A Theory of Tariffs as a Method of Promoting Long-Run Free Trade

Tariffs have been in the news lately. As is typically the case, economists have come to the rescue on social media and op-ed pages to defend the idea of free trade and to discuss the dubious claims that politicians make about protectionist policies. I have no quarrels with these ardent defenses of free trade (although I would note that claims about the supposed importance of New Trade Theory and New New Trade Theory and claims about the global optimality of free trade are potentially contradictory; perhaps economists don’t like NTT or NNTT as much as they claim, but I digress). Despite my general support of free trade, I also think we should take a step back and try to understand the motivations of politicians who embark on protectionist policies. In addition, I think that we should start with the basic premise that politicians are rational (in the sense that they have some objective they want to pursue and their actions are consistent with such a pursuit) and potentially strategic actors. In doing so, we might obtain a better understanding of why politicians behave the way that they do. Once upon a time, this type of analysis was referred to as public choice economics. What follows is a short attempt to do so.

Let’s start with the following basic assumptions:

1. We will refer to the country of analysis as the Home country and a trading partner as Country X.
2. Country X has imposed trade barriers on the Home country that are costly to a particular sector in the Home country.
3. Free trade is unequivocally good and is the long-run goal of all of the politicians in the Home country (I make no assumptions about the goals of Country X).

With these assumptions in mind, I would like to make the following claim:

Given that Country X is imposing a costly trade restriction on an industry in the Home country, the politicians in the Home country would like to reduce this trade restriction. They could try to negotiate the trade restriction away. However, if the Home country does not have trade restrictions of their own that they can reduce, they do not have much to offer Country X. As a result, the Home country might impose trade restrictions on Country X. By doing so, the Home country might be able to induce Country X to reduce their trade restrictions in exchange for the Home country getting rid of its new restriction.

So what is the basis of this claim? And why would politicians do this given the assumption that I made that free trade is unequivocally good and therefore all trade restrictions are bad?

Here is my answer. Without having trade restrictions on Country X, the Home country does not have anything to bring to the bargaining table to induce Country X to reduce trade restrictions (setting aside other geopolitical bargaining). So the Home country needs to create a bargaining chip, but the bargaining chip needs to be credible. For example, one way to create a bargaining chip would be to impose trade restrictions on Country X. However, for this to be a credible threat, these restrictions have to be sufficiently costly for the Home country. In other words, politicians in the Home country have to be willing to demonstrate that the trade restrictions imposed by Country X are so costly to the Home country that the politicians are willing to punish Country X even if their own constituents are harmed in the process. By demonstrating such a commitment, they now have a bargaining chip that they can use to negotiate away trade restrictions and end up with free(r) trade in the long run. At the same time, politicians in the Home country cannot broadcast their strategy to the world because this would undermine their objective. So the politicians will likely adopt typical protectionist rhetoric to justify their position.

The problem, of course, is that this is not a foolproof plan. Once the Home country imposes trade restrictions on Country X, this could turn into a war of attrition. If the Home country is not willing to commit to these trade restrictions indefinitely, then they might eventually unilaterally remove these restrictions without any benefit. Not only that, but by doing so, Country X might now see this as evidence that they can impose additional trade restrictions on the Home country without subsequent retaliation. So make no mistake. This sort of policy can be a gamble because it requires winning a war of attrition. However, some politicians might be willing to make that gamble in order to achieve the long run benefits.

The New Keynesian Failure

In a previous post, I defended neo-Fisherism. A couple of days ago I wrote a post in which I discussed the importance of monetary semantics. I would like to tie together two of my posts so that I can present a more comprehensive view of my own thinking regarding monetary policy and the New Keynesian model.

My post on neo-Fisherism was intended to provide support for John Cochrane who has argued that the neo-Fisher result is part of the New Keynesian model. Underlying this entire issue, however, is what determines the price level and inflation. In traditional macroeconomics, the quantity theory was always lurking in the background (if not the foreground). Under the quantity theory, the money supply determined the price level. Inflation was always and everywhere a monetary phenomenon.

