I find this way of thinking about monetary policy to be quite odd for several reasons. First, conceivably when one talks about the natural rate of interest, the reference is to a real interest rate. New Keynesians, for example, clearly see the natural rate of interest as a real rate of interest (at least in their models). Second, the market rate of interest is a nominal rate. Thus, it is odd to say that the market rate of interest is above the natural rate of interest when one is nominal and one is real. I suppose that what they mean is that given the nominal interest rate and given the expectations of inflation, the implied real market rate is too high. But this seems to be an odd way to describe what is going on.

Regardless of this confusion, what advocates of this approach appear to be saying is this: when the market rate of interest is at the zero lower bound and the natural rate of interest is negative, unless inflation expectations rise, there is no way to equate the real market rate of interest with the natural rate.

But this brings me to the most important question that I have about this entire argument: Why is the natural rate of interest negative?

It is easy to imagine a real market interest rate being negative. If inflation expectations are positive and policymakers drive a nominal interest rate low enough, then the implied real interest rate is negative. It is NOT, however, easy to imagine the natural rate of interest being negative.

To simplify matters, let’s consider a world with zero inflation. The central bank uses an interest rate rule to set monetary policy. The nominal market rate is therefore equal to the real market interest rate. Thus, assuming that the central bank is pursuing a policy to maintain zero inflation, they are effectively setting the real rate of interest. Thus, the optimal policy is to set the interest rate equal to the natural interest rate. Also, since everyone knows the central bank will never create inflation, this makes the zero lower bound impenetrable (i.e. you cannot even use inflation expectations to lower the real rate when the nominal rate hits zero). I have therefore created a world in which a central bank is incapable of setting the market rate of interest equal to the natural rate of interest if the natural rate is negative. My question is, why in the world would we ever reach this point?

So let’s consider the determination of the natural rate of interest. I will define the natural rate of interest as the real rate of interest that would result with perfect markets, perfect information, and perfectly flexible prices (the New Keynesian would be proud, I think). To determine the equilibrium real interest rate, we need to understand saving behavior and we need to understand investment behavior. The equilibrium interest rate is then determined by the market in our perfect benchmark world. So let’s set up a really simple model of saving and investment.

Time is continuous and infinite. A representative household receives an endowment of income, y, and can either consume the income or save it. If they save it, they earn a real interest rate, r. The household generates utility via consumption. The household utility function is given as

where is the rate of time preference and is consumption. The household’s asset holdings evolve according to:

where are the asset holdings of the individual. In a steady state equilibrium, it is straightforward to show that

The real interest rate is equal to the rate of time preference.

Now let’s consider the firm. Firms face an investment decision. Let’s suppose for simplicity that the firm produces bacon. We can then think of the firm as facing a duration problem. They purchase a pig at birth and they raise the pig. The firm then has to decide how long to wait until they slaughter the pig to make the bacon. Suppose that the duration of investment is given as . The production of bacon is given by the production function:

where f’,-f”>0 and b is the quantity of bacon produced. The purchase of the pig requires some initial outlay of investment, , which is assumed to be exogenously fixed in real terms and then it just grows until it is slaughtered. The value of the pig over the duration of the investment is given as

Integration of this expression yields

Let’s normalize the amount of investment done to 1. Thus, we can write the firm’s profit equation as

The firm’s profit-maximizing decision is therefore given as

Given that the firm makes zero economic profits, it is straightforward to show that

So let’s summarize what we have. We have an inverse supply of saving curve that is given as

Thus, the saving curve is a horizontal line at the rate of time preference.

The inverse investment demand curve is given as

The intersection of these two curves determine the equilibrium real interest rate and the equilibrium duration of investment. Since the supply curve is horizontal, the real interest rate is always equal to the rate of time preference. So this brings me back to my question: How can we explain why the natural rate of interest would be negative?

You might look at the equilibrium conditions and think “sure the natural rate of interest can be negative, we just have to assume that the rate of time preference is negative.” While, this might mathematically be true, it would seem to imply that people value the future more than the present. Does anybody believe that to be true? Are we really to believe that the the zero lower bound is a problem because the general public’s preferences change such that they suddenly value the future more than the present?

