The Foreign Exchange Rate Determination Issue and its Empirical Deviations

The discussion about the theories that determine the foreign exchange rate is a recurrent issue in the economic literature. Theoretical and empirical approaches achieved to outline a shaky framework in the past decades.

The mainstream of modern economic literature holds that relative prices of countries determine the behavior of their foreign exchange rate. The most well-known theoretical approach to this explanation is the Purchasing Power Parity (PPP) theory, which asserts that the purchasing power of countries is the same when measure in the same currency.

The reason for the PPP model to hold is the presence of the international arbitrage, which makes prices equal between countries and corrects their purchasing power disparities. This is possible due to when the price of a good is cheaper in the domestic country than in the foreign country, foreign importers and domestic exporters will buy the good in the domestic country in order to sell it in the foreign country to obtain the profit derived from the both countries price imbalance. As a result of this situation, the price of the domestic good would increase while the price of the foreign good would decrease making one price equals to the other. This would lead to assert that when PPP holds, the purchasing power of those countries is the same (constant) over time.

Canada/U.S. Foreign Exchange Rate vs. PPP


*Percentage change relative to the base year 2010

Source (Muñoz-Salido, 2016)

As it can be seen in this graph of the Canada/U.S. foreign exchange rate and the PPP theory, there are consistent patterns regarding to the theoretical relationship of those variables. In general, it can be observed that whenever the value of Canadian dollar falls (so it implies an appreciation of the U.S. dollar against the Canadian dollar) against the value of the U.S. dollar, then always the Canada’s price level falls relative to that in the U.S., and , conversely, whenever there is a depreciation of the U.S. dollar against the Canadian dollar (so there is an increase in the value of the Canadian dollar relative to that in the U.S. dollar) then there is an increase in the Canadian price level relative to that in the U.S., which is strongly consistent with the PPP theory.

The only periods when this pattern is distorted is from 1974 to 1977 and from 2007 to 2013. This is not consistent with the PPP theory and it can be associated with not having the proper conditions for the PPP to hold, concretely. Following Coughlin’s & Koedijk’s (1990) statements, it can be explained by economic shocks, in this case the energy crisis at earlier 1970s which ended in the later 1970s and by the financial crisis which covered the aforementioned period.

Bearing in mind our results in this sample dataset, Stockman (1978) suggests that while a great part of changes in the exchange rate can be explained by inflation rates, there is many substantial changes in the exchange rate that remain unexplained. Stockman tries to justify part of this deviation by the role of the information about the future (id est. an increase in the expected rate of domestic inflation). He asserts that this information role makes a reduction on the demand for domestic money and connotes all nominal prices, including the price of foreign exchange, to rise. Nevertheless, he stresses that this alone cannot account for deviations from PPP unless exchange rates are associated with fluctuations in the ratio of domestic and foreign price levels. Stockman’s (1978) also addresses part of this deviation issue by associating its cause with other policies such a tariffs, quotas and controls on foreign exchange transactions which may affect the exchange rate indirectly by directly affecting the terms of trade.

In light of this ever-present deviation of empirical findings from the theory, Musa (1984) fiercely criticise the stickiness of prices. He addresses the short-run deviations to the slow price adjustment due to they are fixed in the short-run and they don’t adjust immediately to its equilibrium value. Stockman (1978) adds that this fact could be the main cause for the exchange rate to depreciate in the short-run, due to in the long-run good prices have already had time to adjust to a market equilibrium. Nevertheless, De Grauve et al. (1985) associate part of empirical deviations from PPP with the influence of the size of the stochastic disturbances in the money market by setting the assumption that the larger the size of the monetary and inflationary disturbances, the larger the variability of the real exchange rate. They also notice that this relation is not linear connoting an increase in the variability of the real exchange rate when monetary and inflationary disturbance occurs but levelling off after this immediate increase due to the force of goods arbitrage. They also set the international arbitrage as a grader factor when this disturbance arises.

In addition, Coughlin & Koedijk (1990) attribute part of this deviation to the fact that floating exchange rates are relatively new over time, so that the exchange rate determination is trying to be addressed by the convergence of two different type of exchange rate that have different behaviour. Under this assumption, they stress the fact that the relative price ratio of the real exchange rate fluctuates more in the floating-rate period than in the fixed exchange rate period. Also, they hold that another possibility that may explain this deviation is the effect of random shocks of various origins which disturb the real exchange rate theoretical behaviour, such as oil price shocks. As stated above, our results in the graph of Canada/U.S. foreign exchange rate and PPP theory coincide in dates with two economic shocks when the PPP theoretical pattern is distorted from 1974 to 1977 and from 2007 to 2013. Following Coughlin’s and Koedijk’s statements, this fact can be explained by the energy and the financial crisis influence in the aforementioned period.

Taylor & Taylor (2004) try to address this deviation issue by introducing trade costs and real shocks to the model with the aim to correct the deviations of the real from the foreign exchange rate. They hold that in order to improve the better understanding of the volatility of the real exchange rate, it can be combined the PPP theory with transactions costs and nonlinearity (due to, for example, the long-lasting effects made by price rigidities as stated above by Musa and Stockman) to obtain a more consistent empirical results that allow for the theory to properly hold.

Another requirement for the PPP model to hold is that the real version of the exchange rate achieved provided by PPP must show mean-reversion, so the behaviour of the real exchange rate is stable as it returns to a long-run level despite its fluctuations. When this assumption is violated, it entails that there are trends, random walks or cycles that may explain the causality of the foreign exchange rate instead the PPP model. In other words, this doesn’t allow for the foreign exchange rate to be explained or predicted by the PPP. De Gauve et al. (1985) propose an improvement to the stationarity of the series by applying an alternative statistical technique that makes it possible to decompose a time series into cycles of different frequencies, the spectral analysis. The results on this analysis would show how much of the total change is due to an observed cycle (a low-frequency cycle that repeats itself some times) and how much to seasonal movement (a high-frequency cycle that repeats itself predominantly). As a result, it is obtained a regression information on the extent to which the total variability of series is due to cycles of different frequencies.

In light that the theory assumes the trade to be constant, it can be asserted that in some periods of economic weakness the perfect arbitrage cannot play the same role for correcting purchasing power imbalances than when the economic system is not disturbed. Also, there could be potential factors for the international arbitrage to change over time such as the presence of the internet-based trade since 2000s or the development of new technologies, which can accelerate and change the international trade patterns.

In short, some of these hypothetical deviation statements can lie as a suitable explanation for slight deviations of empirical results from the theoretical framework of PPP theory of the literature in the past decades.

A conclusion to be drawn from this analysis is that PPP theory tends to hold with peculiarities. In the light of this evidence, Dornsbusch (1985) asserts that “There can be no objection to the strong or absolute version of PPP as a theoretical statement. Objections arise, however, when it is interpreted as an empirical proposition”. It can be asserted that the more the model simplifies the reality through theoretical assumptions the more the reality can be distorted. By logical thinking, it can be considered that the more this model is corrected for such an inaccuracy the more the deviation can be reverted.

In short, the vicissitudes with which the PPP holds in the literature over time can be considered as a challenging avenue for future research and as a suggestion for developing in depth the assumptions in which theoretical economic models are based.

Enrique Muñoz-Salido
Enrique Muñoz-Salido
Enrique works in the tech industry, computer software, in the City, London. His interests lie at crossroads of human behavior and software. Enrique is an Oxford Masters graduate, Talentia scholarship.