The New Keynesian model dispenses with money altogether. The initial impulse for doing so was the work of Michael Woodford, who wrote a paper discussing how monetary policy would be conducted in a world without money. The paper (to my knowledge) was not initially an attempt to remove money completely from analysis, but rather to figure out a role for monetary policy once technology had developed to a point in which the monetary base was arbitrarily small. However, it seems that once people realized that it was possible to exclude money completely, this literature sort of took that ball and ran with it. The case for doing so was further bolstered by the fact that money already seemed to lack any empirical relevance.

Of course, there are a few fundamental problems with this literature. First, my own research shows that the empirical analysis that claims money is unimportant is actually the result of the fact that the Federal Reserve publishes monetary aggregates that are not consistent with index number theory, aggregation theory, or economic theory. When one uses Divisia monetary aggregates, the empirical evidence is consistent with standard monetary predictions. This is not unique to my paper. My colleague, Mike Belongia, found similar results when he re-examined empirical evidence using Divisia aggregates.

Second, while Woodford emphasizes in Interest and Prices that a central bank’s interest rate target could be determined by a channel system, in the United States the rate is still determined through open market operations (although now that the Fed is paying interest on reserves, it could conceivably use a channel system). This distinction might not seem to be important, but as I alluded to in my previous post, the federal funds rate is an intermediate target. How the central bank influences the intermediate target is important for the conduct of policy. If the model presumes that the mechanism is different from reality, this is potentially important.

Third, Ed Nelson has argued that the quantity theory is actually lurking in the background of the New Keynesian model and that New Keynesians don’t seem to realize it.

With all that being said, let’s circle back to neo-Fisherism. Suppose that a central bank announced that they were going to target a short term nominal interest rate of zero for seven years. How would they accomplish this?

A good quantity theorist would suggest that there are two ways that they would try to accomplish this. The first way would be to continue to use open market purchases to prevent the interest rate from ever rising. However, open market purchases would be inflationary. Since higher inflation expectations puts upward pressure on nominal interest rates, this sort of policy is unsustainable.

The second way to accomplish the goal of the zero interest rate is to set money growth such that the sum of expected inflation and the real interest rate is equal to zero. In other words, the only sustainable way to commit to an interest rate of zero over the long term is deflation (or low inflation if the real interest rate is negative).

The New Keynesians, however, think that the quantity theory is dead and that we can think about policy without money. And in the New Keynesian model, one can supposedly peg the short term nominal interest rate at zero for a short period of time. Not only is this possible, but it also should lead to an increase in inflation and economic activity. Interestingly, however, as my post on neo-Fisherism demonstrated, this isn’t what happens in their model. According to their model, setting the nominal interest rate at zero leads to a reduction in the rate of inflation. This is so because (1) the nominal interest rate satisfies the Fisher equation, and (2) people have rational expectations. (Michael Woodford has essentially admitted this, but now wants to relax the assumption of rational expectations.)

So why am I bringing all of this up again and why should we care?

Well, it seems that Federal Reserve Bank of St. Louis President Jim Bullard recently gave a talk in which he discussed two competing hypotheses. The first is that lower interest rates should cause higher inflation (the conventional view of New Keynesians and others). The second is that lower interest rates should result in lower inflation. As you can see if you look through his slides, he seems to suggest that the neo-Fisher view is correct since we have a lower interest rate and we have lower inflation.

In my view, however, he has drawn the wrong lesson because he has ignored a third hypothesis. The starting point of his analysis seems to be that the New Keynesian model is the useful framework for analysis and given that this is true, which argument about interest rates is correct, the modified Woodford argument? Or the neo-Fisherites?

However, a third hypothesis is that the New Keynesian model is not the correct model to use for analysis. In the quantity theory view, inflation declines when money growth declines. Thus, if you see lower interest rates, the only way that they are sustainable for long periods of time is if money growth (and therefore inflation) declines as well. Below is a graph of Divisia M4 growth from 2004 to the present. Note that the growth rate seems to have permanently declined.

Also, note the following scatterplot between a 1-month lag in money growth and inflation. If you were to fit a line, you would find that the relationship is positive and statistically significant.

So perhaps money isn’t so useless after all.

To get back to my point from a previous post, it seems that discussions of policy need to take seriously the following. First, the central bank needs to specify its target variable (i.e. a specific numerical value for a variable, such as inflation or nominal GDP). Second, the central bank needs to describe how it is going to adjust its instrument (the monetary base) to hit its target. Third, the central bank needs to specify the transmission mechanism through which this will work. In other words, what intermediate variables will tell the central bank whether or not it is likely to hit its target.

