KEYNESIAN ROOTS OF INTERESTPARITY THEOREMS∗

André Cieplinski†, Ricardo Summa‡

April 29, 2015

Abstract

Interest parity theorems, namely the covered interestparity (CIP), uncovered interest parity (UIP) and realinterest parity (RIP), as part of the basic open macroe-conomics framework, are presented in almost every text-book in macroeconomics and international economics. Thisset of theorems explain how international capital flowsmake it impossible for a monetary authority to autonomouslyset their basic real interest rate in relation to the inter-national one. In this work we will trace back the devel-opment of these theorems. We argue that although somepost-Keynesians nowadays reject uncovered and real in-terest parities, even in the long period, these interest par-ity theorems have a Keynesian root. Covered InterestParity first appears in Keynes 1923s’ A Tract on Mon-etary Reform. Uncovered Interest Parity theorem relieson early contributions from Keynes (1936), Kaldor (1939)and Tsiang (1958). But it is only during the 70’s, alongwith the diminished influence of keynesian theory, thatother elements such as Rational Expectations and the Ef-ficient Market Hypothesis are incorporated in this openeconomy framework and together with the PPP lead to

∗The authors kindly thank the comments of Franklin Serrano, Fábio Fre-itas and Anlexander Tobon.†PhD candidate at the University of Siena.‡Associate professor at the Institute of Economics, Federal University of

Rio de Janeiro (UFRJ).

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the Real Interest Parity. Moreover, during the develop-ment of these theorems some interesting questions weretackled such as the role of speculation in destabilizing afloating exchange rate regime and the possibility of set-ting autonomously real interest rates across countries. Fi-nally, we briefly summarize themain results obtained bythe vast empirical literature. While there is great ev-idence in favor of the CIP, the results known as “UIPfailure” and “forward premium puzzle” represent the per-sistent difficulty to falsify the UIP empirically.

1 Introduction

In the following pages we analyze the origins and developmentof interest parity theorems throughout the XX century and ar-gue that their roots may be traced back to the works of JohnMaynard Keynes. While covered interest parity (CIP) was firstpresented in A Tract on Monetary Reform (Keynes, 1923), un-covered interest parity (UIP) relies on a fundamental contributionfrom Tsiang (1958), largely influenced by Kaldor’s (1939) analy-sis of speculation; which, on its turn, is inspired in the portfoliomodel exposed in chapter 17 of Keynes’ (1936) General Theoryof Employment.

Throughout the twentieth century a detachment from thiskeynesian roots is verified by the adoption of typical marginalisthypothesis such as rational expectations and efficient markets,particularly in the case of UIP. Another later development is thereal interest parity (RIP) by the joint assumption of UIP, rationalexpectations and purchase power parity (PPP).

The development of these theorems is also intertwined byother debates, such as the (des)stabilizing role of speculation infloating exchange rate regimes and the possibility to set – andmaintain – different real interest rates across countries, i.e. theeffectiveness of monetary policy in open economies.

The rest of the article is organized in four sections. One foreach interest parity theorem and a final one presenting the majorstylized facts from the empirical literature.

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2 Covered Interest Parity (CIP)

The first presentation of CIP dates back to 1923 in A Tracton Monetary Reform (Keynes, 1923, p.115-139). And the ba-sic premises stablished there would only face small modificationsduring the following decades. In short, financial agents seek thegreatest return possible without incurring in exchange rate risk.The covered interest parity is, therefore, a non-arbitrage condi-tion since its very first formulation.

Keynes’ analysis begins with a precise definition of forwardexchange markets: “A “forward” contract is for the conclusionof a “spot” transaction in exchange at a later date, fixed on thebasis of the spot rate prevailing on the original date.” (Keynes,1923, p.116). Hence, the forward rate is determined in relationto the spot rate prevailing when the forward contract is fixed andbears no relation to the spot exchange rate in the future .

