# Category Archives: Macroeconomic Theory

## How Much Capital?

Recently, it has become very popular to argue that the best means of financial reform is to require banks to hold more capital. Put differently, banks should finance using more equity relative to debt. This idea is certainly not without merit. In a Modigliani-Miller world, banks should be indifferent between debt and equity. I would like to take a step back from the policy response and ask why banks overwhelmingly finance their activities with debt. It is my hope that the answer to this question will provide some way to focus the debate.

It is clear that when banks finance primarily using equity, adverse shocks to the asset side of a bank’s balance sheet primarily affect shareholders. This seems at least to be socially desirable if not privately desirable. The imposition of capital requirements would therefore seem to imply that there is some market failure (i.e. the private benefit from holding more capital is less than the social benefit). Even if this is true, however, one needs to consider what makes it so.

One hypothesis for why banks hold too little capital is because they don’t internalize the total cost of a bank failure. For example, banks are limited liability corporations and covered by federal deposit insurance. Thus, if the bank takes on too much risk and becomes insolvent, shareholders lose their initial investment. Depositors are made whole through deposit insurance. It is this latter characteristic that is key. If bank shareholders were responsible not only for their initial level of investment, but also for the losses to depositors, banks would have different incentives. In fact, this was the case under the U.S. system of double liability that lasted from just after the Civil War until the Banking Act of 1933. (I have written about this previous here.) Under that system bank shareholders had a stronger incentive to finance using equity. In fact, evidence shows that banks with double liability took on less leverage and less risk than their limited liability counterparts.

Along similar lines the existence of Too Big Too Fail similarly creates greater incentives toward risk-taking and leverage because in the event that the bank becomes insolvent, it will be rescued by the government. Finally, the U.S. tax system treats debt finance more favorable than equity finance.

Of course, a first-best policy solution to these incentive problems would be to eliminate deposit insurance, Too Big to Fail, and the favorable tax treatment of debt finance. However, such reform is either politically infeasible or, in the case of eliminating Too Big to Fail, relies on a strong commitment mechanism by the government. Thus, a second-best policy prescription is to impose higher capital requirements.

This second-best policy solution, however, is contingent upon the characteristics above being the only source of the socially inefficient level of capital. I would argue that even in the absence of these characteristics banks might still be biased toward debt finance and that imposing capital requirements could actually result in a loss in efficiency along a different dimension of welfare.

The reason that capital requirements could be welfare-reducing has to do with the unique nature of bank liabilities. Banks issue debt in the form of deposits (and, historically, bank notes), which circulate as a medium of exchange. Thus, bank debt serves a social purpose over and above the private purpose of debt finance. This social function is important. In a world that consists entirely of base money, for example, individuals will economize on money balances because money does not earn a pecuniary yield. As a result, the equilibrium quantity of consumption and production will not equal the socially optimum quantity. Bank money, or inside money, has the potential to be welfare improving. In fact, the main result of Cavalcanti and Wallace was that feasible allocations with outside (or base) money are a strict subset of those with inside money. Imposing strict capital requirements would reduce the set of feasible allocations and thereby reduce welfare along this dimension.

Now some might be quick to dismiss this particular welfare criteria. After all, greater stability of the financial system would seem to be more important than whether the equilibrium quantity of production is the socially optimum quantity. However, this ignores the potential interaction between the two. Caballero, for example, has argued that there is a shortage of safe assets. This claim is consistent with what I argued above. If the supply of media of exchange is not sufficient to allow for the socially optimum quantity of output then there is a transaction asset shortage. As a result, there is a strong incentive for banks to create more transaction assets. This can explain while interest rates were low in early part of the decade and can similarly explain the expansion in the use of highly-rated tranches of MBS in repurchase agreements prior to the financial crisis.

In other words, the shortage of transaction assets described above creates an incentive for banks to create new such assets in the form of new debt finance. Thus, it is possible that banks have a bias toward debt finance that would exist even independent of Too Big To Fail, deposit insurance, limited liability, and the tax system. In addition, one could argue that the desire to create such transaction assets played an important role in the subsequent financial crisis as some of the assets that were previously considered safe become information-sensitive and thereby less useful in this role.

To the extent that one believes that the transaction asset shortage is significant, policymakers face a difficult decision with respect to capital requirements. While imposing stronger capital requirements might lead to greater financial stability by imposing greater losses on shareholders, this requirement can also exacerbate the shortage of transaction assets. Banks and other financial institutions will then have a strong incentive to attempt to mitigate this shortage and will likely try to do so through off-balance sheet activities.

This is not meant to be a critique of capital requirements in general. However, in my view, it is not obvious that they are sufficient to produce the desired result. One must be mindful of the role that banks play in the creation of transaction assets. It would be nice to have an explicit framework in which to examine these issues more carefully. In the meantime, hopefully this provides some food for thought.

P.S. Miles Kimball has suggested to me that capital requirements coupled with a sovereign wealth fund could assist in financial stability and fill the gap in transaction assets. I am still thinking this over. I hope to have some thoughts on this soon.

## Let’s Talk About Interest on Reserves

Recently, there has been a great deal of discussion about paying interest on excess reserves and the corresponding implications for money and monetary policy. While much of this discussion has been interesting, it might be useful to consider the impact of the influence of paying interest on reserves in the context of an explicit macroeconomic model so that we might better understand the dynamics of the effects of such a policy. In addition, a model allows us to be explicit about the assumptions that we are making and also to keep are logic consistent. Fortunately, we do not need to start from scratch on this topic as Peter Ireland has written an excellent paper entitled, “The Macroeconomic Effects of Interest on Reserves.”

