Does the Fed Control Interest Rates?

Casey Mulligan goes to the New York Times to say that monetary policy doesn't work. This annoys Brad DeLong:

THE NEW YORK TIMES PUBLISHES CASEY MULLIGAN AS A JOKE, DOESN'T IT? 

... The third joke is the entire third paragraph: since the long government bond rate is made up of the sum of (a) an average of present and future short-term rates and (b) term and risk premia, if Federal Reserve policy affects short rates then--unless you want to throw every single vestige of efficient markets overboard and argue that there are huge profit opportunities left on the table by financiers in the bond market--Federal Reserve policy affects long rates as well. 

Casey B. Mulligan: Who Cares About Fed Funds?: New research confirms that the Federal Reserve’s monetary policy has little effect on a number of financial markets, let alone the wider economy…. Eugene Fama of the University of Chicago recently studied the relationship between the markets for overnight loans and the markets for long-term bonds…. Professor Fama found the yields on long-term government bonds to be largely immune from Fed policy changes…

Krugman piles on [1]; the only problem with DeLong's post, he says, is that

it fails to convey the sheer numbskull quality of Mulligan’s argument. Mulligan tries to refute people like, well, me, who say that the zero lower bound makes the case for fiscal policy. ... Mulligan’s answer is that this is foolish, because monetary policy is never effective. Huh? 

... we have overwhelming empirical evidence that monetary policy does in fact “work”; but Mulligan apparently doesn’t know anything about that.

Overwhelming evidence? Citation needed, as the Wikipedians say.

Anyway, I don't want to defend Mulligan -- I haven't even read the column in question -- but on this point, he's got a point. Not only that: He's got the more authentic Keynesian position.

Textbook macro models, including the IS-LM that Krugman is so fond of, feature a single interest rate, set by the Federal Reserve. The actual existence of many different interest rates in real economies is hand-waved away with "risk premia" -- market rates are just equal to "the" interest rate plus a prmium for the expected probability of default of that particular borrower. Since the risk premia depnd on real factors, they should be reasonably stable, or at least independent of monetary policy. So when the Fed Funds rate goes up or down, the whole rate structure should go up and down with it. In which case, speaking of "the" interest rate as set by the central bank is a reasonable short hand.

How's that hold up in practice? Let's see:

The figure above shows the Federal Funds rate and various market rates over the past 25 years. Notice how every time the Fed changes its policy rate (the heavy black line) the market rates move right along with it?

Yeah, not so much.

In the two years after June 2007, the Fed lowered its rate by a full five points. In this same period, the rate on Aaa bonds fell by less 0.2 points, and rates for Baa and state and local bonds actually rose. In a naive look at the evidence, the "overwhelming" evidence for the effectiveness of monetary policy is not immediately obvious.

Ah but it's not current short rates that long rates are supposed to follow, but expected short rates. This is what our orthodox New Keynesians would say. My first response is, So what? Bringing expectations in might solve the theoretical problem but it doesn't help with the practical one. "Monetary policy doesn't work because it doesn't change expectations" is just a particular case of "monetary policy doesn't work."

But it's not at all obvious that long rates follow expected short rates either. Here's another figure. This one shows the spreads between the 10-Year Treasury and the Baa corporate bond rates, respectively, and the (geometric) average Fed Funds rate over the following 10 years.

If DeLong were right that "the long government bond rate is made up of the sum of (a) an average of present and future short-term rates and (b) term and risk premia" then the blue bars should be roughly constant at zero, or slightly above it. [2] Not what we see at all. It certainly looks as though the markets have been systematically overestimating the future level of the Federal Funds rate for decades now. But hey, who are you going to believe, the efficient markets theory or your lying eyes? Efficient markets plus rational expectations say that long rates must be governed by the future course of short rates, just as stock prices must be governed by future flows of dividends. Both claims must be true in theory, which means they are true, no matter how stubbornly they insist on looking false.