The CIP is presented assuming the forward exchange pre-mium (ft − st)as an indicator of investors preferences. Capitalsare invested in the currency whose interest paying assets offersthe greater return1 (Keynes, 1923, p.124). Thus, the non ar-bitrage condition is achieved when the interest rate differential(it − i∗t )equals the forward premium2, once the forward exchangecontract mitigates exchange risk.

Regarding the adjestment mechanism tha underlies the CIP,Keynes believed it to be a stable because of speculators acted as acounterpart for arbitrageurs. The formers engage into uncoveredoperations, leading to an excess of buyers in the forward marketand, hence, an increase in ft. The divergence between ft−st andit − i∗t creates arbitrage opportunities in the oposite direction ofthe speculators. In this case it would be profitable to realize two

1Afterwards, in the Treatise on Money, Keynes (1930) called the situationwhen future exceeds spot prices, in our case ft > st, contango and theopposite case (ft < st) normal backwardation.

2In fact, Keynes (1923) and Einzig (1937) believed that due to the fraildevelopment of markets for futures a minimal profit margin of aroung 0.5%was necessary for agents to engage in arbitrage operations of this kind. Later,Peel and Taylor (2002) presented evidences in favor this hypothesis for theperiod preceeding the first world war. Already in the 1950s this rule wasthought to be obsolete (Einzig, 1960).

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simultaneous covered operations: buying exchange rate spot andselling it forward. Thus, the arbitrageurs would push ft downuntil forward premium and interest differential were balancedagain34.

Other contributions in the first half of the century are due toEinzig5 (1937) and Kindleberger (1939). Yet, the 1950s, when“[the] relative importance of hedging operations has greatly in-creased” (Einzig, 1960, p.485), were a more prolific decade in thedevelopment of interest parity theorems. During these years theCIP was revisited in a more formal way by Spraos (1953), Trued(1957) and Tsiang (1959).

Spraos was responsible for the explicit presentation of CIPas a non arbitrage condition between the interest rates of twocountries, as in equantion 1 below.

ft

st

= (1 + it)(1 + i∗t )

(1)

Which may be linearized as:

ft − st = it − i∗t (2)

Provided there is free capital mobility, convertibility betweencurrencies and available resources (funds) for arbitrage capitalswill be invested in the interest rate that yields greater return,thus guaranteeing that 1 holds. According to Spraos, a discrep-ancy in the CIP with the forward premium exceeding the interestdifferential, for example, will lead arbitrageurs to buy exchangespot and sell forward, receiving the foreign interest rate6. Thus,CIP will return to equilibrium due to the increase in the domestic

3It is in this sens that speculators and arbitrageurs have complementaryroles, as Tsiang (1959) would point again later.

4Not only speculation acts as a stabilizing force, it also provides thenecessary liquidity for exchange rate markets. “A free forward market, fromwhich speculative transactions are not excluded, will give by far the bestfacilities for the trader who does not wish to speculate, to avoid doing so.”(Keynes, 1923, p.136)

5Spraos (1953, p.91) points Einzig (1937) as the first to coin the term“ínterest parity” to refer to the relation betwee interest differentials andspot and forward exchange rates.

6 ft

st(1 + i∗t ) > (1 + it)

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and fall in the foreign interest rate. In contrast with Keynes, inSpraos (1953, p.116) the adjustment depends on the endogenousvariation on interest rates. Therefore, it relies fundamentally onthe hypothesis of exogenous money supply.

“Thus the wheel has turned full circle: whereas Keynes,it will be remembered from section I, advocated theadjustment of forward rates to offset interest differ-entials as a menas of monetary management, the newmanagement which was operated in 1952 has workedin the reverse direction by adjusting the interest dif-ferentials to the forward margins” Spraos (1953, 116).

By the end of the 1950s Trued (1957, p.441) postulates an ad-justment mechanism quite similar to Keynes’: “movements ofcovered interest arbitrage funds to a market will normally tendto firm the spot rate for a currency, depress the forward rate, andadd to official and private holdings of foreign currencies.”

