In Defense of Neo-Fisherism

The term neo-Fisherites has arisen to describe people like John Cochrane, who has suggested what New Keynesians believe to be a particularly weird policy conclusion. Namely, he has suggested that the Federal Reserve’s pegging of the interest rate on reserves at a rate very close to zero implies that we will experience deflation. A number of people I would identify as New Keynesians have privately communicated to me that they think this claim is preposterous and that Cochrane doesn’t understand how policy works. However, I would submit that John Cochrane understands the New Keynesian Model better than the New Keynesians and that if his prediction is wrong, then this has more to do with how little New Keynesian models teach us about monetary policy.

Let’s start with a basic premise that I think everyone would agree with. Let’s make three assumptions (1) the real interest rate is positive, (2) the Federal Reserve pegs the interest rate arbitrarily close to zero, and (3) the Federal Reserve pursues a policy of generating positive inflation. If (1), (2), and (3) are true, then the Federal Reserve is pursuing an unsustainable policy. This is the essence of neo-Fisherism. So what is wrong with this conclusion?

New Keynesians seem willing to admit the above policy is unsustainable. However, they think that it works in the opposite direction. In particular, New Keynesians have countered that if the Federal Reserve pegs the interest rate too long, then we should get more inflation and not less. This is certainly in keeping with the argument of Milton Friedman in his 1968 AEA Presidential Address. As Peter Howitt (2005) explains:

Friedman argued that at any given time there is a hypothetical (“natural”) real rate of interest that would generate a full employment level of demand. If the central bank set nominal interest rates too low, given the expected rate of inflation, then the real interest rate would be below this hypothetical natural rate, and this would generate excess aggregate demand, which would cause inflation to rise faster than expected… With inflation running faster than expected, people’s expectations of inflation would at some point start to rise, and if the nominal rate of interest were kept fixed that would just fuel the fire even more by reducing the real rate of interest still further below its natural rate.

I could have easily summarized Friedman’s position myself. However, the quote of Peter Howitt describing Friedman’s position is purposeful. The reason is because a number of observers have claimed that Cochrane and other neo-Fisherites should just read Howitt’s 1992 paper that seemingly shows how the New Keynesian model produces Friedman’s prediction. However, I would submit that this fails to understand Howitt’s paper.

For the interested reader, let me condense Howitt’s paper into a simplified New Keynesian framework. Suppose that there is an IS equation:

y_t = -\sigma (i_t - E_t \pi_{t+1} - r^*)

and a New Keynesian Phillips Curve:

\pi_t = E_t \pi_{t+1} + \phi y_t

where y is the output gap, \pi is inflation, i is the nominal interest rate, r is the natural real rate of interest, E is the expectations operator, and \sigma and \phi are parameters. Suppose that the central bank decides to peg the interest rate and suppose that the Federal Reserve’s desired rate of inflation is \pi^*. In a rational expectations equilibrium, it will be true that \pi_t = E_t \pi_{t+1} = \pi^*. Using this result, we can now combine the two equations to get an equilibrium inflation rate. Doing so yields,

\pi_t = i_t - r^* = \pi^*

Thus, in this New Keynesian model, when the central bank pegs the interest rate, the equilibrium inflation rate is increasing in the nominal interest rate. This is precisely what Cochrane and others have argued!

New Keynesians, however, conveniently ignore this result.* Instead, they immediately jump to a different conclusion drawn by Howitt. In particular, the way in which Howitt argues that we can obtain Friedman’s result in this framework is by starting with a departure from rational expectations. He then shows that without rational expectations, individuals would make forecast errors and that this particular policy would reinforce the forecast errors thereby producing Friedman’s conclusion. Any learning rule would push us away from the unique equilibrium \pi^*.

But the New Keynesian model doesn’t assume a departure from rational expectations. Thus, our result that \pi_t = i_t - r^* is not overturned by Howitt. Those who seek Howitt for support are abandoning the New Keynesian model.

Thus, we are left with an unfortunate conclusion. The New Keynesian discussion of policy doesn’t fit with the New Keynesian model of policy. Thus, either the model is wrong and the discussion is correct or the discussion is wrong and the model is correct. But consider the implications. Much of policy advice that is given today is informed by this New Keynesian discussion. If the model is correct, then this advice is actually wrong. However, if the model is wrong and the discussion is correct, then the New Keynesians are correct in spite of themselves. In other words, they still have no idea how policy is working because their model is wrong. Either way we are left with the conclusion that New Keynesians have no idea how policy works.


