in post-war Okinawa demonstrates that any discussion
on optimal monetary policy in the open-economy NK framework should be recast in the light of a global
social welfare function originating from a state-dependent mechanism of price stickiness. We leave thiscrucial task as an important future research agenda.

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31

Table 1: Mean CPI Inflation Rates in Okinawa and Mainland (% at annual rate)

Okinawa Mainland
USD-Fix
USD-Flex
JPY-Com

5.91
7.82
24.6

5.78
5.78
15.9

Table 2: Descriptive Statistics: Item-level LOP Deviations

Currency regime

Sample size

Mean

S.D.

USD-Fix
USD-Flex
JPY-Com(a) Okinawa pair: Pooled
156,536 0.022
69,638 0.123
236,387 -0.051

0.285
0.264
0.300

USD-Fix
USD-Flex
JPY-Com(b) Mainland pair: Pooled
3,546,841 0.001
1,595,531 0.002
5,524,948 -0.001

0.162
0.153
0.162

(c) Okinawa pair: Fresh Foods
USD-Fix
25,320 0.105
USD-Flex
11,407 0.078
JPY-Com
39,253 -0.09

0.388
0.358
0.393

(d) Mainland pair: Fresh Foods
USD-Fix
300,736 0.005
USD-Flex
222,166 0.007
JPY-Com
702,269 -0.005

0.272
0.273
0.257

USD-Fix
USD-Flex
JPY-Com(e) Okinawa pair: Non-fresh
131,216 0.006
58,231 0.132
197,134 -0.043

0.258
0.240
0.277

USD-Fix
USD-Flex
JPY-Com(f) Mainland pair: Non-fresh
2,968,758 0.000
1,335,041 0.002
4,611,551 -0.001

0.129
0.117
0.135

32

Table 3: Results of DID Analysis: Item-level LOP deviation

Variable
DOkinawac,sDFlex (t)DCom (t)DOkinawa∗ DFlex (t)c,sDOkinawa∗ DCom (t)c,sConstant
Adj. R2
Log-L.
N

Pooledest/s.e.
2.131(.073).135(.015)–.256(.011)
9.943(.124)–7.104(.096).163(.013).006–4.72e+07
11,129,881

Fresh Foods
est/s.e.
10.078(.247).237(.065)–.945(.045)–3.011(.420)–18.646(.318).479(.081).005–8.62e+06
1,827,950

33

Non-fresh Mainland Okinawa
est/s.e.
est/s.e.
est/s.e.
.598
1.198–2.503(.072)(.103)(.105)
.115
.207
.028
(.013)(.018)(.021)
–.121
–.075
–.278
(.010)(.014)(.017)
12.457
11.20015.236(.123)(.172)(.187)–4.855–5.705.361(.095)(.135)(.147)
.087
.055
.141
(.012)(.014)(.037)
.008
.006
.008
–3.77e+07 –2.36e+07 –1.02e+07
9,301,931 5,694,520 2,584,656

Table 4: Descriptive Statistics: Average Absolute Size of Price Changes

Currency regime

Sample size

Mean

S.D.

USD-Fix
USD-Flex
JPY-Com(a) Okinawa: Pooled
668
541
2,138

0.169
0.144
0.121

0.277
0.232
0.253

USD-Fix
USD-Flex
JPY-Com(b) Mainland: Pooled
38,134 0.166
17,633 0.175
85,024 0.148

0.269
0.301
0.230

USD-Fix
USD-Flex
JPY-Com(c) Okinawa: Fresh Foods
370 0.238
197 0.205
721 0.190

0.344
0.290
0.382

USD-Fix
USD-Flex
JPY-Com(d) Mainland: Fresh Foods
19,643 0.243
9,240 0.257
34,270 0.235

0.335
0.377
0.314

USD-Fix
USD-Flex
JPY-Com(e) Okinawa: Non-fresh
298 0.083
344 0.109
1,417 0.085

0.111
0.182
0.137

USD-Fix
USD-Flex
JPY-Com(f) Mainland: Non-fresh
18,491 0.083
8,393 0.086
50,754 0.089

