Why are real interest rates not equalized internationally?

• Author: Chung, S. Young
• Position: Purchasing power parity

1. Introduction

   International financial economists are intensely concerned with several parity conditions that relate goods prices and asset returns across countries. These include purchasing power parity (PPP), interest rate parity (IRP), and variations of these two, such as relative PPP, ex ante PPP, and real interest rate parity (RIP). Each of these parity conditions measures a degree of integration between the economies of the world. The greater the economic integration across countries, the greater the likelihood that the more restrictive of these parity conditions will have empirical support. For example, the strict PPP hypothesis implies that aggregate price levels will be equal in terms of a common currency. This condition is very stringent because it does not allow for even temporary deviations from the equilibrium condition. (1) A less restrictive version is long-run PPP, where price levels, measured in a common currency, across countries converge over some period of time, may be a very long period of time. Recognizing all of the impediments that keep strict PPP from holding, economists have put their efforts in studying the long-run version of this equilibrium condition.

   There is a relatively large literature examining the equality of real interest rates internationally. (2) In all of these studies, the real interest rate is defined by the Fisher equation. These studies then go on to estimate and test for the simultaneous existence of uncovered interest parity (UIP), which is also called the open-economy Fisher relation, and ex ante PPP (EAPPP), the other conditions sufficient for RIP. The problem in this strategy is that the Fisher equation may not hold. Many studies have been devoted to examining the validity of the Fisher relationship for both the U.S. and other economies. (3) The results of this line of inquiry have been decidedly mixed. Even if the Fisher relation does hold, it is unlikely that the Fisher effect will be one-for-one, as implied by defining the real interest rate from the simple Fisher equation. Both Mundell--Tobin and tax effects can drive a wedge between inflation expectations and the effect on nominal interest rates. (4) It would seem more appropriate to treat the Fisher relation as another testable parity condition than as an assumption.

   In this study, we examine the underlying parity conditions sufficient for RIP, treating them as hypotheses to be tested. The four parity conditions or equilibrium relationships upon which RIP is predicated, uncovered interest parity (UIP), ex ante PPP (EAPPP), the Fisher relation in each country (i.e., the Fisher relation in country A and the Fisher relation in country B), imply time series implications for the observable variables. Specifically, if any of the nominal interest rates or inflation rates can be characterized as integrated variables, evidence of which we will provide, then the four parity conditions imply one common stochastic trend between them. Therefore, an initial examination of the sufficient conditions for RIP should include a test for a unit root in the observable variables and then a test for the number of common stochastic trends in a given RIP system.

   Because the power of univariate unit root and stationarity tests is notoriously low, many exploit the power gains available by using panel tests. However, there are serious drawbacks to some of these panel unit root tests, for example, O'Connell (1998), Taylor and Sarno (1998), and Breuer, McNown, and Wallace (2001). We overcome these drawbacks by taking advantage of recent innovations in univariate and multivariate unit root tests that have substantially greater power to reject a false null but are not subject to the size distortions associated with some popular panel-based tests. Our use of these methods leads us to conclude that each RIP system analyzed can be characterized, to some degree, as a system of integrated variables that share more than one common trend. This violates the sufficient conditions for RIP implied by the four parity conditions.

   We extend the analysis to determine which of the parity conditions fail, resulting in the violation of RIP. Our results indicate that no single parity condition can explain the failure of RIP in all cases. But it does appear that the Fisher relation is the least likely to violate the RIP equilibrium. On the other hand, UIP appears to be the most commonly violated of the four conditions, with EAPPP somewhat more consistent with the data.

   The rest of the article is organized as follows: Section 2 discusses the theoretical conditions sufficient for RIP and the time series implications of these conditions. Section 3 describes the econometric methodology and discusses the various hypothesis tests. Section 4 presents the empirical results and Section 5 concludes.

2. Real Interest Rate Parity

   Four Parity Conditions

   RIP is the condition where real rates of return on essentially identical assets are equalized across countries. There are many reasons why real interest rates will not always be equal across countries, for example, country-specific risk, transactions costs, information asymmetries, and/or differential tax treatment. For these reasons, our focus is on long-run RIP.

   The nominal interest rate in country j can be related to the real interest rate by the Fisher relationship given in Equation 1:

   (1) [i.sub.j,t] = [r.sub.j,t] + [[pi].sup.e.sub.j,t+k']

   where [i.sub.j,t] is the nominal interest rate of country j in period t and [[pi].sup.e.sub.j,t+k] is the ex ante inflation in country j over the holding period k of the asset.