* – A subsequent argument is that pegging i_t causing a multiplicity of equilibria even under the assumption of rational expectations. Thus, the equilibrium I describe above might not be unique in more general models in which the expectation of the output gap appear in the IS equation. New Keynesians have argued that you can generate a unique equilibrium by having the central bank increase the interest rate adjust more than one-for-one with changes in the inflation rate. However, Benhabib, et al. have shown that this isn’t sufficient for global uniqueness and that there is a multiplicity of stable equilibria near the zero lower bound on interest rates.

What Do We Want Out of Macroeconomics?

Mark Thoma recently wrote a piece on the failures of macroeconomics and the need for new thinking in macroeconomics. His main criticisms are as follows:

  1. Existing macroeconomic models failed to give warning about the financial crisis.
  2. The models failed to give us policy guidance.
  3. There is too much emphasis on representative agents.
  4. Macroeconomists did not think questions about financial markets were worth asking.
  5. During the Great Moderation, economists didn’t spend enough time thinking about why things were going well.
  6. In 2003, Robert Lucas proclaimed that depression-prevention policy had been solved and this sentiment was shared by others of importance within the profession thereby making it more difficult to get work on such topics published.

I should note that Thoma also criticizes the critics. He argues that the scorn leveled at dynamic stochastic general equilibrium models is misplaced. These models and techniques were developed to answer specific questions. Thus, we should expect them to answer the questions they ask, but we shouldn’t necessarily expect more than that.

Nonetheless, I would like to consider his criticisms point-by-point.

  • Points 1 and 2 above are not (necessarily) fair criticisms of macroeconomics.
  • While I agree that there is too much emphasis on representative agents in RBC models and New Keynesian models, there is considerable work in macroeconomics involving heterogeneous agents.
  • Economists were actually thinking quite a bit about financial markets.
  • Economists were actually thinking quite a bit about the Great Moderation (including yours truly).
  • This discussion of Robert Lucas and his 2003 lecture is unfair to Lucas.

In his first two points, Thoma makes two distinct statements. First, he argues that modern macroeconomics does not equip us with models to explain the financial crisis and recession. Second, he argues that because of these models, economists were able to provide zero guidance to policymakers.

Macroeconomists think about recessions as coming from some exogenous shock. By definition, a shock is unknown and unpredictable. According to Thoma, a successful macroeconomic program would be one that provides models that explain what happens after the shock and provides policy guidance in the event that the policy. The implication thus seems to be that if we economists had the right models, we would know what was going to happen and could prevent the recession from being severe by enacting the necessary policy response.

This certainly sounds reasonable. Nonetheless, I actually think that this is a high bar for what we should expect from macroeconomics and macroeconomists. To understand why, consider the following example. Suppose there is some exogenous shock to the economy. There are two possible scenarios. In Scenario 1, macroeconomists have models that describe how the shock will affect the economy and the proper policy response. In Scenario 2, macroeconomists have no such models.

In Scenario 1, we avoid a severe recession. In Scenario 2, we could possibly have a severe recession. However, note something very important about our example. Given this logic, the only time that we would have a severe recession is when macroeconomists are ill-prepared to explain what is likely to happen and to provide a policy response. Thus, given Thoma’s expectations about macroeconomics, we should conclude that macroeconomics has failed every single time there is a severe recession. This seems like a very high bar.

As a result, I do not think that this is a fair criticism of macroeconomics. No matter how much we know, our knowledge will be imperfect and so long as our knowledge is imperfect we are going to have severe recessions.

This point is important because Thoma argues that the reason that we lacked a proper policy response to severe recessions was because people like Robert Lucas thought we didn’t need to study such things. However, this is a very uncharitable view of what Lucas stated in his lecture (read it here). Thoma quotes Krugman who quotes Lucas as saying “depression prevention has been solved.” Sure enough, the quote is there in the introduction. Lucas said it. Lucas then spends the rest of the paper comparing the welfare costs of business cycles to the welfare benefits of supply-side policies. However, if you read all the way through to the conclusion, you will note that Lucas actually has something to say about macroeconomic stabilization policies:

If business cycles were simply efficient responses of quantities and prices to unpredictable shifts in technology and preferences, there would be no need for distinct stabilization or demand management policies and certainly no point to such legislation as the Employment Act of 1946. If, on the other hand, rigidities of some kind prevent the economy from reacting efficient to nominal or real shocks, or both, there is a need to design suitable policies and to assess their performance. In my opinion, this is the case: I think that the stability of monetary aggregates and nominal spending in the postwar United States is a major reason for the stability of aggregate production and consumption during these years, relative to the experience of the interwar period and the contemporary experience of other economies. If so, this stability must be seen in part as an achievement of the economists, Keynesian and monetarist, who guided economic policy over these years.

