Since the financial crisis began, I have been one of the most vehement supporters of modern macroeconomics. While I have my own quarrels with the current research, I have found much (not all) of the criticism wanting. Nevertheless, there is one notable and glaring failure in the macro literature that has come to the forefront during this recession. That failure is regarding the zero lower bound on nominal interest rates. Not only do I believe that a consensus is needed on this topic, but I also believe that the zero lower bound is of little practical importance.

**Background**

The tool of modern macroeconomics is the dynamic, stochastic, general equilibrium (DSGE) model. Monetary models often consist of the baseline New Keynesian model and extensions thereof. This model is characterized by two equations and an interest rate rule. The first equation is the dynamic IS equation, which is expressed in logarithms as follows:

y(t) = E(t)y(t+1) – (1/a)[R(t) - E(t)P(t+1)]

where y(t) is the output gap at time t, E is the mathematical expectation operator, R is the nominal interest rate, P is inflation, and a is a parameter.

The second equation is the New Keynesian Phillips curve:

P(t) = bE(t)P(t+1) + ky(t)

where b and k are parameters.

The system is then closed by a monetary policy rule. This is typically formulated as a Taylor-type rule in which the monetary authority adjusts the nominal interest rate in response to inflation and the output gap. Together with the assumption of sticky prices, the adjustment of the nominal interest rate leads to a corresponding adjustment in the real interest as well.

It is important to note that money is not part of this model. Rather movements in the interest rate pin down the rate of inflation (so long as the policy rule leads to an increase in the real rate of interest when inflation is higher than its target). The purported benefits of these types of models is that they can neglect any reference to money demand and the interest rate captures the complete transmission mechanism through which monetary policy and monetary shocks influence the system. As it turns out, however, this framework contributes to what I believe to be the failure of modern macro in light of this recession. [I also have quarrels with the empirical evidence that justifies this approach, but I will leave that for a separate post.]

**The Zero Lower Bound**

In the model presented above, monetary policy is conducted by a central bank that adjusts ‘the’ interest rate. The change in the interest rate in turn inversely impacts the output gap through the IS relation. Supposing that we begin from a zero inflation steady state, the increase in the interest rate causes output to fall below the natural rate. As a result, inflation declines in accordance with the New Keynesian Phillips curve.

What this process illustrates is that the interest rate is the sole mechanism through which monetary policy affects the economy. The importance of this point centers on the fact that the nominal interest rate is limited in that it cannot take on a value less than zero. Thus, if we believe this model accurately captures the world in which we live, there exists a precarious position for central banks when the output gap is negative and the nominal interest rate is zero.

The zero bound therefore places a limit on the effects of monetary policy conducted using an interest rate.

**Theoretical Foundations**

As with all modern theoretical macro models, the New Keynesian model is derived from microeconomic foundations. In other words, the IS equation is derived from utility maximization in which a representative household maximizes utility subject to a budget constraint. In the basic New Keynesian model illustrated above, there is a consumption good and one asset (bonds). The analysis can be extended to include money, but for typical money demand functions, money is essentially a mirror for changes in the interest rate. Nonetheless, the existence of only two assets — money and bonds — is at the heart of the problem.

If monetary policy is ineffective at the zero bound, this is referred to as a liquidity trap. Put differently, if the interest rate on bonds is zero, money and bonds become perfect substitutes. Whereas open market operations would typically be used to increase reserves and thereby lower the federal funds rate, in a liquidity trap agents simply hold the additional cash balances in place of the bonds. Increases in the money supply do not result in real changes, only alterations to the composition of portfolios.

So what is the problem with this analysis?

Well, the problem surrounds the fact that there are only two assets in the model. Monetary policy is impotent because money and bonds are perfect substitutes. Contrary to this model (and others), there are actually substantially more than two assets in the real world. Thus, a natural question to ask is whether these other assets matter for our analysis. In their 1968 paper, Karl Brunner and Allan Meltzer do precisely that. They extend the analysis beyond the two asset world. In such a case, the condition for a liquidity trap is that the marginal rates of substitution for money and all other assets must be equal to zero. As Karl Brunner would have said, we simply know this isn’t true.

This condition, I believe, represents substantial reason for pause in considering the possibility and policy implications of a liquidity trap. In fact, I would argue that it suggests that liquidity traps don’t exist. Put differently, as Scott Sumner has suggested:

Zero rates don’t really make monetary policy more difficult, they make interest rate-oriented monetary policy more difficult.

Indeed, in the absence of a liquidity trap, the zero lower bound is merely a signal that monetary policy needs to employ other methods.

**The Evidence . . . Or, Am I alone?**

A subsequent question is whether (a) evidence suggests that monetary policy is impotent, and (b) whether I am alone in suggesting that “unconventional” monetary policy — defined as non-interest rate policy — is useful at the zero bound.

Regarding point (a), I will be brief. In a fairly recent paper, Allan Meltzer examines the monetary transmission mechanism by comparing the behavior of the real interest rate and real money balances during periods of deflation. The impetus behind this reasoning is that during periods of deflation, the real interest rate and real balances will increase. If the monetary transmission mechanism is solely captured by the real interest rate as implied by the New Keynesian framework, then one would expect output to decline as the real interest rate rises. In contrast, the monetarist proposition has long been that the monetary transmission mechanism is reflected by the behavior of real money balances as individuals re-allocate their portfolios thereby inducing relative price adjustments on financial assets and subsequently on non-financial, or real, assets. Thus, the mechanism implies that as real balances rise, output should be expected to rise. He finds that in each case the behavior of real money balances is a much better predictor of movements in output than the real interest rate. This not only suggests that there is little reason to fear the zero lower bound, but there is also reason to doubt that the interest rate represents the correct mechanism for analysis of the monetary transmission process.