But suppose you are willing to believe this. Suppose you think it is perfectly reasonable to assume that people woke up sometime during the recession and their rate of time preference was negative. There are two sides to the market. So what would happen to the duration of investment if the real interest rate was negative? From our inverse investment demand curve, we see that the real interest rate is equal to the ratio of the marginal product of duration over total production. We have made the standard assumption that the marginal product is positive, so this would seem to rule out any equilibrium in which the real interest rate was negative. But suppose at a sufficiently long duration, the marginal product is negative. We could always write down a production function with this characteristic, but how generalizable would this production function be? And why would a firm choose this actually duration when they could have chosen a shorter duration and had the same level of production?

Thus, the only way that one can believe that the natural rate of interest is negative is if they believe that individuals suddenly value the future more than the present and that in a perfect, frictionless world firms would prefer to undertake dynamically inefficient investment projects. And not only that, advocates of this viewpoint also think that the problem with policy is that we cannot use our policy tools to get us to a point consistent with these conditions!

Finally, you might argue that I have simply cherry-picked a model that fits my conclusion. But the model I have presented here is just Hirshleifer’s attempt to model the theories of Bohm-Bawerk and Wicksell, the economists that came up with the idea of the natural rate of interest. So this would seem to be a good starting point for analysis.

P.S. If you are interested in evaluating monetary policy within a framework like this, you should check out one of my working papers, written with Alex Salter.

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As I wrote in my previous post on the topic, I think that macroeconomists tend to look at the negotiations between Germany (and the EU more broadly) and Greece all wrong. Naturally, as macroeconomists, we tend to think about these negotiations in terms of the “big picture”. In other words, when macroeconomists look at the negotiations, they often think about the macroeconomic effects of a financial market collapse in Greece and the possible damage that results from various interlinkages. Those who see these costs as being very large then tend to advocate the importance of coming to an agreement. In addition, those who advocate stabilization policies think that such an agreement should also allow Greece to defer the costs until they have a chance to improve their economy through (you guessed it) stabilization policies.

I think that this is the wrong way to think about the negotiations. The negotiations have to be viewed in the context of game theory. The Germans and the Greeks are playing a dynamic game. Thus, Germany has an incentive to make sure that any deal that is reached between the EU and Greece is one that prevents these types of negotiations from happening in the future. In other words, Germany is trying to minimize the costs associated from moral hazard in the future. This isn’t just about Greece, this is about setting a precedent for all future negotiations. When you think about the negotiations in this context, I think that you come up with a better understanding of Germany’s behavior.

But I also think that once you think about the negotiations in terms of game theory, the supposed German opposition to fiscal stabilization doesn’t hold up very well as an explanation of the German response. For example, suppose that the Germans do believe in fiscal stabilization policies. Wouldn’t it then make sense to use austerity as a punishment mechanism for the bailout? If Germany’s true desire is to prevent such negotiations from taking place in the future, then they have an incentive to enact some sort of punishment on Greece in any deal that they reach. Imposing austerity would be one possible punishment. Even if the Germans don’t believe in fiscal stabilization, they know that the Greeks do. As a result, this threat is still a credible way of imposing costs in the game theoretic context because the expected costs to Greece are conditional on Greece’s expectations.

In short, whether or not Germany believes in economic stabilization policy, they are likely to pursue the same strategy within a game theoretic context. Thus, viewing this strategy on the part of the Germans doesn’t necessarily tell us anything about German beliefs.

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1. Consider a Robinson Crusoe economy. There is one guy on an island with production opportunities, but no market opportunities. For simplicity, think of a two-period model. In the first period, the individual receives an endowment, Y. The individual can invest that endowment to generate future production or consume the endowment. The individual transforms Y into P1, production now, and P2, production later. It follows that investment is defined as I = Y – P1. Savings is defined as S = Y – C1, where C1 is consumption in the first period. Since there is only one guy on the island, it must be true that P1 = C1. These decisions are both determined by the individual’s rate of time preference. Thus, S = I is an identity.

2. Consider the same guy on an island, but who now has market opportunities. Now we have the same definitions for saving and investment. Saving is

S = Y – C1

I = Y – P1

Note that with exchange opportunities, it is very unlikely that C1 = P1. Thus, at the individual level, savings probably doesn’t equal investment. Combining these conditions, we get

S = I + P1 – C1

for the individual. Now sum across all terms and we get

Now in equilibrium, market-clearing requires that total production equals total consumption. Thus, market clearing implies that total savings is equal to total investment:

Saving = Investment is therefore an equilibrium condition.

