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Electronic copy of this paper is available at: http://ssrn.com/abstract=949087
Published in:
Jahrbücher für Nationalökonomie und Statistik, 221/1, 2001, 45-67
A General Refutation of the Law of One Price As Empirical Hypothesis
Eine allgemeine Widerlegung des „Gesetzes des einheitlichen Preises„ als einer
empirischen Hypothese
by
Carsten Herrmann-Pillath
Witten/Herdecke University, Germany, Department of Economics and Management,
Chair, Macroeconomics and Institutional Change, Alfred-Herrhausen-Straße 50, 58448
Witten
phone +49-2302-926-572
fax +49-2302-926-571
e-mail Fehler! Textmarke nicht definiert.
JEL Classification: B41, C80, D52, F19, R10
Keywords: arbitrage, law of one price, integration, non-traded goods and services,
distributed local knowledge, entrepreneurship
Arbitrage, Gesetz des einheitlichen Preises, Integration, nicht-handelbare
Güter und Dienstleistungen, verteiltes lokales Wissen, Unternehmertum
Electronic copy of this paper is available at: http://ssrn.com/abstract=949087
2__Carsten Herrmann-Pillath
Zusammenfassung
Das „Gesetz des einheitlichen Preises„ spielt eine zentrale Rolle in der modernen
Außenwirtschaftstheorie, insbesondere in monetären Ansätzen zu Wechselkurs und
Zahlungsbilanz, aber auch in der Analyse von Dumping und anderen Bereichen des
Außenhandels. Als allgemeines Prinzip der Arbitrage liegt es allen wesentlichen
Theoremen zugrunde, wie etwa dem Faktorpreisausgleichstheorem. Die im letzten
Jahrzehnt wieder intensiver durchgeführten empirischen Tests kommen aber zu keinen
klaren Ergebnissen. Dies hängt zum einen mit methodologischen Problemen
zusammen, nämlich seiner ambivalenten Rolle als „Gesetz„ oder impliziter Definition
z.B. der „Identität von Gütern„. Der Fortschritt der Ökonometrie hat paradoxerweise auch
größere Freiheitsgrade zwischen Daten und Hypothesen geschaffen. Das Papier
argumentiert jedoch, daß über diese Probleme hinaus das „Gesetz des einheitlichen
Preises„ nicht gelten kann, wenn es bei positiven Kosten des interregionalen Handels
für Endprodukte versunkene Kosten der Ermöglichung des intra-regionalen Handels gibt.
Wenn das Wissen über Marktgelegenheiten nicht vollständig diffundiert ist, dann
entstehen solche Kosten durch das Erfordernis, lokal spezifisches unternehmerisches
Wissen als Dienstleistungs-Input für den Handel bereitzustellen. Dieses Wissen ist selbst
nicht-handelbar (auch im starken Sinne der Nicht-Kontrahierbarkeit), so daß die
Arbitrage eingeschränkt bzw. unmöglich ist. Damit ist das „Gesetz des einheitlichen
Preises„ widerlegt, soweit nicht die perfekten Bedingungen des allgemeinen
Gleichgewichts erfüllt sind. Viele empirischen Beobachtungen in der
Außenhandelstheorie stützen diese These, wie etwa zum „Pricing to Market„.
Abstract I
The Law of One Price (LOP) is of prime importance for modern international economics,
in particular in the monetary theory of forward exchange, or in the theory of
international trade, as, e.g., in the analysis of dumping. As a general proposition about
arbitrage, the LOP underlies every core proposition in neoclassical trade theory, e.g., the
factor price equalization theorem. However, the empirical tests conducted in recent
times have not led to conclusive results. There are methodological problems arising
from the indeterminacy whether the LOP is a law or an implicit definition, e.g., of the
„identity of goods“. Paradoxically, progress in econometrics has enlarged the degrees of
freedom for interpreting data. However, this paper argues that the LOP cannot hold in
principle, if there are positive costs of inter-regional trade for final goods, and if sunk
costs are incurred for intra-regional trading. If knowledge about market opportunities
has not dispersed completely, sunk costs result from the need to provide locally specific
entrepreneurial knowledge as a service input into trading. This knowledge is non-
tradable and even non-contractible, so that arbitrage is limited or impossible. Therefore,
the LOP can be refuted unless the conditions of perfect general equilibrium are fulfilled.
Many empirical observations support this hypothesis, for example, as regards „pricing to
market“.
Law of One Price__3
Abstract II
The Law of One Price (LOP) is of prime importance for modern international economics.
However, empirical tests have not led to conclusive results. There are many
methodological problems of measurement and interpretation. This paper argues that
the LOP cannot hold in principle, if there are positive costs of inter-regional trade for
final goods, and if sunk cost of local market entry result from the need to provide locally
specific entrepreneurial knowledge as a service input into trading. This knowledge is a
non-tradable, even in the sense of non-contractability. Hence, the LOP cannot hold inter-
regionally.
4__Carsten Herrmann-Pillath
A General Refutation of the Law of One Price
As Empirical Hypothesis1
1. Intuitive truths about the Law of One Price:
Why it works in principle, and why it fails in reality
The Law of Price (LOP) is duly regarded as one of the earliest hypotheses in economic
science. This most general description of the process and result of market arbitrage
underlay the rudimentary theories on purchasing power parity (PPP) that was developed
by the School of Salamanca (Niehans, 1995, pp. 151ff.). Here we meet for the first time
the assumption that if there are systematic differences between goods prices across
different currency areas, nominal exchange rates will stabilize close to the rate which
equalizes goods prices across areas in terms of a particular currency. In this special
application, the LOP continues to be a crucial building block of modern theories about
international economic relations.
First of all, the LOP has to be an element of the theory of comparative advantage
because without LOP there can be no fully efficient allocation as there would be no
consistent international price vector (cf. Engel/Rogers, 1998, p. 180). In this context, the
Stolper-Samuelson theorem must be conceived of as a close relative of LOP. The
Rybczynsky theorem explicitly presupposes the LOP because international prices have
to be given so that changes in factor supplies are only reflected in changes of output
composition. There are indeed several classes of models which attempt to prove that
because of the interdependence of the arbitrage mechanism even missing markets (in
this case missing factor markets) make no difference to the necessary convergence of
all goods prices in a perfect market system linking spatially separate markets.
Furthermore, the LOP plays a crucial role in the linkage between the real and the
monetary sphere. In particular, the monetary approach to the balance of payments as
well as to the analysis of flexible exchange rates is based on the assumption that the
LOP will lead to PPP, if only in the long run. Freshmen of international macroeconomics
get the lesson with their first steps that there is an intimate link between LOP, PPP and
formally analogous propositions about arbitrage in international financial markets (e.g.
Barro/Grilli, 1994, ch. 11). On a more advanced level, PPP takes on a special role as an
anchor for the formation of expectations about the long-range exchange rate. Since
expectations can turn the current exchange rate into an arbitrary variable, it is important
1 I wish to thank participants at the weekly staff seminar at the University of Konstanz for
illuminating comments, in particular Albert Schweinberger and Martin Kolmar. I have also enjoyed the
advice of my staff at Witten University. The extensive recommendations of one anonymous referee have
been extremely helpful to produce a second version of the original paper. Of course, remaining faults
reflect my stubbornness.
Law of One Price__5
that economic agents adopt rationally the PPP model so that their respective
expectations eventually close the real macroeconomic model guiding their decisions as
well as enlightening the researcher (e.g. Claassen, 1996).2
Viewed from a slightly different perspective, the background of the monetary approach
is the general assumption that the world economy is a fully integrated economy,
independent of the fact of certain „missing markets“. In one of the programmatic
statements about the monetary approach, this connection is eloquently made, with
many references to the LOP as an empirical statement (Johnson/Frenkel, 1975).