Few years later Tsiang (1959) formalized the CIP in a morecomplete frameword. His objective was to explain the forwardrate determination by the joint action of arbitrageurs, specula-tors and hedgers (Tsiang, 1959 p.75). The relation between ar-bitrageurs and seculators is simmilar to Keynes elaboration ex-plained above. Speculators buy forward rate when the expectedspot exchange rate in the future

(se

t+1

)exceeds the ft. Their de-

mand for forward contracts is an increasing function of set+1−ft

7.Such positions will be extended as long as the expected gainsequal the marginal risk of the icreased exposure to foreign cur-rency8.

7The underlying hypothesis assumed are that every uncovered position isin forward and not spot markets and belongs to speculators only. Surpris-ingly, however, Tsiang does not define the determinants of future expectedspot rates - “We shall not be able to go into details of the dynamics of theformation of exchange rate expectations here.” (Tsiang, 1959, p.91) - andonly asserts that such expectations could be positively related to the forwardrate. However, even this is seen with certain skepticism: “the current for-ward rate is unlikely to have a considerable direct influence upon the averagerate of all speculators...” (Tsiang, 1959, p.91).

8This marginal risk is assumed to be an increasing function of the sizeof speculator’s positions in forward exchange markets and of the standarddeviations of their expectations regarding the spot rate in the future.

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The arbitrageurs then take advantage of the disparity in theCIP created by the speculative activity. Therefore, if the specu-lators in average expect se

t+1 > ft they will buy forward currencyand which will lead arbitrageurs to buy spot and sell forward,because ft

st(1 + i∗t ) > (1 + it), while borrowing domestically and

investing abroad. Finally, the hedgers simply protect their ex-posure to currency risk. Their demand (supply) in the forwardexchange market equals the size of net imports (exports)910.

The equilibrium in the CIP is achieved when the demands forforward exchange of the three kinds of agents cancel each other.Hence, the adjustment of the CIP depends on all four variables:ft, st, it, i

∗t (Tsiang, 1959, p.79). That is, once again the non ar-

bitrage conditions depends on the endogenous determination ofinterest rates given exogenous money supply.

This summarizes the basic paradigm of the CIP. Equilibriumis attained by arbitrage and that is why the CIP is sometimesunderstood as a measure of openess and capital mobility. An-other factor that conributes to the lack of alternative theoreticalexplanations of the CIP is its overwhelming empirical confirma-tion. We firther point that in the presentations above there is aconfusion between actually covered positions and uncovered onesin the interpretation of CIP, a vice that dates back to the originalexposition by Keynes.

Withal, there is an alternative explanation, the cambist view,developed by Coulbois and Prissert (1974). They assert thatis actually determined by the cost banks face to deliver foreigncurrency to their clients in the future. And this cost is given bythe interest differential. In this sense, the CIP is no longer a nonarbitrage condition but an identity.

ft ≡ st + (it − i∗t ) (3)

9It is assumed that all currency exposure due to internatinal trade ishedged.

10Tsiang’s presentation is relatively more complex and also includes liq-uidity premia as an increasing function of the arbitrage positions’ size, asystem of equations that represents the agents behaviour and graphic anal-ysis. However, none of these affects the exposure of his arguments presentedabove.

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The cambist view was revisited in the last decade, not only asan alternative interpretation fo CIP but also as part of the theo-retical propositions that explain how basic interest rates are setindependently (exogenous interest rates) by monetary authoritiesin an open economy.

3 Uncovered Interest Parity (UIP)

According to the uncovered interest parity “expected [spot] ex-change rate movements offset nominal interest differentials so asto equalize expected nominal yields internationally” (Cumby andObstfeld, 1984, p.135). Agents are, thus, exposed to exchangerisk which characterizes the UIP as a stronger condition thanthe CIP. It is assumed that interest paying assets from differentcountries are perfect substitutes.