3. Finally, David’s issue is that he doesn’t think that gross domestic income and gross domestic expenditure are the same thing. Empirically, he’s correct. This is why we have GDP Plus.

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In the midst of these negotiations, some have argued that the EU, and Germany specifically, do not appear to understand the magnitude of the situation. Paul Krugman, for instance, writes

As long as it stays on the euro, then, Greece needs the good will of the central bank, which may, in turn, depend on the attitude of Germany and other creditor nations.

But think about how that plays into debt negotiations. Is Germany really prepared, in effect, to say to a fellow European democracy “Pay up or we’ll destroy your banking system?”

[…]

Doing the right thing would, however, require that other Europeans, Germans in particular, abandon self-serving myths and stop substituting moralizing for analysis.

This last statement is particular telling. Many commentators agree with Krugman and view the Germans and other members of the EU as moralizing. In other words, they are not using economic analysis, but rather relying on their own views about right and wrong and how a government should operate. However, I would submit that rather than assuming that the Germans and other members of the EU are vindictive moralizers, an understanding of economics can actually teach us why EU members have taken their current position. But to understand why, we need to know something about rent-seeking.

Suppose that there are two countries, Germany and Greece. In addition, suppose that each of these countries have an endowment of resources, , where will refer to Germany and will refer to Greece. Now let’s assume that each country can devote some amount of resources to production, and some amount of time to fighting with each other, . It follows that each country has a resource constraint:

Now, let’s assume that the total production between the two countries is given as

where is a measure of complementarity in production. One way to think about is that the higher its value, the most closely linked the two countries are in terms of international trade, production, etc.

Thus, we see that the countries can commit their resources to production or to fighting. The more each country contributes to production, the higher the total level of production. However, fighting with one another can also provide benefits (this obviously doesn’t have to refer to actual fighting, it could refer to negotiations like those that are ongoing). However, whereas increased production will cause an increase in the amount of production/income that is generated, fighting will only have an effect on the distribution of income.

Thus, each country faces a trade-off. The more resources they commit to production, the higher the level of income that is generated. The more resources they commit to fighting, the greater the distribution of the existing income they receive (but there is less income as a result). Thus each country has to choose the share of resources that they want to commit to production and fighting.

We will assume that there is a contest success function (as in Tullock, 1980) that is a function of the amount of resources that each country commits to fighting. For Germany, we assume that the contest success function is given as

where is an index of the decisiveness of the conflict. Correspondingly, for Greece .

Given these definitions, we can then define the distribution of income:

Now let’s assume that each country wants to maximize their own income , taking what the other country is doing as given. Thus, each country wants to maximize the following

In equilibrium, it follows that

Now let’s use this equilibrium condition to understand the interaction between Germany and Greece. Suppose that we simply choose resource endowments of $R_1 = 100$ and $R_2 = 50$ thereby assuming that Germany has twice as many resources as Greece. Now let’s consider the implications under two scenarios. First, we will consider the scenario in which . In this case, total production is just the sum of German and Greek production. It follows from equilibrium that

Thus, in this case, Germany and Greece devote the same amount of resources to the fighting. However, since Germany has twice as many resources as Greece, it follows that Greece is devoting a larger percentage of their resources to fighting. In devoting resources to fighting, the two countries produce less total production. To see this, consider that if each country devoted all of their resources to production, total production would be 100 + 50 = 150. If we assume that , then . Thus, total production is 62.5 + 12.5 = 75. And yet this is their optimal choice given what they expect the other country to do!

As a result of the percentage of resources devoted to fighting, Greece gets 1/2 of the resulting production, despite only having 1/3 of the total resources. It should therefore be straightforward to understand why Greece is devoting so many resources to getting a larger bailout without bearing the costs of so-called austerity measures. In addition, it is important to note that it is in Germany’s best interest to devote resources to fighting, given what they expect Greece to do.

It is straightforward to show two other results with this framework. First, as increases, the weaker side has less of an incentive to fight whereas the stronger side has a greater incentive to fight. In other words, when production becomes more complementary, then the poorer side has less of an incentive to fight because of the linkages in production between their production effort and the other country. While the richer country has an incentive to fight more, the total resources devoted to fighting will fall.