Indeed, the LOP is often regarded as the most reliable indicator of economic
integration.3 If a certain region is integrated economically, goods of similar quantity and
quality should be priced similarly in that region, because otherwise gains from trade
would be left unexploited. Hence, the validity of LOP is the touchstone of economic
integration.
Accordingly, violations of LOP may be interpreted as indicators of the lack of integration,
possibly because of policy interference in the arbitrage process. An important
application of LOP which is very relevant for policy issues is the analysis of non-tariff
barriers to trade and investigations into dumping (e.g. Deardorff/Stern, 1998, pp. 14ff.).
In both cases, deviations from conveniently measured international goods prices are
regarded as indicators of the existence of factors interfering with an ordinary market
process. There is the additional presumption that an international convergence of cost
conditions should prevail as a result of competitive forces so that persistent deviations
can be interpreted as a reflection of anti-competitive interventions and strategies.
Without the LOP as the beacon, these assumptions could not be justified in a rigorous
manner.
However, although the LOP plays such a fundamental role in economics, we still do not
have final proof that the LOP holds in reality (Taylor, 2000). Of course, the statement is
disarmingly simple that in a free market with a sufficiently high degree of competition,
goods identical in terms of quality and quantity should always bear the same price tag,
yet both empirical corroboration and empirical refutation are extremely difficult to
2 In that context we also note that the LOP, though regarded as a hypothesis about goods prices, is
applied as a general formal structure in the treatment of the entire set of international markets. In
particular, interest rate parity and international convergence of real interest rates are direct intertemporal
equivalents to the standard LOP. Hence, the common explanations for violations of LOP are also formally
analogous. For example, impediments to trade and arbitrage correspond to differences in riskiness of
international assets so that asset prices need not converge absolutely, although in the hypothetical
absence of risk differentials this would be the case.
3 There are naïve as well as sophisticated versions of that argument. In their assessment of
globalization, Bordo et al. (1999) point to the convergence of prices on international raw materials
markets as one indicator of increasing integration accompanying globalization. This is a naïve statement,
of course, because on the other hand the increasing share of intrafirm trade, counter-trade and other
forms of trade raise doubts regarding the relevance of LOP for measuring integration, all of these
contradicting the standard assumptions about arbitrage. Knetter/Slaughter (1999) exemplify the
sophisticated approach because they vote for the LOP only after assessing the difficulties involved in
applying other indicators of integration. However, they also propose such a complementary indicator of
“market thickness” based on the analysis of trade flows (i.e. relative quantities).
6__Carsten Herrmann-Pillath
achieve. There is a large conceptual and intellectual distance between the intuitive
plausibility and the demanding preconditions of rigorous tests of the LOP. This results
from the fact that the mechanism underlying the LOP is of the equilibrium type, hence
implying the move toward neoclassical equilibrium analysis if viewed in toto.4 Indeed,
the decisive event in linking LOP, PPP and the modern theory of international trade was
Gustav Cassel’s establishment of a general equilibrium framework for the further
development of trade theory (cf. Albert, 1995, ch. one).
It is illuminating to observe that the immediate successors of Cassel and founding
fathers of the modern neoclassical theory of international trade, Ohlin and Haberler,
treated the link between PPP and LOP rather cautiously. Haberler (1970, pp. 30ff.)
believed that PPP would prevail in the short term via the impact of LOP working through
internationally traded goods on the domestic price levels, a presumption that stands in
flat contradiction to our modern textbook view that introduces PPP as a long-term
phenomenon. In the long run, he argued, changes in the composition of tradables
versus non-tradables and, hence, the structure of the international market system will
always disturb the LOP mechanism and destroy the basis for PPP. Furthermore,
impediments to trade will allow prices to diverge within the range defined by the costs
of overcoming those impediments. Depending on the composition of trade, Haberler
even adduces examples where LOP and PPP run into the opposite direction.
Notwithstanding, he regards LOP and PPP as reasonable propositions approximating
reality. Bertil Ohlin (1967, pp. 290ff.) explicitly rejects the linkage between LOP and PPP
even within the setting of a rudimentary monetary approach to forward exchange. He
argues that supply and demand for foreign exchange will be determined by the specific
conditions on the international markets for goods and services, so that the general
domestic price levels are plainly irrelevant for the exchange rate. His extreme example
refers to trade among completely specialized countries with no common production so
that domestic price levels are disconnected, although international trade establishes
mutual interdependence of traded goods prices and hence influences the demand and
supply of foreign exchange and the exchange rate.
Both Ohlin and Haberler accept the arbitrage perspective on the market system, yet
because they have not yet laid down into the Procrustes bed of the general equilibrium
framework, they argue in a differentiated and balanced manner leaving much leeway
between data and theory. But the question arises whether the arbitrage argument
carries the seed of general equilibrium in it anyway. In fact, as smoothly as the LOP is
being accepted if the equilibrium view of the market is adopted, the failure of LOP is
just as easily swallowed if market imperfections and disequilibrium approaches are
taken into serious consideration. Starting with Stigler’s (1961) classic, many economists
would not deny that incomplete information on the demand side will render the LOP
invalid, if consumers stop searching for the least cost providers at an arbitrary point in
4 This means that making the exact conditions explicit for the LOP entails reference to all the basic
laws of neoclassical equilibrium analysis (like optimization, utility maximization etc.) as, for example,
described in Hausman (1992). This fact is somewhat obscured in direct econometric tests focusing
exclusively on price movements.
Law of One Price__7
time. Models demonstrating this basic fact have long been available (e.g. Pratt et al.,
1979). There is also the even more general presumption that non-tatonnement models
will establish equilibria without LOP, which can be demonstrated even with simple
computer simulations based on myopic local interaction modelling (Epstein/Axtell,
1996, pp. 116ff.). Thus, adherence to the LOP does not seem to be an empirical issue,
but a matter of basic beliefs about how the market mechanism works. However, there is
always one strong argument put forward by equilibrium theorists, for example, in
international economics: „in the long run“ there is no compelling reason to believe that
market imperfections persist beyond the level of frictions that is absolutely necessary
under realistic circumstances. That is, if these frictions are reckoned with, the LOP can
be regarded as an almost logically true statement about the market as an equilibrium
process, and only if the equilibrium concept is rejected outright, can the LOP no longer
be accepted as a fundamental principle of arbitrage.
But there is another problem with LOP that is related to the fundamental issue how
arbitrage works, that is, how entrepreneurs discover the opportunities to strike a good
bargain, i.e. how gains from trade are actually realized. The concept of „frictions“
somehow neutralizes this role of entrepreneurial discovery, even implicitly conveying the
impression that frictions are themselves an efficient state in terms of the allocation of
resources. The question may be raised what happens to the LOP if the very process of
discovering and exploiting market opportunities is scrutinized. This kind of
entrepreneurial action is different from the grand Schumpeterian acts of creative
destruction and may be safely regarded as a pervading phenomenon in real market
economies, where myriads of entrepreneurs are recurrently processing market data.5
In this paper, I will briefly review some recent attempts at testing the LOP and its
relatives especially in international economics. Subsequently, I will try to reject the LOP:
My argument rests upon the hypothesis that under the condition of a non-homogenous
and unequal distribution of knowledge across economic agents, empirical analyses of
market transactions can never yield the LOP as a generally valid result. Since unique
availability of knowledge is the core feature of entrepreneurial capabilities,
entrepreneurship and arbitrage according to LOP cannot coexist. I wish to make the
strong point that the very concept of arbitrage is a paradoxical idea, if entrepreneurial
activity is treated as a non-tradable input into the provision of goods traded on the
market. Hence, I claim to be able to reject the LOP within the framework of equilibrium
thinking: It is the very activity of trading that prevents the LOP from holding in reality,
although it is a perfectly logical consequence of equilibrium approaches to the market.
