Unit 7 Macroeconomic policy in the global economy

7.8 Global financial markets and policy interest rates

Members of a common currency area, such as the eurozone, have chosen to abandon their national currency, with the result that they hand over control of the policy interest rate to the central bank of the common currency—in the case of the eurozone, the ECB.

This section is about policy interest rates and therefore only concerns countries with their own currency. On paper, at least, the central bank in all such countries—whether the exchange rate is flexible or fixed—has the power to set its own policy rate. But for countries with their own currency, integrated global financial markets affect the relationship between interest rates and exchange rates, and this puts important constraints on the ability of the central bank to choose its policy interest rate.

For countries that fix, or even attempt to fix, their exchange rate, we will show that the power to set the interest rate independently entirely disappears. The actual power to set rates effectively transfers to the central bank that sets monetary policy for the currency against which the exchange rate is fixed (for example, to the US Federal Reserve if the currency is fixed against the dollar).

To explain this relationship, we first move away from the policymaker’s perspective and consider the viewpoint of a global investor.

In what follows, we assume that financial markets are truly global: that investors can, in principle, buy assets anywhere in the world. That is, we assume there are no capital controls, which limit, or sometimes entirely prevent, investors from investing outside their home country.

The assumption of no capital controls has been quite close to holding in most high-income economies in recent decades. But it typically did not hold in some earlier periods even in richer countries, and even today capital controls are still imposed in quite a large number of countries with lower GDP per capita. It is important to bear in mind that we are making this assumption in what follows.

The policy interest rate from a global investor’s perspective

Imagine that you work for a pension fund in the United States, and your job is to invest your clients’ funds in assets that bring the highest possible expected returns.

You can, if you wish, buy government bonds or other assets in your own country using dollars, but if, for example, you think that the returns on South African government bonds are likely to be higher, you could convert your clients’ dollars into South African rand and invest there instead.

In the absence of capital controls, what will persuade you, and other global investors, to invest in any particular country? Figure 7.18 shows that as of 2022 you appeared, at least, to have a wide range of investments to choose from. Should you invest where the interest rate is highest? This turns out not to be a sensible strategy.

In economics, as in life, when something looks too good to be true, it usually is.

One immediate clue is to consider the countries offering the highest interest rates. At the top of the list is Argentina, which was in a deep crisis in 2022. Most countries on the right-hand side of Figure 7.18 were in some form of distress or crisis, whether long-term or short-term in nature—a feature we will discuss in Section 7.10.

As an investor with clients in the US, who will in due course be paid pensions—and consume—in dollars, you are interested in what you will get back from investment in South Africa, Mexico, or Türkiye in dollars, not rand, pesos, or Turkish lira. This means that you cannot just consider interest rates in any given currency in isolation. You also have to think about what is going to happen to that country’s exchange rate.

Global capital mobility: Interest rates and the exchange rate

Suppose you are considering whether your employer, the pension fund, should invest in South African government bonds. South Africa has a flexible exchange rate. As a global investor, you therefore need to consider both the interest rate and prospects for the exchange rate of South Africa, the rand. If you buy South African bonds, you need rand, but you need dollars to pay out the pensions to your clients. We will show that a high interest rate on rand bonds may be unattractive if you expect the rand to depreciate while you are holding the bonds, leaving you with fewer dollars than if you had invested in US bonds.

What constrains the choices available to policymakers is the behaviour of global investors as a whole, making trades based on comparisons between various available rates of return—taking account both of interest rate differentials between countries and expectations of how exchange rates will move. For now, we assume that your behaviour matches that of the typical global investor.

We will take South Africa to be the policymaker’s home economy, and consider how its policy interest rate and the rand–dollar nominal exchange rate will affect your decision, as a global investor, about whether to invest in South Africa on behalf of your clients at a US pension fund. From the South African perspective, you are a foreign investor, and the US is the foreign economy.

To simplify the analysis, we assume that you need to make decisions about investing over a one-year horizon. Your employer can always invest in risk-free dollar assets, such as a government-guaranteed US bank one-year deposit or a US government bond, which earns interest at the US policy rate, \(i^*\).

As a US dollar investor, you could in principle recommend to your employer that they invest instead in an asset in South African rand, paying the South African policy rate, i, also assumed to be guaranteed, but only in rand terms.

To make things concrete, we assume that the US policy rate (in dollars) is \(i^* = 4\%\), and that the home rate (in rand) is \(i = 6.5\%\).

If you do invest in South African bonds, the payment will be in rand; so in a year’s time, you will need to convert the proceeds of your rand investment into dollars. So what you are interested in is the rate of return you will get in dollar terms. In the extension to this section, we show that this is given, to a good approximation, by:

\[\text{ROR}_n^* \approx i - \delta\]

where \(\text{ROR}^*_n\) is the nominal rate of return in dollars, \(i\) is the home policy rate and \(\delta\) (as in Section 7.4), is the rate of depreciation of the home currency (here, the price of dollars in rand).