As it currently stands, the short term nominal interest rate is the Federal Reserve’s preferred intermediate variable. Nonetheless, the federal funds rate has been close to zero for six and a half years (!) and yet inflation has not behaved in the way that policy would predict. At what point do we begin to question using this as an intermediate variable?

The idea that low nominal interest rates are associated with low inflation and high nominal interest rates are associated with high inflation is the Fisher equation. Milton Friedman argued this long ago. The New Keynesian model assumes that the Fisher identity holds, but it has no mechanism to explain why. It’s just true in equilibrium and therefore has to happen. Thus, when the nominal interest rate rises and individuals have rational expectations, they just expect more inflation and it happens. Pardon me if I don’t think that sounds like the world we live in. New Keynesians also don’t seem to think that this sounds like the world we live in, but this is their model!

To me, the biggest problem with the New Keynesian model is the lack of any mechanism. Without understanding the mechanisms through which policy works, how can one begin to offer policy advice and determine the likelihood of success? At the very least one should take steps to ensure that the policy mechanisms they think exist are actually in the model.

But the sheer dominance of the New Keynesian model in policy circles also leads to false dichotomies. Jim Bullard is basically asking the question: does the world look like the New Keynesian model says or does it look like the New Keynesians say? Maybe the answer is that it doesn’t look like either alternative.

Interest on Reserves and the Federal Funds Rate

The payment of interest on reserves is supposed to put a floor beneath the federal funds rate. Since banks can lend to one another overnight at the federal funds rate, they have a choice. The bank can either lend excess reserves to another bank at the federal funds rate or they can hold the reserves at the Federal Reserve and collect the interest the Fed pays on reserves. In theory, this means that the federal funds rate should never go below the interest rate on reserves. The reason is simple. No bank should have the incentive to lend at a lower rate than they would receive by not lending.

However, the effective federal funds rate has been consistently below the interest rate on reserves. How can this be so? Marvin Goodfriend explains:

The interest on reserves floor for the federal funds rate failed, and continues to fail to this day, because non-depository institutions (such as government-sponsored enterprises (GSEs) Fannie Mae and Freddie Mac, and Federal Home Loan Banks (FHLBs)) are authorized to hold overnight balances at the Fed, but are not eligible to receive interest on those balances. Hence, the GSEs and FHLSs [sp] have an incentive to try to earn interest on their overnight balances at the Fed by lending them to depositories eligible to receive interest on their reserve balances. The federal funds rate is thereby driven below interest on reserves to the point that depositories are willing to borrow from the GSEs and the FHLBs, deposit the proceeds at the Fed, and earn the spread between interest on reserves and the federal funds rate.

More here.

Exchange Rate Volatility and Alternative Money: The Case of Bitcoin

David Andolfatto has written a very good post on Bitcoin and why it might have positive value. In particular, he provides an excellent overview of what Bitcoin actually is (an electronic record of transactions) and how this relates to the insight that “money is memory.” (On this point, see also, William Luther’s paper, “Bitcoin is Memory.”) Nevertheless, I have some questions about the post regarding David’s discussion of the volatility of Bitcoin and how this impacts the choice of what to use as money. In this post, I hope to address this point and perhaps add some additional substance to the issue.

David ends his post talking about whether Bitcoin would make for a good form of money. This is an interesting question and one that often isn’t given sufficient thought. In David’s own research, however, he has emphasized that the characteristic that determines whether an asset is useful as money is whether that asset is information-sensitive (this claim is often prevalent in Gary Gorton’s work as well). The basic idea is that if the value of an asset is sensitive in the short-run to news that has private value, but no social value, then short run fluctuations in the price of the asset will preclude its use as a medium of exchange. Thus, David suggests looking at how the value of Bitcoin has changed over time. In his graph, he plots the price of bitcoins in terms of dollars. As you can see if you read his post (or if you know anything about Bitcoin), the price of bitcoins relative to dollars is quite volatile — especially over the last year.

However, I wonder whether looking at the volatility of the exchange rate between Bitcoin and the dollar is the best way to determine whether Bitcoin would be a good form of money. There are two reasons why I say this.

