Monthly Archives: January 2013

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.

1. The New Dynamic Public Finance by Narayana Kocherlakota

2. The Redistribution Recession by Casey Mulligan

3. The Bretton Woods Transcripts, edited by Kurt Schuler and Andrew Rosenberg

4. Misunderstanding Financial Crises by Gary Gorton

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.