**Exchange Rate Expectations under a Fixed Exchange Rate Regime. **

**An Imaginary Application to the Case of the Cuban Peso. **

** **

Ernesto Hernández-Catá

June 2021

In a recent paper, Luis (2021a) provided a rigorous analysis of Cuba’s exchange rate system. His model, based on portfolio selection theory, features the three currencies that until recently circulated in Cuba: the falsely labeled “convertible peso” or CUC[i]; the non –convertible Cuban peso or CUP[ii]; and the U.S. dollar[iii] [iv]. Luis explained the proportion of wealth held in assets denominated in these currencies in terms of the expected rates of rate of return on each asset, i.e., interest rate differentials and expected changes in exchange rates. The model provides a coherent theoretical tool to analyze the behavior of exchange rates in a multi- currency country, which Cuba was until 2020. In particular, the model can be solved for the expected exchange rate, which turns out to be a function of asset to wealth ratios and is therefore consistent with the equations of the model.

In this paper we show that traditional models are unable to explain expectations about the value of the currency under a fixed exchange rate regime.[v] We derive an alternative model which recognizes explicitly the presence of an officially declared fixed exchange rate. In that model, the expected value of the currency is a function of (i) the probability that the rate will be changed in the following period; and (ii) the equilibrium exchange rate. The model is applied to the official exchange rate of the Cuban peso which was fixed 1:1 to the U.S. dollar until its devaluation in January 2021.

**A complex and distorting multiple exchange rate system.**

Until 2020 Cuba’s exchange system featured not only several currencies, but also rules specifying the sectors in which theses currencies were to be used. In particular, two different rules applied to the CUP.

T**he official exchange rate** (at CUP 1 per U.S. dollar) was earmarked for state enterprises and governments, and used to convert data on transactions with the rest of the world (including exports, imports, and direct investment) into domestic currency. In his excellent summary of past and recent exchange market developments, Vidal (2021) estimates that the official CUP exchange rate accounted for the great bulk of economic transactions in the Cuban economy.[vi]

The other exchange rate—the **CADECA,**** or exchange bureau rate—**applied to households and private transactions, except for official purchases of oil, food, and medicine. It was also used by tourists and by families receiving remittances from Cuban residents abroad.[vii] As shown in Fig. 1, this rate was floated in the early 1990s, depreciated sharply after the catastrophic depression following the end of Soviet/Russian assistance, and then appreciated equally sharply after the implementation of a stabilization and reform plan. The parallel rate was then fixed at CUP24/$, and remained at that level until 2019. Since early 2021 it has depreciated sharply in the black market—although, as Vidal reminds us, not nearly as sharply as it had in the early 1990s.

**Sources**: ONEI, Vidal (2021, Table 1), and author’s estimates. Data for 2021 are part-year numbers (post devaluation exchange rate for the Cuban peso; and black market rate for the exchange bureau rate).

**Expectations**

In Luis’ 2020 model—let’s call it the portfolio balance model—the change in the expected exchange rate (ẽ) is consistent with the equations of the model, and is therefore a function of the ratios to wealth of the three assets considered. Specifically,

(1) ẽ _{t} – e _{t-1 }= h (x)

where ẽ _{t}-e _{t-1 }is the difference between the exchange rate expected to prevail at time t and the actual rate at time t-1; and x is a vector of the explanatory variables mentioned in the first paragraph of this paper. This formulation is topnotch from a theoretical viewpoint, and is particularly well suited to analyze expectations in a flexible exchange rate system. It is not appropriate, however, to deal with a fixed exchange rate, like the Cuban official exchange rate that prevailed from the early 1900s until 2020. In fact, any model that does not explicitly consider the existence of a fixed rate would be inadequate.

To see this, consider a perfectly credible fixed exchange rate system. Perfect credibility means that market participants will expect the official exchange rate to remain unchanged (at least until authorities declare otherwise) at the officially established rate (ϵ). Since ϵ is by definition a constant, it follows that the expected *change* in the exchange rate will always be zero (Δẽ_{t }=0). Any model that ignores this fact would be inconsistent with a credible, fixed exchange rate. This applies in particular to the portfolio balance model, where the expected rate is a variable and continuous function of a set of non-zero variables.

As an alternative, consider an adaptive expectations model, where the exchange rate is expected to change in every period so as to partially fill the gap between the equilibrium rate (ϕ_{t) }and the actual rate:

(2) ẽ _{t} – e _{t-1 }_{=}_{ }_{Ѳ} _{ }(ϕ_{t }– e_{t-1)}

Where Ѳ>0 is a constant. Again, the change in the expected rate is different from zero and therefore the model is inconsistent with a credible fixed exchange rate.