Of course if you want to believe that the inherent risk premium on long bonds is four points higher today than it was in the 1950s, 60s and 70s (despite the fact that the default rate on Treasuries, now as then, is zero) and that the risk premium just happens to rise whenever the short rate falls, well, there's nothing I can do to stop you.

But what's the alternative? Am I really saying that players in the bond market are leaving huge profit opportunities on the table? Well, sometimes, maybe. But there's a better story, the one I was telling the other day.

DeLong says that if rates are set by rational, profit-maximizing agents, then -- setting aside default risk -- long rates should be equal to the average of short rates over their term. This is a standard view, everyone learns it. but it's not strictly correct. What profit-maximizing bond traders do, is set long rates equal to the expected future value of long rates.

I went through this in that other post, but let's do it again. Take a long bond -- we'll call it a perpetuity to keep the math simple, but the basic argument applies to any reasonably long bond. Say it has a coupon (annual payment) of $40 per year. If that bond is currently trading at $1000, that implies an interest rate of 4 percent. Meanwhile, suppose the current short rate is 2 percent, and you expect that short rate to be maintained indefinitely. Then the long bond is a good deal -- you'll want to buy it. And as you and people like you buy long bonds, their price will rise. It will keep rising until it reaches $2000, at which point the long interest rate is 2 percent, meaning that the expected return on holding the long bond and rolling over short bonds is identical, so there's no incentive to trade one for the other. This is the arbitrage that is supposed to keep long rates equal to the expected future value of short rates. If bond traders don't behave this way, they are missing out on profitable trades, right?

Not necessarily. Suppose the situation is as described above -- 4 percent long rate, 2 percent short rate which you expect to continue indefinitely. So buying a long bond is a no-brainer, right? But suppose you also believe that the normal or usual long rate is 5 percent, and that it is likely to return to that level soon. Maybe you think other market participants have different expectations of short rates, maybe you think other market participants are irrational, maybe you think... something else, which we'll come back to in a second. For whatever reason, you think that short rates will be 2 percent forever, but that long rates, currently 4 percent, might well rise back to 5 percent. If that happens, the long bond currently trading for $1000 will fall in price to $800. (Remember, the coupon is fixed at $40, and 5% = 40/800.) You definitely don't want to be holding a long bond when that happens. That would be a capital loss of 20 percent. Of course every year that you hold short bonds rather than buying the long bond at its current price of $1000, you're missing out on $20 of interest; but if you think there's even a moderate chance of the long bond falling in value by $200, giving up $20 of interest to avoid that risk might not look like a bad deal.

Of course, even if you think the long bond is likely to fall in value to $800, that doesn't mean you won't buy it for anything above that. if the current price is only a bit above $800 (the current interest rate is only a bit below the "normal" level of 5 percent) you might think the extra interest you get from buying a long bond is enough to compensate you for the modest risk of a capital loss. So in this situation, the equilibrium price of the long bond won't be at the normal level, but slightly below it. And if the situation continues long enough, people will presumably adjust their views of the "normal" level of the long bond to this equilibrium, allowing the new equilibrium to fall further. In this way, if short rates are kept far enough from long rates for long enough, long rates will eventually follow. We are seeing a bit of this process now. But adjusting expectations in this way is too slow to be practical for countercyclical policy. Starting in 1998, the Fed reduced rates by 4.5 points, and maintained them at this low level for a full six years. Yet this was only enough to reduce Aaa bond rates (which shouldn't include any substantial default risk premium) by slightly over one point.

In my previous post, I pointed out that for policy to affect long rates, it must include (or be believed to include) a substantial permanent component, so stabilizing the economy this way will involve a secular drift in interest rates -- upward in an economy facing inflation, downward in one facing unemployment. (As Steve Randy Waldman recently noted, Michal Kalecki pointed this out long ago.) That's important, but I want to make another point here.