5 The idea of the omnipresence of entrepreneurial behavior is closely related to Austrian
perspectives on the market process. In particular, Mises (1949) developed the notion that „everybody is
an entrepreneur„. However, in Austrian theory, too, there is the split between proponents of the
equilibrium as the final point of convergence of the price mechanism and scholars outrightly rejecting
even the most basic reference to that concept. For a survey, see Kirzner (1997). Hence, the LOP also
seems to be a promising testing ground for selecting between both versions of Austrian theory. In an
earlier version of this paper, I also argued that the topic may be relevant for the debate about the
appropriate understanding of the Schumpeterian approach, especially in his “Theorie der wirtschaftlichen
Entwicklung” where entrepreneurship is regarded as a force which destroys equilibria.
8__Carsten Herrmann-Pillath
2. Some Methodological Problems of Empirical Research Into Arbitrage
2.1 LOP: Law or tautology?
A closer look at the link between LOP and spatial integration immediately reveals that
the logical nature of the LOP is by no means clear, because the LOP may be interpreted
either as a definition of integration or as an empirical hypothesis about real pricing
patterns. Then:
– first, as an empirical hypothesis, every meaningful test would presuppose that there
is an independent measure of integration available because otherwise any refutation
can be accommodated via an appropriate redefinition of the region considered to be
the integrated one. As a definition of integration, LOP can never be refuted or
verified: We can only assess whether or not a region is integrated by applying LOP
and getting consistent interpretations of the data. This problem is formally
analogous the identification of „relevant markets“ in competition analysis. Hence,
there is even a third possible interpretation of the LOP (Knetter, 1997, p. 5), namely
treating the LOP as a definition of „identical goods“, provided that an exogenous
measure of integration is already at hand. The latter problem is mostly stressed in
research into price dispersion where it is very difficult empirically to identify
„identical goods“ in terms of consumer preferences (Kessner/Polborn, 2000).
Correspondingly, there is always a serious problem of under-determination involved,
given the fact that both the economic borderlines of regions and the criteria of the
identity of goods are very difficult to measure.
– second, and related to the last point yet methodologically different, is the logical
flaw underlying most uses of LOP as an indicator of integration, which invert the
conclusion from integration to LOP, thereby inferring the truth of the premise from
the confirmation of the consequence, a fairly common logical error (see, e.g.,
Salmon, 1973, ch. two). There is rarely an explicit exclusion of other explanations for
observing similar prices for similar goods. This is a problem because hence there is
no necessary relation between patterns of prices and the arbitrage process as
envisaged by LOP. For example, spatial theories of imperfect competition imply that
observations on convergence of prices can in fact contradict the assumptions of LOP
because pricing violates the marginal conditions. That is, if there are spatial costs,
empirical validity of the LOP would either imply cost absorption and hence price
discrimination on the part of producers (Greenhut et al., 1987, pp. 102ff., 193,
234ff.) or actual differences in the „full price“ of the goods that would internalize
costs of consumers getting access to the good (ibidem, p. 52). Argued the other way
round, violations of the LOP need not be proof of a lack of integration, but precisely
Law of One Price__9
the result of the perfect competitive integration of a system with spatial costs of
market activities.
Regarding the first point, a crucial empirical problem results to be the measurement of
impediments to arbitrage. For most commentators, LOP is still considered to be valid if
the impediments to arbitrage can be treated as being internalized in its mechanism: for
example, if prices converge interregionally, taking transport costs into consideration.
This argument can also be applied on more complex categories like exchange rate
uncertainty, as for example, considering whether or not markets for hedging against the
exchange rate risk are present (Maloney, 1999). This means the impediments are either
exogenous, yet included in the calculation of costs of arbitrage, or are endogenous to
the arbitrage process, and hence object of the optimization calculus of the agents. In
both cases, the possibility of adducing a complete economic explanation of observed
failures of LOP is regarded as proof of its validity, similar to the treatment of „friction“ in
classical mechanics.
Again, problems arise when we consider the structure of that argument. In the theory of
international trade, exogenous impediments have proven to be the only way of resolving
the problem of indeterminacy of the direction of trade in multi-factor/multi-goods
models, or of determining the spatial distribution of production. In Samuelson’s (1954)
classical approach only so-called „iceberg“ transport costs were introduced in order to
get that result; however, any additional kind of exogenous impediment would evidently
yield the same effect, as transaction costs in the broadest meaning of the term. But
then we are back with the problem of measuring integration independently because
unless we know the entire range of impediments impacting on arbitrage, we would not
be able to test the trade model empirically.6 Again, the LOP could only be used as an
implicit definition of „impediments to trade“.
Endogenous impediments to trade lead to problems of definition, too. Imagine that all
possible impediments to trade were endogenous to the arbitrage process, which means
that agents would not treat the impediments as a given, but rather try to find the
optimal way to diminish the impact of impediments. Then we enter into Dr. Pangloss’s
world because the non-existence of spatial arbitrage could no longer be interpreted as a
lack of integration. If agents do not realize transactions, this would simply have to be
conceived of as an efficient state of the world, which means that the world is indeed a
6 I do not wish to delve into the details here (see Herrmann-Pillath, 2000a). Suffice to mention that
trade theorists have developed fairly complex approaches to tackle the problem. For example,
impediments to trade are introduced indirectly via the estimation of the demand side of Heckscher-Ohlin
models by applying gravity models, see Davis/Weinstein (1998). The indeterminacy problem becomes
apparent in tests of trade models like Harrigan (1995), (1997), where another approach is taken to a
solution, namely introducing absolute advantages in terms of country-specific productivity differences.
The central role of trade impediments for determining trade models is made explicit in
Bernstein/Weinstein (1998) who compare a presumably integrated region (Japanese prefectures) with
the world and re-interpret the large residuals of H-O-estimates in the former case as a confirmation of the
H-O-model, just because of the correlation between the strength of impediments and the degree of
determinacy of the model. Of course, the final proof of the pudding cannot but rely on accurately
measuring the impediments in order to fix the correct estimation framework.
10__Carsten Herrmann-Pillath
fully integrated economic system because both the realization an the non-realization of
transactions are determined by the price system. In other words, in that scenario the
world would be fully integrated in terms of informational linkages so that no opportunity
for arbitrage and, hence, profit would be left aside.7 Therefore, it becomes a matter of
arbitrary definition whether the non-existence of certain transactions is treated as a
state of integration or a state of disintegration unless we are able to accurately describe
the state of information in the economy.
Researchers try to get round all these pitfalls by referring to empirical examples where it
is seemingly easy to identify goods characteristics and markets. A famous example are
the econometric tests of market integration for the journal „Economist“ (on the
following, see Knetter, 1997, and Goldberg/Knetter, 1997). There are differing results
depending on the samples and the respective approach, but, roughly speaking,
symptoms of regional disintegration of world trade in the „Economist“ could be
identified. Yet, there is no unequivocal diagnosis because of two difficulties.
– First, we need to ask whether the position of the outside scientific observer is the
relevant one to compare goods and to select „identical“ ones. In the case of the
„Economist“, this outside position proves to be problematic because even though
copies of the „Economist“ seems to be perfectly identical in terms of content and
layout, this may not be perceived thus by the customer. As is well-known from
competition theory and policy, goods characteristics cannot be assessed in isolation
but only in relation to other goods (complements and substitutes).8 This, however,
means that a physically identical good may assume a completely different position
in the goods space of different territories, hence not in fact being the same good. In
other words, the criterion for assessing the identity of goods cannot be that of the
outside observer but only that of the participating „inside„ economic agents.9
7 It is not always easy to recognize the fundamental importance of full informational integration in
economic theories. For example, although the “New Economic Geography” explicitly takes trade costs
into consideration and therefore could possibly tackle the problem of measuring degrees of integration,
on a more fundamental level the mathematical modelling techniques assume full informational
connectedness, see Schweitzer (1998, p. 110).