Again, this informs the discussion about Germany and Greece in comparison to other countries. If you want to understand why there seems to be a greater conflict between Germany and Greece than between Germany and other EU countries, consider that Greece is Germany’s 40th largest trading partner, just after Malaysia and just ahead of Slovenia. All else equal the model described above suggests that we should expect more resources devoted to conflict.

The second characteristic has to do with the decisiveness of conflict. As increases, the conflict between the two countries can be considered more decisive. As the conflict becomes more decisive, the model predicts that the sides will have more of an incentive to devote to fighting. Thus, if Germany believes that this is (or should be) the last round of negotiations with Greece, then we would expect them to devote more resources to fighting.

So what is the point of this exercise?

The entire point of this exercise is to understand that Germany is, in fact, acting in their own economic interest given what they expect Greece to do. If we want to understand the positions of Germany and Greece, we need to understand strategic behavior. Germany’s refusal to simply give in to Greece’s demands and “do what’s best for Europe” ignores a lot of the aspects of what is going on here. Those who think that Germany is being too harsh ignore some of the key aspects of the framework discussed above.

First, one should note that the distribution of income in the framework above is always more equal to the distribution of resources. Thus, it pays for Greece to fight. However, Germany knows that it pays for Greece to fight and therefore Germany’s best strategic decision is to devote resources to fighting as well.

Second, by claiming that Germany is failing to do what is in the “best interests of Europe”, the critics are presuming that they know the social welfare function that needs to be maximized. Perhaps they are correct. Perhaps they are not. But even if these critics are correct, this doesn’t mean that Germany’s behavior is incomprehensible or that it is based on something other than economics. Rather the confusion is on the part of the critics who fail to understand that a Nash equilibrium may or may not be the socially desirable equilibrium. Germany’s rhetoric might be moralizing, but we can understand their behavior through an understanding of economics. And this is true whether you like Germany’s behavior or not.

[This post is an application of Hirshleifer’s Paradox of Power model. See here.]

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In this post I would like to argue that the problem with the New Keynesian view is that it completely ignores money. By ignoring money, the New Keynesians assume that the central bank need only use the nominal interest rate as a monetary policy tool. Previous generations of monetary economists argued that interest rate policies were not plausible. An earlier generation of economists, such as Milton Friedman and Jurg Niehans, argued that pegging the nominal interest rate would cause ever-increasing inflation. A later generation of economists, such as Thomas Sargent and Neil Wallace, argued that pegging the interest rate would lead to multiple equilibria. The logic of these claims are the same, but the primary difference in their analysis is the treatment of expectations. Under Friedman’s and Niehan’s formulations, expectations were backward-looking. For Sargent and Wallace, agents were assumed to have rational expectations and are therefore forward-looking. The reason for the different predictions are the differences in assumptions about expectations, but the perils of interest rate targeting remain.

New Keynesians, however, seem to believe that they have solved this problem with the Taylor principle, which states that when inflation rises by 1%, the central bank should increase the nominal interest rate by more than 1%. The intuition behind this is that by raising the nominal interest rate by more than the rate of inflation, the central bank is increasing the real interest rate, which reduces demand and thereby inflationary pressures. Using the Taylor principle, New Keynesians were able to show that they could get a unique equilibrium using an interest rate target. In addition, their model showed that they could do this all without money.

Despite the ability of New Keynesians to get a unique equilibrium with an interest rate target and no reference to money, remained critics of the practical application of the model. A number of critics, for example, pointed out that the way in which the Federal Reserve adjusts its own interest rate target, the federal funds rate, is through open market operations. The Federal Reserve increases the supply of bank reserve by making open market purchases and this causes the federal funds rate to fall. Thus, the critics argued, that even when the Fed uses the federal funds rate as its preferred measure of communicating policy, the Fed’s actual policy instrument is the monetary base.