Before we discuss the impact of paying interest on reserves, it might be beneficial to talk about how this impacts the market for reserves using a straightforward supply and demand analysis, as Ireland does. Consider a simple supply and demand graph with the interest rate on the vertical axis and the quantity of reserves on the horizontal axis. Typically, in the market for reserves, the demand for reserves is a standard downward sloping demand curve. This is because a higher federal funds rate means that there is a higher opportunity cost of holding reserves rather than lending them to banks. If the Federal Reserve sets a target for the federal funds rate, the supply curve is horizontal at that interest rate. Where the supply curve intersects the demand curve is where one gets the unique quantity of reserves necessary to clear the market. One can therefore think of the Fed as providing the quantity of reserves necessary to maintain its interest rate target.

Now let’s suppose that the Fed starts paying interest on reserves. In this case, the supply curve remains the same (horizontal at the federal funds rate), but the demand curve changes. In particular, with demand curve for reserves is now downward-sloping for all rates above the interest rate on reserves. At the interest rate on reserves, the demand curve is horizontal. Why? Suppose that the federal funds rate is above the interest rate on reserves. In this case, an increase in the federal funds rate, holding the interest rate on reserves constant, causes a reduction in the demand for reserves. In other words, when the federal funds rate is above the interest rate on reserves, the opportunity cost of holding reserves is now the spread between the federal funds rate and the interest rate paid on reserves.

So why do people think that money doesn’t matter in this context? They think that money doesn’t matter because when the federal funds rate target is equal to the interest rate on reserves, the supply curve is horizontal at the same interest rate at which the demand curve is horizontal. This implies that there is a continuum of values for reserves that can be an equilibrium.

Unfortunately, this is where most of the debate stops in the blogosphere. Those who think that money is irrelevant point to this latter result and conclude that any quantity of base money is consistent with equilibrium and therefore the actual quantity doesn’t matter. However, as Ireland notes, this leaves many questions unanswered:

[The preceding analysis ignores] the effects that changes in output, including those brought about in the short run by monetary policy actions themselves, may have on the demand for reserves. And to the extent that changes in the interest rate paid on reserves get passed along to consumers through changes in retail deposit rates, and to the extent that those changes in deposit rates then set off portfolio rebalancing by households, additional effects that feed back into banks’ demand for reserves get ignored as well. One cannot tell from these graphs whether changes in the federal funds rate, holding the interest rate on reserves fixed either at zero or some positive rate, have different effects on output and inflation than changes in the federal funds rate that occur when the interest rate on reserves is moved in lockstep to maintain a constant spread between the two; if that spread between the federal funds rate and the interest rate on reserves acts as a tax on banking activity, those differences may be important too.

The point of developing a corresponding macroeconomic model is to fundamentally assess whether or not these hypothesized effects are of any significance. To do so, Ireland extends a New Keynesian model to have a banking system and a shopping time specification to motivate the use of a medium of exchange. Since this is a large scale model and this is a blog post, I will spare further details of the model and refer interested readers to the paper. However, I would like to discuss what Ireland finds as it relates to the discussion among econobloggers (there are more results that are of interest as well).

First, and perhaps most importantly for the blogosphere discussion, Ireland’s model demonstrates that even if they pay interest on reserves, the Fed still has to use open market operations to adjust the supply of bank reserves in order to change the price level. In other words, not only does the monetary base remain important, it is still necessary to pin down the price level. Second, there are important implications for how the Fed conducts open market operations. Specifically, in a world without interest on reserves, when the Fed raises its target for the federal funds rate it correspondingly reduces the supply of reserves. However, in Ireland’s model, the impulse response function for reserves following a change in monetary policy is just the opposite. In his model the central bank would have to increase bank reserves in response to a tightening of monetary policy as a result of an increase in the demand for reserves from banks, which in turn are caused by the portfolio reallocations of households. This is because a contractionary monetary policy causes a reduction in the user cost of deposits, which raises the demand for deposits and thereby the demand for reserves.

As noted above, there are other results of interest and I would encourage anyone who wants to have a serious discussion about interest on reserves to read the paper in its entirety. Nevertheless, just to summarize, the importance of Ireland’s paper is to present an explicit macroeconomic model that allows us to talk about the short-run and long-run behavior of the monetary base when the Fed pays interest on reserves. The implications of his model is that the monetary base is important in both the long- and short-run. In the short run, the Fed has to adjust the supply of bank reserves in accordance with their desired interest rate target. This response differs depending on whether interest is paid on reserves, but in either case, this behavior is necessary. In addition, and most importantly, the nominal stock of reserves is essential for influencing the price level in the long run. In other words, the monetary base is not irrelevant.

## Monetary Theory and the Platinum Coin

Yesterday I argued that the platinum coin is a bad idea. In doing so I received a substantial amount of pushback. Some have argued that while the platinum coin might be a dumb idea, it is preferable to being held hostage by recalcitrant Republicans. Others argued that my claims about the potential inflationary effect of the platinum coin were overblown. With regards to the first claim, I have very little to add other than the fact that I don’t subscribe to the “two wrongs make a right” theory of public policy. The second claim, however, is more substantive. It is also something about which economic theory has something to say.

In many contemporary models, money is either excluded completely or is introduced using a reduced form approach, such as including real money balances in the utility function. These models are ill-equipped to tackle the effects of the introduction of the platinum coin because they either assume that money always has value (it generates utility) or that it has no value whatsoever. An analysis of the effects of the platinum coin should be backed by an understanding of what gives money value in a world of fiat money and the conditions necessary to insure a unique equilibrium in which money has value. In doing so, one can show that having the Fed conduct open market sales to offset the increase in the monetary base from the minting of the platinum coin (i.e. holding the money supply constant) might not be sufficient to prevent a significant inflation.

To illustrate the properties of money, I am going to employ the monetary search model of Lagos and Wright. (If you’re allergic to math, scroll down a bit.) The reason that I am employing this approach is because it is built on first principles, its explicit about the conditions under which a monetary equilibrium exists, and can be used to derive a dynamic equilibrium condition that can shed light on the value of money.