8 Goods characteristics are not independent of marketing strategies, either, in particular branding
strategies. The mixed results of highly disaggregated tests of LOP for goods and services in U.S.-Canadian
cross-border comparisons were explained by Rogers/Jenkins (1995, p. 356) with reference to the
distinction between homogenous „auction goods„ and heterogenous „customer goods„. The LOP is mostly
valid for auction goods but not for customer goods. However, the assignation to a certain category cannot
be based on exclusively „objective„ features of goods, but depends on branding strategies and the
provision of complementary services. „Customer goods„ can be created out of „auction goods„ and vice
versa.
9 In the theory of international trade, this problem is mostly defined away with the assumption of
identical homothetic preferences among the economic agents or with the assumption of identical
demand elasticities. The other side of the coin is the introduction of the Armington-bias that simply
assumes that agents treat identical goods differently according to country-of-origin, so that demand
elasticities become goods-specific. If the latter is introduced (as in Trefler, 1995) without making the
causes explicit, we stick to the position of the outside observer, yet simply say that goods are not
identical.
Law of One Price__11
– Second, when reflecting upon the strategy for selling the „Economist“ internationally,
identifying the above differences in the goods space is, of course, the bread and
butter of international marketing. That means there is someone who collects and
processes information about those differences, and who tries to exploit them for the
sake of profit. If the firm selling the journal adapts its pricing policy to that
knowledge, international prices of the identical product will differ. However, should
we conclude that the respective violation of the LOP means there is no spatial
integration? Of course not, because we observe a complete informational
interdependence and a complete interdependence of pricing decisions across all the
markets on which the „Economist“ is sold. This is also true if the comparable product
is sold by independent domestic producers provided they take the potential external
competitive forces into consideration.
Hence, we learn that Dr. Pangloss’s problem indeed affects the interpretation of studies
on the LOP in the case of the „Economist“.10 The same observation can be interpreted
as corroboration or refutation: For example, Knetter (1997) focuses on resale costs and
regionally different distribution channels as an explanation of market segmentation, yet
we could also conclude that the different markets reflect a differently structured goods
space. Dr. Pangloss cannot but note that what we observe must be efficient because
otherwise we wouldn’t observe it, and hence the world is always in a state of perfect
integration. There is only integration possible, and we are free to decide whether we
consider the LOP in the narrow sense to be true or not, independent of the data.
2.2 The disillusionment of econometrics
Recent econometric tests of the LOP are very closely related formally to the tests of PPP
and of the factor price equalization (FPE) theorem. Of course, the simple reason is that
all of these hypotheses are propositions on equilibrium arbitrage processes. Hence,
progress in empirical tests has followed a similar pattern in these different fields.
Step 1: Testing absolute price convergence
Step 2: Testing relative price convergence
Step 3: Testing the random walk hypothesis in the longer run
Step 4: Testing structural interdependence (co-integration approaches)
Each of these steps is a result of previous failures to confirm LOP, PPP and FPE on the
preceding step. Of course, there are differences among the theorems regarding more
specific sequences of testing approaches. For example, the FPE allows different
interpretations, depending on whether convergence is required as a result of resource
10 My argument can easily be applied to other cases, too, like Haskel/Wolf’s (1999) analysis of
IKEA pricing in different countries. The fact that local managers apply widely diverging pricing policies for
single items can be explained in different ways, and the basic point remains true that the simple identity
of goods and catalogues does not imply that the items are located at the identical structural position in
the local goods spaces.
12__Carsten Herrmann-Pillath
allocation or as a tendency following certain policy measures (liberalization of the trade
regime) (see Leamer/Levinsohn, 1995, pp. 1354ff.; Slaughter, 1998). However, this only
introduces even more degrees of freedom because, for example, dynamic effects can
also result from technological change (Baldwin, 1999). Furthermore, in spite of being
structurally related, the different theorems also require different data sets, with PPP
tests, for example, only relying on price level data, whereas direct LOP tests require
single goods prices, which is very demanding. Furthermore, this distinction between
single prices, averages of prices and levels is also of theoretical importance, because
there are different interpretations, for instance, of FPE that focus on only one of these
aspects, like the „friends/foe“ version (Deardorff, 1994). The distinction between
averages and single prices is also of econometric importance, because inevitably the
data collection procedures only produce time-period averages or mixed point-of-time
prices across regions and countries. The specific relation between these data features
and the length of the period considered can lead to substantial biases in estimating the
time needed for the arbitrage process to work its way through (mean-reversion half-
time) (Taylor, 2000).
The major methodological problem is that in most applications the peculiar role of
econometrics is not made explicit. In the debate about the status of econometrics in
economic theorizing, there are, basically speaking, two parties, one treating
econometrics as a sophisticated method with which to organize data and to observe
reality, and the other arguing that econometrics generates law-like statements (for a
critical survey see Woodward, 1995). Even if there is almost universal agreement that
testing without theory does not make much sense, these conflicting approaches are still
difficult to assess in terms of their relative merit. This is easily discernible in LOP tests
because, to put it simply, estimating pricing patterns could be interpreted as either a
sophisticated method for observing price movements (which means that there is not yet
any explanation involved) or as a straightforward justification of the LOP as a general
causal hypothesis.
From our perspective on LOP both interpretations lead to a number of methodological
problems. One reason is the well-acknowledged fact that econometrics introduces
increasing degrees of freedom in the arrangement of data and the formulation of
specific propositions about data, so that, paradoxically, better instruments for empirical
research do not necessarily imply increased power to falsify.11 Applying different
techniques, using different kinds of data, adapting scales and other devices serve to
weaken the impact of bad results on either our assessment of the accuracy of
observation or of the validity of the law-like statement. These degrees of freedom
11 Indeed, Sawyer et al. (1997) make the very strong point that the Duhem-Quine thesis is true for
economic theory, precisely because of the (growing) complexities of empirical testing in econometrics.
This means we can only reject or accept full sets of hypotheses, conditions and supporting theories of
testing, but cannot check single constituents as in fact suggested by the tests themselves. From that
perspective, there is no such thing as “testing of theories” because tests and theories can only be
assessed as integrated wholes. On a more earth-bound level, Mayer (1993) presents a bleak picture of
the practice of testing in economics, which, however, reflects these methodological dilemmas exactly. For
a revealing case study referring to competing tests of FPE, see Slaughter (1998).
Law of One Price__13
actually amplify the difficulties involved in measuring the impediments of arbitrage
which are the object of the core antecedent assumptions of LOP.12
This problem is very important for the interpretation of the stepwise progress of
empirical tests. In the original formulation of LOP, interregional prices clearly had to be
identical in the same currency, which is plainly wrong. Moving ahead to checking
relative LOP means that there should be some common determinant of levels of prices
between different regions which can be separated from movements of relative prices
which should be closely correlated if the LOP holds (e.g. Engel/Rogers, 1996). Then,
econometrics focuses on movements of relative prices and their correlation across
regions, that is, the LOP is referred to „relative-relative prices„. Clearly, if there were only
determinants of price levels with limited reach and divergent strength in both the goods
space and the geographical space, econometric analysis would never identify those
patterns if the units of analysis did not fit the spatial scope of these absolute
determinants.13
Furthermore, at a closer look we recognize that the hypothetical introduction of such
determinants is highly dependent on other theoretical assumptions. For example, in
tests of the FPE theorem it is common to introduce Hicks-neutral technology differences
between regions which allow us to stick to the assumption of identical technology
matrices in the Heckscher-Ohlin-Vanek model. This assumption is not only very difficult
to separate observationally from a Ricardian scenario, but even more important, in
empirical tests based on factor content analysis we cannot translate goods into factor
contents without that assumption, so that the very criterion of observing the goods
space is dependent on the assumption which is at the same time an explicit
precondition for testing FPE.14 Hence, Max Albert (1995, pp. 243ff.) argues that the
12 Indeed, there is an increasing trend toward shifting the battle ground in LOP and PPP on to the
methodological level of proper econometric techniques. As an example, see O’Connell (1998) who
discusses the effects of cross-sectional dependencies among real exchange rates which result from the
common numeraire country, and which impair the use of panel studies for measuring PPP. He also
discusses the high probability of sample selection bias in existing studies.
