Typically, though, when low real interest rates are discussed in policy circles, the discussion does not revolve so much around

*actual*real rates of interest, but some other real interest rate concept. And there are several such concepts, which is bound to make things confusing, if not totally impenetrable. Let's try to sort this out.

(1) The

**natural real rate of interest**: For the average macroeconomist, this measure is well-defined, though not necessarily useful. The natural real rate of interest, or

*Wicksellian natural rate*is the real interest rate in a New Keynesian (NK) macroeconomic model, if we remove all wage and price stickiness. For simplicity, early NK models were built so as to leave out all sources of inefficiency, except for wage stickiness (sometimes) and price stickiness (usually). These models may have efficiency loss due to monopolistic competition, but that's a by-product of the approach to price stickiness. So, essentially, the natural real rate of interest is the real rate of interest in the underlying real business cycle model with flexible wages and prices. Why am I saying this concept is "not necessarily useful?" First, while there is some complacency among NK practitioners that NK is all we need to think about in understanding monetary policy, that's a dangerous idea. The basic model has many faults, not least of which is that it neglects the essential details of monetary policy - assets actually play no role in the model, in that there is no central bank balance sheet, no open market operations, no banks, no role for credit, for money, etc. Second, the baseline NK model cannot explain why the natural real rate of interest might be low. For example, low-real-interest-rate NK macroeconomics, such as Eggertsson and Woodford's work or Werning's, typically assumes the real interest rate is low because the subjective discount factor is high. That is, the low natural rate results from a contagious attack of patience. As is well-known, preference shock "explanations" for economic phenomena aren't helpful. If you like explaining the financial crisis as a contagious attack of laziness accompanied by an increased dislike for some assets and an infatuation with some other assets, most people aren't going to listen to you - and those that do listen shouldn't. I think some NK practitioners think of the high discount factor as a stand-in for something else. If so, it would be more useful to develop explicitly what that something else is.

(2) The

**equilibrium real interest rate**: I'll let Ben Bernanke explain this one:

...it helps to introduce the concept of the equilibrium real interest rate (sometimes called the Wicksellian interest rate, after the late-nineteenth- and early twentieth-century Swedish economist Knut Wicksell). The equilibrium interest rate is the real interest rate consistent with full employment of labor and capital resources, perhaps after some period of adjustment. Many factors affect the equilibrium rate, which can and does change over time. In a rapidly growing, dynamic economy, we would expect the equilibrium interest rate to be high, all else equal, reflecting the high prospective return on capital investments. In a slowly growing or recessionary economy, the equilibrium real rate is likely to be low, since investment opportunities are limited and relatively unprofitable. Government spending and taxation policies also affect the equilibrium real rate: Large deficits will tend to increase the equilibrium real rate (again, all else equal), because government borrowing diverts savings away from private investment.This is where the confusion starts. Bernanke tells us this is a synonym for the "Wicksellian interest rate," suggesting that the "equilibrium rate" is the same as the "natural rate." And he says that the equilibrium real interest rate is the "rate consistent with full employment of labor and capital resources," which would tend to steer the reader in the direction of thinking this is an NK natural rate of interest. But, the remainder of the paragraph appears to describe what happens in an IS-LM model, so Bernanke is mixing theories - never a recipe for clarity. Further, "equilibrium real interest rate" is bad language for describing the natural rate of interest in the NK model, as the sticky-prices-and-wages real interest rate is in fact an equilibrium real interest rate - but it's a non-standard equilibrium concept.

(3) The

**neutral real interest rate**: Janet Yellen covered this one in a recent speech:

Gauging the current stance of monetary policy requires arriving at a judgment of what would constitute a neutral policy stance at a given time. A useful concept in this regard is the neutral "real" federal funds rate, defined as the level of the federal funds rate that, when adjusted for inflation, is neither expansionary nor contractionary when the economy is operating near its potential. In effect, a "neutral" policy stance is one where monetary policy neither has its foot on the brake nor is pressing down on the accelerator. Although the concept of the neutral real federal funds rate is exceptionally useful in assessing policy, it is difficult in practical terms to know with precision where that rate stands. As a result, and as I described in a recent speech, my colleagues and I consider a wide range of information when assessing that rate. As I will discuss, our assessments of the neutral rate have significantly shifted down over the past few years.To clarify, here's what I think she means. It's common to think of monetary policy in terms of a Taylor rule, which we can write as:

*R = r* + a(i-i*) + b(y-y*) + i*,*

where

*R*is the fed funds rate,

*r**is a constant,

*i*is the actual inflation rate,

*y*is the actual level of output,

*i**is the inflation target, and

*y**is full-employment output. It's typical for people to assume that

*a > 1*and

*b > 0*. Then, if there is full employment and the central bank is hitting its inflation target, we have

*R = r* + i**. So, in the Taylor rule,

*r**is the neutral real interest rate, and

*r* + i**is the neutral nominal fed funds rate before we have "adjusted for inflation," as Janet Yellen says.