   Nominal interest rates across countries are related via the UIP relationship. UIP relates the nominal interest rate differential to the expected exchange rate depreciation as in Equation 2:

   (2) [i.sub.j,t] - [i.sub.i,t] + [DELTA][S.sup.e.sub.t+k']

   where [s.sup.e.sub.t+k] is the log of the ex ante spot exchange rate in period t + k and [DELTA] is the first difference operator.

   Inflation rates are related across economies via the EAPPP relationship. EAPPP relates the expected inflation differential to the expected exchange rate depreciation as in Equation 3:

   (3) [[pi].sup.e.sub.j,t+k] - [[pi].sup.e.sub.i,t+k] = [DELTA][S.sup.e.sub.t+k']

   Combining Equations 1, 2, and 3 yields the real interest parity relationship

   (4) [r.sub.j,t] = [r.sub.j,t.]

   If Equations 1, 2, and 3 are true, then real interest rates will be equalized internationally. RIP is itself based on the validity of four equilibrium relationships, a Fisher relation in both the foreign and domestic countries relating nominal rates to real rates, the UIP equation relating nominal rates across countries, and EAPPP relating expected inflation rates across countries.

   Time Series Implications

   We start the discussion of the time series implications of the previous section from the assumption that the observable variables [i.sub.j,t], [i.sub.i,t], [[pi].sub.j,t+k], [[pi].sub.i,t+k], and [s.sub.t+k] are integrated of order one or I(1). (5) This assumption implies that these variables have no tendency to revert toward a constant mean or deterministic trend. Such series may wander without bound.

   Previous studies have used Equation 1 as the basis for testing the Fisher relation by noting that economic theory suggests that [r.sub.j,t] should be a stationary or I(0) variable. (6) In order for the Fisher relation to hold empirically when [i.sub.j,t] and [[pi].sub.j,t+k] are I(1) processes, they must be cointegrated. Cointegration implies that, while both individual variables will wander aimlessly through time, some linear combination of the two tends toward a constant value, that is, they share a long-run equilibrium. (7)

   Similarly, if nominal interest rates and the spot exchange rate are first-order integrated or I(1), then the log difference of the spot exchange rate is I(0), and Equation 2 implies that the two nominal interest rates are also cointegrated. (8)

   Finally, if [[pi].sub.j,t+k] and [[pi].sub.i,t+k] are both I(1) variables, then they must also be cointegrated if the EAPPP relation is to be empirically valid. Real interest rates will be equalized internationally if these four equilibrium relationships or parity conditions are satisfied in each two-country pairing, a Fisher relation in each country, UIP, and EAPPP. There are four observable variables in these four parity relationships: [i.sub.j,t], [i.sub.i,t], [[pi].sub.j,t+k] and [[pi].sub.i,t+k]. Because only three of the four parity conditions are independent, that is, if three hold, then the fourth must also be true, there should exist three stationary relations among the four variables in each RIP system. This means, as shown by Stock and Watson (1988), that there must be one common stochastic trend among the four variables.

   In order to see this result more clearly, it is convenient to appeal to a vector autoregressive (VAR) model in the four observable variables as in Equation 5,

   (5) [PHI](L)[X.sub.t] = [[mu].sub.t] + [[mu].sub.t],

   where [X.sub.t] is the 4 x 1 vector of the observable variables: [i.sub.j,t], [i.sub.i,t], [[pi].sub.j,t+k], and [[pi].sub.i,t+k]. [PHI](L)is a pth-order matrix polynomial in the lag operator, [[mu].sub.t] is a vector of deterministic components, and [[mu].sub.t] is a vector of white-noise error terms. Equation 5 can be rewritten in error-correction model form as in Equation 6:

   (6) [DELTA][X.sub.t] = [[mu].sub.t] + [PI][X.sub.t-1] = [p-1.summation over (i=1)][[GAMMA].sub.i][DELTA][X.sub.t-1] + [[mu].sub.t],

   where the long-run impact matrix [PI] is of particular interest. There are three possibilities with respect to the rank of the [PI] matrix: (i) [PI] is of zero rank, implying that all of the variables in [X.sub.t] are I(1) and not cointegrated; (ii) [PI] is of full rank, implying that all of the variables in [X.sub.t] are stationary in levels; and (iii) [PI] is of reduced rank, implying that at least some of the variables in [X.sub.t] are integrated and...