13 For example, this problem does not arise if country-specific differences in absolute levels are
introduced so that their scope matches the scope of national statistics. In FPE studies Hicks-neutral
productivity differentials between countries are introduced (Trefler, 1995), or in studies of LOP
distribution costs are assumed to be reflected in common levels of distribution costs. For PPP, the
Balassa-Samuelson hypothesis assumes country-specific productivity differentials between the
production of tradables and non-tradables. Formally speaking, the assumption of more constricted
determinants of goods price levels would be closely linked to the use of a specific-factors model that
necessarily impairs FPE. Therefore, assuming country-specific differences in levels is a very strong
empirical hypothesis, which, however, is mostly introduced by way of assumption.
14 An interesting application is Hanson/Slaughter (1999) who analyze the impact of immigration on
U.S. wages and composition of trade along the lines of the Rybzcynski theorem. Via the factor content
approach (for a survey, see Bhagwati et al., 1998, pp. 118ff.) they try to predict factor endowments by
applying the identical technology matrix linking the goods vector with factor contents. If relative FPE
holds, regions should always feature the same factor requirements for the same output vector. However,
FPE as a mere observational statement on factor prices can also hold if technology does not match the
neoclassical standard assumptions, as if, for example, there are externalities or increasing returns to
scale. Therefore, the test is only valid if all these alternatives are straightforwardly excluded. This is
another example of the equivocal conclusion from consequence to premise.
14__Carsten Herrmann-Pillath
currently fashionable tests of trade theories based on the HOV-theorem are highly
suspect from a methodological point of view because they need to adopt FPE as a valid
empirical proposition. That is, the econometric tests introduce a law-like statement into
the antecedent conditions, which is directly linked to the theory to be tested.
Therefore, tests of relative LOP and its relatives suffer from a fundamental ambiguity
arising just out of the movement away from the strict absolute version of LOP. This is
true if only national data are considered. For example, Engel/Rogers (1999) show that
relative-relative price movements seem to manifest a violation of the LOP for tradables
and just the opposite for non-tradables, which flies in the face of any sensible
understanding of LOP. Their explanation rests upon the argument that the non-tradables
prices are much stickier in nominal terms than the prices of tradables. Methodologically,
this means that after shifting to the relative version of LOP, there is a loss of information
because a lack of relative price volatility can be interpreted as a manifestation of LOP,
even though the underlying arbitrage mechanism does not even exist in the case of non-
tradables. Furthermore, we face the problem of the erroneous step backward from the
conclusion to the validity of the premises. The move from absolute to relative PPP is by
no means innocuous because the first can only be true if the LOP also holds, whereas
the latter can also be true, for example, if only the quantity theory of money holds in
both regions so that changes of price levels always need to be parallel if there are
similar changes in the quantity of money, given an arbitrary absolute price level for each
region. The exchange rate will reflect PPP, even if there are no trade but only capital
flows (see Niehans, 1995, p. 155). This is not a problem if we are only concerned with
the theory of forward exchange, but it affects our assessment of the LOP directly. The
same can be said regarding the relation between the boundaries of the integrated
region and the relative role of direct arbitrage versus indirect price linkages mediated
via third countries: LOP can be held between two countries without any direct
integration (Kindleberger, 1989, p. 74f.).
In tests of the PPP, step 3 played a very prominent role in the past because PPP is the
alternative to the random walk hypothesis as a crystallization of non-systematic
determinants on prices. The major problem surfacing in that literature is indeed related
to Haberler’s viewpoint that PPP and LOP may only be valid in the short run. Now, given
the fact that everybody knows that PPP does not hold in the short run, bookshelves of
articles have been published trying to test the random walk hypothesis in the long run.
However, precisely in the long term it becomes increasingly difficult to assess the results
of estimation procedures (for a well-balanced survey, see Froot/Rogoff, 1995). To put it
simply, the slower the reversion to PPP, the more diffuse the distinction vis-à-vis random
walk and the longer the time period needed to estimate mean reversion, the more
probable are structural impacts on PPP that cause deviations in the long run even
though tendencies to reversion might be strong, yet slowly working, in the short run
(which was exactly Haberler’s belief, as we have seen in the first section). These
complex relations between relative speed of changes in variables, determinants and
background conditions render the interpretation of estimates difficult, if not arbitrary. To
put it differently, if LOP is a propensity of certain real causal constellations as suggested
Law of One Price__15
by Cartwright (1995), which, however, can never work out fully because the time scale is
too long to justify a ceteris paribus assumption, we may be right in accepting the LOP as
a law, but at the same time we have to admit that no empirical falsification is possible.
Accordingly, accepting LOP or not does not depend on facts but on methodological
beliefs.
These problems become even more pronounced in step 4, where co-integration tests
have been introduced in order to investigate structural interdependence. Here, aside
from the increasing number of special technical assumptions, the fundamental issue is
how to interpret a possibly positive result of the tests without any clear idea about the
actual working of structural interdependencies (for example, see Burgman/Geppert,
1993, on FPE). Very often tests yield results that cannot be interpreted economically in a
straightforward manner (Froot/Rogoff, 1995, p. 1662ff.). Co-integration techniques
actually raise the requirements of providing good reasons for selecting lag-structures,
omitting or including certain variables, and separating causality and correlations (e.g.,
Cheng, 1999, on PPP). At the same time, the Haberler problem of identifying „virtual“
long-run forces in short-run phenomena is solvable in principle, yet at the price of an
ever-increasing degree of technical complexity (e.g., Culver/Papell, 1999). There is the
additional problem that some important determinants and variables cannot be
observed directly, as in the most simple case that arbitrage may not be reflected in price
movements but only quantities on which no data are available (cf. O’Connell/Wei,
1997).
All this means that econometrics takes us a full circle to the problems of measuring
integration without reference to LOP and PPP: The more complex the estimation
procedures become, the more important is the inclusion of detailed descriptions of the
institutional and structural background of the economic process. These descriptions
need to complement the econometric results as theoretical propositions about
structures of reality that generate propensities of complex events which, in turn,
underlie the presumed working of the LOP beneath the surface of a bewildering
multitude of market transactions (again, see Cartwright, 1995). That is to say, in sharp
contrast to the common stance of trade theorists, complex historical descriptions
actually attain a theoretical status that is as important as the tested hypothesis.
However, there is no guarantee that these structures might eventually lend support to
reasonable reference to the LOP.15 Moreover, these problems affect not only the
application of sophisticated econometric techniques, but also the more down-to-earth
issue of data collection and interpretation. Considerable doubts have to be raised
whether the existing data match the requirements of econometrics at all, and certain
15 An example of such complex historical accounts is Walter (1996) who analyzes the situation in
19th century Germany. For example, price movements were strongly influenced by railway tariffs which
were administered. This part of the story alone makes exclusive analysis of quantitative data elusive.
Walter argues that most determinants of integration at the same time contributed to disintegration,
albeit on a different geographical scale (i.e. integration by agglomeration versus disintegration by
peripherization). Hence, “integration” as an aggregate measure is very difficult to define.
16__Carsten Herrmann-Pillath
defects of the data, which are rarely made explicit or even known to the theorists, might
strongly bias the results (Taylor, 2000).
