What's Wrong With the Taylor Rule?

John Taylor, a Stanford University professor, senior fellow at the Hoover Institution, and former Treasury Department official, came up with the rule that bears his name in 1993. Nearly all central banks nowadays conduct monetary policy by targeting an interest rate (often referred to as the policy rate) daily. The Taylor Rule offers a guide to setting this target in a way that simultaneously keeps inflation in check and dampens the business cycle. Although most developed countries’ central banks, including the Fed, regularly look at what the rule prescribes, none of them are tightly bound by it. Unfortunately, interest-rate targeting poses major empirical difficulties, and the Taylor Rule ultimately fails to overcome all of them.1

To begin with, there is the crucial distinction between nominal and real interest rates. Nominal interest rates are the rates at which loans are made, and they are the rates we observe. Real rates are the rates we compute by adjusting either ex-post for actual inflation or ex-ante for anticipated inflation. Thus, it is now well understood that the short-run and long-run effects of a loose (or tight) monetary policy have opposite impacts on nominal rates. The long-run impact of an expansionary policy is to raise nominal rates, in what is known as the Fisher effect. Once higher inflation is fully anticipated, nominal interest rates will rise to offset the negative effect of inflation on real rates. But an expansionary policy in the short run usually lowers interest rates, in what is known as the liquidity effect.

Although economists disagree about the magnitude, extent, and duration of the liquidity effect, the bottom line is that the initial impact of monetary policy on interest rates is self-reversing. Therefore, depending on inflationary expectations, low nominal interest rates can be a sign of either tight or easy money. This dilemma bedeviled monetary policy until the work of Milton Friedman and the Great Inflation of the 1970s brought widespread acceptance of the Fisher effect. Indeed, it was not until the Taylor Rule that central banks had an explicit model for adjusting their interest-rate target for this effect. That this rule took so long to develop should be a source of both embarrassment and epistemic humility for economic policy makers.2

Actually, one should refer to Taylor Rules, plural, because there are different versions. But they all adhere to the same generalized form: the central bank’s target nominal interest rate should equal the underlying equilibrium real rate plus the rate of inflation, with one weighted adjustment for the gap between actual and desired inflation, and another weighted adjustment for the gap between the economy’s potential and actual real output:

target nominal interest rate = equilibrium real interest rate + inflation rate + α(inflation gap) + β(real output gap)

By including the actual inflation rate, Taylor Rules do compensate for the Fisher effect. The two terms for the inflation and output gaps then employ the liquidity effect. If either inflation or output is too low, the central bank should lower its target interest rate to stimulate the economy. And if either is too high, it should raise its target. There are different ways to calculate these gaps, determine the inflation rate, and set the weights (α and β), but Taylor’s estimates of the weights were 0.5 for each. By adjusting for both inflation and output, Taylor Rules become a kind of indirect nominal Gross Domestic Product targeting, given that nominal GDP constitutes total real output times the price level.3

When formulating this rule, Taylor used the Federal funds rate (the rate at which banks lend each other reserves overnight) as the target. He estimated the underlying real Federal funds rate at two percent in long-run equilibrium (given a particular inflation target in the neighborhood of two percent). Although Taylor derived all of his estimates from historical data, he has been quite explicit that the rule is not a positive description of what central banks actually do but a normative prescription for what they should do. This hasn’t stopped macroeconomists from developing fancy New Keynesian models that replace the traditional aggregate demand curve with a monetary response function in which the central bank, in fact, automatically follows a Taylor Rule, with complete control over real rates. In other words, many New Keynesians, at least in their models, regard the Taylor Rule as a description of central bank behavior. During the Great Inflation of the 1970s, the actual Federal funds rate was very far from what the Taylor Rule would have prescribed, but it was much closer during much of what has been termed the Great Moderation, while Alan Greenspan was Fed chair. 4

The differences among Taylor Rules arise from various ways of estimating the coefficients and variables. For the inflation rate, should the central bank use current (which amounts to past) inflation, as Taylor did, or expected inflation? And if it uses expected inflation, which of the alternative methods of measuring inflationary expectations should it choose? The same questions plague estimates of the gap between actual inflation and whatever is chosen as the desired inflation rate. Finally, in order to determine the real output gap, the central bank needs to know precisely what potential output would be at the natural rate of unemployment. But neither of these two variables is directly observable. The aftermath of the financial crisis dramatically illustrates what a tricky and controversial problem the determination of potential output and the natural rate of employment can be.