0.130
0.137
0.114

34

Table 5: Results of DID Analysis: Average Absolute Size of Price Changes

Pooledest/s.e.
–.004(.010)
DFlex (r).005(.002)
Com
D (r)
–.000
(.001)
Okinawa
FlexDs∗ D (r) .002(.014)
OkinawaComDs∗ D (r) –.012(.011)
Constant.135(.011)
2
Adj. R.213
Log-L.
11917.187
N
144,138
Variable
DOkinawasFresh Foods
est/s.e.
–.002(.016).009(.004)–.003(.003)–.030(.027)–.035(.021).095(.003).138–1.55e+04
64,44135

Non-fresh
est/s.e.
–.006(.006).000(.002).002(.001).025(.011).001(.007).132(.011).110
59544.054
79,697

Mainlandest/s.e.
–.018(.008).000(.002)–.005(.002).025(.013).012(.010).139(.011).079
31192.573
47,565

Okinawa
est/s.e.
.030(.015).006(.002).01(.001).033(.036)–.029(.016).038(.002).184
20052.091
22,424

Table 6: Descriptive Statistics: Average Frequency of Price Changes

Currency regime

Sample size

Mean

S.D.

USD-Fix
USD-Flex
JPY-Com(a) Okinawa: Pooled
178
178
176

0.212
0.356
0.441

0.278
0.301
0.283

USD-Fix
USD-Flex
JPY-Com(b) Mainland: Pooled
8,183 0.264
8,129 0.356
8,185 0.353

0.316
0.301
0.302

USD-Fix
USD-Flex
JPY-Com(c) Okinawa: Fresh Foods
31 0.703
31 0.769
31 0.877

0.307
0.220
0.196

USD-Fix
USD-Flex
JPY-Com(d) Mainland: Fresh Foods
1,425 0.813
1,417 0.810
1,423 0.853

0.284
0.290
0.229

USD-Fix
USD-Flex
JPY-Com(e) Okinawa: Non-fresh
147 0.109
147 0.269
145 0.348

0.113
0.236
0.199

USD-Fix
USD-Flex
JPY-Com(f) Mainland: Non-fresh
6,758 0.148
6,712 0.143
6,762 0.248

0.166
0.180
0.189

36

Table 7: Results of DID Analysis: Average Frequency of Price Changes

Variable
DOkinawas
DFlex (r)DCom (r)DOkinawa∗ DFlex (r)sDOkinawa∗ DCom (r)sConstant
Adj. R2
Log-L.
N

Pooledest/s.e.
–.052(.010)–.005(.002).089(.002).148(.020).139(.016).009(.004).809
13941.070
25,029Fresh Foods
est/s.e.
–.110(.034)–.002(.005).040(.004).069(.054).134(.044).836(.014).781
2843.593
4,358

37

Non-fresh
est/s.e.
–.039(.010)–.006(.002).099(.002).165(.021).140(.017).006(.004).428
11239.023
20,671

Mainland Okinawa
est/s.e.
est/s.e.
–.023
–.096
(.013)(.017)–.010–.004(.003)(.005).097.080(.003)(.005).216.075(.026)(.032).140.154(.020)(.031).007.315(.004)(.023).384.420
6990.182 2959.956
12,7805,638

Table 8: Descriptive Statistics: Average Frequency of Price Up and Down

Price Up
Mean S.D.

Price Down
Mean S.D.