We consider Tsiang (1958) as the pioneer presentation ofthe UIP as it applies previously developed speculation condi-tions directly to the exchange rates. Former contribution byKeynes (1936) and Kaldor (1939) were alse paramount for thedevelopment of the UIP. Tsiang’s presentation also considers the(des)stabilizing role of speculation on a flexible exchange rateregime following the debate between Nurkse and Friedman, whichwe present in the next section.

Keynes’ presentation of a good’s own rate of return on thechapter seventeen of the General Theory (Keynes, 1936) is thestarting point for the analysis of speculation tha would later leadto the UIP. In this portfolio model the return of different goods,including money, tends to be equalized. An asset’s own rate ofinterest (i) is defined by the sum of its expected appreciation (a), marginal return (q), and liquidity premia (l), minus its marginalcarrying cost (c).

a+ q − c+ l = i (4)

Kaldor presents the speculation in goods and assets, whichis defined as “the purchase (or sale) of goods with a view to re-sale (re-purchase) at a later date, where the motive behind such

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action is the expectation of a change in the relevant prices rel-atively to the ruling price and not a gain through their use...”(Kaldor, 1939, p.1). Altough not considering directly exchangerates, Kaldor describes the necessary conditions for an asset to besucject to speculation: the existence of a perfect or semi-perfectsecondary market for it11 and low carrying cost12. Undoubtfully,these apply to currencies and make exchange rates almost anideal locus for speculative activity.

The equilibrium condition for a speculative asset is repre-sented in equaltion (5). The expect change in the price - expected(EP ) minus current price (CP ) - must equal the sum of interest(i), liquid carrying cost (c− q), which may be both positive ornegative, and a risk premia (r)13.

EP − CP = i+ c− q + r (5)

The next and crucial step on the development of UIP wasdue to Tsiang (1958)14 by applying (5) to exchange rates, takinginto account the impact of speculative demand for moneis oninternational capital flows (Tsiang, 1958, p.399). His presentationof the UIP derive directly from (5). Assuming the carrying costof foreign exchange is negligible and that its return is the foreigninterest rate

(ift

)we have:

ERt −Rt

Rt

= h(it − ift + rt) (6)

This is the equilibrium condition for an individual agent inthe foreign exchange market, its aggregate version is obtained byaveraging the sum of all individual conditions. If speculators, in

11That is, liquid secondary markets. This definition bears no relation tothe later concept of efficient markets.

12Any asset that fulfills these conditions should be higly standardized, anarticle of general demand and with high value in proportion to its bulk.

13According to Kaldor “Mr. Keynes’ “liquidity premium” on the holdingof short-term assets is merely the negative of our marginal risk premium onthe holding of long-term bonds.” (Kaldor, 1939, p.41)

14Other works also contributed to stablish the UIP, but none of them ascomplete and simmilar to the contemporaneous version as Tsiang’s. Wemention Trued (1957), for instance, whose brief analysis of speculation illus-trate how an uncovered parity was not of great interest at the time, mainlybecause of the large dominance of fixed exchange regimes.

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average, expect a appreciation (ERt < Rt)larger than the interestdifferential

(it − ift

)augmented by the risk premia (rt) they will

increase their positions in domestic currency15.The equilibrium um (6) is guaranteed by three different mech-

anism accoring to the author. The first a more relevant one isagain the (i) endogenous variation of the two interest rates as aresponse changes in the monetary basis caused by capital flows.The other two adjustment mechanisms are the (ii) principle of in-creasing risk, that is, the risk perception of agents increase withthe size of their positions and (iii) a high elasticity of interestrates to supply (demand) of money16. In summary, an increasein the speculative demand for foreign exchange increases the in-terest differentias more or equal to the expetec appreciation ofthe exchange rate.

In the beggining of the first and second sections we pointedout the contributions of Keynes to the covered and uncoveredinterest parities, respectively. Yet, while this contribution wasfundamental for the CIP we can not ascribe the UIP theoremdirectly to Keynes. In fact, passages of the Treatise on Money(Keynes, 1930) illustrate how the uncovered parity possibly di-verge from Keynes’ original ideas.

