Following the Leader: The Central Bank and the Markets
Following the Leader: The Central Bank and the Markets
Abstract and Keywords
This chapter focuses on the complex and evolving relationship between central banks and the financial markets. It argues that central banks, which used to pride themselves on lording it over the markets, have been showing them increasing deference in recent years. Some modern central bankers seem to have become so deeply respectful of markets that a new danger is emerging: that monetary policymakers might be tempted to “follow the markets” slavishly, essentially delivering the monetary policy which the markets expect or demand. The chapter argues that many more central bankers now view the markets as repositories of great power and wisdom—as sages to be listened to rather than merely as forces to be reckoned with. However, when it comes to foreign exchange operations, central banks still strive to catch the markets off guard—even to push them around, if possible.
Qver the past decade or so, central bank independence has been the subject of a vast outpouring of academic literature,1 a great deal of real-world debate in political and public policy circles, and a substantial amount of legal and institutional change in a wide variety of countries (not including the United States). Alex Cukierman (1998), who knows more about this subject than almost anyone else, has taken note of the strong worldwide trend toward greater central bank independence: Since 1989, more than two dozen countries have increased the independence of their central banks substantially. It seems that none have moved in the other direction. This trend has been widely applauded by economists, and for good reasons. Greater central bank independence appears to be associated statistically with superior macroeconomic performance,2 although questions have been raised about the direction of causation.3
Just about 100 percent of this voluminous academic and realworld attention to central bank independence has been devoted to independence from politics and, in particular, from political influence over monetary policy. But there is another kind of independence that at least some strains of modern central banking may actually be endangering: independence from the financial markets.
(p.66) What? you say. How can a central bank be independent of the markets when its policy actions work through markets, and when many of its most important indicators are market prices of one sort or another? Both objections are, of course, correct. When I speak of independence from the markets, I do not mean that central banks should either ignore market signals or rely on nonmarket methods for implementing monetary policy (for example, quantitative credit controls). What I do mean is that some modern central bankers seem to have become so deeply respectful of markets that a new danger is emerging: that monetary policymakers might be tempted to “follow the markets” slavishly, essentially delivering the monetary policy that the markets expect or demand.4
Who's the Boss?
It was not always thus. If I may be forgiven for indulging in stereotypes for a moment, the older tradition viewed the central bank more as the stern schoolmarm disciplining the markets when they got out of line than as the eager and respectful student studying at the markets' knee. As both a positive and normative matter, there was little question about who was the leader and who was the follower. Part of the central banker's job was believed to be surprising or even bullying the markets.
Attitudes today are radically different. Modern central bankers pay rapt attention to what markets think they are up to—often as embodied in futures prices that flash across the Bloomberg screen in real time. Normally, the bank is loathe to deviate from what the markets expect it to do. This is a two-way street, of course. Markets today scrutinize the central banks with an intensity once reserved for the Kremlin; and “don't fight the Fed” is a well-ingrained piece of Wall Street wisdom. But the point I want to make is that many more central bankers now than previously view the markets as repositories (p.67) of great power and wisdom—as sages to be listened to rather than merely as forces to be reckoned with. As I will discuss later, there is one major exception to this new rule: When it comes to foreign exchange operations, central banks still strive to catch the markets off guard—even to push them around, if possible. But by and large, the evolving norm of behavior is just the opposite. Central banks often listen to the markets in both senses of that verb.
For the most part, this is a healthy development. Investors and traders do, after all, back up their beliefs with huge amounts of money—although skeptics will note that most of it is OPM (other people's money). Furthermore, as we economists are fond of pointing out, market prices succinctly summarize the collective wisdom of a vast number of people with diverse beliefs and access to different information. To believe that you can outwit the markets on a regular basis requires an extreme hubris that few if any modern central bankers have. Nor should they have it.
That said, I'd like to raise a question about whether the pendulum may perhaps have swung too far, whether the roles of leader and follower may have been reversed too sharply, whether what began as a healthy respect for markets may be in danger of devolving into worship of a false hero. In brief, whether the quiet revolution in modern central banking may have taken a good thing too far.5
I have one particular hazard in mind. Imagine a stereotypical monetary policy committee that scrutinizes the term structure of interest rates or the futures markets or both, observes what the markets expect it to do on a meeting-by-meeting basis, and then delivers precisely that policy. Such behavior may sound like the proper outcome of central bank transparency that I discussed and extolled in chapter 1. But it is actually something quite different. A fully transparent central bank keeps the markets well informed, teaches them about its way of thinking, and offers appropriate clues to its future behavior—thereby making the markets better predictors (p.68) of the central banks' decisions. But in all these ways, the monetary authorities are leading the markets to what they see as the right conclusions. My concern is with a central bank that follows the markets rather than leads them.
On the surface, it might seem that following the markets should produce a pretty good policy record. After all, the resulting decisions would embody the aforementioned collective wisdom, which presumably far exceeds the combined wisdom represented on any monetary policy committee. But I fear that following the markets might lead to rather poor policy nonetheless—for several reasons.
One is that speculative markets tend to run in herds and to overreact to almost any stimulus,6 whereas central bankers need to be cautious and to act prudently. I have often had occasion to cite Blinder's Law of Speculative Markets, which is based on a truly colossal amount of armchair empiricism. It is this: When they respond to news, the markets normally get the direction right but exaggerate the magnitude by a factor between three and ten. (Three connotes calm markets, ten, volatile ones.) Central banks, by contrast, must not get carried away. They should have the personality of Alan Greenspan, not of Jim Morrison.
I am aware that Bob Shiller's provocative original work on overreaction in the stock and bond markets (Shiller 1979, 1981) spawned a huge literature, some of which establishes that Shiller-like evidence may not actually demonstrate that markets typically overreact. There are alternative explanations of the data that are consistent with the efficient markets hypothesis. Maybe the daily dose of news absorbed by the stock market really does change the present discounted value of future dividends by about 1 percent—and by 23 percent on that fateful October day in 1987! (If you believe that, I have an efficiently priced dot.com I'd like to sell you.)