Currency regime

Sample size

USD-Fix
USD-Flex
JPY-Com(a) Okinawa: Pooled
178 0.121
178 0.209
176 0.287

0.140
0.175
0.162

0.092
0.146
0.154

0.157
0.181
0.159

USD-Fix
USD-Flex
JPY-Com(b) Mainland: Pooled
8,183 0.160 0.173
8,129 0.148 0.183
8,185 0.236 0.171

0.104
0.111
0.117

0.176
0.186
0.164

USD-Fix
USD-Flex
JPY-Com(c) Okinawa: Fresh Foods
31 0.337 0.151
31 0.373 0.148
31 0.481 0.117

0.366
0.396
0.396

0.200
0.200
0.183

USD-Fix
USD-Flex
JPY-Com(d) Mainland: Fresh Foods
1,425 0.410 0.179
1,417 0.400 0.188
1,423 0.461 0.127

0.403
0.411
0.392

0.196
0.219
0.175

USD-Fix
USD-Flex
JPY-Com(e) Okinawa: Non-fresh
147 0.075 0.084
147 0.175 0.160
145 0.246 0.139

0.034
0.094
0.102

0.050
0.124
0.091

USD-Fix
USD-Flex
JPY-Com(f) Mainland: Non-fresh
6,758 0.107 0.116
6,712 0.095 0.130
6,762 0.189 0.138

0.041
0.048
0.059

0.082
0.094
0.083

38

Table 9: Simulation Results: Menu Cost and Calvo Models

Currency regime

Data (Non-fresh) Menu Cost

Calvo

USD-Fix
USD-Flex
JPY-Com(a) Average LOP Deviation: Okinawa
0.006
0.000
0.132
0.103
-0.043-0.0460.000
0.123-0.067

USD-Fix
USD-Flex
JPY-Com(b) Average LOP Deviation: Mainland
0.000
0.000
0.002
0.000
-0.001
0.000

0.000
0.000
0.000

USD-Fix
USD-Flex
JPY-Com(c) Average Absolute Size: Okinawa
0.083
0.075
0.109
0.081
0.085
0.090

0.131
0.198
0.141

USD-Fix
USD-Flex
JPY-Com(d) Average Absolute Size: Mainland
0.083
0.065
0.086
0.065
0.089
0.077

0.053
0.051
0.141

USD-Fix
USD-Flex
JPY-Com(e) Average Frequency: Okinawa
0.109
0.087
0.269
0.146
0.348
0.206

0.117
0.121
0.119

USD-Fix
USD-Flex
JPY-Com(f) Average Frequency: Mainland
0.148
0.114
0.143
0.120
0.248
0.182

0.116
0.116
0.118

39

370.00

Okinawa Reversion

Nixon Shock360.00350.00340.00330.00320.00310.00300.00290.00280.00270.00Figure 1: The JPY/USD exchange rate around the Nixon Shock and the reversion

200

180

160

140

120

100
Naha CPI (in terms of JPY)
Mainland CPI
80

60

Figure 2: CPI: Okinawa and the mainland

40

(a) Okinawa pairs

410(b)Mainland pairs
USD-Fixed
USD-Flex
JPY Com

9

3.5

8
3
7
2.5

6

2

5

4

1.5

3
1
2
0.5

0
-1.5

1

-1

-0.5

0

0.5

1

1.5

0
-1

-0.5

0

0.5

1

Figure 3: Kernel-smoothed densities of item-level LOP deviation: pooled sample(a) Okinawa pairs

410(b)Mainland pairs
USD-Fixed
USD-Flex
JPY Com

9

3.5

8
3
7
2.5

6

2

5

4

1.5

3
1
2
0.5

0
-1.5

1

-1

-0.5

0

0.5

1

1.5

0
-1

-0.5

0

0.5

1

Figure 4: Kernel-smoothed densities of item-level LOP deviation: Non-fresh items

41

Figure 5: Item-level LOP deviation: Menu cost model

Figure 6: Item-level LOP deviation: Calvo model

42

1.3
Data
Mean
+68%
-68%

1.25

1.2

1.15

1.1

1.05

1

0.95

0.9

0.85

0.8
1970:M1

1971:M8

1972:M5

1973:M1

1974:M1

1974:M10

Figure 7: Real exchange rate simulation: Menu cost model

1.5
Data
Mean
+68%
-68%

1.4

1.3

1.2

1.1

1

0.9

0.8
1970:M1

1971:M8

1972:M5

1973:M1

1974:M1

Figure 8: Real exchange rate simulation: Calvo model

43

1974:M10