The question I have addressed in this lecture is whether stabilization policies that go beyond the general stabilization of spending that characterizes the last 50 years, whatever form they might take, promise important increase in welfare. The answer to this question is no.

So when Lucas says that the depression-preventing policy problem has been solved, he actually provides examples of what he means by depression-prevention policies. According to Lucas preventing severe recessions occurs when policymakers stabilize the monetary aggregates and nominal spending. This is essentially the same depression-prevention policies advocated by Friedman and Schwartz. Given that view, he doesn’t think that trying to mitigate cyclical fluctuations will have as large of an effect on welfare as supply-side policies.

Nonetheless, Thoma’s quote and his remark imply that Lucas was wrong (i.e. that we haven’t actually solved depression-prevention). Of course, in order for Lucas to be wrong the following would have to be true: (1) Lucas says policy X prevents severe recessions, (2) We enacted policy X and still had a severe recession. In reality, however, we never got anything that looked like Lucas’s policy. The growth in monetary aggregates did not remain stable. In fact, broad money growth was negative. In addition, nominal spending did not remain stable. In fact, nominal spending declined for the first time since the Great Depression. We cannot conclude that Lucas was wrong about policy because we didn’t actually use the policies he advocates.

This brings me to a broader point. Thoma argues that Lucas’s thinking was indicative of the profession as a whole (or at least the gatekeepers of the profession). This ties directly into his argument that economists spent far too little time trying to explain the Great Moderation. This simply isn’t true. John Taylor, Richard Clarida, Mark Gertler, Jordi Gali, Ben Bernanke, and myself all argued that it was a change in monetary policy that caused the Great Moderation. Others, like Jonathan McCarthy and Egon Zakrajsek argued that improvements in inventory management due to innovations in information technology were a source of the Great Moderation. James Stock and Mark Watson argued that the Great Moderation was mostly result of good luck. Thus, to say that people didn’t care about understanding the Great Moderation is unfair.

Similarly, his criticism that economists simply didn’t care enough about financial markets is unfounded. Townsend’s work on costly state verification and the follow-up work by Steve Williamson, Tim Fuerst, Charles Carlstrom, Ben Bernanke, Mark Gertler, Simon Gilchrist, and others represents a long line of research on the role of financial markets. Carlstrom and Fuerst and well as Bernanke, Gertler, and Gilchrist found that financial markets can serve as a propagation mechanism for other exogenous shocks. These frameworks were so important in the profession that if you pick up Carl Walsh’s textbook on monetary economics there is an entire chapter dedicated to this sort of thing. It is therefore hard to argue the profession didn’t take financial markets seriously.

The same thing can be said about representative agent models. Like Thoma, I share the opinion that progress means moving away from representative agents. However, the profession began this process long ago. While the basic real business cycle model and the New Keynesian model still have representative agents, there has been considerable attention paid to heterogeneous agent models. Labor market and monetary search models contain heterogenous agents and not only get away from a representative agent framework, but also dispense with Walrasian market clearing.

But perhaps more important for this discussion is the work of the late Bruce Smith. Throughout his career, Smith was trying to integrate monetary models in which money and banking were actually essential to the model with growth and business cycle models. Look at a list of Smith’s work, which encompasses over 20 years of thinking about money, banking, and business cycles in frameworks with heterogeneous agents and in which money and banks are essential for trade to take place. It is hard to argue that the profession doesn’t take these issues seriously when one can establish such a long, quality research record doing so.

I agree with Thoma that we need to make progress in macroeconomics. We live in a complex and uncertain world and are tasked with trying to understand how millions of individual decisions produce equilibrium outcomes. It is a complex task and we do need to ask the right questions and develop frameworks to answer these questions. Nonetheless, to argue that macroeconomists aren’t already asking these questions and working on these tools does a disservice to macroeconomists and macroeconomics more generally.