The basic setup is as follows. Time is discrete and continues forever. There are two types of agents, buyers and sellers. Each time period is divided into two subperiods. In the first subperiod, buyers and sellers are matched pairwise and anonymously to trade (we will call this the decentralized market, or DM). In the second subperiod, buyers and sellers all meet in a centralized (Walrasian) market (we will call this the centralized market, or CM). What makes buyers and sellers different are their preferences. Buyers want to purchase goods in the DM, but cannot produce in that subperiod. Sellers want to purchase goods in the CM, but cannot produce in that subperiod. Thus, there is a basic absence of double-coincidence of wants problem. The anonymity of buyers and sellers in the DM means that money is essential for trade. Given this basic setup, we can examine the conditions under which money has value and this will allow us to discuss the implications of the platinum coin. (Note that we can confine our analysis to buyers since sellers will never carry money into the DM since they never consume in the DM.)

$E_0 \sum_{t = 0}^{\infty} \beta^t [u(q_t) - x_t]$

where $\beta$ is the discount factor, $q$ is the quantity of goods purchased in the DM, and $x$ is the quantity of goods produced by the buyer in the CM. Consumption of the DM good provides utility to the buyer and production of the CM good generates disutility of production. Here, the utility function satisfies $u'>0 ; u''<0$.

The evolution of money balances for the buyer is given by:

$\phi_t m' = \phi_t m + x_t$

where $\phi$ denotes the price of money in terms of goods, $m$ denotes money balances, and the apostrophe denotes an end of period value. Now let's denote the value function for buyers in the DM as $V_t(m)$ and the value function for buyers entering the CM as $W_t(m)$.

Thus, entering the CM, the buyer's value function satisfies:

$W_t(m) = \max_{x,m'} [-x_t + \beta V_{t + 1}(m')]$

Using the evolution of money balances equation, we can re-write this as

$W_t(m) = \phi_t m + \max_{m'} [-\phi_t m' + \beta V_{t + 1}(m')]$

In the DM, buyers and sellers are matched pairwise. Once matched, the buyers offer money in exchange for goods. For simplicity, we assume that buyers make take-it-or-leave-it offers to sellers such that $\phi_t d = c(q_t)$ where $d \in [0,m]$ represents the quantity of money balances offered for trade and $c(q_t)$ represents the disutility generated by sellers from producing the DM good. The value function for buyers in the DM is given as

$V_t(m) = u(q_t) + W_t(m - d)$

Using the linearity of $W$ and the conditions of the buyers' offer, this can be re-written as:

$V_t(m) = u(q_t) - c(q_t) + \phi_t m$

Iterating this expression forward and substituting into $W$, we can then write the buyer's problem as:

$max_{m} \bigg[-\bigg({{\phi_t/\phi_{t + 1}}\over{\beta}} - 1\bigg)\phi_{t + 1} m + u(q_{t+1}) - c(q_{t+1}) \bigg]$

[If you're trying to skip the math, pick things up here.]

From this last expression, we can now place conditions on whether anyone will actually hold fiat money. It follows from the maximization problem above that the necessary condition for a monetary equilibrium is that $\phi_t \geq \beta \phi_{t + 1}$. Intuitively, this means that the value of holding fiat money today is greater than or equal to the discounted value of holding money tomorrow. If this condition is violated, everyone would be better off holding their money until tomorrow indefinitely. No monetary equilibrium could exist.

Thus, let's suppose that this condition is satisfied. If so, this also means that money is costly to hold (i.e. there is an opportunity cost of holding money). As a result, buyers will only hold an amount of money necessary to finance consumption (in mathematical terms, this means $d = m$). This means that the buyers' offer can now be written $\phi_t m = c(q_t)$. This gives us the necessary envelope conditions to solve the maximization problem above. Doing so, yields our equilibrium difference equation that will allow us to talk about the effects of the platinum coin. The difference equation is given as

$\phi_t = \beta \phi_{t + 1}\bigg[ \bigg(u'(q_{t + 1})/c'(q_{t + 1}) - 1 \bigg) + 1 \bigg]$

Since money is neutral in our framework, we can assume that there is a steady state solution such that $q_t = q \forall t$. Thus, the difference equation can be written:

$\phi_t = \beta \phi_{t + 1}\bigg[ \bigg(u'(q)/c'(q) - 1 \bigg) + 1 \bigg]$

This difference equation now governs the dynamics of the price of money. We can now use this assess claims that the platinum coin would not have any inflationary effect.

Suppose that $u$ and $c$ have standard functional forms. Specifically, assume that $u(q) = {{q^{1 - \gamma}}\over{1 - \gamma}}$ and $c(q) = q$. [I should note that the conclusions here are robust to more general functional forms as well.] If this is the case, then the difference equation is a convex function up to a certain point at which the difference equation becomes linear. The convex portion is what is important for our purposes. The fact that the difference equation is convex implies that the difference equation intersects the 45-degree line used to plot the steady-state equilibrium in two different places. This means that there are multiple equilibria. One equilibrium, which we will call $\phi_{ss}$ is the equilibrium that is assumed to be the case by advocates of the platinum coin. They assume that if we begin in this equilibrium, the Federal Reserve can simply hold the money supply constant through open market operations and in so doing prevent the price of money (i.e. the inverse of the price level) from fluctuating.

However, what this suggestion ignores is that the difference equation also intersects the 45-degree line at the origin. Coupled with the range of convexity of the difference equation, this implies that there are multiple equilibria that converge to an equilibrium in which money does not have value (i.e. $\phi = 0$). Put in economic terms, there are multiple equilibria that are decreasing in $\phi$, which means that they increasing in the price level. It is therefore possible to have inflation even with a constant money supply. The beliefs of economic agents are self-fulfilling.

In terms of the platinum coin, this implies that the explicit monetization of the debt by minting the platinum coin can potentially have disastrous effects even if the president states that the infusion is temporary and even if the Federal Reserve conducts open market operations to offset the increase in the monetary base caused by the deposit of the coin by the Treasury. In short, if the debt monetization were to have a significant impact on inflation expectations, it is possible that the United States could experience significant inflation even if the Federal Reserve tried to hold the money supply constant. The very idea that this represents a possible outcome should render the platinum coin to be a bad idea.