The intuition for this formula is as follows: if \(\delta > 0\), the South African rand depreciates and this means that in a year’s time any payment in rand will be worth less in dollar terms. So the more rapid the rate of depreciation (the higher is \(\delta\)) the worse the return will be in dollar terms.

So, knowing this, should your pension fund invest in South African bonds? Clearly this depends crucially on what you expect to happen to the rand–dollar exchange rate.

Suppose that over the course of the next year, you expect the rand to depreciate against the dollar by 2.5%. This implies that:

\[\delta^E = 0.025 = 2.5\%\]

where \(\delta^E\) is the expected depreciation. In other words, you expect that in a year’s time, \(e\), the price of a dollar in rand, will have increased by \(2.5\%\).

Given your expectation of depreciation, should you invest in rand assets? It would only make sense if you get a higher interest rate, \(i\), on rand investments, than on dollar investments. If the interest differential, \(i \text{ } – \text{ } i^*\), is 2.5% or more, this would compensate you for the expected depreciation. So, in this case, you would not consider investing in rand assets unless the policy interest rate set by the South African central bank is at least \(i = 0.04 + 0.025 = 6.5\%\).

If this was not the case, and, for example, your expected rate of depreciation was higher, say \(\delta^{E}= 5%\), your expected return on investing in South African bonds would be considerably less than the return on investing in dollar bonds, so you would be very unlikely to recommend the investment. Conversely, if you did not expect the rand to depreciate at all, that is, \(\delta^{E}= 0\), South African government bonds would be a very good investment indeed.

Therefore your expectations of exchange rate depreciation, and those of all other global investors, are crucial.

Comparing expected returns on investing in assets in different countries

More generally, the expected rates of return on domestic and foreign assets (in our example, rand and dollar assets) will be the same if the gap between the interest rates precisely offsets expected depreciation:

\[\text{Equal expected return} \Rightarrow i = i^* = \delta^E\] \[\begin{align*} \text{Interest gain to a foreign investor from holding home currency} \\ = \text{Expected loss from exchange rate depreciation} \end{align*}\]

When we observe interest rate differentials in the data (sometimes, as illustrated in Figure 7.18, very large ones), one way to interpret these gaps is that they represent a compensation to investors for expected depreciation. But how does this come about?

Uncovered interest parity: Trading by global investors equalizes expected returns on assets in different countries

The formula in the previous subsection shows the implications of expected returns on different currencies being equal.

uncovered interest parity, UIP

When interest rates and expected depreciation of the exchange rate are such that the expected rates of return on domestic and foreign assets are equal, we say that the uncovered interest parity (UIP) condition holds.

The ‘equal expected returns’ relationship is called the uncovered interest parity (UIP) condition. What we call the ‘principle of uncovered interest parity’ is the argument that trading in financial markets will always ensure that this relationship holds.

The algebra underlying this relationship is set out in the extension to this section, and the intuition is as follows: if \(i > i^*\), then the gain that you, as a dollar investor, make from the higher rand interest rate will precisely offset the expected loss due to the rand depreciating against the dollar.

In terms of our numerical example, if:

\[i^* = 4\%\]

then UIP implies:

\[\delta^E = i \text{ } – \text{ } i^* = 2.5\]

which therefore implies:

\[i = i^* + \delta^E = 4 + 2.5 = 6.5\]

Note that the same relationship works in the opposite direction, for a South African investor: if they invest in dollar assets, they’ll get a lower interest rate, but this will be compensated for by the expected depreciation of the rand, which will mean that every dollar they get back will buy them more rand.

This is a reminder of a key assumption underlying the UIP: that both dollar and rand investors can freely choose to invest in both currencies: that is, we are assuming there are no capital controls. Extension 7.8 shows how to derive the UIP condition, and that it does appear to be consistent with what we observe in the data.

Why would we expect UIP to hold? To answer this question, advocates of UIP would flip the question the other way around, and ask: what if it doesn’t hold?

Suppose, for example, that we observe that the South African central bank has set an interest rate of 6.5%. What if we made a different assumption about the expected rate of depreciation of the rand, and assumed \(\delta^E = 5\%\), instead of \(\delta^E = 2.5\%\)? If this combination was sustained, this would imply that the interest differential was not providing sufficient protection to compensate global investors for expected depreciation. So global investors would be expecting a lower return from investing in rand assets than they could earn by investing in risk-free dollar assets. The principle of UIP argues that this simply could not be a market equilibrium. No one would want to invest in rand assets at the prevailing rand–dollar exchange rate.

But if we observe that, in reality, global investors are prepared to hold rand assets, then the principle of UIP says that the assumption that \(\delta^E = 5\%\) must be incorrect. The same would apply if we guessed a lower value, like \(\delta^E = 0\%\): that would imply that expected returns on rand assets were higher on a sustained basis. So, as long as we assume that global investors are only motivated by expected returns, the only value of \(\delta^E\) that is consistent with what we observe is the value, \(\delta^E = 2.5\%\), implied by UIP.