Much of this debate is highly technical, and this is neither the time nor the place to summarize, extend, or adjudicate it. Nor am I (p.69) the person best qualified to do so. Let me just point out that Ptolemaic astronomy also had its ingenious defenders, whose cleverly constructed epicycles held back the Copernican tide for a while. As you can probably tell, I cast my vote with Shiller—as, by the way, do most market participants. As Fischer Black, who lived successfully in both worlds, once put it, markets look far more efficient from the banks of the Charles than from the banks of the Hudson.7
Taking it as a fact that financial markets frequently overreact, an interesting question is why. One presumptive explanation is herding behavior. Even people from Connecticut and New Jersey know this much about cattle and sheep: that while they may be individually rational, the behavior of the herd sometimes produces results that, shall we say, stray pretty far from group rationality. Just as lemmings follow their leaders over cliffs, the seventeenth-century Dutch placed their faith in tulip bulbs, and the early-eighteenth-century French followed John Law into oblivion. Lest we think that modern-day Americans are vastly more sophisticated than those simpletons of yore, it was not so very long ago that gullible investors scrambled to fork over literally unbelievable sums for shares of Internet companies that never had any realistic ideas about how to make money. (Remember the idea of “paying for eyeballs”?—that is, valuing companies on the number of website “hits” rather than on profits or even sales.)
There is by now a substantial theoretical and empirical literature on herding, most of which—having been produced by economists—pertains to what might be called rational herding, that is, cases in which A follows B for reasons that are perfectly (individually) rational.8 For example, herding might be based on the belief that others have valuable private information. I learn that Warren Buffet has bought a stock, believe it is because he knows something I don't know, and therefore buy the stock myself. That may be quite rational. But if everyone emulates Buffet, the stock price may get (p.70) pumped up way beyond anything that Buffet's private information (if he really has any) can plausibly justify. Other models of rational herding are based on the reputations of fund managers and the way they are compensated (for example, it may pay to stay with the pack). In such cases, rational behavior by individuals may (but need not) lead to inefficient market outcomes.
But models of rational behavior may not capture the most important reasons for the herding phenomenon we observe in real markets. For example, so-called momentum investing—which means buying a stock just because it has recently gone up—is plainly irrational by standard definitions because, in efficient markets, stock prices are supposed to approximate random walks. Thus a recent run-up in the price of a share per se offers no reason to believe that above-normal returns will accrue to those who buy in today. Yet the existence of a substantial amount of momentum investing is well known anecdotally and has been documented by several scholars.9
Detecting herding empirically is a daunting task for several reasons. First, there may be good “fundamental” reasons for everyone to rush for the exits—or for the entrances—at once, without having contracted the urge just by watching others. Think about Enron stock once the bad news became public in 2001. Or Argentina's slowmotion default in 2000–01. Or, on the upside, the reaction of a pharmaceutical company's stock to its announcement of a new blockbuster drug. Investors are not necessarily acting like a herd just because many of them do the same thing at the same time. Second, devising a measure of herding is no simple task.10 Third, it may be next to impossible to distinguish between rational and irrational herding. On the other hand, this last distinction may not be too important for present purposes since either type of herding behavior can lead to overreaction in markets—the phenomenon that concerns us here.
Although I have dwelt on it, herding behavior is just one of (p.71) several possible explanations for systematic overreaction in speculative markets. Another, related explanation is that financial market participants frequently succumb to fads and fancies, producing speculative bubbles that may diverge sharply from fundamentals.11 If learning that buying shares of stupid-idea.com is the in thing to do makes you too long for shares in the company, then the market may display positive feedback loops that produce more volatility than the fundamentals can justify. But central bankers must steadfastly resist such whimsy and inoculate themselves against the faddish behavior that so often dominates markets. That may be why central bankers are not much fun at parties.
Last, but certainly not least, there is the nasty matter of time horizons. Homo economicus has a long (perhaps infinite) time horizon and a reasonable discount rate. So, I hope, do most central bankers. But traders in real-world financial markets seem to have neither. One might hope that Darwinian mechanisms would select for patient, long-term investors—but they do not appear to do so in markets that are dominated by daily mark-to-market, quarterly reporting, and compensation based on short-term performance.
Here is a stunning quantitative example that I have cited before.12 According to the standard theory of the term structure of interest rates, about which I will have critical things to say shortly, the thirty-year bond rate should be the appropriate average of the one-year bill rates that are expected to prevail over each of the next thirty years. Only one of these, today's one-year rate, is currently observed in the market. But the others—the so-called implied forward rates—can be inferred from the term structure. I will explain this in more detail shortly. But, for now, a simple example will do.
Suppose today's observed one-year interest rate is 3 percent and the two-year rate is 4 percent. Together, these imply that the one-year rate expected to prevail one year from now must be about 5 percent. The reason is straightforward. Investing in the two-year (p.72) bond will leave you with (1.04)2 two years later, after compounding. On the other hand, investing in two consecutive one-year bonds will be expected to earn you (1.03)(1+r), where r is the one-year rate expected to prevail a year from today. Since arbitrage dictates that the two returns must be more or less equal, r must be approximately 5 percent.13 Proceeding similarly, one can use the term structure to deduce all the implied forward rates, as I will demonstrate shortly. But now back to the time horizon issue.
One day in 1995, while serving as vice chairman of the Federal Reserve Board, I was wondering about bond market overreaction—which I thought I was witnessing all around me. So I asked the Fed staff to do a calculation. What, I inquired, is the correlation between daily changes in the one-year interest rate on U.S. Treasuries and daily changes in the implied one-year forward rate expected to prevail twenty-nine years from now? I was pretty sure I knew the theoretically correct answer to this question: essentially zero, because hardly any of the news that moves interest rates on a daily basis carries significant implications for interest rates twenty-nine years in the future. Modern-day Ptolemaists will, of course, insist that I am wrong about this. They will argue that things often happen that should have similar effects on both current interest rates and rates twenty-nine years from now. Oh? Name two.14
In any case, the statistical answer for the year 1994 was +0.54.15 Taken literally, this correlation means that you can explain 29 percent of the variance of changes in the one-year interest rate 10, 585 days from now by using nothing but today's change. Don't bet Yale's endowment, or even your own, on that!