The New Keynesians, however, countered that they didn’t need to use open market operations to target the interest rate. For example, Michael Woodford spends a considerable part of the introduction to his textbook on monetary economics to explaining the channel system for interest rates. If the central bank sets a discount rate for borrowing and promises to have a perfectly elastic supply at that rate and if they promise to pay a rate of interest on deposits, then by choosing a narrow enough channel, they can set their policy rate in this channel. In addition, all they need to do to adjust their policy rate is to adjust the discount rate and the interest rate paid on reserves. The policy rate will then rise or fall in conjunction with the changes in these rates. Thus, the New Keynesians argued that they didn’t need to worry about money in theory or in practice because they could set their policy rate without money and their model showed that they could get a determinate equilibrium by applying the Taylor principle.

Nonetheless, what I would like to argue is that their ignorance of money has led them astray. By ignoring money, the New Keynesians have confused cause and effect. This confusion has led them to believe that they know something about how interest rate policy should work, but they have never stopped to think about how interest rate policy works when the central bank adjusts the nominal interest rates in a channel system versus how interest rate policy works when the central bank adjust the nominal interest rate using open market operations.

The standard story about the impact of monetary policy on nominal interest rates as follows. Suppose that the central bank increases the growth rate of money. Assuming that we are initially in equilibrium, this increase in the growth rate of money initially increases the nominal supply of money such that the real value of money balances is greater than individuals desire to hold. As a result, the nominal interest rate must fall to induce individuals to hold these higher money balances. This decline in the interest rate is referred to as the liquidity effect. Over time, however, this increase in money growth causes inflation to increase. Thus, as inflation expectations rise, this puts upward pressure on the nominal interest rate. This is referred to as the Fisher effect.

Keynesians tend to focus on the liquidity effect as the source of the transmission of monetary policy. For example, this decline in interest rates (coupled with the assumption of sticky prices) should increase both consumption and investment as the real interest rate also declines. Thus, the New Keynesians view the nominal interest rate as a tool in and of itself. However, New Keynesians are confusing cause and effect. It is called the liquidity effect because the decline in interest rates is *caused* by a change in the money supply.

This distinction is eminently important when one considers the implications of paying interest on reserves. For example, consider the world without interest on reserves. The standard story about the market for reserves is that the Federal Reserve determines the supply of reserves and therefore the supply curve for reserves is vertical. The demand for bank reserves is decreasing in the nominal interest rate. Thus, an increase in the quantity of bank reserves shifts the supply curve to the right. At the old interest rate, banks want to hold less reserves than are supplied. Thus, the interest rate has to adjust downward to get us back to equilibrium. This is shown in the figure below.

Now consider the effects of this change within the following basic framework. Recall that the equation of exchange can be expressed in logarithms as

where m is a broad measure of the money supply, v is velocity, p is the price level, and y is real income. The equation of exchange is identically true. However, we can use the equation of exchange to discuss the implications of the quantity theory of money if we have some theory of velocity. Suppose that we adopt the standard Keynesian liquidity preference view of money demand:

Thus, the demand for real money balances is increasing in real income and decreasing in the nominal rate of interest. Assume for a moment that . It is straightforward to show that we can solve this expression for the demand for money to get a theory of velocity:

Thus, velocity is an increasing function of the nominal interest rate. Substituting this into the equation of exchange, we have:

Now consider the effects of a change in the money supply. As illustrated in the figure above, the increase in the money supply causes the interest rate to decline. This means that when the money supply increases, velocity declines. However, the interest elasticity of velocity is often estimated to be rather small. The initial effect of the increase in the money supply is that the nominal interest rate to fall and nominal spending to rise. The decline in the nominal interest rate is an effect of the change in the money supply, but note that it is not the cause of the change in nominal spending.

However, now consider what happens if the central bank pays interest on reserves. We now have to re-draw our market for reserves. Specifically, the demand for reserves will now be kinked. This is because interest on reserves imposes a floor on the interest rate in this market. Nonetheless, since the interest rate on reserves is set by central bank policy, they can adjust this rate without open market operations. If the quantity of reserves in the banking system is sufficiently large, an increase in the interest rate paid on reserves will not have an effect on the equilibrium quantity of reserves. To see this, consider our modified market for reserves presented below.