But the deeper, more critical flaw in Taylor Rules is that the long-run, equilibrium real rate of interest—or what is alternatively called the natural or neutral rate—is also unobservable. Yet these rules make the astonishing assumption that their estimates are not only correct but also relatively fixed and unchanging over extended periods. In short, Taylor Rules virtually preclude any factor, other than central banks, from affecting the equilibrium real rate of interest. A standard rationale for this assumption is what is known as the Ramsay-Cass-Koopmans model. This model estimates the natural interest rate for a closed economy with a fixed number of infinitely-lived households, all identical. Each household has the same rate of time preference, the same declining marginal utility of consumption, and the same rate of population growth. This almost rules out any fluctuations in the natural rate that might arise from alterations in how individuals discount the future, from how consumption preferences may differ among individuals or alter over time for one individual, or from differences in the distribution of wealth. 5

As David Laidler emphasizes, this way of estimating the natural rate of interest, therefore, does not extend

… to more complicated structures where agents are diverse in their tastes and opportunities… What if different agents have different outlooks concerning the amount of consumption goods that will be available to them in the future? What if individuals’ rates of pure time preference are not constant, but vary with their wealth—poorer people might, for example, be less patient than richer? What if individuals’ rates of time preference vary with age, so that demographics affect its average value for the economy as a whole? But if agents are heterogeneous along any or all of the above lines, any economy-wide value for the rate of time preference will vary, among other things, with the prevailing distribution of income and wealth, and will therefore vary with the structure of relative prices.6

At one time, complications of these kinds intrigued and troubled economists as diverse as Knut Wicksell, Irving Fisher, John Maynard Keynes, and Friedrich Hayek. More recently, David Romer’s graduate macro text concedes that “the equilibrium or natural real interest rate presumably varies over time,” and, therefore, a constant rate should be replaced with one that is “time-varying.” But the only major modifications introduced by some Taylor Rule variants are a weighted variable for the exchange rate (slightly relaxing the assumption of a closed economy) or a lag in the change of the target interest rate (which can create as many problems as it solves).7

One striking case where these unrealistic assumptions are likely to have gone awry is the period prior to the financial crisis. According to the Taylor Rules, Greenspan’s excessively expansionary policy was holding the Federal funds rate too low by as much as two percentage points or more (estimates vary). Yet inflation was low, and all the monetary growth measures were steadily falling. From 2001, the annual year-to-year growth rate of MZM (money of zero maturity) fell from over 20 percent to nearly zero percent by 2006. During that same period, M2 growth fell from over ten percent to around two percent, and M1 growth fell from over ten percent to negative rates. As for the measure that the Fed actually controls day-to-day, the monetary base (consisting of banks’ reserves plus currency in circulation), after 2001, its growth rate fell from ten percent to below five percent in 2006.8

So, if one rejects any of these monetary measures as a reliable gauge of the Fed’s policy, how does one avoid the following meaningless circularity: “Why were interest rates so low? Because of Greenspan’s expansionary monetary policy. How do we know that Greenspan’s policy was expansionary? Because interest rates were so low.” To anchor the claim that Fed policy caused undesirably low interest rates, one must turn to Taylor’s estimate that the equilibrium, real Federal funds rate of two percent remained constant throughout this period. Doing so arbitrarily excludes by assumption any alternative explanation for the period’s low interest rates, including the one that both Ben Bernanke and Greenspan offered. Somewhat misleadingly referred to as the “global saving glut” thesis, it was supported by the fact that the net inflow of savings from abroad dwarfed the Fed’s increase of the monetary base. In 2006 alone, that annual inflow was about $800 billion, far exceeding the mere $200 billion increase in the base for the entire half-decade beginning in 2001. Total net inflows for 2001 through 2006 came to $3.5 trillion. This inflow peaked at six percent of GDP. Whether or not one finds the global-saving-glut thesis convincing, the important point is that nearly all versions of the Taylor Rule, by basing their estimates of the natural rate on a closed economy, deny that international factors can have any significant impact on domestic interest rates.9