So why is the correlation so high? My hunch, which I will develop in greater detail shortly, is that it reflects overreaction stemming from excessively short time horizons. The men and women who traded the thirty-year bond in 1994 (like the folks who do it today) were probably not thinking about the implications of various (p.73) bits of news for the economy in the year 2024. Indeed, many of them probably had a hard time getting their arms around the concept of thirty years, having not yet attained that august age themselves. Instead, I believe, traders were buying and selling the long bond as if it were a much shorter instrument.
If this hunch—and I admit that it is no more than that—is correct, there is a supreme irony here. One of the chief arguments for making central banks politically independent is that monetary policy requires a long time horizon, not the notoriously short time horizons of elected politicians. But if the central bank follows the market too slavishly, it will tacitly and inadvertently adopt the market's short time horizon as its own. Politicians may focus on the next election, which is bad enough. But bond traders may focus on their positions at the end of the trading day, or perhaps a half-hour from now, which is much worse. A politically independent central bank that follows the whims of the markets may thus wind up with an effective time horizon even shorter than that of a politician.
It is also very likely to overreact, just as the markets frequently do. Here is a simple example. Suppose something happens that should, on rational grounds, induce the central bank to raise interest rates, but only very slightly—say, by 25 basis points. Perhaps the government issues a bad-looking inflation report for a single month, or something like that. The market sees this new information but exaggerates its significance. It therefore begins to embody expectations of, say, a 75-basis-point rate hike into asset prices. The central bank reads the market's expectations from the term structure and feels compelled to deliver something closer to what the market expects, say, 50 basis points, rather than “disappoint the markets?” In this instance, the central bank's reaction is twice as large as it should be. While this is an exaggerated example, it serves to make the general point: If markets overreact and central banks follow the markets, then central banks are likely to overreact, too.
(p.74) More analytically, my Princeton colleagues Ben Bernanke (who is now a Fed governor) and Michael Woodford (1997) have built a rational expectations model in which a central bank can create a multiplicity of equilibria by reacting to the market's forecast of inflation rather than to its own. They emphasize the importance of the central bank using its own inflation forecast rather than relying on the market's, which, in the context of their model, is the only way the bank can maintain its independence from the market.
A Case in Point: The Term Structure of Interest Rates
I just used the term structure of interest rates to illustrate the general phenomenon of overreaction. This was no idle choice. In fact, one does not get very far in discussing central banking practice without mentioning the term structure. The so-called expectations theory of the term structure, to which I alluded earlier, is the vehicle almost always used to assess what the markets expect the central bank to do. It is therefore critical to communication between the central bank and the markets—in both directions. The question I want to deal with next is whether the markets are communicating well-considered wisdom to the central bankers or something rather less valuable. If the latter, of course, the central bank should listen rather selectively.
The role of the term structure is also central to the transmission mechanism of monetary policy, and for a very simple reason. Monetary policymakers generally have direct control over only the overnight interest rate. In the United States, that is the federal funds rate, the interest rate at which some banks lend reserves to others. At any one time, only a small minority of banks is active in this market. More fundamentally, as I noted earlier, no economic transaction of any importance takes place at the federal funds rate. If the Fed's (p.75) monetary policy is to succeed in influencing the interest rates and asset prices that really matter—such as loan rates, bond rates, exchange rates, and stock market valuations—then changes in the funds rate must somehow be transmitted to these other financial variables. The expectations theory of the term structure provides the standard linkage.
The theory itself starts with a simple arbitrage argument. As in the numerical example above, an investor can buy a two-period bond and hold it to maturity or buy a one-period bond and roll it over into another one-period bond when the first one matures. If each strategy has adherents, the expected returns on the two strategies must be equal. That means that, roughly,16 the two-period interest rate must be equal to the average of the two one-period rates—the first of which is actually observed in the marketplace today and the second of which is an (implicit) expectation. Using obvious symbols,17
where r1,t and r2,t are, respectively, the one- and two-period interest rates prevailing at time t, and the superscript e indicates an expectation. In this case, re1,t+1 is the one-period rate expected to prevail one period from now. In the simple numerical example, the two-year rate was 4 percent, the one year rate was 3 percent, and we deduced that the one-year rate expected to prevail one year from now had to be 5 percent because 4% = ½(3% + 5%). Note that this relationship should hold whether time is measured in days, weeks, months, or years.
Similar relationships hold for three-period interest rates, four-period interest rates, and so on. Thus r1,t, r2,t, r3,t and so on—the constituent parts of what is called “the yield curve”18—depend crucially on expectations. If you think of time as measured in days, it is clear that the entire term structure should, in principle, be driven by (p.76) expectations of what future monetary policy will be. For example, the one-year interest rate should embody today's one-day rate and the next 364 expected one-day rates; the ten-year interest rate should embody the next 3,649 expected one-day rates (forgetting about leap years); and so on.
As we move out along the yield curve to longer maturities, a term premium—variously rationalized as a risk premium or a liquidity premium—is generally added to the right-hand sides of equations like (3.1) to represent what investors demand to be paid to compensate them for the higher risk or lower liquidity of longer-dated instruments. In practice, the use of these premiums sometimes borders on the tautological: If the two sides of an equation like (3.1) appear to move differently, you can always square the circle with the appropriate time-varying risk premium. But the main point for present purposes is that interest rates on medium- and long-term debt instruments should depend mainly on expectations of future central bank policy.
This little detour into term structure theory explains why expectations are so central to the monetary policy transmission mechanism. A Federal Reserve action that strongly affects expectations of future short-term interest rates will, according to the theory, have a much greater impact on long-term interest rates than an action that moves today's short rate but leaves expected future short rates largely unaffected.