On the Price of Money and Monetary Policy

It has become commonplace recently to discuss quantitative easing in the context of a comparison between the rates of return on T-bills with the interest rate paid on excess reserves. Money, however, is defined vaguely and the comparison of reserves with T-bills is a limiting case considering the scope of open market purchases conducted by the Federal Reserve in recent years. In all of the discussion, however, there is a neglected aspect of analysis and that aspect is in regards to the price of money.

Initially, it might seem odd to think about the “price of money.” Goods are priced in terms of money. So what is meant by the price of money? Often times, people think of the price of money as simply the reciprocal of the price of the good. In other words, if a banana costs 50 cents, then the price of a dollar is two bananas. Others see the price of hold money as an opportunity cost. In other words, by holding money, I am giving up some amount of rate of return. Thus, “the” interest rate is often considered the price of money. The interest rate, however, is not the price of money. The interest rate is the price of credit. So what is a meaningful definition of the price of money? Fortunately, the literature on monetary aggregation provides an answer to this question that is actually based on economic theory.

To define the price of money, we first need to define what we mean by money. Money consists of a lot of different things. Currency is money, a checking account or a savings account is money, and some have argued that due to things like repurchase agreements, even T-bills can be considered money. So if all these things can be considered money, how can we begin to define the price of money. As it turns out, each different type of money has its own price and every definition of a monetary aggregate has a corresponding price index.

Before getting to this, let’s first take a detour through monetary theory.

Traditional courses on monetary theory often start with a discussion about fiat money. Why would anybody hold fiat currency? It is clearly dominated in rate of return. Thus, shouldn’t people hold something else, like capital? Monetary theory has a lot of different answers to this question. For example, currency is assumed to be more liquid than other assets (i.e. there are lower transaction costs associated with using currency than other assets) or individuals value the constant (zero) rate of return in comparison to a stochastic (perhaps negative) rate of return, etc. Regardless of the reason, the general theme is that there are characteristics that currency has and that other assets do not have. Those characteristics create a non-pecuniary yield.

This is not only true of a comparison of say currency and capital, but also true of a comparison of currency with other types of things that we often consider “money”, such as a checking account or savings account, or a certificate of deposit. While these other forms of money might bear interest, some places refuse to accept checks, getting money out of a savings account might require a trip to the bank, withdrawing money from a certificate of deposit requires a transaction fee, etc. Thus, there is a trade-off between money and non-money, but there is also a trade-off between different forms of money. Less liquid forms of money yield higher rates of return, but the transactions costs associated with spending that money are higher.

These characteristics of different types of money are important. The reason that they are important is because they highlight the fact that different types of money and different types of assets more generally are imperfect substitutes for one another, a characteristic that is important when thinking about monetary policy. In addition, consider the counterfactual. If all different types of money were perfect substitutes, then individuals would only hold the money asset with the highest rate of return.

So what does this have to do with the price of money?

When we think about money, it is important to think about money in the way that we think about durable goods. Money provides a flow of services over time. As a result, the proper way to think about the price of money is to think about money in terms of its user cost. As Barnett (1978) derived, the real user cost of a given monetary asset i at time t is given as

u_{it} = {{R_t - r_{it}}\over{1 + R_t}}

where u_{it} is the user cost of asset i at time t, R_t is some benchmark rate of return, and r_{it} is the rate of return of asset i. Thus, the user cost of holding a given type of money is the discounted present value of the opportunity cost of holding that asset rather than the benchmark asset that doesn’t provide any sort of monetary services. It is important to note that this captures the features of money describe above. An asset that is more liquid will have a lower rate of return and therefore a higher user cost. Nonetheless, individuals will be willing to hold assets with different user costs because the assets are imperfectly substitutable. The price of a monetary aggregate is then given by the share-weighted average of each of the components in a given monetary aggregate.

So why is this important for monetary policy?