Taylor Rules do have one thing going for them. As mentioned above, they indirectly target nominal GDP. In that respect, they have an advantage over the explicit inflation targeting adopted by several central banks throughout the world, including New Zealand’s, Canada’s, and Britain’s. Inflation targeting can do a better job of dampening shocks to aggregate demand than of dampening shocks to aggregate supply. That is because a negative supply shock pushes output and prices in opposite directions, decreasing output growth while simultaneously increasing inflation. If the central bank tries to suppress the resulting inflation with a tighter policy, it will aggravate the hit to output. An ideal policy should allow the price level to rise in response to a supply-side shock, and inflation targeting does not do this. Note that with a Taylor Rule, a negative supply shock will result in a negative output gap and a positive inflation gap. The first calls for lowering the target interest rate and the second for raising it, with the two tending to offset each other.10

However, most advocates of targeting nominal GDP (or some related measure of national income), such as Scott Sumner and other Market Monetarists, call for looking at this measure directly, rather than trying to break it down into its price level and output components. This still requires an estimate of where nominal GDP ought to be heading, and the economy’s performance after the financial crisis provides an acute example of some potential problems. Not only has real GDP been growing at a slower rate than before the crisis—but with no increase in inflation—nominal GDP has also. And both of them experienced a large, one-time fall in their level that never reverted to the previous trend line, as in most recessions. Sumner’s suggested solution is to create a market for nominal GDP futures to provide the target. Despite these empirical obstacles, direct targeting of nominal GDP at least does not necessarily require any static assumptions about the unobservable natural interest rate.11

John Cochrane, of the University of Chicago and the Hoover Institution, has pointed out an even more important difference between Taylor Rules on one hand and inflation or direct nominal GDP targeting on the other. Both of the latter would establish general, limited goals for the Fed. This would leave the Fed free to use whatever operating means it thought appropriate to meet those goals, whether its focus would be on interest rates, on monetary measures, or on some complex mixture. Fed compliance with the goal could easily be monitored. But the Taylor Rule specifies the exact means by which the Fed should pursue its goal. As Cochrane puts it:

Inflation targeting is like ‘go to Minneapolis, not St. Louis, and don’t get distracted by shopping along the way. The rest is up to you, wake me up when we’re there.’ A [Taylor] rule is like ‘Stay on I-94. When the white line gets too close to the right wheels, turn a bit to the left; when the dashed line gets too close to the left wheels, turn a bit to the right. If you need to go to the bathroom, wake me up and tell me why we’re getting off the freeway.’12

In other words, a legislated Taylor Rule would involve Congress micro-managing how the Fed, in turn, micro-manages the economy. Moreover, it would, in practice, probably be less binding on the Fed than a goal such as inflation or nominal GDP targeting. Whenever the Taylor Rule variant that the Fed uses fails to produce a desired economic outcome, there will be overwhelming pressure to accede to Fed discretion. Particularly ironic is that enthusiasm for the Taylor Rule has emerged in a period of such low nominal rates that many believe that a “zero bound” has completely undermined the effectiveness of interest-rate targeting altogether.13

As long as we are stuck with the Fed, congressional imposition of inflation targeting, direct nominal GDP targeting, or, perhaps, price-level targeting would all be small steps in the right direction, along with repeal of the dual Fed mandate to keep inflation and unemployment low. Any one of these actions would help constrain the Fed while the debate continues over which goal is the best at mitigating recessions and depressions. I have long opposed expansive and ever-expanding Fed discretion. But locking the Fed into some kind of interest-rate rule based on questionable assumptions would be a step in the wrong direction.