# Modeling interest rate parity: A system dynamics approach.

 Author: Harvey, John T.

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The theory of uncovered interest rate parity has enjoyed very little empirical support. Despite the fact that global financial markets trade seven days a week, twenty-four hours a day, and communication takes place almost instantaneously, there are strong indications that differences in expected rates of return across countries can be non-zero and large for extended periods of time.

However, these deviations display a pattern within which there is an important clue regarding their cause. Changes in the differences between expected rates of return across countries largely correspond to changes in the differences between national interest rates. In other words, when agents expect the rate of return (taking into account both interest rates and forecast exchange rate movements) to be higher in one country than another, that country also tends to have the higher interest rates. This means, as will be demonstrated below, that deviations from uncovered interest rate parity cannot be explained (as has been argued elsewhere) by relying on the assumption that agents perceive some assets to be riskier than others. A model of international financial flows that incorporates John Maynard Keynes' concept of forecast confidence, however, has no difficulty explaining this commonly observed phenomenon.

The purpose of this paper is to show the superiority of Keynes' approach by comparing three system dynamics models of the relationship among interest and exchange rates: one based on traditional uncovered interest rate parity, one with risk, and one with forecast confidence. It will be demonstrated that only the last produces patterns consistent with those observed in the real world. This paper is an extension of the empirical study undertaken in Harvey 2004.

Uncovered Interest Rate Parity

Uncovered interest rate parity makes the seemingly innocuous claim that the return on interest-bearing assets throughout the world must be identical once expected exchange rate movements are taken into account. This can be expressed (using the dollar and the euro to make the example more concrete) as shown in equation (1):

(1 + [r.sub.\$]) = ([euro]/\$)(1 + [r.sub.[euro]])[(\$/[euro]).sup.e] (1)

where [r.sub.\$] is the rate of interest paid on dollar deposits, [r.sub.[euro]] is the rate of interest paid on euro deposits, ([euro]/\$) is the spot price of dollars in euros, and [(\$/[euro]).sup.e] is the market's expectation of the spot price of the euro (in dollars) at some future date (where the time horizon of the interest rates and the exchange rate expectation are the same). If one side exceeds the other it is then assumed that this sets into motion forces that will restore the equilibrium. Were the left side of (1) to exceed the right side, for example, this would create capital flows from the euro to the dollar, driving [r.sub.\$] down (as capital becomes less scarce), [r.sub.[euro]] up (as capital becomes more scarce), and ([euro]/\$) up (as agents buy the dollar with the euro, causing the former to appreciate).

Figure 1 shows a system dynamics model (written in Vensim) of the basic uncovered interest rate parity relationship introduced in equation (1). At the center is UIRP Deviation, which is measured as (1 + [r.sub.\$]) - ([euro]/\$)(1 + [r.sub.[euro]])[(\$/[euro]).sup.e] (i.e., the amount by which the market expects that U.S. returns will exceed foreign). If this number is zero, equilibrium prevails and nothing is transmitted along the single arrow emanating from UIRP Deviation. If instead, for example, U.S. returns are expected to be greater than those of foreign assets, this will lead to a rise in...