The logic behind (3.2) is straightforward. If you earn the two-year rate for two years, you get (approximately) 2r2,t. If you earn the one-year rate for one year, you get r1,t. Equation (3.2) then answers the (p.77) question How much must investors be expecting to earn in the second year?
More complicated versions of (3.2) will produce any implied forward rate you want. For example, I will shortly look at the nine-year-ahead forecasts of the one-year interest rate, in which case:
In words, if a prospective investor can earn r10,t annually for ten years with one strategy and r9,t annually for nine years with the other strategy, then she must be expecting to earn 10r10,t - 9r9,t in the remaining year. Since everything on the right-hand sides of equations like (3.2) and (3.3) can be observed directly in the market, the implied forward rates are easily computed, and financial specialists do so routinely.19
So far, so good. But here's the rub. The implied interest rate forecasts (expectations) that can be deduced from the yield curve bear little resemblance to what future interest rates actually turn out to be. There is no space here—and probably even less patience among readers—for a thorough review of the empirical evidence on the term structure of interest rates.20 Suffice it to say that the abject empirical failure of the expectations theory of the term structure of interest rates is a well-established fact.
I will offer just two kinds of simple evidence here. The first is for ordinary people—simple pictures. The second is designed for professionals—simple regressions. Both derive from the same sort of equation—versions of (3.2) and (3.3).
Look first at figure 3.1, which offers a kind of eyeball test of equation (3.3). The right-hand side of (3.3), which is observable every day in the market, is a forecast of the one-year rate expected to prevail nine years from today. We can assess the accuracy of such forecasts historically by comparing them to the one-year interest rates that actually obtained nine years later, provided we are willing (p.78)
On the horizontal axis, I plot the forecasted one-year bond rate nine years (that is, 108 months) later, computed from equation (3.3) for each month in the sample period. On the vertical axis, I plot the actual one-year rate 108 months later. In principle, the two should be equal, except for random forecasting errors. The straight line shown in the graph is not the best-fitting regression line, but rather a line with a slope of one—indicating the theoretically correct relationship.22 You do not need advanced training in statistics to see that the forecasts are pretty terrible. In fact, there appears to be little relationship between the two variables.
For those who do have such training, I offer two regressions. The first regresses the actual interest rate, r1,t+9, on the forecast, re1,t+9, as defined by equation (3.3), and tests the restriction that the slope coefficient is 1.0. Unsurprisingly given the picture, the null hypothesis is easily rejected. In fact, the resulting point estimate of the slope is just 0.27 (with standard error 0.037).23 The second comes from the existing literature—in particular, from a paper by John Campbell (1995, 139). It uses a variant of the term structure logic in which this month's yields on one-month and twelve-month zero-coupon bonds are used to forecast how the one-month yield should change over the ensuing eleven months.24 Once again, his equation has the feature that the estimated slope parameter would be 1.0 under the expectations theory. But his estimate is only 0.25 with standard error 0.21. That point estimate, which is quite close to mine, is significantly different from the theoretically correct value of 1.0 but not significantly different from zero.
In brief, what we seem to have found is that the expectations theory of the term structure performs miserably over moderate (one-year) and long (ten-year) time horizons.25 The empirical (p.80) failure of the expectations theory of the term structure raises an obviously interesting question: Why? Why does a theory that seems so obviously correct in principle work so poorly in practice?
There is another, equally fascinating question, however. The theory's abject failure is not some deep, dark secret that we professors know about but have somehow kept from the rest of the world. Central bankers realize that the expectations theory does not work. So do market participants, who nonetheless appear to use it to guide billion-dollar interest rate bets each day. Yet, in what appears to be a stunning example of pretending that the emperor is still fully dressed, academic economists, central bankers, and market participants alike all proceed as if the expectations theory really underpins the term structure. It's a curious case of mutually agreed selfdelusion, and the question is how and why it persists.
Freed, as I am in this book, from the heavy burden of peer review, I would like to suggest tentative answers to each of these questions.
First, why do experts continue to use the expectations theory of the term structure despite overwhelming evidence against it? My answer is that doing so is an act of desperation—they have no alternative. On a priori grounds, it is hard to understand how the expectations theory could be wrong. If expectations of future short rates do not determine long rates, then what does? I must admit that I have a hard time answering that question myself, and so I frequently find myself using the expectations theory to interpret the yield curve anyway. It's a bad habit that is hard to kick. Rarely has the old saw “it takes a theory to beat a theory” been leaned on so hard.
Second, why does the theory fail so miserably in explaining the facts? That may be the harder question. It is also the one most relevant to thinking through what the central bank can (or cannot) learn from the yield curve. I want to offer two candidate answers, while leaving the ultimate resolution of the issue, as usual, to the proverbial subsequent (p.81) research. The two answers are consistent with one another. Each denies that expectations are rational. And each explains why the implied forward rates—the expectations—are overly sensitive to current rates, and therefore why long rates overreact to short rates.
My first candidate answer, which I offer with some trepidation and only because both New Haven and Princeton are so far from the Great Lakes, was suggested earlier; but let me repeat it now. I believe that, when it comes to pricing long-term bonds, market participants do not peer as far into the future as the theory says they should. Instead, they are systematically myopic and extrapolative, treating and trading longer-term instruments as if they were much shorterdated instruments. One consequence is that the current situation and the latest news get far too much weight in setting today's longterm interest rates.
If this is so, then the amazingly high correlation between the one-year interest rate and the implied forward rate twenty-nine years from now becomes understandable. If traders treat the thirty-year bond as if it were, say, a three-year bond, then it is not hard to see why its price should respond strongly to short-term influences. Generalizing this example, we see that artificially short time horizons offer a straightforward explanation of Shiller's (1979) evidence for the overreaction of long rates to short rates.