## The Debt Ceiling, Platinum Coins, and Other Nonsense

In the coming months, it is very likely that the president and Congressional Republicans will once again go to battle over the debt ceiling. Like many others, I am already lamenting the idea of more “negotiations” between the president and Congress. However, unlike others I see this as a problem with the debt ceiling itself, not the Congressional Republicans. So long as it is within their power to use the debt ceiling as a bargaining chip, they should be free to do so if they wish. (They should recognize, of course, that this is not as strong a bargaining chip as they realize, however. A refusal to raise the debt ceiling without spending concessions from the president is simply a game of chicken. Anti-coordination games are unlikely to be the best strategy for achieving one’s objective.)

Nonetheless, a growing subset of individuals who believe that the Congressional Republicans are recalcitrant have suggested that the president authorize the Treasury department to mint a $1 trillion platinum coin (because this is within constitutional authority) and deposit it with the Federal Reserve to enable the payment of the federal government debt. The argument is that in doing so the president can circumvent the debt ceiling within constitutional limits. In addition, advocates argue that, since the coin will never circulate, the minting of the coin will not be inflationary. If this idea sounds ludicrous, that is because it is. Minting a platinum coin sufficient to pay off the deficit is what is traditionally known as monetizing the debt. To put it bluntly, large-scale debt monetization is bad. This is traditionally how hyperinflations start. Nonetheless, we are told that we needn’t be concerned because the coin won’t circulate. This would seem to ignore two factors: (1) the point of the coin is to pay for the debt, and (2) money is fungible. Thus, if the Treasury minted a$1 trillion platinum coin and deposited it at the Federal Reserve, the entire point of doing so would be to allow the Federal Reserve to make payments on behalf of the Treasury for government spending that exceeds tax revenue. Even if the coin itself doesn’t circulate (how could it?), the money supply can still increase substantially as the Treasury writes checks out of its account at the Federal Reserve.

Advocates, however, dismiss this possibility. Josh Barro, for example, argues:

[Inflation] is a more serious objection, and it gets at what the platinum coin strategy really is — financing the federal government’s operations by printing money instead of borrowing it. The trillion- dollar coin will never circulate, but it will be used to back cash payments coming from the Treasury that would have otherwise been financed by bond purchases.

If the government financed itself this way in general, that would absolutely be inflationary. But the president can hold inflation expectations steady by making absolutely clear that the policy will not lead to a net change in the money supply over the long term. Obama should pledge that once Congress authorizes additional borrowing, he will direct the Treasury to issue bonds to cover the government’s coin-backed spending and then to melt the coin.