Under a fixed exchange rate regime with perfect capital mo-bility Keynes (1930, p.271) claims interest rates should be equalbetween two countris, otherwise, there would be capital flows

15The demand for foreign exchange is equal to the size of the variation ofspeculators positions. Tsiang proceeds to evaluate impact of speculation ona floating exchange regime. Full employment of all factors is assumed as asimplifying hypothesis. The spot exchange rate (Rt) depends on the levelof domestic prices, the speculative demand for foreign exchange and otherexogenous variables that shift the demand for domestic exports (Dt). Theeffect of exchange rates on the domestic price - exchange rate pass-trough - isbriefly mentioned, but its effect is deemed “substatially smalle than unity”,because “to analyze the effect of speculation on the exchange rate under suchan inherently unstable monetary and price system [when pass-through is coleto unity] is rather pointless.” (Tsiang, 1958, p.404).

16This last condition holds if the elasticity of the domestic interest rate toinflation expectations is greater than one. Therefore, Tsiang (1958, p.412-413) asserts that this is “no more than the required for the stability of theeconomy even in the absence of any foregin-exchange speculation” and, thus,the system would be stable. He also recognizes that “considerble elasticityin the supply of credit money with respect to the interest rate may preventthe interest rate from rising.” (Tsiang, 1958, p.413).

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to the country with the higher interest rates. These equalities,however, were not observed because interest paying assets arenot equal in different countries, not perfect substitutes, due tocost and risk factors. These “imperfections” allow each countrya certain level of autonomy to set their interest rates even underfixed exchange rates (Keynes, 1930m p.286). It should be recog-nized that this equality in interest rates, in spite of its apparentsimmilarty with UIP, depends on the maintenance of the peg andon its credibility.

“If we deliberately desire that there should be ahigh degree of mobility of international lending, bothfor long ans short periods, that this is, admitedly, astrong argument for a fixed rate of Exchange and rigidinternational standards.” (Keynes, 1930, p.299).

The quote above depicts Keynes skepticism about the existenceof a self equilibrating mechanism between interest and (floating)exchange rates as proposed by the uncovered interest parity.

The canonical textbook presentation of the UIP17 is essen-tially a linear version of (6). It is a non arbitrage conditionin which the expected appreciation (deppreciation) of exchangerates offsets gains from borrowing in one country and investingin a second one, again considering a risk premia (ρ).

set+1 − st = it − i∗t − ρ (7)

We illustrated several times how important is the endogenousdetermination of interest rates for the correct functioning of inter-est parities. It seems relevant, then, to mention that this hypoth-esis has been questioned by both heterodox economists (Kaldor,1984 and Moore, 1988) and authors from some branches of main-stream macroeconomics such as the New Keynesians (New Con-sensus) for a closed economy (Romer, 2000). Indeed, as statedby Pivetti (2001, p.104) the origin of endogenous money sup-ply/exogenous interest rates can be traced back to classical economistslike William Petty, Thomas Tooke and Karl Marx and is still

17See, for instante, Gandolfo (2002) or McCallum (1996).

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present in some neoclassical authors such as Wickseel, Myrdaland Tobin.

Although equantion (7) resembles equation (6) the underly-ing hypothesis of the modern uncovered interest parity are sub-stantially different. Starting from the 1970s authors like Frenkel(1976) and Bilson (1978) applied the hypothesis of rational ex-pectations and efficient markets to the UIP in an economy withperfectly flexible prices. This new interpretation is contained inthe asset view interpretation of exchange rates, which also in-cludes Dornbusch’s (1976) overshooting model.

An exchange rate is the relative price of two monies and its ex-pected value, therefore, depends on the supply and demand for it.“When the domestic interest rate rises relative to the foreign in-terest rate, it is because the domestic currency is expected to losevalue through inflation and depreciation.” (Fankel, 1979, p.610).In contrast to the previous UIP interpretations, in Frenkel (1976)the variations in domestic interest rates and expected exchangerates - which guarantee that the UIP holds - have a commonorigin: inflation expectations.