In place of a summary if both methodological sub-sections, we may finally observe that
all these problems are long familiar from other so-called „laws“ in economics like the
quantity theory of money. The law-like hypothesis is in fact under-determined regarding
the empirical identification of its constituents, so that we cannot fix its character in
terms of either law or definition.16 This means that in spite of seemingly rigorous
attempts at measuring the LOP empirically, these efforts can lead neither to
falsification nor to confirmation because the logical essence of the LOP is close to a
tautology. From this perspective, the LOP is a logical necessity, yet without any
empirical content.
3. Entrepreneurial local knowledge as trading input:
a necessary cause for the failure of LOP
So far, we have focused on the methodological problems that arise when testing the
LOP as an empirical proposition. As we have seen, these problems do not yet preclude
adherence to the law as a theoretical hypothesis, although there is a strong suspicion
that the LOP might be a non-falsifiable proposition. Subsequently, we will investigate
some more fundamental theoretical reasons why the LOP might not hold. I wish to focus
on one explanation for the failure of LOP that highlights the interaction between missing
markets and non-tradable goods.
Engel and Rogers (1998) examine the case of final consumer goods which are not
traded across the border of a region and of intermediary inputs in the production of final
goods which are traded between regions. The „missing market“ for final goods should
nevertheless allow the working of the LOP via the market for intermediary goods,
provided there is no local impact on the final goods price which cannot be traded away.
They show that a sufficient condition for the LOP to fail is the existence of
geographically separated distribution systems for final goods which need to be set up by
incurring sunk cost, and which at the same time allow a monopolistic mark-up for the
16 I should mention that this is by no means a fundamental flaw, depending on the methodological
and epistemological position. From the viewpoint of so-called “new structuralism” in the philosophy of
science, this ambiguity is reflected in the interdependence of procedures of measurement and the
respective theory to be tested which is typical for highly developed axiomatic theories. For this, see
Stegmüller (1986) and my application on neoclassical growth theory Herrmann-Pillath (1998). However,
there are clear consequences for assessing the role of empirical methods and theory selection, as for
example regarding the impossibility of falsification. Hence my argument in the text would remain valid.
Law of One Price__17
seller.17 The assumption of sunk cost is reasonable if we imagine that distribution
requires certain destination-specific capabilities that cannot be transferred to other
regions (like knowledge of the local language) or that investment in immobile facilities
is necessary which can only be re-sold with a substantial loss (like special retail outlets
adapted to local taste). If these barriers to entry exist, cost conditions can differ, and
hence the LOP will fail for final goods because there will be no cross-border transactions
between the distribution areas, even though intermediary products are being traded
across the border.
The crucial idea, thus, is that trade is always linked with certain services, the most
obvious one being trading services proper. Hence, spatially diverging costs of trading will
influence the working of LOP if there are certain impediments to the equalization of
those costs, and if at the same time there are impediments to the interregional resale
of the final good. The entire gamut of impediments to trade-specific services will
therefore exert impact on goods trade. On closer scrutiny, this consideration deals a
final blow to the LOP as an empirically meaningful hypothesis.18
Hirsch (1989) develops a simple and clear analytical framework. The point is that
superficially the costs of services that make the good tradable will be included as an
additional cost factor formally similar to transportation costs or tariffs. However, the
latter presuppose that goods are first produced and then traded, so that these costs are
clearly separable from production costs. Services that are strictly complementary to
goods, however, cannot be separated because the good would never have been
produced without taking into consideration the possibility of full transformation into
final use. This assertion is a special conclusion from the even more general statement
by North (1990, p. 28) that production costs consist of (technological input/output)
transformation costs and transaction costs, both being inextricably intertwined. Neither
the economic agents nor the outside scientific observer are able to measure either of
these costs separately to the full extent. However, this means at the same time that
there are „missing markets“ by which the two components could be priced and traded
separately. Hence, the LOP can never fully work for any good that is traded because the
mere activity of trading drives a wedge between hypothetical producer’s prices and end-
user prices. The very activity of trading prevents the LOP from holding for trade, if there
are non-tradable inputs into trading.
17 We note that sunk costs of market entry also play an important role in the explanation of
exchange rate hysteresis put forward by Baldwin/Krugman (1989). Hence the mechanism described by
Engel and Rogers can be even more complex. This is important for analyzing the LOP because empirically
we always face the problem how to calculate prices in same currencies. This means that factors
influencing the nominal exchange rate can lead to systematic deviations of the real exchange rate from
PPP which in turn leads to violations of the LOP.
18 O’Connell/Wei (1997) analyze product prices across U.S. cities and argue that the movements of
prices are influenced by the complex interaction between fixed and variable costs of distribution.
However, here we find the same logical flaw as involved in the use of LOP as a measure of integration.
The authors deduce the structure of costs from econometrically identifiable price patterns. They do not
exclude other possible explanations explicitly.
18__Carsten Herrmann-Pillath
It is precisely in this context that the role of the entrepreneur comes to the fore, if we
distinguish between the outside observer and the participating agent. The
Samuelsonian „iceberg„ concept conflates outside and inside observer with the implicit
assumption that transport costs are known to everybody and perceived identically.
However, although this might seem to be sensible for transport costs, we cannot take it
for granted for the majority of other categories of transaction costs.19 The spectrum of
causes of transaction costs reaches from linguistic differences and diverging normative
backgrounds of social behavior to special knowledge about local demand conditions or
contractual uncertainty. In the case of transaction costs we have to differentiate sharply
between the observable impediments to trade and the subjective perceptions of those
impediments which in turn are linked with the individual assessment of the respective
capabilities to overcome these obstacles to spatial transactions. Before transactions are
realized, these perceptions are based on subjective expectations; after transactions they
continue to be different among various sets of individuals, depending on their specific
experience, and until all the information about the impediments is completely dispersed
among the economic agents.20
As we see, for the observation of actual arbitrage processes the measurement of
impediments to arbitrage is only possible if the information about their nature as well as
the distribution of capacities to overcome them is identical among the set of economic
agents as well as scientific observers. Of course, this would be tantamount to the
standard assumptions on perfect and complete information in equilibrium models. In all
other cases, we cannot accurately measure and identify impediments to trade without
detailed knowledge of the information sets and capacities of the participating economic
agents.
If we now return to the Engel/Rogers explanation of the failure of LOP, we conclude that
trade must necessarily be linked with activities to overcome impediments to trade.
Generally speaking, trading with goods is always linked with the provision of certain
services. These services include transport, insurance, communication, advice,
marketing, legal counseling and everything related to the incurring of transaction costs,
that is and most importantly, the costs of discovering and preparing opportunities for
19 Indeed, even Paul Krugman (1995, p. 1273), who applies the iceberg concept extensively in his
“New Economic Geography”, expresses serious doubts whether it makes sense to compare transaction
costs with iceberg transport costs. A systematic argument against this equation is presented by
Streit/Wegner (1992). They argue that the very essence of transaction costs lies in the fact that they
result from a lack of information in the sense of true uncertainty. Hence there cannot be ex ante
knowledge about these costs before transactions are realized, which implies that agents cannot optimize.
They learn about transaction costs by means of transacting, that is, ex post. In comparison, under normal
circumstances information about transport costs is available ex ante.
20 I wish to mention that there is vast empirical literature referring to this theoretical argument in
the field of international marketing, in particular regarding the widely diverging capabilities of firms to
export. The so-called “export-development process” is nothing but the peculiar way to enter that system of
transactions which is in part described by the concept of arbitrage. For a survey, see Leonidou/Katsikeas
(1996).
