RDP 9101: The Effect of Steady Inflation on Interest Rates and the Real Exchange Rate in a World with Free Capital Flows 1. Introduction

This paper presents a model to help explain important aspects of the behaviour of the Australian macroeconomy over the recent past. Figure 1 shows inflation^[1] from March 1984 to June 1990 in Australia, in the US and in four large OECD economies (the figure shows an arithmetic average of inflation in the US, Japan, West Germany and the UK). Figure 2 shows both short and long-term real pre-tax interest rates^[2] over the same period and Table 1 provides summary statistics. Figure 3 shows the Australian real exchange rate and terms of trade over the 1980s.^[3]

As Figure 1 shows, for over six years, Australian inflation has been fairly steady and well above US or ‘large four’ inflation. As Figure 2 shows, real short-term interest rates in Australia have been substantially above world real interest rates for most of this six year period – on average, over p.a. above world rates – and real Australian long bond rates have also been somewhat above world rates.

Since Australia is a small open economy operating, over the last six years, with no impediments to the movement of capital into or out of the country, Australian interest rates should satisfy international arbitrage conditions.^[4] With these arbitrage conditions in mind, there are two possible explanations for the fact that Australian short-term pre-tax real interest rates have averaged over p.a. above comparable world rates for over six years. Either there has been a sizable risk premium^[5] demanded by foreign investors to hold Australian short-term nominal assets, or the market has continually expected significant real depreciation of the Australian dollar – or, perhaps, a combination of these two explanations.

Smith and Gruen (1989) rejected the possibility of a large risk premium for the Australian dollar. The volatility of the return on short-term Australian nominal assets is similar to the volatility of the return on comparable assets from other countries,^[6] and the risk premium required by foreign investors to compensate them for that volatility should also be similar. Both theoretical calculations (extending the work of Frankel and Engle (1984) and Frankel (1988)) and estimates based on surveys of the exchange rate expectations of market participants (using the approach of Froot and Frankel (1989)) suggest that, on average, the risk premium is much too small to account for the short-term real interest differential between Australia and the world over the last six years.^[7]

This paper provides an alternative explanation for the consistently high Australian short-term pre-tax real interest rates, and examines its consequences. The main body of the paper presents a formal model, but the key ideas can be set out descriptively.

With relatively high domestic inflation and a tax system which is not inflation-neutral, the monetary authorities will find it necessary to maintain high domestic short-term pre-tax real interest rates simply to keep inflation steady.^[8] Domestic lenders will receive a nominal interest return high enough to at least partly compensate them for being taxed on their full nominal interest receipts. Similarly, domestic borrowers will be willing to pay these interest rates because they can deduct the full nominal value of their interest costs when calculating their taxable income.

In contrast to their domestic counterparts, to the extent that foreign lenders are taxed, their tax is levied on their nominal $A interest receipts adjusted for any depreciation.^[9] Hence, foreign lenders will find the high domestic short-term interest rates attractive even when they anticipate that the domestic exchange rate will depreciate to offset the domestic/foreign inflation differential. In the process of satisfying their demand for Australian nominal assets, foreigners will cause the domestic nominal and real exchange rate to appreciate. When this happens, foreign lenders will be aware of two things: that domestic real interest rates are relatively high, and that the domestic real exchange rate is over-valued (compared with its level if domestic real interest rates were equal to world real rates). Equilibrium is established when the marginal foreign investor's assessment is that the excess return on the high domestic interest rates is offset by the expected loss should the domestic currency depreciate in real terms.

Thus, while the relatively high domestic inflation persists, foreign lenders continue to receive an exchange-rate-adjusted return higher than the world interest rate. This does not cause them to invest so heavily in domestic nominal assets that the domestic pre-tax real interest rate is driven down to the world level because foreigners remain wary of the possibility that the persistent real exchange rate over-valuation will unwind – which would occur if, for example, the domestic inflation was to end.

To summarize, while the combination of relatively high steady domestic inflation, a non-inflation-neutral domestic tax system and free global capital flows persists, domestic short-term pre-tax real interest rates remain above comparable world rates and the domestic real exchange rate remains over-valued.

To support this intuitive argument, the paper develops a formal model. The development proceeds in two stages. In the first stage (Section 2 of the paper) we consider a small open economy with steady inflation and a non-inflation-neutral tax system in a world with no inflation and free global capital flows. A critical assumption is that there is no future uncertainty – both the steady domestic inflation and the tax system are expected to remain unchanged. Then, international investors force domestic real pre-tax interest rates to equal world real pre-tax interest rates. This is a standard result, and clearly such a model cannot explain Australia's high short-term real interest rates over the past six years.