Of course, full credibility and its implication (Δẽ_{t }= 0), is an extreme assumption. Therefor an adequate fixed rate model must also take into account the possibility that the *expected* rate is variable, even if the *actual* rate always remains unchanged. If credibility is imperfect, i.e., if market participants are uncertain about the authorities’ willingness *and* *ability* to defend the rate, they could envisage the *possibility* of a devaluation. (This uncertainty characterizes the Cuban official peso regime ended in 2021, particularly in view of the gigantic overvaluation of the currency). However, the fixed rate constraint would still be relevant, except if and when a devaluation appeared to be certain. Clearly, equations (1) and (2) cannot deal with these possibilities. A different model is needed.[i]

**Expectations under fixed rates. Fixed, but not immutable. **

Under a fixed rate regime market participants do not know with certainty if and when the currency will be devalued, but they can gauge the *probability* that it will. Thus the expected change in the exchange rate will depend on two principal factors:

- the probability of a devaluation in the next period (λ), which is inversely related to the perceived ability of the authorities to defend the official rate, for example by using its foreign exchange reserves; and
- the level of the exchange rate expected to prevail in the next period
*if*a devaluation does in fact occur, which can be interpreted as the equilibrium exchange rate (ϕ).[ii]

These conditions are represented in equation (3).

(3) (ẽ_{t}** – **e_{t-1) }**/** e_{t-1 }= λ_{ t-1}** ^{ } **(ϕ – e

_{t-1) / }e

_{t-1})

The right hand side of the equation is the expected change in the official exchange rate (measured in percentage terms for computational convenience). The variable λ is a* probability* and therefore must lie between zero and one. If λ = 0 the rate is expected to remain unchanged; if λ =1 it is expected to depreciate all the way to its equilibrium level ϕ. In this particular exercise, ϕ is assumed to be the CADECA exchange rate applicable to households (at CUP24/$). This rate was often believed to be close to equilibrium, and it became the official rate of the new, unified peso in early 2021. It was constant over the sample period 2002 to 2020.

Rearranging equation 3 and noting that the official rate e was always equal to one during the sample period, we obtain:

(4) ẽ_{ t }= λ_{ t-1}^{ . }(ϕ_{t} – 1) + 1

The expected level of the exchange rate is a function of the probability of a devaluation and the estimated equilibrium level of the rate. The variable λ depends on the perceived ability of the authorities to defend the currency by using foreign exchange reserves. Reserves were proxied by the size of Cuba’s claims on foreign countries, as reported by the Bank for International Settlements (BIS). Specifically,

(5) λ _{t-1} = 1 – (a / a^{max })

**Source: **Author’s estimates, Bank for International Settllements, ONEI.

**Note.** The boken line is the subective probabilty of a devaluation based on the avilablty of foreign exchange assets, multiped by the exchange bureau (CADECA) exchnge rate.

The variable a/a^{max }is the level of Cuban claims on the BIS divided by the maximum value of these claims (which serves to transform the original data for *a* from millions of dollars into a probability ranging from 0 to 1). The right hand side of equation (5) is now represents the probable magnitude of a devaluation.

The combined model of equations (4) and (5) is illustrated in Fig. 2 for the case where the expected probability of a devaluation in the next period is inversely related to the level of Cuba’s foreign assets. The expected depreciation of the official rate falls to zero in 2010 (after the financial crisis of 2008-09), meaning that the rate was expected to remain unchanged in the following year. But the expectation of a depreciation then rises, reaching a peak in 2020, just before the formal devaluation of January 2021.

A similar exercise was performed using the fiscal deficit as the variable guiding the probability of a devaluation and thus the expected official exchange rate. This is not an indicator of the government’s ability to defend the rate, but a more intuitive gauge of pressure on the current account and therefore on the value of the currency. It is also more readily available to Cuban residents than the indicator based on BIS data. Fig. 2 and 3 have a few things in common. The lowest expectation of a devaluation occurs after the financial crisis of 2008-09; and this is followed by a rise through 2020—which is considerably more pronounced in the model using the fiscal deficit, where a devaluation is expected with almost certainty in 2017-18 and again in 2020.

**Source: **Author’s estimates and ONEI.

**Note.** The broken line represents the subective probabilty of a devaluation (based on Cuba’s fisal deficit), multiplied by the exchange bureau (CADECA) exchnge rate.

This model cannot be tested for the simple reason that actual data for ẽ do not exist. So the model is imaginary and its only merit is that it is based on reasonable assumptions about the formation of expectations under a fixed rate regime and involves explanatory variables that can be obtained from published sources.

*** * ***

** **

As shown in Fig.1, the official exchange rate of the peso was devalued from 1 to 24 pesos per dollar in January 2021. If coupled with measures to a phase out the subsidies and controls that have distorted the economy for decades, significantly expand the list of sectors opened to private enterprise, and cut down fiscal deficits to more reasonable levels than those prevailing in recent years, there would be a substantial improvement in resource allocation and economic performance and, in particular, an end of the discrimination against exports inherent in the old system.