If the primary influence on current long rates is the expected future value of long rates, then there is no sense in which long rates are set by fundamentals.  There are a potentially infinite number of self-fulfilling expected levels for long rates. And again, no one needs to behave irrationally for these conventions to sustain themselves. The more firmly anchored is the expected level of long rates, the more rational it is for individual market participants to act so as to maintain that level. That's the "other thing" I suggested above. If people believe that long rates can't fall below a certain level, then they have an incentive to trade bonds in a way that will in fact prevent rates from falling much below that level. Which means they are right to believe it. Just like driving on the right or left side of the street, if everyone else is doing it it is rational for you to do it as well, which ensures that everyone will keep doing it, even if it's not the best response to the "fundamentals" in a particular context.

Needless to say, the idea that that long-term rate of interest is basically a convention straight from Keynes. As he puts it in Chapter 15 of The General Theory,

The rate of interest is a highly conventional ... phenomenon. For its actual value is largely governed by the prevailing view as to what its value is expected to be. Any level of interest which is accepted with sufficient conviction as likely to be durable will be durable; subject, of course, in a changing society to fluctuations for all kinds of reasons round the expected normal. 

You don't have to take Keynes as gospel, of course. But if you've gotten as much mileage as Krugman has out of the particular extract of Keynes' ideas embodied in the IS-LM mode, wouldn't it make sense to at least wonder why the man thought this about interest rates, and if there might not be something to it.

Here's one more piece of data. This table shows the average spread between various market rates and the Fed Funds rate.

Spreads over Fed Funds by decade
	10-Year Treasuries	Aaa Corporate Bonds	Baa Corporate Bonds	State & Local Bonds
1940s		2.2	3.3
1950s	1.0	1.3	2.0	0.7
1960s	0.5	0.8	1.5	-0.4
1970s	0.4	1.1	2.2	-1.1
1980s	0.6	1.4	2.9	-0.9
1990s	1.5	2.6	3.3	0.9
2000s	1.5	3.0	4.1	1.8

Treasuries carry no default risk; a given bond rating should imply a fixed level of default risk, with the default risk on Aaa bonds being practically negligible. [3] Yet the 10-year treasury spread has increased by a full point and the corporate bond rates by about two points, compared with the postwar era. (Municipal rates have risen by even more, but there may be an element of genuine increased risk there.) Brad DeLong might argue that society's risk-bearing capacity has decline so catastrophically since the 1960s that even the tiny quantum of risk in Aaa bonds requires two full additional points of interest to compensate its quaking, terrified bearers. And that this has somehow happened without requiring any more compensation for the extra risk in Baa bonds relative to Aaa. I don't think even DeLong would argue this, but when the honor of efficient markets is at stake, people have been known to do strange things.

Wouldn't it be simpler to allow that maybe long rates are not, after all, set as "the sum of (a) an average of present and future short-term rates and (b) [relatively stable] term and risk premia," but that they follow their own independent course, set by conventional beliefs that the central bank can only shift slowly, unreliably and against considerable resistance? That's what Keynes thought. It's what Alan Greenspan thinks. [4] And also it's what seems to be true, so there's that.



[1] Prof. T. asks what I'm working on. A blogpost, I say. "Let me guess -- it says that Paul Krugman is great but he's wrong about this one thing." Um, as a matter of fact...

[2] There's no risk premium on Treasuries, and it is not theoretically obvious why term premia should be positive on average, though in practice they generally are.

[3] Despite all the -- highly deserved! -- criticism the agencies got for their credulous ratings of mortgage-backed securities, they do seem to be good at assessing corporate default risk. The cumulative ten-year default rate for Baa bonds issued in the 1970s was 3.9 percent. Two decades later, the cumulative ten-year default rate for Baa bonds issued in the 1990s was ... 3.9 percent. (From here, Exhibit 42.)

[4] Greenspan thinks that the economically important long rates "had clearly delinked from the fed funds rate in the early part of this decade." I would only add that this was just the endpoint of a longer trend.