So, given that

*r**is low, what implications does this have for monetary policy? Of course, the answer to that question should depend on why it is low. Economists have discussed several reasons for low real interest rates:

1.

*Low productivity growth*: In standard models, the real interest rate falls when consumption growth falls. Lower growth in total factor productivity growth implies lower growth in consumption in the long run, which implies a lower real interest rate.

2.

*Demographics*: Demographic structure matters for savings behavior, which in turn matters for the real interest rate. In particular population growth and longevity are important. For example, lower population growth tends to increase capital per worker and lower the real interest rate, and people save more if they expect to live longer, which also will tend to increase capital per worker and reduce the real interest rate. A paper by Carvahlo et al. is an attempt to disentangle some of those effects.

3.

*Higher demand and lower supply of safe, liquid assets*: The low real interest rates we observe are interest rates on government debt, and such assets have functions that go well beyond providing a safe vehicle for savings. Government debt is widely traded in financial markets, and is the principle form of collateral in the market for repurchase agreements, which is a key part of the "financial plumbing" that helps financial markets run efficiently. Much like money, government debt bears a liquidity premium - market participants are willing to hold government debt at lower rates of return than if they were holding it purely for its associated payoffs. Then, the higher the demand for government debt relative to its supply, the higher the liquidity premium, and the lower the real interest rate on government debt. The supply of safe collateral fell as a result of the financial crisis - some types of private collateral and sovereign debt were no longer considered safe. As well, the crisis engendered an increase in demand for safe collateral due to an increase in perceived crisis risk, and because of new financial regulations, associated with Dodd-Frank and Basel III, for example.

I tend to think that (3) is most important, but that's based on working through some models, like this one and this one, and my own informal views on what is going on in the data. On that note, I should add a fourth factor:

4.

*Monetary policy*: Indeed, the real rate of interest on government debt may in part be low because of monetary policy. First, conventional monetary policy can make the real interest rate permanently low. For example, in this paper, if safe collateral is scarce, a reduction in the nominal interest rate also reduces the real interest rate - permanently. That's because the open market operation that reduces the nominal interest rate is a purchase of good collateral (same effect under a floor system with reserves outstanding). Second, an expansion in the central bank's balance sheet can reduce the real interest rate, as I show in this paper. Basically, swapping reserves for government debt reduces the effective stock of safe collateral, as reserves are an inferior asset to government debt (why else would the interest rate on reserves exceed the T-bill rate?). Thus a central bank balance sheet expansion exacerbates the problem of collateral scarcity - quantitative easing may be a bad idea.

What we need to evaluate what is going on is a model that can incorporate these factors, and can be used both to evaluate quantitatively how (1)-(4) matter, and the implications for optimal monetary policy. So what are economists in central banks up to in this respect? At the most recent Brookings paper conference, there are a couple of papers that deal with the problem, one by Kiley and Roberts, at the Federal Reserve Board, and the other by Del Negro et al. at the New York Fed.

Let's look first at the Kiley and Roberts (KR) paper. The key monetary policy problem KW perceive with low

*r**- and this, not surprisingly, is consistent with mainstream policy views - is that this will cause the effective lower bound (ELB) on the nominal interest rate to bind more frequently. As they say,

ELB episodes may be more frequent and costly in the future, as nominal interest rates may remain substantially below the norms of the last fifty years.Why would this happen? Going back to our Taylor rule, a lower

*r**implies that, when the central bank is hitting its targets, then the nominal interest rate has to be lower. So, if the economy is being hit by shocks which cause the central bank to move the nominal interest rate up and down, and if the average nominal interest rate is lower, then the central bank will find itself more frequently constrained by the ELB. Then, periods at the ELB will be periods when the central bank departs from its goals, and there is nothing (other than unconventional policy) that the central bank can do about it. Faced with this perceived problem, some policymakers contemplate increases in the central bank's inflation target - inflation would on average be higher, which may imply a welfare loss but, as the argument goes, there are benefits from being constrained by the ELB less frequently.