The second explanation dispenses with rational expectations in a different way. A long-neglected paper by my Princeton colleague Gregory Chow, published in 1989, starts with the usual finding: The data he studies resoundingly reject the joint hypothesis that the expectations theory of the term structure holds and that expectations are (statistically) rational.26 Furthermore, the estimated parameters make no sense. Chow (1989) then inquires into which is the weak sister. His answer is clear. When he replaces the assumption of rational expectations with adaptive expectations, he finds that the estimated parameters in the term structure equation are reasonable (p.82) and that the joint hypothesis is not rejected. In other words, the expectations theory fails under rational expectations but works just fine under adaptive expectations.
Interesting. But how does that relate to the short-time-horizons idea? Simple. It turns out empirically that, compared to rational expectations, adaptive expectations place much greater weight on current short rates. In Chow's estimated example, under rational expectations a sustained 100-basis-point increase in the one-month rate has no effect on the twenty-year rate in the same month, only an 11-basis-point effect after three months, and only a 21-basis-point effect after six months.27 But under adaptive expectations, the contemporaneous reaction is 20 basis points, the three-month reaction is 33 basis points, and the six-month reaction is 45 basis points.28
In sum, relative to rational expectations, both adaptive expectations and, I would suggest, actual human behavior put far too much weight on current market conditions. This finding will not surprise anyone who has not been unduly influenced by advanced training in economics. And if it is true, delivering the monetary policy that is expected, if not indeed demanded, by the (myopic) markets could lead a too-compliant central bank down a primrose path. So this is one case—and an important case at that—in which it is important that the central bank not take its lead from the markets.29
Another Case in Point: Uncovered Interest Rate Parity
An analogous problem with interpreting market signals—and imbuing them with too much wisdom—arises in an international context. Instead of thinking about the arbitrage-like relations that arise in choosing among instruments of different maturities, as we do in the term structure, now think about choosing among instruments denominated in different currencies (over the same maturity). To start (p.83) once again with a simple concrete example, suppose one-year U.S. Treasury bills are paying 4 percent in dollars at a time when equallysafe one-year German government bills are paying 3 percent in euro. The theory of uncovered interest rate parity is based on the following simple but compelling insight: If some investors choose the U.S. paper while others choose the German, then the two must have (approximately) equal expected yields—whether you measure that yield in dollars or in euro. For that to be the case, the euro must be expected to appreciate by 1 percent over the year relative to the dollar.
Let's be more precise. If you invest $100 in the U.S. paper, you will get back $104 at the end of the year, with certainty. Alternatively, you can (a) purchase 100 euros (using an exchange rate of $1 = 1 euro, and ignoring commissions), (b) invest that money at 3 percent to get back 103 euro after a year, and then (c) convert those euro into dollars at whatever exchange rate, X, then prevails. Doing all this will earn you 103/X dollars. A simple arbitrage-like argument says that, with risk-neutral investors, these two investment strategies must offer the same expected return—which is the basic insight underlying uncovered interest parity. In the specific example, 103/Xe must be approximately equal to $104, so that Xe must be 0.9904.30 Thus, for the 4 percent U.S. interest rate and the 3 percent German interest rate to coexist in financial market equilibrium, the euro must be expected to appreciate from $1 per euro to $1/0.9904=$1.0097 per euro, or by approximately 1 percent.
Generalizing this simple example, uncovered interest rate parity states that, for two equally risky instruments denominated in different currencies but covering the same time period (any time period will do):
where rd is the domestic-currency interest rate, rf is the foreign-currency interest rate, and xe is the expected rate of appreciation of (p.84) the foreign currency. (xe is negative if the foreign currency is expected to depreciate.) Equations like (3.4) tie interest rates and exchange rate expectations tightly together. The age-old question is, Which moves which?
To see why this question is relevant to monetary policy, let's consider an application that is near and dear to the hearts of central bankers. Think of rd and rf as very short term interest rates, more or less controlled by the Fed and the ECB, respectively. Now suppose the Fed raises rd, but the ECB does not change rf. By the logic underlying (3.4), the expected change in the exchange rate must adjust upward. Specifically, the euro must now be expected to appreciate more or depreciate less than was the case just prior to the Fed's move. If the exchange rate expected to prevail a year from now is not changed by this event, as theoretical models generally assume, that means the dollar must rise now in order to create the expectation that it will fall later. On the other side of the Atlantic, of course, the ECB may be less than thrilled by the immediate depreciation of the euro. But, according to the logic behind equation (3.4), there is not much it can do about it—short of raising its domestic interest rate to match the Fed's. Like it or not, uncovered interest parity puts central banks in bed with one another. This is one-worldism in the extreme.
Now to the bad news. Think of equation (3.4) as a way to forecast changes in the exchange rate. It says, for example, that the expected rate of appreciation of the euro must be equal to the interest rate differential.31 Thus, by examining interest rates here and abroad, you can read an implicit forecast of where exchange rates are expected to go from market prices—just as interest rates on short- and long-term debt imply a forecast of where short rates are expected to go. Thus, equation (3.4) is a market-based forecasting equation, similar in spirit to equation (3.2). Having read that, you can probably guess the punch line. Yes, the exchange rate forecasts implied by uncovered interest rate parity are truly terrible.32 Don't bet a nickel on them.
(p.85) Once again, there is a substantial scholarly literature on this point. And, once again, I'll gloss over this literature and offer just two pieces of supporting information. The first is a pair of simple graphs comparing the forecasts of exchange rate changes based on interest rate differentials to the exchange rate changes that actually occurred. Figures 3.2 and 3.3 both use data on the dollar/yen exchange rate and interest rate data on government debt in Japan and the United States. In figure 3.2, I compare the actual three-month change in the exchange rate to the forecast implied by three-month Treasury bill rates in the two countries three months earlier. Not only is the relationship not tight, it is actually perverse: Amazingly, the yen typically depreciated when its short-term interest rate was below the U.S. rate. Figure 3.3 compares ten-year exchange rate forecasts derived from equation (3.4) with actual realizations. There appears to be virtually no relationship between the two.