But Fig. 1 also shows that in the first half of this year the black market rate has surged to about 70 pesos per dollar. The authorities cannot be blamed for not wanting to further devalue the now unified rate all the way to the black market level. That level most likely reflects the unusual circumstances faced by Cuba in recent years—some probably temporary, like the effects of the pandemic on tourism, exports and remittances; some probably permanent like the fall in the compensation of Cuban doctors in Venezuela and Brazil. But hopefully the authorities will not fall asleep in the false belief that 24 pesos per dollar is necessarily the end of the ball game and try to restore a “fixed” exchange rate that nobody will expect to be fixed for long. The officially declared fixity will give an appearance of stability, but again will conceal a growing overvaluation of the currency fueled, among other things, by a continued massive absorption of saving by the central government.

History tells us that, unless you are nearly perfect in the policy area, a fixed exchange rate will be like the seeming virginity of a courtesan, a ruse that helps to hide her sins for some time, until they become obvious and then the only solution is an earthquake.

The Canadian system of floating while leaning against the wind should get considerable attention.

** **

**References**

BIS (2021). Bank for International Settlements. International Banking, location statistics, bis.org.

Hernández-Catá, Ernesto (2017). “Reforming Cuba’s Exchange System. The Perils of Gradualism”. Association for the Study of the Cuban Economy.

Luis Luis R, (2020a). “Cuba, Dollar Crunch, Dollarization and Devaluation”. Association for the Study of the Cuban Economy. (January).

Luis, Luis R. (2021b). “Recent Inflation Trends and Peso Devaluation in Cuba.” Association for the Study of the Cuban Economy. (May).

Luis Luis R. (2021c). “Monetary Bang and Inflation after the January 2021 Devaluation of the Peso”. Association for the Study of the Cuban Economy. https//www.ascecuba.org/monetary=abank-inflation-january 2021dvaluation-cuban-peso/

Mesa-Lago, Carmelo (2021). “La unificación monetaria y cambiaria en Cuba: normas, efectos, obstáculos y perspectivas.” Real Instituto Elcano. Documento de trabajo 2/2021. (Febrero).

Oficina Nacional de Estadística e Información. Anuario Estadístico de Cuba. Various issues.

Vidal Alejandro, Pavel (2021). “Five Factors to Understand the Cuban Peso Devaluation”. Columbia Law School. Cuba Capacity Building Project. (May).

[i] Furthermore, some within the government may come to realize that the distortions caused by the overvaluation of the official rate damage economic performance. Eventually they will prevail on those who defend the existing system (by stupidity or by self-interest). In the end, reason will prevail and the government will announce that the currency will be devalued. This is what the Cuban government announced in 1920 and executed in early 2021. As this story unfolds, expectations will be inexorably influenced by official pronouncements, even before the devaluation occurs, although certainty will not materialized until definitive actions are taken.

[ii] The idea behind this model germinated in early 1992 when I was working on Mexico. In those days, the Mexican peso was fixed at 12.49 per dollar, but was occasionally subject to speculative attacks.

[i] The multiple rate system was introduced in the early 1990s. The CUC, which was at first paraded as convertible, was a sort of currency board, fixed at par to the U.S. dollar. Later, the king was deemed to have no clothes, and the CUC was (properly) declared unconvertible; but it continued to circulate. On the basis of ONEI data, which, for the first time, included holdings of CUCs in the total money supply numbers, Luis estimated that in 2017 CUCs amounted to 39% of M2A—an aggregate that includes currency and bank deposits but excludes enterprise holdings. As part of the reforms implemented in early 2021, the CUC is scheduled to disappear, although for some time holders will be allowed to exchange them for the now unified Cuban peso at 24 pesos per CUC, the same rate that prevailed before the CUIP devaluation.

[ii] To further complicate things, the authorities introduced several additional exchange rates (less overvalued than the official rate) applicable to the sugar sector, hotels and restaurants, and a few other enterprises. See Hernández-Catá (2017).

[iii] The Cuban authorities have gone back and forth in allowing the circulation of dollars. The dollar was de-criminalized in the early 2000s as part of package of measures implemented to deal with the post-Soviet crisis, but this was reversed later on. Since the turn of the century, the dollar holdings of the population, obtained from remittances and tourist outlays, have mounted. In October 2020 the government allowed Cubans to obtain dollars and other convertible currencies in state stores and use them to purchase high priced goods. The government’s goal, of course, was to capture foreign currency at a time of severe liquidity shortages.

[iv] A more complete description of the evolution of these currencies before and after the January 2021 devaluation is provided in Mesa-Lago (2021).

[v] This paper does not deal with the distinction between tradable and non-tradeable goods and its important implications for exchange rate effects on the domestic economy. These issues are analyzed extensively by Luis (1921c).

[vi] The paper does not deal with the distinction between tradable and non-tradeable goods and its important implications for exchange rate effects. These issues are analyzed extensively by Luis (1921).

[vii] This rate is sometimes described as a “parallel exchange rate” because it originated in an informal market in the early 1990s. However, the rate transacted in exchange bureaus from the turn of the century until 2019 almost never changed and therefore it may be more correctly labeled fixed* o*r *pegged*.