3.1 Speculation and Stability

Parallel to the above mentioned developments of the UIP, theincrease in speculative activity and adoption of floating exchangerates through the XX century also fostered debates about the(de)stabilizing effects of speculation.

Following Nurkse’s (1944) assertion that speculation woulddestabilize exchange rates Friendman (1953, p.173-180) took theopposite position in defending free floating exchange rates andspeculation18. Friedman’s argument is based on the idea thatspeculators buy assets when the price is low and sell when itis high, which makes speculation a stabilizing force over assetprices.

“People who argue that speculation is generally18Other authors working on the same topic were Polak (1943), Haberler

(1949) and Machlup (1949).

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seldom realize that this is largely equivalent to say-ing that speculators lose money, since speculation canbe stabilizing in general only if speculators on the av-erage sell when the currency is low in price and buywhen it is high.” Frieadman, 1953, p.175

The argument above is an example of what kaldor (1939) denom-inated traditional theory of speculation, but before presentingKaldor’s argument it should be noticed that even the conceptof equilibrium adopted by Friedman is dubious. As argued byBaumol:

“Because most of the mathematical analysis of spec-ulation and stability has been conducted in static terms,it has failed to get to the heart of the stability ques-tion which, of course, refers to propertiesof the pricemovements.” Baumol, 1957, p.263

Therefore, in this sense, speculation would be actually desta-bilizing once, even if it is in the “right” direction as Friedmanbelieved, it amplifies the price variations of exchange rates19.

The traditional theory of speculation, according to Kaldor,assumes that speculators are only a small part of the market and,hence, can’t change the price trend direction. It is also implicitthat they are able to predict eschange rate variations better thanother types of agents acting in the same market. When the firstcondition doesn’t apply it is sufficient that some speculators arebetter than others so that “they can live on each other.” (Kaldor,1939, p.2)20.

The true effect of speculative activities could be both stabi-lizing or destabilizing in the general case for Kaldor. The reasonis that the price expectations tend to be less elastic the more dis-tante the market price is from the normal price of an asset. Thus,

19This argument relies, correctly in our opinion, on the premisse thatspeculators can’́t predict accurately the future and, thus, “[they] can onlyhope to identify price peaks and troughs in retrospect after the price trendhas been well established.” (Baumol, 1967, p.263)

20Another critique to the traditional theory of speculation is found onKindleberger (2011).

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speculation could be destabilizing if the actual current price isclose to the normal one21 and stabilizing otherwise.

Such conclusion, however, doesn’t apply directly to foreignexchange markets as in this case “there is no such “external”determinant of normal price as the producers’ supply price as inthe case of commodities.” (Kaldor, 1939, p.12). This arugmentis more precisely defined by Baumol (1957, p.270):

“...the relative price of one consumers’ good asagainst another is determined by costs of production.If this price ratio is out of line with costs, capital willfind it profitable to flow from the production of oneitem to the other and move prices back toward theirequilibrium ratio in accord with the well-known anal-ysis. But the peculiarity of the exchange mar-ket is that the cost of production of the com-modities traded is, for all practical purposes,nil. Governments or the central banking sys-tems can, at nearly zero cost, expand theircurrencies at will, and frequently they do notresist that temptation.”.

In this regard exchange rates would have an unstable a erraticbehaviour. The absence of a production price of moneis makesany reference value for exchange rates depend solely on agentsexpectations and actions of the monetary authority. Which leadsBaumol (1957, p.271) to conclude:

“. . . I can see no way of constructing a sys-tematic explanation of turning points of truly flexibleexchange rates. If, as I believe, Viner is right, ex-change rate movements will be erratic and these turn-ing points will be erratic, or rather, they will be ex-plainable only in terms of the political circumstances

21The normal price “is determined by different factors in different mar-kets” (Kaldor, 1939, p.9) and the “normal price in the future will not be verydifferent from the normal supply price of the past; it is ultimately a belief inthe stability of money wages” (1939, p.10).