I similarly believe that expectations are important. However, Barro seems to fall into the growing category of folks who think that expectations are all that matters and that policymakers can perfectly affect expectations. An announcement from the president that the increase in the money supply isn’t permanent does not guarantee that the minting of the coin is seen as such. In order to believe that the money supply would not increase, we would not only have to believe that the Treasury would commit to borrowing money in the future once the debt ceiling was lifted, but also that the Treasury would borrow enough money to finance the previously financed cash payments necessary to enable them to withdraw the 1 trillion coin. In other words, we would have to believe that the Treasury could perfectly commit itself to actions it would prefer not to take. Or we would have to assume that the Federal Reserve would conduct large scale asset sales to prevent increases in the money supply. Put differently, in the midst of conducting large scale asset purchases, the Fed must commit to large scale asset sales to prevent the money supply from growing by more than they wish as a result of the minting of the coin. The policy would not only tie the hands of monetary policymakers, but forcing the Federal Reserve to conduct such policy is a threat to its independence. And if inflation expectations became unanchored, this could exasperate the effects of the increased money supply and the coin could be particularly harmful. Advocates think that it gives the president an upper hand in debt ceiling negotiations. However, all it does is increase the stakes of the chicken game. The platinum coin is a bad idea. ## On Fiscal Policy In recent weeks, there seems to have been a resurgence in the discussion of the relative effectiveness of counter-cyclical fiscal policy. This discussion is clouded by the fact that there are some whose political ideology seems to get in the way of reasonable discussion of evidence (and who believe that only those who disagree with them are biased!). In this post I would like to make the following points: (1) there is no such thing as “the” fiscal multiplier, (2) empirical and theoretical estimates are highly sensitive to assumptions about monetary policy — assumptions that seem to be violated by the behavior of central banks, and (3) New Keynesian models are flawed models for estimating a fiscal multiplier (especially in the context of log-linearized equations). The most fundamental point surrounding the discussion of the fiscal multiplier is that there is, in fact, no such thing as “the” fiscal multiplier. Put differently, the fiscal multiplier is not a structural parameter that can be identified through careful theoretical or empirical work. To the extent that it is possible for a fiscal multiplier to exist, such a multiplier is likely to be dependent on a number of other factors such as the monetary regime and the composition of spending, to name two. This point is important as it pertains to interpretations of empirical work designed to measure the magnitude of response of a change in fiscal policy. For example, in order to empirically estimate the magnitude of the effect of fiscal policy on output, one needs to find some sort of exogenous change in government purchases to avoid problems of endogeneity in estimation. To avoid the problem of endogeneity, many researchers have used military purchases since military build-ups in the face of war can be considered exogenous (i.e. the government isn’t building tanks to increase GDP, but to fight a war). These types of studies provide estimates of a multiplier effect of military purchases on real output. However, it is important to note that these estimates do not necessarily provide an estimate of a fiscal multiplier that corresponds with all forms of government spending. The composition of spending matters. This point is particularly important when we consider the differences between the these estimates and the likely effects of the American Recovery and Reinvestment Act (ARRA), or as it is commonly referred as “the stimulus package.” The ARRA is not made up of a significant chunk of military spending. In fact, a significant portion of the ARRA consists of transfer payments. Even in the Keynesian income-expenditure model that is unfortunately still taught to undergraduates to understand macroeconomics, transfer payments have no effect on GDP. Thus, the multiplier effect of these provisions is zero. It follows that it would be incorrect to take an estimate of a fiscal multiplier from studies that use military spending as an explanatory variable and apply that multiplier to the total amount of spending. In addition, there is no obvious reason to apply this multiplier to the non-transfer payment fraction of the ARRA as it is not obvious that the marginal impact on real output from building a road, a bridge, or a school or buying a new fleet of government vehicles is equal to the marginal impact of military spending. Even if we ignore the issue of the composition of spending on estimates of the multiplier, it is necessary to consider the effects of fiscal policy in light of monetary policy. If monetary policy responds actively to changes in economic conditions, then a purportedly effective fiscal policy will cause monetary policy to be more contractionary that it would have been otherwise. Put differently, monetary policy will offset, either in whole or in part, the effects of fiscal policy. Recent theoretical and empirical work seems to appreciate this point, but argues that at the zero lower bound on nominal interest rates, monetary policy is ineffective and therefore fiscal policy can be effective. But how valid is this assumption? Central bankers certainly don’t believe that monetary policy is ineffective at the zero lower bound. If so, there would be no debate about quantitative easing because none would have taken place. In addition, this assumption requires that monetary policy work solely through the nominal interest rate (or the expected time path of the nominal interest rate). However, if this is the case, then monetary policy is always relatively ineffective because interest rates do not have strong marginal effects on variables like investment. Empirical work on monetary policy over the last 20 years seems to refute that ineffectiveness proposition. In fact, Ben Bernanke’s work on the credit channel is motivated by the very fact that the federal funds rate seems insufficient to understand transmission of monetary policy. Once we dispense with this notion of the ineffectiveness of monetary policy at the zero lower bound, we realize that empirical studies that estimate a fiscal multiplier by holding monetary policy constant are really estimating a strict upper bound. These empirical estimates, however, have been informed by the predominant framework for monetary policy and business cycle analysis, the New Keynesian model. In the NK model, monetary policy works solely through changes in the interest rate. As a result, at the zero lower bound, fiscal policy can be effective — quite effective in some cases. Nonetheless, there are reasons to doubt these estimates of the fiscal multiplier. First, if monetary policy works through alternative transmission mechanisms, then the assumption that we can hold monetary policy constant is flawed. Second, even if we believe that the zero lower bound is a legitimate constraint on policy there is reason to believe that the estimated marginal effect of fiscal policy in the NK model is flawed. The most compelling reason to doubt the multipliers that come from NK models, even imposing the constraint of the zero lower bound, is that these estimates are driven by the particular way in which these models are solved. For example, Gauti Eggertsson (and others) have pointed out that in the NK model at the zero lower bound, there is something called the paradox of toil. Intuitively, the paradox of toil refers to the characteristic in which the labor supply actually declines following a decrease in taxes. A paradox indeed! (Upon hearing this a commenter who shall remain nameless at a recent conference at the St. Louis Fed found it interesting that presumably it would be possible to increase government spending and fund the increase through higher taxes on labor income all while generating a multiplier effect.) This characteristic is part of a broader conceptualization of the world at the zero lower bound. In short, things look profoundly different than when the interest rate is positive. But is the world really that different at the zero lower bound? The answer turns out to be no. As Tony Braun and his co-authors have shown, the funny business that goes on at the zero lower bound (i.e. the conclusions that run counter to the conventional wisdom in the discipline) is a figment of the way in which NK models are solved. In particular, the standard way to solve models in the literature is to take a set of non-linear equations that summarize equilibrium and log-linearize around the steady state. One can then generate theoretical impulse response functions from the log-linearized solution to the model. The impact multiplier from the change in government spending in the NK model is therefore a theoretical estimate of the fiscal multiplier. However, it turns out that when the models are solved through non-linear methods the counter-intuitive results disappear and the theoretical estimates of the multiplier are substantially lower — again, even imposing the zero lower bound as a constraint. The general takeaway from all of this is that there is reason to be skeptical about the discussions and the purported precision of estimates of the fiscal multiplier — whether theoretical or empirical. (And that is to say nothing about the political constraints that go into devising the composition and allocation of spending!) However, what I have written does NOT necessarily imply that there is no role for fiscal policy during a recession. If some form of infrastructure investment by the government passes the cost-benefit test, I think that it is certainly reasonable to move such