For readers who are regression-minded, notice that (3.4) suggests the following linear regression:
A regression fitted to the data underlying figure 3.2 has a slope coeffcient of minus 3.3 (with a Newey-West standard error of 0.79), whereas the theoretically correct coefficient is 1.0. Surprisingly, the best fitting regression for figure 3.3 has a slope of 1.04 (standard error 0.22)—so, of course, we cannot reject b = 1. But a glance at figure 3.3 reminds us that the interest rate differential has a terrible forecasting record.
This finding is not special to the dollar/yen exchange rate or to the time horizons I have selected. Shusil Wadhwani (1999), while a member of the Bank of England's Monetary Policy Committee, called attention to the failure of uncovered interest parity by running regressions similar to (3.5) for several different exchange rates over a one-year horizon. Not only are his estimates of b not equal to (p.86)
So once again we have a major intellectual puzzle: A theory with seemingly impeccable logical credentials fails miserably in empirical tests. Interest rate differentials turn out to be horrible forecasters of changes in exchange rates. In fact, random walk models—which simply assume that exchange rates will never change—make better forecasts. Economists have been aware of this annoying fact ever since Meese and Rogoff's (1983) important paper. But they have yet to explain it.
So let me speculate about reasons. Once again, short time horizons and extrapolative behavior by traders probably play major roles, in stark contrast to the assumptions of rational expectations models. For example, more than twenty years ago, studies of the profitability of trading on exchange rate forecasts from three different sources—chartists, services based on “fundamentals,” and forward exchange rates—found that the chartists' forecasts did best and the fundamentals-based services did worst.34 I must say that this corresponds to my own casual observations of markets—they appear to be extrapolative in the short run. Note that since chartists base their predictions solely on recent price movements, any evidence of profitable trading based on chartist analysis represents a clear refutation of market efficiency—just as momentum trading does for stocks.
It is, furthermore, fascinating to note that the failure of uncovered interest parity is much more spectacular at short time horizons—where trading based on extrapolative expectations may dominate—than it is at long time horizons. This finding is consistent with our two graphs, which showed much worse performance of uncovered interest parity over three months than over ten years. It is also consistent with the scholarly literature.35
(p.89) From a central banker's point of view, the routine violation of uncovered interest parity at short horizons creates a serious problem. Suppose you are the Fed, thinking about cutting interest rates (rd in equation [3.4]) and wondering what impact this action will have on the economy. One of the standard channels of monetary transmission is, of course, through the exchange rate. So one of the things you are wondering about is how your action will affect the value of the dollar. If you believe that the other major central banks will not match your rate cut, equation (3.4) says that reducing the federal funds rate will make the dollar fall first in order to create expectations of a subsequent appreciation. A cheaper dollar should help U.S. exports and discourage U.S. imports, thereby boosting aggregate demand and giving your monetary policy an assist. But as a well-educated central banker, you are also aware that exchange rate forecasts generated by uncovered interest parity are terribly inaccurate. So you have little confidence that any of this will actually happen. How, then, do you reckon the exchange rate channel into your calculations?
In practice, this intellectual puzzle seems to have deepened in recent years. The new conventional wisdom is that boosting the economy by cutting interest rates may actually make the currency appreciate immediately, presumably because a stronger macroeconomy improves prospects for (mostly financial) investment and attracts larger capital inflows. Notice that this new “model” of how the exchange rate reacts to monetary policy is precisely the opposite of what the textbooks teach.36 I was brought up to believe that easier money made your currency depreciate. (Of course, in those days we also walked barefoot over glass to get to school—uphill in both directions.) Nowadays, what I used to deride as the “macho theory of exchange rates”—the idea that the exchange rate reflects the nation's virility—is looking better and better.
I hasten to say that the macho theory is now the market's belief (p.90) only for major countries like the United States, Europe, and Japan. No one to my knowledge has suggested it for Argentina or Turkey. Yet recent evidence questions even the standard view that emerging-market countries can defend their exchange rates by jacking up interest rates. They may just kill their economies instead.37
The Special Case of Foreign Exchange Intervention
Up to now, I have been speaking about central bank operations that are designed to change interest rates—which, of course, is what we generally mean by monetary policy. Exchange rate movements were only a by-product, although perhaps an important one. But sometimes a central bank—either on its own authority or under orders from the Treasury or Finance Ministry—intervenes in the foreign exchange market with the expressed intent of changing the (otherwise floating) exchange rate without changing the domestic interest rate.38 Economists call such operations sterilized interventions because they insulate domestic monetary conditions from exchange rate intervention.39 The question is, Can sterilized foreign exchange interventions work?
To someone who has not studied economics beyond the 101 level, the answer may seem self-evident. If the Fed enters the market to sell dollars, the dollar falls. If it buys dollars, the dollar rises. Right? Well, maybe not. Remember equation (3.4) again. In a sterilized intervention, rd does not change—under the assumption that domestic and foreign assets are perfect substitutes. Presumably, rf doesn't either. In that case, xe should not change, and so neither should the exchange rate.40
To readers unfamiliar with such arguments, this may seem a bit like pulling a rabbit out of a hat. So here is an analogy for noneconomists. Suppose Coke and Pepsi are perfect substitutes in the eyes of (p.91) consumers. That means that, at equal prices, they do not care which one they drink—but if the price of either soft drink rises by even a penny, customers will move en masse to the other drink. Now suppose the government tries to drive up the price of Pepsi (and drive down the price of Coke) by offering to buy Pepsi and sell Coke. Can this intervention possibly succeed? Not under the hypothesis of perfect substitutability, for then even the slightest price advantage for Coke will give virtually the entire market to Coca-Cola. So the two prices cannot differ, except fleetingly. If the government sells Coke to buy Pepsi, private parties will do just the reverse. The prices must remain equal.