Regarding point (b), consider some recent papers that examine the zero lower bound. First, Marco Del Negro, Gauti Eggertson, Andrea Ferrero, and Nobuhiro Kiyotaki (HT: David Beckworth):

This paper extends the model in Kiyotaki and Moore (2008) to include nominal wage and price frictions and explicitly incorporates the zero bound on the short-term nominal interest rate. We subject this model to a shock which arguably captures the 2008 US financial crisis. Within this framework we ask: Once interest rate cuts are no longer feasible due to the zero bound, what are the effects of non-standard open market operations in which the government exchanges liquid government liabilities for illiquid private assets? We find that the effect of this non-standard monetary policy can be large at zero nominal interest rates. We show model simulations in which these policy interventions prevented a repeat of the Great Depression in 2008-2009.

Next, Michael Woodford, the founder of the moneyless approach exemplified by the New Keynesian model, and Vasco Curdia:

We extend a standard New Keynesian model both to incorporate heterogeneity in spending opportunities along with two sources of (potentially time-varying) credit spreads and to allow a role for the central bank’s balance sheet in determining equilibrium. We use the model to investigate the implications of imperfect financial intermediation for familiar monetary policy prescriptions and to consider additional dimensions of central bank policy—variations in the size and composition of the central bank’s balance sheet as well as payment of interest on reserves—alongside the traditional question of the proper operating target for an overnight policy rate. We also study the special problems that arise when the zero lower bound for the policy rate is reached. We show that it is possible to provide criteria for the choice of policy along each of these possible dimensions within a single unified framework, and to achieve policy prescriptions that apply equally well regardless of whether financial markets work efficiently or not and regardless of whether the zero bound on nominal interest rates is reached or not

And finally, Paul Krugman:

Even if the economy is in a liquidity trap in the sense that the nominal interest rate is stuck at zero, the monetary expansion would raise the expected future price level P*, and hence reduce the real interest rate. A permanent as opposed to temporary monetary expansion would, in other words, be effective – because it would cause expectations of inflation.

An astute reader will note that I have chose these authors because they are supporters of or seem content with the interest rate view of monetary policy. Nevertheless, in each case, they find that monetary policy can be effective at the zero lower bound.

Taken together with the evidence by Meltzer above, I think that we have sufficient reason to doubt the existence of liquidity trap.

**Brief Conclusion**

The zero lower bound represents a key failure of modern macro in that there is little consensus or agreement about the effects of monetary policy in such a circumstance. The issue is of central importance for determining the correct policy prescriptions — both monetary and fiscal. It is my hope that the recent surge in research on the zero lower bound will ultimately reach a consensus. What’s more, I hope that this consensus takes into account that we live in a world with more than two assets and, as a result, that the zero lower bound is nothing more than an intellectual curiosity.

**Further Reading**: For those interested in the topic, I think that these papers might be of use as well:

Sumner, Scott. 2002. “Some Observations of the Return of the Liquidity Trap.” Cato Journal.

Goodfriend, Marvin. 2000. “Overcoming the Zero Lower Bound on Monetary Policy.” Journal of Money, Credit, and Banking.

Meltzer, Allan. “Monetary Transmission at Low Inflation: Lessons from Japan.” (.doc link here).

Great post.

I suppose the output gap takes into account level imbalances, but I still think modern macro is too oriented to growth rates.

I think that recovery shifts the IS curve to the right and raises interest rates is related to the Brunner and Meltzer argument. Interest rate policy rules appear disruptive of that process.

I think the interest rate oriented solution to the output gap at zero nominal interest rate, that nominal interest rates should be kept “too low” after the recovery and allow higher inflation, and so higher expected inflation result in lower real interest rates and more aggregate demand now is too speculative. How are market participants supposed to learn about that? And this inflationary boom after the bust appears to be a cost of interest rate oriented policy rather than a necessary consequence of closing the output gap.

My preference is a policy that commits to expanding the money base whatever amount needed to get nominal expenditure back to its growth path, with an announcement that with the economic recovery, nominal interest rates should be expected to rise.

To me, the notion that.. “but central banks like to control short term interest rates,” doesn’t count for much.

Good post Josh!

Thanks guys! I have been meaning to write this post for some time.

Bill: The output gap is measured as the percentage deviation of real GDP from potential and so it is concerned with the level of output. Your overall point on growth rates, however, is correct.

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Your modelling is based on covering only part of the complete macroeconomics system which has 7 entities to cover the functional activities of land-lords, capitalists (whose activities are not the same), householders, producers, government, banks and the rest of the world.

The model I use does allow for these functions (a total not exceeding 21 money flows). So it is not surprising that the conclusions ate haywire!

Hey man,

Nice article! I’m actually writing a paper on how modern macroeconomics is generating a general glut. Is it possible if you can explain the connection between them. I tried to look for the answer on your post, but I couldn’t seem to find that connection.

Cheers,

I think if you go back and read the General Theory you will find the the idea of a liquidity trap is that at some point you can a state of expectations that monetary policy will not effectively raise investment levels, which is what Keynes was interested in. It seems to me that we are in such a situation now. But given that Keynes theory is based on historical time, the use of a general equilbrium framework is never going to be able to depict his ideas. Its like trying to explain Jimi Hendrix use of feedback on an acoustic guitar.

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