First, as David points out, this volatility could be the result of the fact that people view the supply of Bitcoin as being fixed (the supply of Bitcoin will eventually be fixed), but the demand for Bitcoin is fluctuating. David notes that this is consistent with the type of behavior we observe under commodity standards. When there is a change in the demand for gold, the purchasing power of gold varies (at times considerably) even though the long run purchasing power is constant.

I have heard others make this argument as well and this seems very plausible. Nevertheless, it is useful to recall the way in which free banking systems operated. For example, in a free banking system in which banks issued notes that were backed by gold, the supply of bank notes fluctuated with demand. Increases in the demand for money caused an increase in the supply of notes. These changes in the supply of notes, however, needn’t imply any change in the purchasing power of gold. Issuing bank notes redeemable in gold was thereby capable of reducing the volatility of the purchasing power of gold. Similarly, a financial intermediary today could issue bank notes redeemable in bitcoins and reduce the volatility of the purchasing power of bitcoins.

[A quick note: It is perhaps true that the U.S. government might decide that they don’t want to allow financial intermediaries to issue bank notes, in which case my proposed solution to this source of volatility would not be operable. I would add though that it is not operable because of a legal restriction and not the volatility of the asset price.]

Second, and perhaps much more importantly, in models with competing money supplies the exchange rate does not factor in to the choice of allocation or welfare analysis. This is true even of David’s own research. For example, in quoting the price of bitcoins in terms of dollars, David is citing an exchange rate. However, in his research, the price volatility that matters for an asset is the own rate of return volatility. I think that this distinction matters.

To illustrate why I think that this distinction matters, let’s consider a simple overlapping generations model. There are two types of agents, young and old. Each lives for two periods. At any point in time, there is a generation of young and a generation of old. The population is assumed to be constant. There is one good to trade and it is non-storable. The young receive an endowment, y, of the consumption good. The old do not receive an endowment of goods. Thus, money is essential. There are two assets that can be used as a possible medium of exchange. The first is fiat currency. The second is bitcoins. The initial old carry both currency and bitcoins into the first period. The aggregate supply of bitcoins is fixed. The aggregate supply of currency, , is assumed to grow at the gross rate (i.e. ).

Let’s consider the first and second period budget constraints for future generations in our model (i.e. everybody except the initial old). In the first period, future generations can use their endowment for consumption or they can sell some of this endowment for money and/or bitcoins. Thus, the first-period budget constraint is:

where denotes the consumption when young in period t, is real currency balances, and denotes real balances of bitcoins.

Denote as the price of currency in terms of goods at time t. Similarly, denote the price of bitcoins in terms of goods as . Thus, the rate of return on currency is . Now let’s assume that there is some cost, that individuals have to pay when they use bitcoin to make a purchase. The rate of return on bitcoins is then given as . Thus, the second-period budget constraint can be written as

But we can derive a precise definition of the rate of return on money. It follows from our first period budget constraint that we have:

where denotes nominal currency balances. Define the total nominal currency stock as and the size of the population, which as assumed to be constant as . This implies an aggregate demand function for currency:

Thus, the rate of return on money is

From above, we know that the currency supply grows at a gross rate . This implies that in a stationary allocation (i.e. where consumption paths a constant across generations), the rate of return on currency is

By similar logic, it is straightforward to show that in a stationary allocation because the supply of bitcoins was assumed to be fixed.

Thus, our stationary allocation budget constraints are:

In the present model, money and bitcoins are perfect substitutes (i.e. there only purpose is to serve as proof of a previous transaction when trading with future young generations). Thus, the real rates of return on money and bitcoins must be equal for both to exist in equilibrium. In other words, it must be true that . We can re-write the second-period constraint as

Combining these budget constraints, we have a lifetime budget constraint:

Now let’s consider the basic implications of the model. First, the conditions under which both currency and bitcoins would be held in equilibrium is dependent on their relative rates of return. If these rates of return are equal, then both assets are held. This condition is independent of the exchange rate. Second, lifetime budget constraint outlines the feasible set of allocations available given the agents’ budget. Assume that utility is a function of consumption in both periods. The allocation decision in this case is dependent on the rate of return on currency, which is the same as the rate of return on bitcoins. The allocation decision is therefore contingent on the equilibrium rate of return. The exchange rate between currency and bitcoins plays no role in the allocation decision. In addition, one can show that this is the identical lifetime budget constraint that would exist in a currency economy (i.e. one in which Bitcoin doesn’t circulate). This last characteristic implies that neither the existence of bitcoins nor the exchange rate between bitcoins and currency have any effect on welfare.