Law of One Price__19
business.21 Now, these services can only be integrated in the LOP if prices are publicly
known and if they are traded at least on the respective local markets with inputs traded
interregionally (for example, non-tradable local marketing services would use
interregionally mobile labor). In abstract terms, this means that transaction costs would
be valued at equilibrium prices. However, this is a contradiction in terms: If knowledge is
unequally distributed across agents, and if transaction costs result from incomplete
knowledge, there can be no equilibrium valuation of the services needed to overcome
impediments to trade.22 This means that any valuation of services includes a non-
reducible and non-separable component of remuneration for the individual readiness to
overtake entrepreneurial risk, i.e. coping with uncertainty.23
Here is the most general refutation of the LOP:
The LOP can only be a true empirical proposition if knowledge about impediments to
trade is fully dispersed across all economic agents. If the individual states of
information differ, as well as individual capabilities to overcome those impediments,
arbitrage cannot result in the LOP being valid for empirical pricing patterns. Observable
goods prices reflect different cost conditions across space which include an inseparable
component of remuneration of entrepreneurial services which is a non-traded good.
These entrepreneurial services focus on the discovery and realization of transaction
opportunities and hence determine the transaction costs specific to every single
transaction. Differences among those costs render the LOP invalid.
This argument is very closely related to the subjectivist approaches by Shackle and to
the analysis of entrepreneurship by Kirzner. In the recent literature, Casson (1997, pp.
80ff.) proposed a theory of entrepreneurship that stresses the role of tacit knowledge
about market opportunities as a non-tradable. Metaphorically speaking, the LOP cannot
be valid because real arbitrage is inseparably intertwined with entrepreneurial activity,
21 Casson (1997, p. 282ff.) offers a list of factors determining the “information intensity of
transactions” that illustrates this point in more detail. Of course, this is closely related to the standard
distinction between homogenous and heterogenous goods in trade theory. But here we talk about a
continuum of goods properties where only a very small part would be close to the feature of homogeneity.
22 As we can see, our argument does not preclude that certain organizational and technological
changes lead to the emergence of markets on which a part of those services will eventually be traded and
measured. Yet, this is different from standard equilibrium analysis which takes the set of markets as a
given. For a theory on the emergence of markets that transform transaction cost into measurable
production (transformation according to North) cost (like traded services) see Wegehenkel (1981).
23 We should add that in the attempts to measure purchasing power parity directly for the sake of
comparing national income calculations, services are regarded as being the most “comparison-resistant”
category, see Kravis/Lipsey (1991, p. 443). Though this is a different point, it reflects the strong impact of
local knowledge on demand and supply of services. Anderson/Marcouiller (1999) lend some support to
my hypothesis because they show that different degrees of insecurity across countries may be reflected
in destination-specific price mark-ups of exports. These mark-ups are equivalent to the remuneration for
the special services enabling the agents to realize the transactions. My approach also fits in with the
analysis of the IKEA case by Haskel/Wolf (1999) who argue that the price differences for identical IKEA
products in different countries do not result from location-specific non-traded costs because these have to
affect the set of goods in a similar way. However, entrepreneurial knowledge has to be regarded not only
as location- but also goods-specific, so that their explanation based on strategic mark-ups can be
regarded as a corroboration of my argument.
20__Carsten Herrmann-Pillath
and because there can be no arbitrage for the latter.24 Entrepreneurial activity uncovers
the information that might eventually disperse among the population of agents and
which might provide the base for the LOP to work out its effects. However, if there are
changing external circumstances and other impacts on the arbitrage process, the LOP
can never be fully recognizable in empirical data, because the general state of
uncertainty and unequal distribution of knowledge is recurrently restored.
Within the context of the Engel/Rogers explanation, this abstract reasoning can be
easily fleshed out into more concrete hypotheses. The crucial ingredient is the
introduction of sunk cost in terms of investment in entrepreneurial „local knowledge“.
Now, any kind of information specific to a certain destination of trade goes hand in hand
with incurring sunk cost of collecting that information. Hence, spatial entrepreneurship
will always feature behavioral phenomena linked with sunk cost. This is a simple
generalization of the scenario with separate distribution systems resulting in a scenario
of separate, entrepreneur-centered information and communication systems. There are
many concrete bases for such information systems that are structurally very similar to
distribution systems. In particular, any kind of social network specific to locations is an
impediment to trade linked with sunk cost. For example, if an entrepreneur has to
establish personal communication channels in order to access information about the
local market, this investment cannot be transferred to other locations. We can speak of
location-specific social capital which,formally, can be treated analogous to a distribution
network à la Engel/Rogers (1998). This idea entails many important consequences
because trade will always reflect a complex interaction between fixed and variable
costs, presumably with strong non-linearities involved: a far cry from LOP!
Finally, our argument can be linked to the theory of incomplete contracts.25 The
standard use of the LOP presupposes that even if there are frictions like transport costs
that cause markets to miss, the network of contracts will allow a complete linkage
among the prices of existing markets. However, it there are certain markets missing
because the underlying economic activities are not contractible, this conclusion is no
longer valid, because the reason is not linked with spatial costs that are transparent for
every agent. That is, there is a fundamental difference between „non-tradability“ arising
from spatial costs and „non-tradability“ because of incontractability, even if the latter
results from spatial phenomena (like spatially dispersed local knowledge). So the
question is whether entrepreneurial activity is contractible. Obviously, this is not the
case if there is true uncertainty, because ex ante no valuation can be agreed upon, and
24 The spatial competition models developed by Greenhut et al. (1987, esp. chpt. 19) also introduce
special rents that are reaped by entrepreneurs who cope with uncertainty (which is different from the
mark-up in monopolistic equilibrium models). Here, in the short run a certain price pattern will correspond
with a variable distribution of firm sizes reflecting divergent entrepreneurial capabilities as well as
individual perceptions of the individual opportunity costs of entrepreneurship. In the long run, there will be
an efficient equilibrium because location is endogenous and complete factor mobility is realized. In that
setting, LOP will be discernible if no further changes of data take place. But this scenario transcends the
conventional one by far.
25 I am grateful to Martin Kolmar, Konstanz, for drawing my attention to this argument.
Law of One Price__21
no market can be set up: If the entrepreneur revealed his special knowledge to the
buyer, the latter would no longer need the service which is based precisely on that
knowledge – if the buyer does not have that knowledge, he or she is not able to decide
about his or her reservation price. However, on the other hand the entrepreneur who
invests, for example, in location-specific social capital may run into a hold-up problem
when trying to recover those costs. As Underlain and Fell have demonstrated in a couple
of related papers (1998a,b), if there is such a hold-up problem involved in contracting
with the sunk costs of preparing the contract, there is no way to add another contract
that arranges for the measures to solve this hold-up problem. Now, every
entrepreneurial activity that is linked to specific investments in particular destinations
would face such a hold-up problem if a contract needed to be designed that separately
established a market transaction for these investments. That is, if alternatively local
consumers were also to invest in the specific knowledge about possible locations of
producers that might deliver the locally needed goods, there is the problem how to
share these ex-ante costs of setting up the contract among the two sides. This sharing
arrangement is in turn a contract that gives rise to ex-ante costs, and so on ad infinitum.
Therefore, our refutation of the LOP can be justified by many different arguments that
have one crucial idea in common, namely: trading in a particular space is an
entrepreneurial activity if knowledge about market opportunities is not perfect and
complete across all economic agents. This activity is a location-specific, non-tradable
input into the provision of goods, so that the LOP cannot hold in principle.
Let us conclude with some observations on empirical issues in international trade which
lend support to our abstract reasoning. One of the hot topics in empirical research into
exchange rates is the analysis of „pricing to market“ (PTM) and the extent of exchange
rate pass-through. In the empirical data, pricing to market is reflected as a violation of
LOP and, hence, as a deviation from PPP. The problem, however, is that PTM cannot
simply be explained by barriers to trade in the narrow sense of the term. In their recent
survey Goldberg and Knitter (1997) show that it is very difficult to identify the reasons
behind PTM even in the broadest sense, given the serious difficulties in separating and
measuring factors like market power, demand elasticities, non-tariff barriers to trade
and last but not least intangible impediments to trade. This is, of course, directly
relevant to the most general and at the same time tautological explanation of the
failure of LOP: If markets are segmented, LOP cannot hold. But why, when and how are
markets segmented?