A lot of the analysis of quantitative easing focuses on the fact that the Fed is now swapping an interest-bearing asset for another interest-bearing asset. From the perspective of a bank, reserves are more liquid than T-bills since banks can use reserves to settle payments, but not (directly) using T-bills. Thus, consider how monetary policy ordinarily works according to what Ben Bernanke refers to as the portfolio channel of monetary transmission. Suppose that we begin in equilibrium. A bank is holding a given amount of reserves and a given amount of T-bills. The Federal Reserve then purchases T-bills, reducing the supply of T-bills and the increasing the supply of reserves. Assuming that the bank was content with its allocation, it then decides to re-allocate its portfolio (i.e. get rid of the reserves by purchasing other stuff). This re-allocation then has real effects on the economy.

Some have argued that with the Federal Reserve paying interest on reserves, however, banks have no incentive to do this. In other words, the bank receiving the reserves actually gets a marginal increase in liquidity without sacrificing the rate of return. Thus, there is no reason to re-allocate and no corresponding real effects. However, this ignores the fact that quantitative easing has taken a variety of forms. Not all rounds of quantitative easing has entailed buying T-bills. Nevertheless, some have claimed that buying 10-year Treasury bonds instead of T-bills has no effect other than to change the slope of the yield curve.

Regardless of whether the critics of quantitative easing have been correct in the context of the argument above, there is one thing that hasn’t been discussed: the price of money. What effect do large scale purchases of MBS have on the price of money? Is the price of money more sensitive to the purchases of long term bonds or mortgage-backed securities? The counter-argument to the portfolio view espoused by Bernanke suggests quantities don’t matter because relative prices adjust without any corresponding real effects. However, even if we take that view as true, then it must be the case the price of money is changing. This would seem to matter since shocks to the price of money have been shown to have significant effects on real output.

Anyway, just some food for thought.

The Index Number Problem and Inflation

Nick Rowe asks whether or not housing prices should be included in the inflation rate that the Bank of Canada targets. His discussion focuses on whether or not housing prices are sticky or whether they are flexible. His discussion is a standard story that follows from Woodford’s textbook on monetary theory and policy. The idea is that the price index that the central bank uses to target inflation should consist only of sticky prices. However, I find this viewpoint (while commonly accepted) to be counter to the conclusion of the index number problem discussed by Samuelson, Niehans and many others. In addition, I think that there is something to learn from the latter.

Consider a standard microeconomic story. An individual receives income, I, and gets utility from consuming goods x and y. Let p_x denote the price of x and p_y denote the price of y. Further, suppose the utility function is given as u(x, y) and has the usual properties. Thus, the consumer maximization problem is

\max\limits_{x, y} u(x, y)

s.t. p_x x + p_y y \leq I

The optimal allocation is therefore given as

{{u_x}\over{u_y}} = {{p_y}\over{p_x}}

where u_x is the marginal utility of x and correspondingly for y.

Now you are probably wondering, what does this have to do with inflation? Well the answer is quite simple. In the problem above, there was no discussion of money. This was a real economy. Suppose instead that we are dealing with a monetary economy. In this case, income is money income (i.e. the number of dollars that you earn). In order to solve the allocation problem, we now need to deflate money income by some price index such that income is expressed in real terms. If a change in the money supply has an equiproportional impact on all prices, the choice of the price index is entirely arbitrary. The price of any individual good will suffice as a price index. In other words, we could re-write the budget constraint as

x + {{p_y}\over{p_x}} y = {{I}\over{p_x}}

Solving the consumer’s maximization problem yields the same equilibrium condition as that above. In addition, since changes in the money supply have an equiproportionate effect on all prices, the relative price of good y to good x remains unchanged and doesn’t have any effect on the allocation of goods. Additionally, so long as p_x is held constant, then money income will not have any effect on the allocation either.

However, suppose that changes in the money supply do not have equiproportionate effects on prices. To use Nick’s example, suppose that the price of x is sticky and the price of y is flexible. In this case, a change in the money supply will also affect relative prices. In this case, one cannot simply solve the allocation problem by deflating money income by the price of one of the goods. In this case, changes in the money supply will distort the allocation of goods. In addition, this means that it is not sufficient to simply target the sticky price.

The solution to this problem is to choose a price index to deflate money income such that when that index is held constant, there is not any distortion in the allocation of goods. In other words, the objective to choose P such that the budget constraint can be re-written as

{{p_x}\over{P}} x + {{p_y}\over{P}} y = {{I}\over{P}}

Given the correct choice of P, it is straightforward to show that (1) the allocation of goods is determined by the relative prices of the goods, and (2) when P is constant, money income is constant as one moves along an indifference curve.