[**Updated:** Scott Sumner made clear to me in the comments that what initially followed this point was hard to understand. As a result, it has been edited to be more clear. –JH]

Thus, let’s accept the New Keynesian idea that the change in the interest rate on reserves can be done in the absence of a change in broad measures of the money supply (we’ll return to this point later). Recall that the Keynesian liquidity preference of the money supply implies that the income velocity of the money supply is . Then, returning to our equation of exchange we have:

Now consider what happens if the central bank increases the interest rate paid on reserves, holding the money supply constant. According to the expression above nominal spending increases when the interest rate rises. To understand why, consider that the interest rate on excess reserves reduces the demand for currency. Since the supply of currency doesn’t change, individuals increase spending to alleviate attempt to alleviate this excess supply. However, the excess supply is alleviated only once prices have risen such that real currency balances are back in equilibrium. It is important to note that this increase in velocity results only because individuals are pushed off of their demand curve (i.e. the individual is temporarily off of their currency demand curve). This disequilibrium is a characteristic of most supply and demand analyses. The supply and demand for reserves, however, is given by a cross. There is never a point of disequilibrium. As a result, the velocity of reserves is unchanged.

Note here that this result comes entirely from adopting New Keynesian-type assumptions in a static model. There is no role for expectations and I haven’t done any fancy tricks with difference equations.

So is the New Keynesian model wrong and, if so, where does it go wrong? My own view is that the New Keynesian model is likely incorrect. And the New Keynesian model is likely incorrect for two reasons. First, the New Keynesians have no theory of the money supply process. In other words, how do changes in the interest rate paid on reserves affect the supply of broader measures of the money supply? The New Keynesian view seems to be that since the change in the rate doesn’t affect bank reserves, then it doesn’t affect the money supply, more generally. I think this needs to be fleshed out in a formal model rather than in a static partial equilibrium graph of the market for reserves.

Second, the typical New Keynesian liquidity preference view of money demand is wrong (this is by the way, the New Keynesian view, you can find it in Gali’s book on the NK model). The money demand equation should be a function of the price of money, not “the” nominal interest rate (see my recent post on the price of money here). This is important because the implications of paying a higher rate of interest on reserves for the opportunity cost of holding broad measures of money is not obvious.

Taking these points slightly more seriously, we could re-write the equation of exchange as

where is the money multiplier, is the price of money, and is the monetary base. A model of broad money demand would imply that a higher interest rate on reserves would increase the opportunity cost of holding currency and reduce the opportunity cost of holding deposits. The former would increase whereas the latter would reduce . Thus, the effect on inflation would depend on the relative magnitude of this effect. If the effects were of equal magnitude in absolute value, then the inflation rate wouldn’t change. This is precisely the outcome shown in Peter Ireland’s model of interest on reserves which appends the standard NK model to have a role for broad money:

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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:

and a New Keynesian Phillips Curve:

where is the output gap, is inflation, is the nominal interest rate, is the natural real rate of interest, is the expectations operator, and and 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 . In a rational expectations equilibrium, it will be true that . Using this result, we can now combine the two equations to get an equilibrium inflation rate. Doing so yields,

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 .

But the New Keynesian model *doesn’t assume a departure from rational expectations*. Thus, our result that 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 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.

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- Existing macroeconomic models failed to give warning about the financial crisis.
- The models failed to give us policy guidance.
- There is too much emphasis on representative agents.
- Macroeconomists did not think questions about financial markets were worth asking.
- During the Great Moderation, economists didn’t spend enough time thinking about why things were going well.
- 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.

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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

where is the user cost of asset i at time t, is some benchmark rate of return, and 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.

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

The optimal allocation is therefore given as

where is the marginal utility of and correspondingly for .

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

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 to good remains unchanged and doesn’t have any effect on the allocation of goods. Additionally, so long as 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 is sticky and the price of 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 such that the budget constraint can be re-written as

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

So how do we construct ? 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:

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

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:

Suppose the price index is given as , then this can be re-written as

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

Substituting this into the budget constraint yields

Thus, when 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, was a sticky price and was a flexible price, targeting would be insufficient. Doing so would prevent money income from affecting utility, but it would not prevent an adjustment in the relative prices of and 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.

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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 . They assume that this constraint is binding such that young agents always borrow an amount, . The key equation in their framework is the equilibrium condition in the savings market, given by

where is the real interest rate, is the discount rate, is the rate of population growth, and 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 permanently declines (i.e. young agents find it harder to borrow). In this case, the real interest falls in period and falls again in period . 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

which is a contradiction since we've assumed that .

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.

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