Some Hypotheses | RDP 9104: Cross-Country Relationship Between Interest Rates and Inflation over Three Decades

RDP 9104: Cross-Country Relationship Between Interest Rates and Inflation over Three Decades 3. Some Hypotheses

Michele Bullock and Mark Rider

June 1991

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In this section, an attempt is made to explain the empirical regularities observed in section 2b. How can the positive relationship between real short-term interest rates and inflation in the second half of the 1980s be explained? And how can the break with previous periods be justified? Before discussing these issues though, it is worth highlighting some simple hypotheses upon which much of the literature of inflation/interest rate relationships is built.

(a) The Fisher Hypothesis

Theory on the relationship between inflation and interest rates for closed economies has revolved around the Fisher hypothesis and variants on this. Fisher (1930) decomposed the nominal interest rate (i_t) into two parts: a real component (r_t) and inflationary expectations (π^e_t).^[8]

Fisher argued that over the longer term, the real rate of interest is determined mainly by individual time preference and will be approximately constant. Nominal interest rates will hence reflect movements in inflationary expectations one-for-one.

This simple analysis neglects taxes which are now recognised (beginning with the contribution of Darby (1975)) as having an important influence on interest rates. When taxes are taken into account, the simple Fisher hypothesis alters. Assuming a proportional income tax, taxable nominal interest receipts and deductible nominal interest payments,

where r^a_t is the real after-tax interest rate, and τ is the (proportional) tax rate. Therefore, if the real after-tax rate of return is constant in the long run, the nominal rate of interest is given by

So if π^e_t rises by one percentage point, the nominal interest rate rises by 1/(1−τ) > 1 percentage points. That is, the nominal interest rate must rise not only by enough to cover the higher inflation rate but also by enough to cover the increased taxation burden. Note also what this implies for the real pre-tax interest rate: it increases with the expected inflation rate and the nominal interest rate. Assuming the real after-tax interest rate is constant, equation 3 implies

where r_t is defined in equation 2. The real pre-tax interest rate will rise proportionately with the expected inflation rate, the proportional tax rate determining the size of the response.

The discussion above proceeded on the basis of a closed economy and said nothing about the relationship between interest rates in different countries. If we assume uncovered interest parity (UIP) and an ex-ante version of purchasing power parity (EAPPP), real pre-tax interest rates will be equalised across countries^[9]. Applying the Fisher equation, it is easy to see that high inflation countries will have higher nominal interest rates than low inflation countries.

It appears relatively easy then to reconcile the relationship between nominal interest rates and inflation across countries. But the simple model above suggested that pre-tax real interest rates would be equalised across countries. The data presented in section 2b are not entirely consistent with this prediction: prior to the 1980s, real pre-tax interest rates were not equal across countries at either the short end or the long end. Furthermore, in the 1980s, there was an apparent change in the relationship between inflation and real short and long-term interest rates. Although real long-term interest rates appeared to be equalised across countries in this period, real short-term interest rates were not. The following section discusses possible explanations for these observations.

(b) Short-Term Interest Rates

A simple explanation for the inequality of short-term real interest rates is that prior to the 1980s, countries with high inflation rates were experiencing their inflation because of loose monetary policies (represented by relatively low or negative real short-term interest rates). In the 1980s, central banks around the world became more conscious of reducing inflation. As a consequence, countries with high inflation ran tight monetary policies (high real short-term interest rates) in an attempt to reduce inflation.

Why were these real interest differentials not arbitraged away? In the context of a Dornbusch(1976) overshooting model, real interest rates may differ across countries in the short run if the authorities have adjusted monetary policy. In such a model, the price level is assumed to be sticky and the exchange rate adjusts quickly. If a country loosens monetary policy, at the initial level of prices, the domestic interest rate will fall. The exchange rate will depreciate but it overshoots so that the expected appreciation in the exchange rate offsets the interest differential between home and abroad. As the domestic price level adjusts upward, the domestic interest rate will rise and the exchange rate will appreciate to its long run equilibrium. In long-run equilibrium, the price level and exchange rate will be at their new equilibrium levels and the (real) interest rate will once again be equal to the foreign (real) interest rate^[10].

In this model then, some countries can run lower real interest rates than the rest of the world in the short run. Likewise, if a country tightens monetary policy, it can keep its real interest rates above those in the rest of the world in the short run. In terms of the relationships we observed in section IIb, countries with high inflation were loosening monetary policy in the 1970s and tightening monetary policy in the 1980s.

An alternative explanation is that a country with high inflation must run a higher pre-tax real interest rate than a country with no inflation simply to keep inflation from accelerating. Equation 5 showed that in a closed economy, if the real after-tax interest rate is to remain constant in an environment of rising inflationary expectations, the real pre-tax interest rate will have to rise. If the real pre-tax interest rate does not rise, the real after-tax interest rate will fall. Since saving and investment decisions in the domestic economy are made on the basis of real after-tax interest rates, a fall in the real after-tax interest rate will encourage investment and discourage saving (or, equivalently, encourage consumption). If the authorities want the real after-tax interest rate to remain constant in the face of rising inflation, they will have to run higher pre-tax real interest rates. This is a product of the non-neutrality of the tax system.

Thus, the non-neutrality of the tax system implies that higher inflation countries will have to run high pre-tax real interest rates simply to maintain a given stance of monetary policy. This is consistent with the real short-term interest differentials observed in section 2b. But why are these differentials not arbitraged away as is predicted in the standard open economy model? Gruen (1991) introduces some uncertainty into the standard model. Without going into details, the result is that real interest rates are higher in a high inflation country simply to keep inflation steady.^[11] Furthermore, these differentials are not arbitraged away.

