## More on Germany

Tony Yates has a new post speculating on Germany’s attitude toward fiscal policy. Tony’s assumption is that the German’s opposition to a deal with Greece is rooted in their beliefs about the macroeconomy. In particular, the New Keynesian consensus never really took hold in Germany and therefore they don’t tend to look favorably on stabilization policies. Some might view Tony’s post as a condemnation of Germany, but I don’t view it as such. If you’re a New Keynesian, you probably think this is a bad thing. If you’re not a New Keynesian, or if you’re otherwise opposed to stabilization policy, you probably think this is a good thing. But regardless of whether it is good or bad, this is a possible explanation. Nonetheless, I don’t find this explanation all that convincing.

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.

## Resolving the Glasner-Sumner Dispute

David Glasner and Scott Sumner are arguing about whether saving = investment is an identity or an equilibrium condition. So I thought I would step in and resolve this dispute. Instead of using textbook accounting identities, let’s consider a framework everyone is familiar with — a two-period consumption model.

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

$\sum S = \sum I + \sum P1 - \sum C1$

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

$\sum S = \sum I$

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.

## Germany, Greece, and Rent-Seeking

Greece is currently seeking a bailout from the European Union. However, negotiations (at least as I write this) are at a standstill. Greece wants a bailout, but the new Greek government has indicated that it is unwilling to enact so-called austerity reforms. During the negotiations, the European Central Bank has given emergency funding to the Greek financial system. However, this funding is conditional on the negotiations between Greece and the EU. The finance ministers of various EU countries want Greece to commit to reducing their debt in line with their 2012 commitments. Since Greece appears unwilling to meet those requirements, the support from the ECB is likely to stop by the end of the month. Thus, Greece could face a significant financial crisis if no deal is reached.

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, $R_i$, where $i=1$ will refer to Germany and $i=2$ will refer to Greece. Now let’s assume that each country can devote some amount of resources to production, $P_i$ and some amount of time to fighting with each other, $F_i$. It follows that each country has a resource constraint:

$R_i = P_i + F_i$

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

$Y = (P_1^{1/s} + P_2^{1/s})^s$

where $s \geq 1$ is a measure of complementarity in production. One way to think about $s$ 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

$\mu_1 = {{F_1^m}\over{F_1^m + F_2^m}}$

where $m$ is an index of the decisiveness of the conflict. Correspondingly, for Greece $\mu_2 = 1 - \mu_1$.

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

$Y_1 = \mu_1 Y$
$Y_2 = \mu_2 Y$

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

$\max\limits_{P_i, F_i} {{F_i^m}\over{F_i^m + F_j^m}} [(P_1^{1/s} + P_2^{1/s})^s]$
$\textrm{s.t.} \hspace{2mm} R_i = P_i + F_i$

In equilibrium, it follows that

${{F_2 P_2^{(1-s)/s}}\over{F_1^m}} = {{F_1 P_1^{(1-s)/s}}\over{F_2^m}}$

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 $s = 1$. In this case, total production is just the sum of German and Greek production. It follows from equilibrium that

$F_1 = F_2$

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 $m = 1$, then $F_1 = F_2 = 37.5$. 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 $s$ 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 $m$ 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.]

## More on Interest Rates and Inflation

In my previous post, I argued that New Keynesians do not understand monetary policy. The New Keynesian model predicts that if one pegs the interest rate, then increases in the interest rate cause increases in the rate of inflation. New Keynesians, however, argue that in order to stimulate economic activity and increase inflation, the central bank needs to reduce nominal interest rates. Thus, I argued that either their policy advice is wrong and their model is correct or their model is correct and their policy advice is wrong.

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

$m + v = p + y$

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:

$m - p = \alpha y - \beta i$

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 $\alpha = 1$. It is straightforward to show that we can solve this expression for the demand for money to get a theory of velocity:

$v = \beta i$

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

$m + \beta i = p + y$

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 $\beta i$. Then, returning to our equation of exchange we have:

$m + \beta i = p + y$

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

$mm(MB) + v(\phi) = p + y$

where $mm$ is the money multiplier, $\phi$ is the price of money, and $MB$ 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 $mm$ whereas the latter would reduce $v$. 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:

## 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.