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of the countries in questions.”22

In summary, we believe the absence of a normal price of cur-rencies cast serious doubts on the possibility of speculation as astabilizing force over free floating exchange rates.

4 Real Interest Parity (RIP)

The RIP theorem has a distinct origin in relation to the two pre-vious ones. It was first present in moenatrist models of exchangerate determination, as a secundary result. In contrast to the cov-ered and uncovered parities, this is not an equilibrium conditionbut rather the outcome of two other parities. If both the UIPwith rational expectations and flexible prices and the PPP holdsimultaneously than the RIP also holds. Hence, this is a strongercondition as noted by Mishkin (1984, p.1345): “If is is true [theRIP], then domestic monetary authorities have no control overtheir real rate relative to the world rate, limiting the impact oftheir stabilization policies.”

These monetarist models are included in the asset view men-tioned in the last section and according to Frankel (1979) maybe separated in two classes: Chicago and keynesian models. Inboth cases the spot exchange rate is determined by the moneysupply in the two countries. They diverge in their assumptionsabout price flexibility. While the “Chicago” models assume fullyflexible prices (Frenkel, 1976 and Bilson, 1978), the keynesianmodels like Dornbusch (1976) exhibit sticky prices in the shortterm. Therefore, the market adjust slower in the goods marketin relation to the currency and financial markets.

And this stickyness is why in the overshooting model it is pos-sible to maintain, at least for some time, a positive real interestrate differential. Thus, generating a temporary inflow of capitalthat appreciates the exchange rate. On the other hand, adjust-ment is instantaneous in models with efficient markets. Then,RIP holds always in the “Chicago” modesl and only in the long

22For a discussion about exchange rates as conventional prices see Ver-nengo (2001).

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term on the “keynesian” models. The true difference of these twoclasses of models is that with flex price exchange rates are alwaysequal to their equilibrium value, given by the PPP and rigiditiescreate the conditions for divergence between current and equilib-rium value of the exchange rate.

However, the PPP, in its absolute or relative versions, lacksempirical confirmation23. Another, more popular, version of theRIP is obtained combining the UIP with the expected or ex-ante PPP. In this version it is enough that the agents believe thePPP will hold, in other words, it doesn‘t actually need to holdempirically (Roll, 1979 and Adler & Lehman, 1983). The ex-antePPP is compatible with exchange rates that behave like randomwalks and variable real exchange rates24.

Bellow we present the RIP (11) obtained by the joint as-sumption of UIP (8) and ex-ante PPP (9) which result in theequality between nominal interest rates minus expected inflation(10). This is Fisher‘s (1930) definition of real interest rate, whichleads us to the RIP.

set+1 − st = it − i∗t + ρ (8)

set+1 − st = πe

t − π∗et (9)

it − πet = i∗t − π∗e

t + ρ (10)

rt = r∗t + ρ (11)

23From the late 1980s and early 1990s, some works present more favorableevidence for the PPP on the very long run, usually more than 100 years,see Rogoff (1996). However, this studies treat the causality from prices toexchange rates only, ignoring the possible influence of exchange rate pass-through.

24Although many believe exchange rates are actually random walks Engeland Hamilton (1990) present evidence of trends or long swings on exchangerates.

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5 Empirical Evidence

The theoretical developments of interest rate parities was natu-rally followed by atempts to verify their empirical soundness.

The CIP has been largely confirmed, including in periods ofrelative market uncertainty (Taylor, 1995, p.19). Even for the1920s, Peel and Taylor (2002) detect only small deviations fromthe CIP, small enough not to trigger significant capital flows be-tween London and New York, which they call the Keynes-Einzigconjecture in reference to the minimal profit margin necessary tolead agents into arbitrage operations mentioned in section (2).They also point further evidence in favor of the CIP in the latenineteenth century for Europe and the U.S.A25.