So what does this mean? Basically what all of this means is that the exchange rate between currency and bitcoins is irrelevant to the decision to hold bitcoins, to the allocation decision, and to welfare. [Note: This isn’t new, Neil Wallace taught us this type of thing over 30 years ago.]

The analysis above is a bit unfair to David for two reasons. First, the framework above skirts David’s main point, which is that Bitcoin is information sensitive whereas currency is not. Second, David doesn’t necessarily mean that the exchange rate between the dollar and bitcoins is relevant for the type of analysis above. Rather, what he means is that since the dollar is relatively stable, the exchange rate serves as a proxy for the own price of bitcoins in terms of goods.

What I would like to do now is to amend the framework above to make bitcoins information sensitive. The results regarding the exchange rate of bitcoins into dollars remain. However, an interesting result emerges. In particular, one can show that it is the risk premium associated with bitcoins that can help us to understand the choice of whether to hold bitcoins or dollar-denominated currency as well as factor into the allocation decision. I will then speculate as to whether this risk premium is sufficient to explain the differences in rates of return between bitcoins and dollar-denominated currency.

For simplicity, let’s now denote the rate of return on bitcoins as . In addition, we will assume that is stochastic. In particular the assumption is that the rate of return is entirely determined by random news events. Thus, we can re-write our first- and second-period budget constraints, respectively, as

The objective of future generations is to maximize subject to the two constraints above. Combining the first-order conditions with respect to and and using the definition of covariance, we have the following equilibrium condition:

where the second term on the right-hand side measures the risk premium associated with bitcoins (note that this is in fact a risk premium since the covariance between the rate of return on bitcoins and the marginal utility of consumption is negative). If both assets are to be held in equilibrium, then the equibrium condition must hold. If the risk premium is too high, it is possible that nobody would hold bitcoins and they would only hold currency. This confirms David’s view that information sensitivity could affect the decision to hold bitcoins. However, this does not show up in the exchange rate, but rather in the relative rates of return. The risk premium similarly affect the allocation decision. Consider, for example, that the lifetime budget constraint can now be written as

where is used to simplify notation and denote the risk premium and the aggregate supply of bitcoins has been normalized to one. It is straightforward to see that when the risk premium is zero (i.e. bitcoins are not information sensitive) then the lifetime budget constraint is the same as that outlined above. The existence of a positive risk premium alters the budget set.

So what does all of this mean?

Essentially what it means is that looking at the exchange rate between bitcoins and the dollar is not a useful indicator about whether or not bitcoins would actually make for a good money. Even if we view the exchange rate between bitcoins and dollars as a useful proxy of the price of bitcoins in terms of goods, the exchange rate is not the correct measure for analysis. Rather, to evaluate whether bitcoins are a viable alternative/substitute for dollars, we need to know the relative rates of return on bitcoins and dollars and the risk premium associated with the fact that bitcoins are information sensitive.

This might all seem like semantics, after all, if we think the exchange rate is a good proxy of the price of bitcoins in terms of goods, then the rate of return could just be measured as the rate of change in the exchange rate. Nonetheless, this distinction seems especially important given the nature of the exchange rate between bitcoins and dollars. In particular, just looking at David’s graph of the exchange rate, it is plausible that the time series follows a random walk with a drift (I had trouble acquire actual data rather than ready-made graphs on this so if anybody has the data please send it along). This is important because if this is correct, the variance of the exchange rate is time-dependent. However, in terms of rates of change, the data would be stationary and therefore have some constant, finite variance. Thus, in this hypothetical example, looking at the exchange rate using David’s criteria about information sensitivity would indicate that bitcoin is a very bad money because the variance of the exchange rate is time dependent. In contrast, if the rate of return on bitcoin is stationary, then it is not immediately clear from the data whether or not bitcoin is a good money. This is why we need the model as it helps us to understand what properties the rate of return must possess to make a good money.