So how do we construct P? Well, Samuelson gave us a class of examples where there was a specific price index that could solve the problem. And it turns out that the correct price index to use is dependent on the preferences of the representative consumer in the model. In particular, consider the following utility function:

u = \sqrt{xy}

It is straightforward to show that the correct price index to use in this case is

P = \sqrt{p_x p_y}

Here is a brief sketch of why this is true. In a real economy, when there is an increase in income, the individual moves to a higher indifference curve (i.e. utility increases). Thus, when an individual moves along an indifference curve, it must be true that income is constant. A different way of stating the problem above is that the objective is to choose a price index such that when that index is held constant, money income is constant when an individual moves along an indifference curve. We can now show that this is true for the utility function and price index above.

Consider the budget constraint:

I = p_x x + p_y y = p\bigg({{p_x}\over{p}} x + {{p_y}\over{p}} y\bigg)

Suppose the price index is given as P = \sqrt{p_x p_y}, then this can be re-written as

I = p\bigg({{\sqrt{p_x}}\over{\sqrt{p_y}}} x + {{\sqrt{p_y}}\over{\sqrt{p_x}}} y\bigg)

Given the preferences assumed above, the equilibrium condition for the consumer is

{{p_x}\over{p_y}} = {{y}\over{x}}

Substituting this into the budget constraint yields

I = p(2\sqrt{xy}) = p(2U)

Thus, when p is constant, a movement along an indifference curve is associated with a constant amount of money income.

So what does all of this mean?

What this means is that if changes in the money supply result in changes in the relative price of goods, then the optimal policy is one in which there is no inflation. However, the choice of how to measure inflation is not arbitrary in this case. Rather, there is a precise index number that must be used to calculate inflation.

Nick’s point, and the accepted wisdom of many in the discipline, is that when changes in the money supply distort relative prices due to price stickiness, the best thing to do is to target the sticky prices and let the flexible prices adjust. However, the example above rejects this idea. If, say, p_x was a sticky price and p_y was a flexible price, targeting p_x would be insufficient. Doing so would prevent money income from affecting utility, but it would not prevent an adjustment in the relative prices of x and y and would therefore distort the allocation.

What the index number problem suggests is that the choice of the proper price index does not depend on which price is sticky or the source of the relative price variability. Instead, the index number problem suggests that the proper price index is derived from the preferences of the consumer. Thus, when asked if housing prices should be included in the price index used to calculate inflation, the relevant question is not whether housing prices are sticky, but rather whether housing enters a representative consumer’s utility function.

On Secular Stagnation and Money

Gauti Eggertsson and Neil Mehrotra have a new paper that seeks to provide a formal model of secular stagnation. The paper is a welcome addition to a debate that, prior to their paper, was mostly muddled thoughts sprinkled throughout speeches and blog posts. The purpose of this post is to express doubts about some of the features of their model and also talk about the role of money (which is absent from the choices made in the model, but somehow prevents policy from going below the zero lower bound).

The basic idea in the Eggertsson and Mehrotra (henceforth EM) paper is that some sort of shock, like a de-leveraging shock, can cause the real interest rate to fall below zero. Since monetary policy is limited by the zero lower bound, the central bank (potentially) cannot equate the real interest rate with the real natural rate of interest. The only solution is for the central bank to increase its inflation target until the real interest rate is equal to the natural rate. In fact, EM argue that there is no equilibrium possible if the inflation rate isn’t raised to minus the real natural rate of interest.

Essentially, my problem with the model is as follows. As I will discuss below, the zero lower bound is only a constraint if individuals can hold currency. However, if individuals are capable of holding currency, when the real interest rate on savings is less than the real rate of return on currency (minus the rate of inflation), then everyone will hold currency. Thus, it is not true that no equilibrium exists when the inflation rate is less than minus the real rate of interest. The inclusion of money has important implications for their model in terms of the welfare effects of the shocks generating the so-called secular stagnation.