projects closer to the present because even in the absence of a multiplier effect these projects provide something of value to society. If there is an additional effect on output, then all the better. ## Quote of the Day “Unusual state’? Is that what we call it when our favorite models don’t deliver what we had hoped? I would call that our usual state.” ## Re-Focusing the Federal Reserve The Shadow Open Market Committee is scheduled to meet next week in New York City. In anticipation of the meeting, I would like to draw attention to SOMC member Peter Ireland’s position paper on Federal Reserve policy that he recently posted on his website. The paper is excellent and I would like to quote a few passages at length. Ireland’s paper begins by assessing the current policy “predicament” of the zero lower bound: With their federal funds rate target up against its lower bound of zero, Federal Reserve officials have been led — some would say forced — to experiment with a variety of new approaches to policymaking. Chairman Bernanke (2012) mentioned several of these novel strategies in his comments at Jackson Hole this past August; the minutes from the September meeting of the Federal Open Market Committee (2012) mention them again. They go by the names “maturity extension,” “forward guidance,” and “large-scale asset purchases.” To be honest, the whole situation seems really, really complicated. But does it have to be? Or might the apparent limitations of more conventional policy measures reflect, not so much the constraints imposed by the zero lower bound on nominal interest rates, but instead the inadequacies of common intellectual framework that places far too much emphasis on the behavior of interest rates to begin with? Might it be more helpful, in these circumstance, to refocus on other variables that have always played key roles, but have been neglected in popular discussions for far to long? Ireland’s paper does a great job of answering these questions. For example, changes in Federal Reserve policy are often communicated through changes in the federal funds rate in normal times. However, as Ireland points out, the fact that changes in the federal funds rate communicate policy changes does not mean that the federal funds rate is the only tool of monetary policy or the only variable capable of communicating the stance of policy. In fact, interest rates might provide incorrect interpretations about the stance of monetary policy. Ireland explains: Under ordinary circumstances, like those that prevailed in the halcyon days pre-2008, the Federal Reserve eased monetary policy by lowering its target for the federal funds rate and tightened monetary policy by raising its target for the federal funds rate. That is why most economists and financial market participants, even now, associate Federal Reserve policy most closely with changes in interest rates. But it is important to recall that even during normal times, the Fed does not control market rates of interest like the federal funds rate by fiat. Instead, Federal Reserve officials must act to bring about their desired outcomes, in which the actual federal funds rate moves in line with changes in their target. These monetary policy actions take the form of open market purchases and sales of US Treasury securities that change the dollar volume of reserves supplied to the banking system. That is, first and foremost, what a modern central bank does, as the one and only agent in the economy with the authority to change the supply of bank reserves. And so it is the dollar quantity of reserves supplied that the Fed really controls. [...] Thus, during normal times, interest rates and money offer two ways of looking at exactly the same thing. One can view a monetary policy easing as either a decline in short-term interest rates or as an expansionary open market operation that increases reserves and the money supply. And one can view a monetary policy tightening as either an increase in short-term interest rates or as a contractionary open market operation that decreases, or at least slows down the growth rates of, reserves and the money supply. Under more extreme circumstance, however, these tight links between interest rates and money may break down. An economy experiencing chronically high inflation, for instance, will very likely have high nominal interest as well, as these become necessary to compensate investors for the loss in purchasing power they would otherwise experience while holding nominally-denominated bonds. But those high interest rates certainly don’t signal that monetary policy is too tight! To the contrary, rapid growth in bank reserves and the broader monetary aggregates will correctly reveal that the inflation itself is being driven by an inappropriately expansionary monetary policy. At the opposite extreme, Milton Friedman and Anna Schwartz (1963) observe that when deflationary expectations take hold, as they did in the United States during the Great Depression, nominal interest rates can be very low. But these low interest rates do not mean that monetary policy is too loose. Instead, declining growth rates or even levels of reserves and, especially, the broader monetary aggregates will correctly indicate that monetary policy is much too tight. Those who keep these considerations in mind will then feel puzzled that new terms like “quantitative easing” are even needed to describe some of the Federal Reserve’s policy actions over the recent period when the funds rate has been stuck at zero. For those observers will be quick to remind us that in both normal and extreme times, all monetary policy easings are quantitative,” in that they are associated with — and, in fact, originate in — expansionary open market operations that increase reserves and the money supply. One reason that focus on the interest rate has become paramount is because of the logic of the New Keynesian model. According to the standard NK model, the interest rate is the sole mechanism available for monetary policymakers. When the nominal interest comes up against the zero lower bound, this model suggests that the main tool of monetary policy is in communicating the future time path of the nominal interest rate. Ireland, drawing on some of his own recent work, argues that this story is incomplete: Furthermore, while Federal Reserve statements providing forward guidance have mentioned only short-term interest rates, they can be read as having implications for open market operations and the supply of reserves in the future as well. In particular, although these details are typically relegated to the background in most New Keynesian analyses, my own recent work (Ireland 2012) extends the basic model to account for the activities of a private banking system that demands reserves, accepts deposits, and makes loans. This extended model highlights that even under New Keynesian assumptions, movements in the federal funds rate are associated with — some might even say caused by — open market operations that add or drain reserves from the banking system, give rise to subsequent movements in the broader monetary aggregates, and lead ultimately to changes in the price level and all other nominal variables. Viewed from this broader perspective, forward guidance regarding the future path of the funds rate also signals the Fed’s intentions for future open market operations and the future path for the money supply. Unlike maturity extension, therefore, forward guidance appears as a coherent part of a genuine monetary policy strategy. But while the logic behind forward guidance certainly seems strong, one might still worry that, when it comes to a policy initiative that relies exclusively on promises for the future, the devil is in the details. Even as it argues, most forcefully and persuasively, in support of stronger and sharper forward guidance, for instance, Michael Woodford’s (2012) own paper from the Jackson Hole symposium must concede that central banks around the world have had mixed success in using their words alone to influence expectations of future monetary policy actions. Reflecting on this, one might wonder, as well, if the New Keynesian view that the short-term interest rate is all that matters is excessively narrow. To cite just one alternative: a long traditional of monetarist thought, summarized by Allan Meltzer (1995), asserts that the channels through which monetary policy actions impact on the economy are far too varied and complex to summarize using a single variable like the short-term interest rate. Efforts to encapsulate these monetarist ideas into a modern macroeconomic model that might compete more directly with the New Keynesian framework has thus far yielded mixed results — here again, therefore, we have an important topic for future research! Yet, consistent with the monetarist view, Eric Leeper and Jennifer Roush (2003) and my own paper with Michael Belongia (Ireland and Belongia 2012c) show that even in the most recent data, strong statistical information about the stance of monetary policy appears in the monetary aggregates that is not in contained in interest rates alone. But, above all, one might ask: why try so hard to finesse things, by making ever more audacious promises about future open market operations, when it remains perfectly feasible, even with short-term interest rates stuck at zero, to conduct those same open market operations today, for all to see as well as to believe? In addition to the passages quoted above, the paper also addresses large-scale asset purchases, maturity extension through operation twist, and how the Federal Reserve can re-focus itself on nominal variables. I realize that I have quoted this paper at length, but I would encourage blog readers to read the paper in its entirety. ## We Are Not Entitled to Our Own Facts Contrarianism is running rampant. Go to a local bookstore and you will note countless “what you know just ain’t so”-type arguments. I am beginning to wonder if this type of trend downplays serious analysis and leaves us open to any argument regardless of whether it is blatantly incorrect. A case in point is a recent op-ed in the New York Times entitled, “Why