Monetarism, Debt, and Observational Equivalence

I have heard a number of people say over the years that one of the best things about reading Adam Smith and Henry Thornton and other classical economists is that they argued their points fairly. In particular, Smith and Thornton argued in favor of their own views and against opposing views while taking these opposing views at face value. They did not attack straw men. They did not caricature their intellectual adversaries (in fact, Thornton and Smith were intellectual adversaries to some extent in their views on the role of bank notes, bills of exchange, and the operation of the monetary system).

This characteristic is, at times, missing from contemporary discourse. This doesn’t mean that modern disagreements are fraught with malice. However, sometimes ideas are not given the proper understanding sufficient for critique. Franco Modigliani, for example, once joked that what we would now call real business cycle theory blamed recessions on mass outbreaks of laziness. Similarly, when Casey Mulligan published his most recent book on the recession in which he argued that expansions of the social safety net can explain a significant fraction of the increase in unemployment, others shrugged this off by saying that this was akin to saying that soup lines caused the Great Depression.

My point is not to defend Casey Mulligan or the real business cycle theorists. It is perfectly reasonable to view real business cycle theory as unconvincing without referencing mass outbreaks of laziness. Rather my point is that more care needs to be taken to understand opposing theories and views of business cycles, growth, etc. so that one can adequately articulate criticisms and rebuttals to such views.

The fact that there is little understanding of (or perhaps just little credit given to) opposing viewpoints is never more apparent than when predictions of two different theories are observationally equivalent. To give an example, consider two explanations of the cause of the most recent recession. Please note that these are not the only two explanations and that the explanations that I give are sufficiently broad to encapsulate a number of more nuanced views.

The first explanation of the recession is what I will refer to as the Debt Theory. According to this view, the expansion that preceded the recession was fueled by an unsustainable accumulation of debt. There are many varieties of this theory that emphasize different factors that caused the run-up of debt, such as monetary policy, policies that subsidize housing, etc. Regardless of the reason that “too much” debt was accumulated, the debt eventually reached a point (most often argued as the beginning of the collapse in housing prices) that was unsustainable and hence the beginning of a recession. The recession is largely the result of de-leveraging.

The second explanation is what I will refer to as the Money Theory. According to this view, it is a deviation between the supply and demand of money (broadly defined) that ultimately results in reduced spending and, as a result, a lower level of real economic activity. As a result, when the large haircuts became apparent in the market for mortgage-backed securities, this reduced the supply of transaction assets thereby causing a deviation between the supply and demand for money. The Federal Reserve, in its failure to provide a sufficient quantity of transactions assets, thereby allowed this deviation to persist and resulted in decline in nominal, and ultimately, real spending.

As these brief descriptions imply, there doesn’t appear to be much overlap between the two views. However, they actually produce a number of observationally equivalent implications. For example, advocates of the Money Theory point to the negative rates of money growth in broad measures of the money supply as evidence that the Federal Reserve failed to provide adequate liquidity. Nonetheless, this observation is consistent with the Debt Theory. According to this view, de-leveraging reduces the demand for credit and therefore reduces the need of financial intermediaries to create new debt instruments that are used as transaction assets. Thus, we would expect a decline in money growth in both cases.

On the other hand, advocates of the Debt Theory point out that there is a strong relationship between counties that had higher levels of debt prior to the recession and the reductions in consumption during the recession. Nonetheless, this observation is also consistent with the Money Theory. Most advocates of the Money Theory are intellectual descendants of Milton Friedman. In Friedman’s theory of money demand, money is considered similar to a durable good in that individuals hold a stock of money to get the flow of services that come from holding money. Thus, contra the transactions view of money demand, individuals do not draw down money balances during a recession. Instead individuals make adjustments to different parts of their portfolio, most notably consumer debt. In other words, we would observe de-leveraging under both frameworks.

To distinguish between the two views it is not sufficient to point to characteristics that they have in common (although those observations are still important). It is also necessary to find areas in which the theories differ so that one is able to develop an empirical approach to assess each framework’s validity.

The examples given above are obviously simplifications, but this is what makes being an economist difficult. It is not enough to use inductive reasoning to support one’s theory. One must be able to differentiate between other theories that would produce observationally equivalent results. Admittedly, this is a problem that exists to a greater extent in the blogosphere than it does in academic journals. The reason is obvious. If one submits a paper to an academic journal, a good reviewer is able to spot the ambiguities between testing the predictions of a particular theory and contrasting the predictions of theories with observationally equivalent predictions. In the blogosphere, the “reviewers” are commenters and colleagues. However, the differences don’t often get resolved. Perhaps this is because there is no gatekeeper that prevents the blog post from being published. (Ironically, the lack of a gatekeeper is perhaps the best quality of the blogosphere because it allows discourse to take place in public view.) Nonetheless, given the degree to which blog posts and debates in the blogosphere ultimately spill over into the popular financial press and public debate, it is important to be careful and considerate regarding opposing views.