The EM model can be summarized as follows. The model is an overlapping generations model in which agents live for 3 periods. Thus, at any one point in time, there are three generations living — young, middle-aged, and old. Agents are assumed to only receive an endowment (or produce) in middle-age. Thus, in order to consume when old, agents have to save some of their endowment for old age. To consume when young, agents have to borrow from middle-aged agents. Middle-aged agents save by lending their endowment to young agents. When young agents become middle-aged, they repay their debt to the now old agents who use the repayment to consume. The model is a pure credit economy in the sense that money serves as a medium of account, but not a medium of exchange. The key feature of the model is that young agents are debt constrained. EM assume that young agents can only borrow an amount less than or equal to D_t. They assume that this constraint is binding such that young agents always borrow an amount, D_t. The key equation in their framework is the equilibrium condition in the savings market, given by

1 + r_t = {{1+\beta}\over{\beta}} {{(1+g_t)D_t}\over{Y_t - D_{t -1}}}

where r_t is the real interest rate, \beta is the discount rate, g_t is the rate of population growth, and Y_t is the size of the endowment. Secular stagnation results when the real interest rate falls below zero and the central bank cannot reduce the nominal interest rate sufficiently to clear the market. One potential cause of this phenomenon is de-leveraging. For example, suppose that D_t permanently declines (i.e. young agents find it harder to borrow). In this case, the real interest falls in period t and falls again in period t+1. If the decline is large enough, this can cause the real interest rate to be negative.

Now in a pure credit economy, this shouldn’t be a problem. The market rate of interest should just become negative. However, EM assume two things. First, they assume that the central bank determines the nominal interest rate. Second, they assume that “the existence of money precludes the possibility of a negative nominal rate.” The assumption they seem to be making is that nobody holds currency, but the threat that people could hold currency prevents the nominal rate from going below zero. The reason that this is important is because they make the following statement: “…it should be clear that if the real rate of interest is permanently negative, there is no equilibrium consistent with stable prices.” This argument follows directly from the Fisher equation. If prices are constant, the Fisher equation implies that

i_t = r_t < 0

which is a contradiction since we've assumed that i \geq 0.

However, if we are to take currency seriously, we should consider the conditions under which people would hold currency. To do so, consider a simple modification to their model. Assume that we endow the initial old agents with currency and assume that the supply of currency is constant such that the price level is constant. Now, middle-aged agents face a portfolio allocation decision. They can lend to young agents at the real rate of interest or they can sell their endowment to old agents for money.

In this modified environment there are three possible equilibria. For both debt and currency to be used in equilibrium, it must be true that the rate of return on debt and the rate of return on currency is equal (it is straightforward to show this by adding money to the EM choice problem and solving out the Kuhn-Tucker conditions). If the rate of return on debt is higher than currency, then nobody holds currency and everybody issues debt. If the rate of return on currency (technically, in an OLG model with a constant supply of currency, this is equal to the rate of population growth) is greater than the rate of return on debt, then everybody holds currency.

This point is not a mere formality. The reason is because EM argue that the world blow up with price stability (actually when they say there is no equilibrium, I think they actually mean that autarky is the equilibrium result). However, the simple addition of currency to the model implies that if the real interest rate ever became negative, all middle-aged agents would simply sell their endowment to old agents in exchange for currency rather than lend to young agents. Thus, if young agents become sufficiently debt constrained, nobody lends to young agents and young agents do not consume. Nonetheless, there is an equilibrium consistent with stable prices.

The importance of the explicit inclusion of currency is as follows. The central bank therefore faces a trade-off. If the central bank increased the growth rate of currency and thereby the inflation rate, they could increase the inflation rate sufficiently such that the inflation rate was equal to minus the real rate of interest. In this case, individuals would be indifferent between debt and currency and the debt market would clear at the desired negative real interest rate. This allows young agents to borrow, which given the assumption of diminishing marginal utility of consumption, means that welfare increases. However, this increase in welfare comes at the expense of a reduction in welfare via inflation. It is well-known that in OLG models, the optimal policy is a constant money supply.

This point might seem subtle, but I think it is important. The reason that I think it is important is because by arguing that the zero lower bound causes autarky when the real rate of interest is sufficiently negative, this overstates the welfare losses from the so-called secular stagnation. Introducing a constant supply of currency in this environment, significantly improves welfare relative to autarky. In fact, in standard OLG models, a constant supply of currency produces an optimal allocation.