This is basically Fisherian logic. Over the long run, a higher nominal interest rate will be associated with higher inflation. Perhaps curiously, KR studiously avoid mention of Irving Fisher, though Jonas Fisher gets several mentions. The one callout to I. Fisher is this:

According to the Fisher equation, higher average inflation would imply a higher average value of nominal interest rates, and so the ELB would be encountered less frequently.By the "Fisher equation" they mean the long-run Fisher effect, I think. Supposing that the long run real interest rate is a constant,

*r**, the long run relationship between the nominal interest rate and inflation is

*R = r* + i*. But, of course, in the quote they have the causality going the wrong way. In their models, it's the central bank that controls inflation by controlling the nominal interest rate, so it's the nominal interest rate that's causing the inflation rate to be what it is, not the other way around. That's basic neo-Fisherism.

So what do KR do? They simulate a couple of models to determine what the potential losses are from retaining a 2% inflation target in a low-

*r**environment. The first model (and this won't surprise you if you know anything about quantitative policy analysis at the Board) is the FRB/US model. For the uninitiated, the FRB/US model is basically a relic of the 1960s - the type of large-scale econometric model that Lucas convinced us in 1976 should not be used for policy analysis. And, 41 years later, here's FRB/US - being used for policy analysis. As KR say:

As emphasized in Brayton, Laubach, and Reifschneider (2014) and Laforte and Roberts (2014), the FRB/US model is extensively used in monetary-policy analysis at the Federal Reserve and captures features of the economy that reflect consensus views across macroeconomists, but is not strictly “micro-founded” in the manner used in many academic analyses.So, apparently, economists at the Board choose to ignore academic standards (no reputable academic journal would - or should - publish an article about the policy predictions of FRB/US), and go about "extensively" using FRB/US to think about policy.

And you can see where it goes wrong. Here's what FRB/US tells us about what happens in a low-

*r* world:*

... the ELB binds often and inflation falls systematically short of the 2 percent objective; in addition, output is, on average, below its potential level.Basically, FRB/US is an extended IS/LM/Phillips curve model. In it, long-run inflation is exogenous (2% basically), and inflation will deviate in the short run from its long run value due to Phillips curve effects. So, not surprisingly, in this type of framework, when the ELB binds, output is below "potential" and this causes inflation to fall short of its target. But, by neo-Fisherian logic, if on average the nominal interest rate is too high, because it keeps bumping up against the ELB, inflation should, on average, be

*exceeding*its target. For example, in recent history in the US, some people think that the inflation rate was persistently below target because the nominal interest rate was effectively at the ELB, and we could have done better (have had higher inflation) if the nominal interest rate were permitted to go below zero. Not so. The fact that inflation was persistently below target indicates that the ELB was not a binding constraint. The nominal interest rate was

*too low.*

What else are KR up to? They also use an off-the-shelf DSGE model, developed by Linde, Smets, and Wouters, to address the same policy question. Is this model an better-equipped to answer the question than the FRB/US model? No. Such models, though smaller and more manageable than old-fashioned large-scale macroeconometric models like FRB/US, certainly can't lay any claim to structural purity - there are plenty of ad-hoc features (adjustment costs, habit persistence) thrown in to fit the data, and the model certainly was not set up to capture the phenomenon at hand. Though this DSGE model can certainly capture a decline in productivity (feature (1)) there's nothing much in there with regard to (2)-(4), and the monetary policy detail is shockingly weak. So, I don't think we should take the results seriously.

The second paper, by Del Negro et al. (DGGT) is more of a straightforward time series exercise - but there's some DSGE in this one too. This paper confronts the data in a useful way, focusing on the "convenience yield" on government debt (which I called a "liquidity premium" above), and showing, for example, that corporate debt does not share this convenience yield, which is important. The analysis documents a fall in the real rate of interest beginning in the 1990s, and the estimate of the current real interest rate is 1.0-1.5%. The econometrics in DGGT is sophisticated, but ultimately I'm not sure if I trust it more than what I see in the chart at the beginning of this post. Currently, the 3-month T-bill rate rate is about 0.80%, and the last reading for the twelve-month pce inflation rate is 1.9%. So, by my crude measure, the current real interest rate is -1.1%. If someone is giving me an estimate of 1.0-1.5%, I'm going to think that's way too high. If, given current policy settings, inflation is roughly at target, as is labor market tightness, then the nominal interest rate must be about right, if we follow our Taylor-rule logic.