[Note: For an example of someone who tries to disentangle the issues surrounding the Debt View and the Money View, see Robert Hetzel’s The Great Recession: Market Failure or Policy Failure?]

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.

Armen Alchian, 1914 – 2013

Armen Alchian passed away today at the age of 98. Others have chimed in with their thoughts on Alchian and his work (see here and here, for example) and I thought that I would as well. As many others have noted, Alchian was insightful and clever. He had a unique ability to communicate clever, unique, and insightful ideas in a way that suggested that these ideas were obvious. In fact, these ideas were often profound in both clarifying topics and in inspiring the work of fellow economists.

The aspect of Alchian’s work that I have found most insightful and most challenging is thinking about the economy as a coordination problem. There are few, if any, economists who have done as much in terms of thinking about economics in this light as Alchian did and the profession is much better for his insights.

No doubt, in the next couple of days, there will be excellent discussions of his great works as a scholar and a teacher, but what is perhaps the best biographical information about Alchian is found in his “Principles of Professional Advancement”, in which he provides a light-hearted guide to success in academia and also discusses some of his important papers. I think that this excerpt in which Alchian details an experience during his time as a consultant at RAND does a lot to summarize the inquisitive nature of Alchian’s mind and his astute ability to use the economic way of thinking to analyze the problems at hand:

I like to brag that I did the first “event study” in corporate finance, bank in the 1950s and 1960s. The year before the H-bomb was successfully created, we in the economics division at RAND were curious as to what the essential metal was — lithium, beryllium, thorium, or some other. The engineers and physicists wouldn’t tell us economists, quite properly, given the security restrictions. So I told them I would find out. I read the U.S. Department of Commerce Year Book to see which firms made which of the possible ingredients. For the last six months of the year prior to the successful test of the bomb, I traced the stock prices of those firms. I used no inside information. Lo and behold! One firm’s stock prices rose, as best I can recall, from about $2 or $3 per share in August to about $13 per share in December. It was the Lithium Corp. of America. In January, I wrote and circulated a memorandum titled “The Stock Market Speaks.” Two days later I was told to withdraw it. The bomb was tested successfully in February, and thereafter the stock price stabilized.

That entire speech is filled with similar anecdotes that demonstrate the way in which Alchian thought and how that influenced his research.

Today is a day to sit down with Economic Forces at Work and appreciate the brilliance of Armen Alchian.

Re-Thinking Financial Reform

Over at National Review Online I advocate reviving double liability for banks. Here is an excerpt:

The banking system in the U.S. hasn’t always been like this. Between the Civil War and the Great Depression, banks did not have limited liability. Instead, they had double liability. When a bank became insolvent, shareholders lost their initial investment (just as they do under limited liability today). But in addition, a receiver would assess the value of the asset holdings of the bank to determine the par value of the outstanding shares. Shareholders had to pay an amount that could be as high as the current value of their shares in compensation to depositors and creditors.

Shareholders and bank managers (who were often shareholders themselves) thus had a stronger incentive than they do today to assess the risk of investments accurately, because they were risking not just their initial investment but the total value of the banks’ assets. Shareholders also had an incentive to better monitor bank managers and the bank balance sheet.

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.)

Suppose that buyers have preferences:

where is the discount factor, is the quantity of goods purchased in the DM, and 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 .

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

where denotes the price of money in terms of goods, 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 and the value function for buyers entering the CM as .

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

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

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 where represents the quantity of money balances offered for trade and represents the disutility generated by sellers from producing the DM good. The value function for buyers in the DM is given as

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

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

[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 . 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 ). This means that the buyers' offer can now be written . 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

Since money is neutral in our framework, we can assume that there is a steady state solution such that . Thus, the difference equation can be written:

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 and have standard functional forms. Specifically, assume that and . [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 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. ). Put in economic terms, there are multiple equilibria that are decreasing in , 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.