On Pegging the Interest Rate

Back in 2010, Narayana Kocherlakota was subjected to a great deal of criticism about his comment that the FOMCs decision to peg the interest rate at zero for an extended period of time would ultimately lead to deflation. Economists, especially those in the blogosphere, became near apoplectic that Kocherlakota, a distinguished scholar and voting member of the FOMC, would say something so seemingly egregious. Criticism largely came from two camps. The first camp, mostly filled with New Keynesians, argued that this was wrong because what mattered was the market interest rate relative to the natural rate. The second camp, mostly those whose views are consistent with Monetarism, suggested that this was preposterous because Friedman’s 1968 speech to the American Economic Association taught us that attempts to peg the interest rate would lead to inflation, not deflation.

Steve Williamson has taken a lot of flak from fellow economics bloggers because he has relentlessly defended this statement over the years. So last week I did a radical thing, I talked to Steve about this very controversy. In doing so, Steve confirmed what I believed to be his view all along and one that I think is correct: Kocherlakota was correct in his statement AND so was Milton Friedman. To understand why, we need to think about the Fisher equation and the behavior of monetary aggregates.

The entire debate centers around the Fisher equation:

i_t = r_t + E_t \pi_{t+1}

where i is the nominal interest rate, r is the real interest rate, and E_t \pi_{t+1} is expected inflation. In the long run, we tend to think of the real interest rate as being determined by real factors, like productivity and preferences. The reason that the Fisher equation is important is because to understand Friedman’s point, we need to understand the effects of monetary policy in the short run and the long run. Thus, we need to understand both the liquidity effect of monetary policy and the Fisher effect.

Suppose, for example, that the central bank increased the rate of money growth. The liquidity effect implies that the short term interest rate would initially decline. However, over time, the Fisher effect implies that expectations of future inflation would increase and push the nominal interest rate higher. Thus, Friedman’s point was as follows. Suppose the current nominal interest rate was 3% and the central bank wanted to peg the nominal interest rate at 2%, in the short run they could achieve this by increasing money growth (i.e. through the liquidity effect). However, the Fisher effect would ultimately push the nominal interest rate higher. Thus, the only way that the central bank could achieve this interest rate peg would be through continuously increasing the rate of money growth to produce lower rates through the liquidity effect. The result of this sort of policy would then be one of ever-increasing rates of money growth and inflation. This result was largely viewed as unsustainable and therefore central banks could not peg the interest rate in this manner.

Kocherlakota’s point was that pegging the nominal interest rate would ultimately lead to deflation. This sounds contradictory to Friedman because he arrives at the opposite conclusion. However, the two points are actually two sides of the same coin. What Kocherlakota is effectively (or perhaps not so effectively, given the outcry) saying is that if the central bank wanted to peg the interest rate at a particular level, then this would require that the central bank start reducing money growth. In fact, for the case in which the central bank kept the nominal interest rate pegged at zero, a positive real interest rate would imply that the central bank would have to pursue a negative rate of money growth to maintain the target.

Thus, Kocherlakota is taking the objective of holding the interest rate constant as given and asking how it is that the central bank can maintain this policy. Friedman, on the other hand, is thinking about how the central bank is likely to try to pursue this policy.

What both Kocherlakota’s argument and Friedman’s argument have in common are what is important. The common element of the argument is that if the Federal Reserve adopts an interest rate peg over a long period of time, the ability to maintain that peg is dependent on the rate of money growth. The central bank can either adopt the rate of money growth consistent with the interest rate peg or they cannot maintain the interest rate peg.

What seemed to confuse people about this entire issue is that their understanding of Federal Reserve policy clearly contradicted any prediction of deflation. Nonetheless, this is the wrong way to interpret Kocherlakota’s argument. The argument he was making was essentially that if the Federal Reserve chose to leave the interest rate at zero for an extended period of time, this would imply that eventually they would have to pursue a policy that was deflationary. If they didn’t pursue that type of policy, they couldn’t maintain their peg of the nominal interest rate. In addition, since we don’t expect the Federal Reserve to pursue a policy consistent with negative rates of money growth, the statement should be seen as a criticism of the Federal Reserve’s original attempt at forward guidance which suggested that the FOMC would keep the interest rate at zero for an extended period of time.

There is an important lesson to be learned from this controversy and debate. The lesson is that even though policy is conducted with the federal funds rate as an intermediate target or with interest on reserves as an instrument, it is still necessary to know the underlying path of the money supply associated with this interest rate policy.

Review of Piketty’s Capital in the 21st Century

My review of Piketty’s Capital in the 21st Century will run in the May 5 issue of National Review. In the meantime, here is a link to a longer version of the review.