Perfect substitutability works in the same way to negate the effects of a sterilized foreign currency intervention. The central bank, for example, buys domestic Treasury bills and sells foreign Treasury bills of equal market value. In principle, that should lower the domestic interest rate and raise the foreign interest rate. But if foreign and domestic bills are perfect substitutes in the eyes of investors, private investors will willingly sell as much of the domestic issue as the government offers to buy and buy as much of the foreign issue as the government offers to sell—all with virtually no change in any price. Neither rd nor rf nor xe need move.
So the issue comes down to one of substitutability in the portfolios of private asset holders.41 If, say, U.S. and Japanese government debt instruments are perfect substitutes, then sterilized intervention cannot move the dollar/yen exchange rate at all. If they are very strong but not quite perfect substitutes, it cannot move the exchange rate much. But if the two types of bonds are rather imperfect substitutes, there is real scope for exchange rate intervention to work.
Which theoretical case is most relevant to the real world? In truth, most economists are skeptical that sterilized interventions either should work in principle or do work in practice. Some (not (p.92) including me) elevate this belief to a quasi-religious status. Substitutability is almost perfect, they insist. And a central bank's foreign exchange portfolio is so small relative to even the daily volume of foreign exchange transactions that it can do little more than spit in the ocean.
Take these two arguments in turn, starting with perfect substitutability. I do not believe that, say, Bill Gates is indifferent to whether his portfolio includes $10 billion of U.S. Treasury bills or $10 billion worth of Japanese government bills. Even if the expected returns are identical (as uncovered interest parity suggests), the risk characteristics are quite different.
But the point about magnitudes is even more apposite, I think, and it may go a long way toward explaining why official interventions seem to have such small effects. Rarely do central banks intervene on the scale that would be necessary to move what have become truly enormous markets in the major currencies: the dollar, the yen, and the euro. With typical interventions of $1 or $2 billion in a foreign exchange market that routinely handles over a trillion dollars each day, it is hardly surprising that central bank operations do not move markets very much. In what market does a 0.1 percent change in supply move the price notably?
In fact, the amazing thing may be that such small interventions move markets at all. A decade or so ago, the weight of the academic evidence clearly held that they did not—that sterilized intervention was ineffective.42 But studies of the 1970s and 1980s may have been hampered by the lack of detailed data on the exact timing and magnitude of interventions. More recent studies, published in the 1990s, find more evidence that intervention works, at least somewhat.43
To be sure, it would be foolish for any modern central bank in a country with a floating exchange rate to believe that it has tight control over its currency value—whether via sterilized intervention or otherwise. Market folk wisdom holds, variously, that you (p.93) shouldn't stand in front of a speeding freight train or try to catch a falling knife. (But it also holds, Don't fight the Fed. Oh, well. Who ever said that markets were consistent?) No sensible person believes that small-scale foreign exchange interventions can reverse the direction of a big market that is hell-bent on moving in a particular direction. That is, indeed, tantamount to standing in front of a speeding freight train.
But market participants do not always hold strong convictions about which way the exchange rate should go. After a big run-up, for example, traders may become nervous that the dollar (or the yen or the euro) is overbought and is therefore due for a “correction.” Under such circumstances, a loud, clear intervention by the authorities, especially if concerted and sprung as a surprise, may succeed in pushing the market around without committing terribly much money. On those rare occasions when markets are not united in their view of the direction in which the exchange rate should be going, but governments are (and they show it), official intervention may be able to influence exchange rates substantially.44 The Plaza Accord in 1985 may have been one such example. Robert Rubin's successful turnaround of the dollar in 1995 may have been another.
My second obvious point is that not all markets are very deep. A $1-billion intervention in dollar/yen may, under most circumstances, be a futile gesture. But if $1 billion is applied to the cross-rate between, say, the British pound and the Czech crown, it may look like the Czech authorities have brought out the heavy artillery. I am concerned that too many governments of (economically) small countries may be afraid of adopting a floating exchange rate in part because they think that any subsequent intervention efforts are doomed to failure. That may not be so. No one will expect them to be able to move the dollar/yen exchange rate.
To return to our main theme, a modern central bank might well question how much wisdom is embodied in foreign exchange (p.94) markets that can't even get uncovered interest parity right as an ex ante relationship—that is, as a way to forecast exchange rate movements. Nor need the central banks of the world feel tightly constrained by uncovered interest parity in an ex post sense. Puzzling as it may be, exchange rates and interest rates seem to lead separate lives.
I can review, encapsulate, and perhaps integrate the main messages of this chapter by pointing out the shortcomings of a straw man. Imagine a central bank so enraptured by modern thinking that it dutifully follows the signals emitted by the financial markets. This hypothetical (and, you might say, wimpy!) central bank would read what the markets expect it to do from the term structure of interest rates, from prices observed in the federal funds futures market and, perhaps, from the foreign exchange markets. Then it would deliver precisely that policy. Monetary policy decisions would effectively be privatized.
What's wrong with such a system? Many things. To start in a strictly rational expectations framework, following the markets in this way can lead to a kind of “dog chasing its tail” phenomenon that may not have a well-defined equilibrium. At the very least, it is likely to produce excessively volatile monetary policy and therefore excessively volatile markets. This is perhaps the most fundamental criticism of the strategy of following the markets.
Now allow a few not-so-rational, but probably quite realistic, elements to creep into the story. A central bank that tries too hard to please currency and bond traders may wind up adopting the market's ludicrously short effective time horizons as its own—thereby succumbing to the very danger that central bank independence was supposed to guard against.
(p.95) And then there are those allegedly invaluable signals from the all-knowing financial markets. According to the predominant economic theory, the term structure embodies the best possible forecasts of future short rates and thus the best possible forecasts of what the market thinks the central bank will (or is it should?) do. In practice, however, forecasts of future short rates derived from the term structure prove to be wide of the mark—perhaps because of myopia, or perhaps for other reasons. At the very least, the collective wisdom that is supposedly embodied in the term structure appears to be greatly overrated.