Note that unlike the Dornbusch model, this is a longer-run equilibrium position. It explains why high inflation countries may have high real interest rates even if they are not attempting to reduce inflation. But the Gruen model only explains the positive relationship between real short-term interest rates and inflation observed in the second half of the 1980s. As will be discussed below, the model does not fit the world of the 1960s and 1970s.

(c) Long-Term Interest Rates

The previous section focussed on the relationship between short-term interest rates and inflation. But it was noted in section 2c that real long-term interest rates are not necessarily equal across countries either. The relationship between real long-term interest rates and inflation tended to be negative over the 1970s. By the 1980s though there was no relationship between real long-term interest rates and inflation. Can this be explained in the context of the hypotheses put forward in the previous section?

In the Dornbusch model, there is no distinction between short and long-term interest rates. But Gruen's model makes this distinction so it is possible to make some predictions about long-term interest differentials. The relationship between domestic and foreign real long-term interest rates is not as clear cut as for real short-term interest rates. Under some assumptions high inflation countries could be expected to have a higher long-term real interest rate than low inflation countries. Under other assumptions, the real long-term interest rate in the high inflation country might be lower than the rate in low inflation countries. But the Gruen model consistently predicts that real long-term interest rates will not be as high as real short-term interest rates in the high inflation country.

The data in section 2c are consistent with the model's prediction of a downward sloping yield curve in high inflation countries. The relationship between real long-term interest rates and inflation over the second half of the 1980s is much weaker than that for real short-term interest rates and inflation over the same period.

(d) Why the Change in the Relationship?

In the previous sections, some hypotheses were offered as to why there is a positive relationship between real interest rates and inflation over the second half of the 1980s. But in the 1960s and 1970s it was observed that pre-tax real interest rates were either equal across countries or exhibited a negative relationship with inflation. Why did the predicted relationship show up in the data only in the 1980s?

In the Dornbusch overshooting framework, there is no difficulty explaining this change. In this model, real interest differentials are only a short run phenomena induced by changes in monetary policy. A negative relationship between inflation and real interest rates is consistent with this model, as is no relationship.

In Gruen's model, the explanation could be the difference in regulatory regimes between the periods. Through the 1960s and 1970s, monetary policy in most countries operated in a regulated environment. Policy operated through direct controls on the amount and direction of lending, controls on interest rates and a variety of reserve requirements. Although what market determined rates there were would have risen as policy was tightened, this was not the principal channel through which policy had its impact. Furthermore, capital was not nearly as mobile as it is these days. Many countries had fixed or managed exchange rates and capital controls. These restrictions impeded the flows of capital which would tend to arbitrage away interest differentials.

But in the 1980s, most countries undertook substantial deregulation of their financial systems. Monetary policy came to operate increasingly through the markets and changes in interest rates. Capital controls were progressively abolished, allowing increasingly free movement of capital across national borders. Furthermore, communication improvements and financial innovation encouraged global capital flows.

The Gruen model is imbedded in the deregulated environment. In this model, short-term interest rates respond to changes in the stance of monetary policy and exchange rates float. The impact of monetary policy on the economy comes through the interest rate channel and the associated exchange rate channel. Capital is mobile and flows to equalise expected returns between countries. It is not surprising then that the predictions from this model are inconsistent with the data for the regulated period.

In addition, the tax-adjusted Fisher effect might only be expected to show up in a deregulated environment. Carmichael and Stebbing (1983) argued that provided there is some degree of regulation of interest rates and a relatively high degree of substitution between money and financial assets, the Fisher hypothesis may be completely inverted (i.e. the after-tax nominal interest rate is approximately constant while the after-tax real rate moves inversely one-for-one with the rate of inflation). The implication is that the tax-adjusted Fisher effect may only begin to show up in the deregulated period, that is, the 1980s.

A more general explanation for the change in the relationship between the 1970s and the 1980s relates to the adaptive nature of investors expectations. As argued in footnote 4, the inflation rates experienced in the 1970s were well outside the experience of most investors. Investors were probably expecting much lower rates of inflation during this period. But their expectations turned out to be very wrong. As shown in Graphs 9,10,16 and 17, the ex-post returns to investors at both the long end and the short end turned out to be negative in many cases over the 1970s. Furthermore, returns tended to be more negative in the higher inflation countries as shown by the negative relationship between inflation and real interest rates. This suggests that the higher the inflation rate, the larger the “mistake” on inflation expectations.

Eventually, investors adapted their expectations to this higher inflation climate. Not wanting to be caught out as they were in the 1970s, investors demanded higher nominal returns in the 1980s. The higher the inflation rate, the more the adjustment since the worst errors in the 1970s had been made in the high inflation cases. This resulted in higher ex-post returns across the board. The graphs showed that in contrast to the 1970s, ex-post real returns tended to be positive in the 1980s. In effect, investors expectations “caught up” with the change in the inflation environment and this produced a change in the relationship between ex-post returns and inflation.

Footnotes

Continuous compounding is assumed. This allows equation 2 to be written without the cross-product term, r_t.p^e_t. [8]

To see this:

where i_t and p_t are defined as in the text, s_t is the log of the spot exchange rate and ^* refers to a foreign variable. Subtracting (F2) from (F1),

That is, ex-ante real interest rates will be equalised across countries. [9]

In the original Dornbusch model, nominal interest rates would also be equalised across countries because there is no money growth and no inflation in the long-run equilibrium. [10]

An accompanying result is that the exchange rate is overvalued. [11]