All the research reported by Goldberg and Knetter tries to apply a certain explanatory
scheme which assumes that eventually objective determinants of market segmentation
can be discovered which are reflected in the behavior of the agents simply following
their optimization calculus. This is exactly the belief that the positions of the outside
observer and the participant agent can be conflated. However, from the perspective of
the argument presented in the preceding paragraphs this will never yield a clear result
because observed market data always reflect entrepreneurial inventiveness in creating
transactions and hence at least one crucial determinant for which the LOP cannot hold
in principle.
22__Carsten Herrmann-Pillath
In an important recent contribution to this topic, Clark et al. (1999) adopt a viewpoint
focusing on that entrepreneurial determinant, too. One of the causes implying PTM is a
different degree of exchange rate pass-through. Empirically, this is very difficult to
explain in a systematic fashion, because there are clear differences in pricing patterns
across industries as well as across countries of destination. In terms of system exporters
from certain countries sometimes seem to behave differently from those of other
countries (which, by the way, also reflects different domestic pricing patterns). Now
Clark et al. argue that these observations can only be explained via an explicit
consideration of pricing strategies of single firms.26 If this is true, systematic aggregate
PTM phenomena can only occur if firms behave similarly. Pricing strategies, of course,
are part and parcel of the entire entrepreneurial approach to the creation and
realization of transactions. In the light of our former argument, we may say that pricing
strategies are based on location-specific knowledge about market opportunities and,
hence, have to be regarded as part and parcel of the set of service inputs making trade
possible at all.
Indeed, the authors show that there are systematic differences in pass-through
depending on the general strategy of the firms. For example, firms may adopt different
price/cost strategies, as for example, cost-plus pricing or incremental export pricing.
From the perspective of LOP, the latter strategy possibly leads to perceived dumping
because firms are satisfied if export earnings only cover the additional costs of
exporting. However, this is a completely sensible pricing policy for firms operating over
an extended territory and aiming to open up new regional markets. In the same vein,
pass-through will be strongly influenced by the choice of distribution system, because
the market reactions of independent distributors will be different from direct exporters,
in particular if there are several steps in the distribution system involved, and if
distributors deal with many different products. Furthermore, Clark et al. present
arguments that pass-through will be asymmetric for certain strategies. For example, if
firms have been successful in building up a strong brand image in the importing country,
an appreciation of the exporter’s currency will allow gains to be reaped because import
demand is inelastic to a certain degree, and a depreciation will be passed through to the
customers.
All in all, these sketchy observations on PTM demonstrate that there are indeed
concrete empirical starting points for a better understanding of the impact of
entrepreneurship on the ongoing market process. PTM can be regarded as an important
cause of LOP failure that goes back on this kind of all-pervading entrepreneurial activity.
Entrepreneurial strategies are always context-dependent so that this match between
individual entrepreneurial competencies and certain local conditions rule out any
generalized hypotheses on arbitrage.
26 This is also true of more general perspectives on pricing in theories of imperfect spatial
competition. Greenhut et al. (1987, pp. 19ff., 65f.) distinguish between different kinds of strategic
behavior on the part of new entrants and incumbents, depending on the assumptions about mutual
reaction patterns. As a result, pricing patterns can differ considerably, although there is complete
integration.
Law of One Price__23
In the recent literature on international trade, therefore, we meet many phenomena that
refer to singular patterns of market relations, which on their part are not explainable
within the established equilibrium framework (for a survey, see Herrmann-Pillath,
2000). There is the literature on border effects on trade where researchers have not
been able to eliminate that effect by introducing almost every possible economic
determinant (see Helliwell, 1997). There is the need to acknowledge the strong impact
of singular country characteristics on trade, which is tantamount to introducing specific
absolute advantages into trade models (Hummels/Levinsohn, 1995; Trefler, 1995).
Even in domestic trade, there is the „home bias„ in demand and an additional „home
market effect„ on related exports systematically favoring goods produced in
geographically closer locations (Wolf, 1997). Although many of those contributions
apply methods like gravity equations that are not directly designed to analyse arbitrage,
we can duly regard all these results as indirect symptoms of substantial deviations of
real market processes from the ideal-typical equilibrium approach to arbitrage. All these
observations refer to impediments to trade and hence to factors impeding the free
working of the LOP, too. Furthermore, there is strong evidence of the importance of
individual determinants of trade.
4. Conclusion: whither the LOP?
I have presented a fairly general argument against the empirical possibility of the Law
of One Price that is based on the assumption that individual entrepreneurial knowledge
differs among the set of economic agents as well as across the set of geographically
separate markets. This rejection also implies that we cannot use price and quantity data
in order to assess the degree of integration in a certain region, but have to rely on much
more detailed descriptions and analyses of institutional and structural conditions.
Moreover, we have shown that there are serious methodological problems involved in
applying the LOP, because there is a fundamental ambiguity between definition and
law, and because econometrics produces the paradoxical result that the leeway for
interpreting the data is ever-increasing.
Therefore, we realize that there is indeed a match between the more complex view of
entrepreneurship and the analysis of markets. The reasons why the LOP fails ultimately
refer to the interaction between missing markets and arbitrage and to the dynamic
process of overcoming impediments to trade, i.e. of creating markets by entrepreneurial
action. Evidently, the LOP only refers to existing markets where there is no longer any
special entrepreneurial input needed for making transactions possible. The LOP
presupposes an automatically running market process. If entrepreneurs are operating in
a market environment where specific investments in knowledge formation and
transmission are needed, prices will reflect uncertainty which in turn gives rise to true
24__Carsten Herrmann-Pillath
entrepreneurial profits. The ultimate reason why the LOP fails is the fact that
entrepreneurship cannot be the object of arbitrage.
Therefore, we may venture a final thought. The increasing complexity of modern
production and consumption processes, and the growing informational requirements for
arranging transactions imply that the market process will in fact diverge even more
from the ideal-typical arbitrage model inherent in the LOP (see also Dunning, 1995, pp.
177ff.). Regions are being integrated via complex solutions to the division of labour
which transcend conventional trade arrangements. Entrepreneurial inventiveness
creates new and complicated solutions to the challenge of making markets work. In
that context, LOP should be regarded as a completely misplaced idea.27 However, we
face serious problems in grasping this reality with the available data because the
categories of standard trade and international price statistics simply do not fit into the
emerging new structures of the international division of labor. As a consequence,
economists should exercise great care when investing in the test of theories and models
unless they are very sure that the data are indeed the required ones. Otherwise,
research activities will be misled by the delusion of stepwise empirical progress which in
fact is only based on an increasing ingenuity in match-making between theory and data.
In the case of LOP, there is a strong suspicion that the emerging structures of global
trade simply give less and less space for the LOP to work out – and not the other way
round, as some observers would have it (for example, Bordo et al., 1999). Continuing all
these efforts to test the LOP may end up proving Ronald Coase’s quip: „If you torture the
data long enough, Nature will confess.“ (according to: www.etla.fi/pkm/JokEc/).
27 For example, Feenstra (1998) argues that production location is no longer distributed spatially
along the lines of established trade theories, because the production process is “fragmented”, that is to
say, split along steps in the value chain. Hence, as Knetter/Slaughter (1999) show, if trade is no longer
between ”production sites” but between different locations of “activities”, there is no longer any
necessary correlation between integration and LOP as measured in price dispersion across countries.
Law of One Price__25
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