Chavez Was Re-Elected.” The op-ed purports that Chavez was re-elected because his policies have been successful. According to the op-ed: Since the Chávez government got control over the national oil industry, poverty has been cut by half, and extreme poverty by 70 percent. College enrollment has more than doubled, millions of people have access to health care for the first time and the number of people eligible for public pensions has quadrupled. According to survey evidence by the World Bank, poverty has fallen in Venezuela. However, it is important to put this in context. The earliest data that we have available on poverty from the World Bank is from 2002 and according to the survey the poverty rate was around 60%. It has come down appreciably since. However, this statistic and the corresponding claims in the op-ed ignore what is driving these measured changes and the long-run implications thereof. Throughout Chavez’s tenure, he has seized thousands of businesses and imposed controls on foreign exchange as well as strict price controls. Any improvement in economic statistics in this type of regime is meaningless. The reason is because Venezuela is experiencing extractive growth. We know from economic theory and historical experience that extractive growth cannot last. (We need only look to the last 15 or so years of research by Daron Acemoglu and James Robinson to understand this conclusion.) The improvement in the statistics that the author highlights are merely the result of the fact that Chavez has seized control of the oil companies and uses revenues to finance social programs. Extractive growth, however, deters foreign direct investment and it reduces the incentives to innovate and re-invest in existing businesses. More broadly, higher risks of expropriation lead to lower income per capita. Meanwhile, according to Bloomberg, price controls have created shortages in “everything from electricity to sugar and beef.” The author, however, seems to believe that Chavez and others like him have discussed some alternative to “neoliberalism” to foster growth. This view is misplaced. Where so-called neo-liberalism has tried and purportedly failed is in countries that have insufficiently inclusive societal institutions. Yet the author seems to accept correlation as causation in these cases. If this is where the op-ed ended, I would conclude that the author’s assertions were misguided, but would be content to agree to disagree. However, the author’s claims only become more dubious as the op-ed proceeds. For example, he argues: Not surprisingly, the leftist leaders have seen Venezuela as part of a team that has brought more democracy, national sovereignty and economic and social progress to the region. Yes, democracy: even the much-maligned Venezuela is recognized by many scholars to be more democratic than it was in the pre-Chávez era. I’m not sure what I am to make of such a dubious statement. Chavez controls the voter rolls. There have been no external audits of the election. In addition, according to this piece in the Wall Street Journal, there are 10,000 voters who are registered between the ages of 111 and 129. Perhaps Chavez has also improved longevity! Markets and migration also tell a different story. Since 2000, approximately 120,000 Venezuelans have migrated to the United States. To put that in perspective, that represents a 125% increase in the number of Venezuelans in the United States. In addition, Chavez’s victory was met with a sharp decline in the price of Venezuelan bonds, which had previously rallied on the prospect of his defeat. Curiously, there was also no mention of lawlessness, violence, and kidnappings under the current regime. One Venezuelan criminologist says that there have been over 155,000 murders in Venezuela during Chavez’s tenure. Gangs rule the streets of Caracas and many crimes go unsolved. This is evident in news reports, but I also know this from talking to Venezuelans who have left. The op-ed seemingly seems impervious to facts as well: After recovering from a recession that began in 2009, the Venezuelan economy has been growing for two-and-a-half years now and inflation has fallen sharply while growth has accelerated. According to the World Bank, inflation has been very high. Over the last three years, consumer price have risen by 27.1%, 28.2%, and 26.1%, respectively. When measured by the GDP deflator, inflation has been even worse. Over the last five years, annual inflation by this metric has been 15.4%, 30.1%, 7.8%, 45.9%, 28.1%, respectively. And this is in the context of a regime of strict price controls and therefore there might be reason to believe that these number understate the actual inflation rate. To put this in perspective, Bloomberg reports that out of all of the countries that they track, only Iran and Belarus have higher rates of inflation than Venezuela. Venezuela is not prospering and Chavez has not discovered an alternative path toward economic growth and prosperity. The Chavez regime is an extractive regime. There are no incentives for long-run growth, inflation is high, lawlessness is rampant, and there are serious reasons to doubt the validity of the election process. This is the reality. And all of this is contrary to the recent New York Times op-ed. ## Observational Equivalence, Again Suppose that prior to the recession, I told you that I had a theory of the business cycle. My theory suggested that shocks to net worth were a significant explanation of the business cycle. Following a shock to net worth, consumption, investment, and hours worked would decline. Suppose that I also told you that increases in the monetary base by the Federal Reserve would keep inflation close to the implicit objective, but have little effect on consumption, investment, and real GDP. Given the events of the last four years, this theory seems to fit pretty well with what we have actually observed. What might surprise you, however, is that the framework I am describing is a real business cycle model with financial market frictions. This view seems largely consistent with James Bullard’s interpretation of events. Suppose instead that I told you that I had the following theory of the business cycle. My theory suggested that liquidity shocks were a significant explanation of the business cycle. Following a shock to liquidity, and without appropriate Federal Reserve policy, nominal and real GDP would decline and unemployment would rise. In addition, suppose that I told you that if the Federal Reserve increased the monetary base without an explicit target or goal that such an expansion would have little effect on real economic activity. Given the events of the last four years, this theory seems to fit pretty well with what we have actually observed. This view is largely consistent with Scott Sumner’s interpretation of events. I have used these two examples to illustrate a couple of points. First, neither Bullard nor Sumner (or anybody else associated with similar views) are crazy. They have logically consistent ideas that are consistent with casual observation. Second, confirmation bias is dangerous. It is very tempting to have a theory, look at the world, observe events consistent with your theory, and conclude that your theory is correct. But that is just confirmation bias. What is necessary is to provide evidence to support your theory in light of other theories that have observationally equivalent observations. This is substantially harder to do — even for those who realize it is necessary. Third, and perhaps most importantly, the ability to distinguish between these and other competing theories is incredibly important given the vastly different monetary policy implications. ## QE3 and the Optimality of Nominal GDP Targeting The Fed’s announcement last week that they intend to conduct open-ended open market purchases has been seen as a victory for advocates of nominal GDP level targeting, especially market monetarists. Scott Sumner has received praise from a number of publications for leading the charge (see here and here). Scott has long advocated nominal GDP level targeting and was criticizing tight monetary policy from the beginning of the recession. The shift toward open-ended open market purchases is therefore certainly a change in the direction of policy and one that is much more in line with a level target. Nonetheless, I don’t think that this is as much of a victory for level targeters as is being claimed. Thus, I would like to take this post to describe my differing view and also the recent discussion of optimal monetary policy. The intuition of a level target runs as follows. The purpose of the level target is to anchor long run expectations. Thus, suppose that the central bank announces that their objective is to target 5% trend growth in nominal GDP consistent with the trend from essentially 1983 – 2008. This policy announcement suggests that the central bank would like to create nominal GDP growth in the short term that is higher than 5% (since we have been below that trend since 2008), but once nominal GDP returns to trend, growth will return to 5%. So long as the central bank has a good degree of credibility in committing to these actions, this should help to anchor expectations. Thus, if nominal GDP is significantly below the long run trend, the policy suggested by this intuition is for the central bank to announce its intention to conduct open market purchases sufficient to achieve its target. In other words, the central bank announces a plan to conduct open-ended open market purchases (i.e. whatever it takes to hit its target). The recent Fed statement represents a stark change from previous policies specifically as it pertains to its efforts at quantitative easing. Specifically, rather than announcing particular dollar values of assets that they intends to purchase, the Fed has changed their statement to reflect their desire to “increase policy accommodation by purchasing additional agency mortgage-backed securities at a pace of40 billion per month.” That’s clearly open-ended. However, advocates of a nominal GDP level target and similar objectives should NOT see this a clear victory.