A market-friendly central bank is also informed, and supposedly constrained, by uncovered interest parity, which links short-term interest rates tightly to near-term exchange rate expectations. Look up the expected dollar/ euro exchange rate and the European interest rate, and the market will tell you what the corresponding U.S. interest rate should be. But once again, this source of market wisdom fails the empirical test. Its implied exchange rate forecasts err badly. Odd as it may seem, interest rate differentials and exchange rates frequently go their own ways.
The upshot of all this is that it may not be wise for a central bank to take its marching orders from the markets. But that does not mean that modern central bankers should emulate King Canute and pretend they can command the markets. Plainly, they cannot. Rather, an astute central banker nowadays should view the markets as a powerful herd that is sometimes right, sometimes wrong, always a force to be reckoned with, but sometimes manipulable. Most fundamentally, the markets need to be led, not followed.
For a central bank to be the leader, it must set out on a sensible and comprehensible course—or else the putative followers may refuse to fall in line. Furthermore, being transparent about its goals and its methods should help the central bank assume this leadership role by teaching the markets where and how it wants to lead them. (p.96) We have thus come full circle. The greater transparency explained and extolled in chapter 1 should, it appears, help put the monetary authorities in the position of leader, rather than follower. It's a nice symbiosis—or, as Shakespeare once put it, “a consummation devoutly to be wished?”
Appendix to Chapter 3: The Expectations Theory of the Term Structure
Start with the two-period example mentioned in the text. Arbitrage implies that, ignoring possible risk or liquidity premiums, the two-period interest factor must be the product of today's one-period interest factor and the one-period interest factor expected to prevail one period from now:
Here ri is the i-period interest rate (expressed at an annual rate), t measures time, and the superscript e indicates an expectation.
Proceeding similarly, the three-period interest factor should be the product of today's one-period interest factor and the next two expected one-period factors:
and so on—except for possible term premiums—for longer maturities. By (3.6), this last expression can be written more compactly as
which relates the current two-period and three-period interest rates.
Because both r2,t and r3,t are observable, equations like (3.7) can be used to deduce the implied forward rates mentioned in the text, although the actual calculations are bedeviled by the question of (p.97) how to handle term premiums. For example, ignoring any term premiums:
In words, the one-period interest factor expected to prevail two periods from now is the ratio of the three-period interest factor divided by the two-period factor.
The corresponding equation for nine- and ten-year bonds is
and, as reported, estimating this equation leads to a resounding rejection of the null hypothesis b = 1.
(5) . For example, a few observers have gone so far as to claim that central banks should simply let markets determine interest rates. See, for example, Ely (1998). Fortunately, this is not the dominant view.
(7) . I have tried several times to track this quotation down. Several of Black's friends remember hearing him say it, but none have been able to point me to a published source.
(13) . This statement assumes risk neutrality.
(14) . One possibility (which I owe to Christopher Sims): If the short-term interest rate literally follows a first-order autoregressive process (so that only its own lagged value matters), an interest-rate shock today will move the expectations of all future short rates, making the short rate and the implied forward rates perfectly correlated. But the correlation drops away from 1.0 as more lags and/or more variables are added.
(15) . The thorough Fed staff calculated this correlation for several earlier years as well. Sometimes it was higher than 0.54, sometimes lower.
(16) . The word “roughly” refers to the fact that the approximation log(1+x) ≈ xis used. See the appendix to this chapter.
(17) . This equality ignores any possible risk or liquidity premiums, which are mentioned below.
(18) . The yield curve is a graph relating the rate of interest to the maturity of the instrument.
(19) . This account leaves out the aforementioned term premium, which is what makes such exercises complicated.
(22) . The line is not forced to go through the origin to allow for different term premiums on nine-year and ten-year bonds.
(23) . The estimate of the standard error uses the Newey-West correction.
(25) . A plot similar to figure 3.1 for three-month and six-month Treasury bill rates using daily data from January 1982 through November 2001 (not shown here) looks much better. It appears that the expectations theory works better at the very short end of the yield curve.
(27) . The long-run asymptotic effect is 97 basis points, insignificantly different from 100.
(28) . In this case, the long-run asymptotic effect is 106 basis points.
(29) . There is a bright side, however. If myopia leads the markets to overreact to the central bank's decisions, the power and speed of monetary policy will thereby be enhanced.
(30) . Purists will note that E(1/X) is not equal to 1/E(X), which is one reason for the word “approximately.” But it has never been clear—at least to me—what to make of this Jensen's inequality problem, for while the American investor presumably cares about E(1/X), the German investor presumably cares about E(X).
(31) . Once again, there are potential complications owing to such things as liquidity premia. These are relevant to levels but should mostly wash out when we deal with changes.
(32) . Over durations and currencies for which forward markets exist, there is a version of (3.4) called covered interest rate parity. Unlike its uncovered brother, covered interest rate parity must hold because people can actually carry out all the necessary transactions to ensure that the arbitrage relation holds.
(33) . His regressions pertain to the following exchange rates: pound/DM, dollar/pound, pound/French franc, pound/yen, dollar/DM, $/yen, and DM/yen. They all end in December 1998, and they begin at various dates from January 1976 to October 1978.
(36) . Meredith (2001) and Alquist and Chinn (2002) both emphasize the roles of productivity and profitability in attracting foreign capital. But there is still a leap to connect capital inflows to expansionary monetary policy.
(38) . Interest rate parity, whether covered or uncovered, reminds us that such an operation may have implications for foreign interest rates.
(39) . By contrast, an unsterilized intervention (e.g., buying a foreign bond and paying for it with newly created high-powered money) should move both the exchange rate and the domestic interest rate.
(40) . This leaves out the logical possibility that today's exchange rate and tomorrow's expected exchange move up or down in proportion, leaving xe unchanged. But in that case, one wonders what will ultimately happen to the country's current account balance.
(41) . There are other mechanisms via which economists have sometimes argued that sterilized interventions might work—for example, if forex operations signal future changes in (domestic) monetary policy. This mechanism muddies the waters, in my view, because it argues that sterilized interventions create expectations of future unsterilized interventions.