At the second stage of development (Section 3) we introduce uncertainty. In turn, we examine three sources of uncertainty – the possibility that, firstly, the steady domestic inflation will end, or secondly, the non-inflation-neutrality of the tax system will be eliminated, or thirdly, a ‘real interest equalization tax’ will be introduced. Then, as the model demonstrates, for as long as the combination of steady domestic inflation, a non-inflation-neutral domestic tax system and free global capital flows (hereafter referred to as “the combination”) persists, the domestic short-term pre-tax real interest rate will be higher than the comparable world real rate. Furthermore, the model predicts that while “the combination” persists, the domestic yield curve will be inverse (i.e., with short rates higher than long rates) – as has been the case for most of the last six years in Australia.

In both the Section 2 and Section 3 versions of the model, the interaction of steady inflation with a non-inflation-neutral domestic tax system and free global capital flows leads to an over-valued domestic real exchange rate.

To conclude this introduction, we highlight the quite different implications of the two alternative explanations for the high Australian real interest rates. If the high Australian real interest rates were a consequence of a risk premium, two things would follow. Firstly, the real interest differential would remain for as long as the risk factors causing the risk premium remained. Secondly, the high domestic real interest rates would not cause the Australian real exchange rate to be over-valued, because, adjusted for risk, Australian real interest rates would be the same as world real interest rates. By contrast, if the explanation presented in this paper is correct, while “the combination” persists, the real exchange rate is continually over-valued – which has resource mis-allocation consequences.

Footnotes

To avoid the problems associated with the consumer price index (CPI) – particularly the inclusion of mortgage interest payments – we use each country's implicit price deflator for private consumption to derive inflation. [1]

Real interest rates are derived by deflating nominal rates by the 12 month ended inflation rates calculated for Figure 1. For short rates, we use 3 month Euro-currency rates for all countries other than Australia. Because of data limitations, for Australia we use the 90-day bank bill rate. Over the period for which Australian Euro-rates were available (since December 1987), the average difference between the 90-day bank bill rate and the mid-point of bid and offer Australian 3 month Euro-rate was 0.36%p.a. Long rates are long-term government bond yields from International Financial Statistics, IMF. [2]

The real exchange rate is the trade-weighted index published by the Reserve Bank of Australia, deflated using the ratio of Australian ‘Medicare adjusted’ CPI to OECD G7 CPI. An increase in the index represents an appreciation of the Australian dollar. The terms of trade is for goods and services. See the Discussion Section for further analysis on the level of Australia's real exchange rate. [3]

Expressed formally, for a representative investor from country j, the arbitrage condition in terms of real interest rates is

View MathML

where r^A and r^j denote the real pre-tax interest rates on comparable Australian and country j assets (r^k ≡ i^k − π^k, where i^k and π^k denote the nominal interest rate and the inflation rate in country k, and k denotes either Australia or country j); S is the bilateral real exchange rate (Australian currency price of country j currency, deflated by the ratio of Australian to country j consumer price indices), and ΔS is the change in S over the life of the asset. The risk premium, rp, is the real excess return demanded by the foreign investor to hold the Australian denominated asset. Part 1 of the Appendix justifies the focus on an arbitrage condition expressed in terms of pre-tax interest rates. [4]

The term ‘risk premium’ is often used loosely to mean the excess return demanded by investors to compensate them for the ‘risk’ of an exchange rate fall. Here, we use the term in its technical sense. For a given expectation of the return on an asset, the risk premium is the excess return required because of the expected volatility of the return and the expected correlation of the return with the returns on other assets. [5]

Over a four-week horizon, an investment in short-term Australian nominal assets by a US investor has experienced a variance of real returns of 0.00119 (Smith and Gruen, (1989)). This may be compared with the average variance of real returns (over a month) for a US citizen investing in short-term nominal assets in the UK (0.00080), France (0.00099), Germany (0.00113) or Japan (0.00099) – Frankel, (1985). [6]

The theoretical calculations suggest that the risk premium a utility-maximizing investor should demand to hold short-term Australian nominal assets is at least a factor of ten smaller than this average real interest differential. An alternative possibility is that a risk premium exists because of a default risk on Australian short-term nominal assets. Over the six years under study, the real interest differential between Australian and US 3-month Treasury bills has also averaged more than 2.5% p.a. Since the Australian Federal Government has a low level of debt and, over the last three years, has been running large budget surpluses, it seems highly unlikely that a ‘default risk premium’ explains the high short-term Australian interest rates. [7]

The monetary authorities control short-term interest rates, while long-term rates are determined by the market. [8]

See Part 1 of the Appendix for further details. [9]