As the description of the intuition behind level targeting makes clear, the use of open-ended open market purchases should be coupled with an explicit objective for policy. There is no such objective in the Fed’s statement. The duration of policy is not defined in terms of objectives, but rather time:

To support continued progress toward maximum employment and price stability, the Committee expects that a highly accommodative stance of monetary policy will remain appropriate for a considerable time after the economic recovery strengthens. In particular, the Committee also decided today to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that exceptionally low level ofs for the federal funds rate are likely to be warranted at least through mid-2015.

The federal funds rate is not the objective of monetary policy, it is the intermediate target. In addition, and perhaps more importantly, we need the Fed to define what they mean by “after the economic recovery strengthens.”

The closest the FOMC statement comes to an objective is the following statement:

The Committee will closely monitor incoming information on economic and financial developments in coming months. If the outlook for the labor market does not improve substantially, the Committee will continue its purchases of agency mortgage-backed securities, undertake additional asset purchases, and employ its other policy tools as appropriate until such improvement is achieved in a context of price stability. In determining the size, pace, and composition of its asset purchases, the Committee will, as always, take appropriate account of the likely efficacy and costs of such purchases. [Emphasis added.]

This is hardly an explicit objective for policy. In addition, not only does the statement leave out an explicit objective, its one mention of a criteria for adjusting policy is a reference to the labor market. Does the Fed now believe that they can target employment? So some less skeptical of the Fed, this question might seem facetious. However, the Fed explicitly put in the statement that they will judge policy in accordance with fluctuations in the labor market. What is an acceptable amount of unemployment to the Fed? To what extent do they think that they can reduce unemployment?

Note here the important difference between the nominal GDP targeting example given above and the actual policy that is being implemented. The adoption of a nominal GDP level target would lead to higher nominal GDP growth in the short run which, given non-neutralities, would lead to a corresponding short run increase in real GDP thereby reducing unemployment. Thus, the objective of the policy would be to increase nominal GDP growth. The result of the policy (assuming that it is successful) would be to reduce unemployment. The actual policy of the Fed, however, seems to be to use unemployment as their objective. This is not the same thing.

This brings me to my final point. Throughout the discussion above, I was comparing the difference between actual Fed policy and a hypothetical nominal GDP target. This latter type of policy has become substantially more popular in the public conversation thanks to Scott Sumner. Its popularity in the economic literature has been somewhat lagging, but once had the support of Ben McCallum, Greg Mankiw, and others. More recently, Michael Woodford quasi-embraced nominal GDP targeting in his recent talk in Jackson Hole. However, Woodford also stated that he doesn’t see nominal GDP targeting as optimal policy. Rather, flexible inflation targeting in which the central bank targets inflation, but gives some weight to the output gap is optimal within the New Keynesian framework.

On this last point, Woodford is clearly correct — he wrote the book on optimal monetary policy in New Keynesian models, literally. Nominal GDP targeting can be consistent with optimal monetary policy in these models, but it depends on the particular characteristics of the model and the value of the parameters. Nonetheless, it is in the New Keynesian framework that nominal GDP targeting should find much of its support. Optimal monetary policy within these frameworks is defined as the policy that minimizes fluctuations in utility around the steady state. By performing a second-order Taylor series expansion of the utility function around the steady state and some mathematical manipulation, it can be shown that the optimal monetary policy is one that minimizes the weighted average of deviations of inflation from its target and output from its “natural” level. (This, by the way, is contrary to the assertions by Scott Sumner and George Selgin that the welfare criteria in these models is ad hoc.) Woodford is obviously correct that in this context that flexible inflation targeting is the optimal monetary policy. However, how should one use this criteria to practically guide monetary policy? I would argue that New Keynesians should advocate nominal GDP targeting because flexible inflation targeting places a large knowledge burden on central bankers as it requires that they know what natural (or potential) output is an any given point in time. In fact, we have very poor estimates of the output gap in real time — a point highlighted in work by Athanasios Orphanides.

Regardless of what policy is optimal, however, recent Fed policy is only a minor step in the direction of the desired policy of advocates of more expansionary monetary policy.