In relation to the theoretical explanations of CIP, if we con-sider the traditional theory presented by Keynes, Spraos, Tsiangand others, its confirmation points to almost perfect capital mo-bility in very different periods and places. In our opinion, thisvast evidence in favor of the CIP is in accordance with the cam-bist view, as it regards the CIP as an identity instead of anequilibrium condition.

Recently, however, in the beginning of the current financialcrisis, some researchers identified failures in the CIP Mancini-Grifolli & Ranaldo (2010), Coffrey, Hrung & Sarkar (2009) andBaba & Packer (2008). This, however, doesn’t affect the validityof the CIP once the availability of funds for arbitrage, a necessarycondition, clearly failed to hold early in the crisis.

We now turn to the UIP, largely used to test the efficient mar-ket hypothesis. Provided the CIP holds and agents have rationalexpectations the expected future spot rate should be equal to theforward rate. As expected rates are not observable, the observedspot rates are usually tested against past forward rates (X).

(st+1 − st) = α + β(ft,t+1 − st) + εt (12)

Taylor (1995) provides a survey on the different tests of the

25Further empirical evidence in favor of the CIP is found on Frenkel andLevich (1975); Peel and Taylor (2002); Taylor (1987a, 1995).

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UIP since the late 1960s. For our purpose it is enough to men-tion that the overwhelming evidence rejects the UIP26. “Indeed,it is stylized fact that estimates of β, using exchange rates againstthe dollar, are generally closer to minus unity than plus unity.”(Taylor, 1995, p.15). In this way, “the so-called “uncovered in-terest parity failure” or “forward premium puzzle” refers to theparadoxical negative and insignificant empirical UIP coefficientlinking changes in exchange rates and interest rate differentials.”(Yuen, 2006, p.14). The fact is that “no economic hypothesis hasbeen rejected more decisively, over more time periods, and formore countries, than UIP” (1993, p. 73 apud Yuen, 2006 p.2).

Different conjunctures about this failure were put forward.The first of them points to a failure of rational expectations. Thisled some authors to test the UIP with other rules for expectations(Marrey, 2004; Frankel, 1987).

Nonetheless, foreign exchange and financial markets in gen-eral seem to be the natural candidates for rational expectationsas they have both highly specialized agents and plenty of in-formation available. Consequently, neoclassical authors, such asFama (1984), often ascribe this failure to a time varying risk pre-mium27; otherwise its effect would bem captured by the interceptin equation (12). Withal, he admits “A good story for negativecovariation between pt [the risk premium] and st+1− stis difficultto tell.” (Fama, 1984, p.327).

The RIP was also subject of extensive testing. Since the early1980s the empirical evidence has shown, to say the least, littlesupport to it. In fact, the real parity was strongly rejected fordifferent currencies over different periods. This result should notsurprise the reader as both of the RIP building blocks, UIP andPPP, rely on very limited empirical support.

Cumby & Obstfeld (1984) test the equality of ex-ante real in-terest rates for five currencies against the American dollar with

26More evidence on the failure of UIP is provided by Froot and Tahler(1990), Cumby and Obstfeld (1984), Taylor(1987b), Hansen and Hodrick(1980) and Marston (1976). A rare defense of UIP is found in McCallum(1996).

27Froot and Tahler (1990) conclude in favor of both time variable riskpremia and rational expectations failure to explain the failure of UIP.

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monthly and quarterly data, using two different price indexes todiscount nominal interest rates. They find “Econometric tests ofthese propositions [equality of ex-ante real interest rates as thecorollary of UIP and ex-ante PPP] within a rational expectationsframework provided significant evidence against them.” (Cumby& Obstfeld, 1984, 146), they believe the UIP and the ex-antePPP do not constitute an appropriate framework to explain thebehavior of macroeconomic variables in a world of diversified as-sets and commodities.

In another study Mishkin (1984) encounters strong evidenceagainst the RIP, and according to him this will not render mon-etary policy useless in an open economy context. Mark (1985,p.205) gives further evidence in the same direction, accountingfor tax differences: “By and large, the hypothesis of net of taxreal rate equality has not been well supported.”

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