Maturity Diversification

In an earlier post I linked to a provocative proposal by Andy Harless in which he argues that the Treasury should be shortening the maturity structure of government debt. His reasoning is roughly as follows:

1. At current interest rates, money and bills are virtually identical assets: holders of bills are requiring no compensation for the additional liquidity or safety that money would provide. This makes conventional monetary policy (exchanging cash for bills) ineffective. On the other hand, an increase in the issue of bills can have expansionary effects, putting the Treasury effectively in charge of monetary policy.
2. In addition to its expansionary effects, a shift to shorter maturities on government debt should lower the expected value of the costs of debt service, since there is a liquidity premium to be paid on longer term bonds. However, it would also increase the vulnerability of the Treasury to unexpected increases in short term rates (expected increases are already implicit in the yield curve). 
3. Maintaining long maturities to insure against this risk would be hedging against good news, assuming that an unexpected increase in short term rates would signal a more rapid recovery than is currently forecast. In this case (unexpectedly) higher rates would be accompanied by (unexpectedly) greater federal revenues and lower benefit payments, so the financial position of the Treasury need not be worsened despite the greater costs of debt service.
   

That's his argument, if I understand it correctly.  The proposal is similar in some respects to one made recently by Joe Gagnon, in which he argues that the Fed should be buying substantial amounts of long term debt. Both proposals would result in roughly the same mix of short and long term securities in the hands of the public, and would lower long term interest rates. But there are two important differences. First, as Gagnon notes, "it would be better for the Fed to do it because they have the staff and expertise for gauging how much to do and when to stop." Second, there would be greater maturity diversification in Treasury issues, raising the expected value of debt service costs but reducing the vulnerability to unexpected fluctuations in interest rates.

How important is the issue of maturity diversification? A commenter (identified only as JKH) on Harless' blog thinks that it would be irresponsible to ignore it:

As far as the Treasury is concerned, it’s just acting according to prudent interest rate risk management considerations in locking in some interest cost on such a massive prospective debt load. It’s just a matter of judgement on how to diversify maturities, given the “risk” that the Fed may want to start tightening some time. Ignoring the issue of maturity mix is irresponsible. From there it’s judgement on the right mix.

This is fair enough as far as it goes, but what are the principles on the basis of which such judgment ought to be exercised? The trade-off here is between the expected costs of debt service and the risk of facing a situation in which costs are much greater than forecast. The basic problem was expressed very succinctly by Richard Roll (1971) as follows:

For example, consider a government agency borrowing for a specific long term project at currently high rate levels. It might be able to reduce the total expected interest payments (and expected taxes) by financing the project partly with short-term bonds rather than entirely with bonds whose term-to-maturity matches the project's life. On the other hand, even though the agency expects lower rates in the future, it would not feel secure in funding the entire project with short-term bonds that would require a later refinancing. It would prefer to pay the higher expected rate on a portfolio of long- and short-term bonds rather than accept the risk that rates will go higher contrary to expectations.

Given some specification of Treasury preferences and expectations about the future course of interest rates, this is a fairly standard optimization problem. But it is not obvious (at least to me) how the desired maturity structure should vary with changes in uncertainty about future rates. Other things equal, greater uncertainty should lengthen maturities. However, greater uncertainty will also steepen the yield curve and raise the expected costs of long-term (relative to short-term) financing, and this effect should reduce desired maturities. In any case, these effects should be possible to identify, given some specification of Treasury objectives.

Much more difficult is the question of what those objectives ought to be. How much weight should by placed on risk as opposed to the expected costs of debt service? And should the desired maturity structure of government debt be sensitive to macroeconomic conditions?

I don't have answers to these questions but (as I said in a comment on Mark Thoma's page) it is important to resist the temptation to view the problem solely from a corporate finance perspective. There will be a significant shortfall in government revenues over outlays for many years to come, so short-term Treasury issues will have to be rolled over repeatedly for an indefinite period, or converted to long-term debt at some point. If this were a corporation, such financial practices would be madness (for the company as well as its creditors). The company would be engaged in massive maturity transformation, and be highly vulnerable to changes in short term interest rates and credit availability. It would be unable to meet even interest obligations without borrowing - which is Hyman Minsky's definition of Ponzi finance.  

But the Treasury is not a private corporation, and it faces very different constraints and objectives. Matching maturities to expected net revenues is simply not an option, nor should it necessarily be a goal. This much is straightforward. Much less clear is the set of principles that ought to guide the decisions that ultimately determine the maturity structure of government debt.

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Update (12/28). In an email to me (posted with permission), Joe Gagnon adds:

Since the government includes the Treasury and the central bank, we could have one objective function and find the optimal policy from first principles. But I suspect the same result would obtain if the Treasury acted as first mover and followed a reasonable, modestly risk-averse, cost-minimizing strategy for maturity of issuance given the Congressionally set taxes and spending. Then the central bank would take Treasury behavior as given when it decides on the optimal maturity structure from the overall social welfare viewpoint, taking into consideration unemployment and inflation as well as risks to government finance and likely future behavior of Congress.

My own sense (buttressed by Table 6 in my paper) is that the risks to government finance from shifting into short maturities is very small compared to the benefits, and much less costly than outright fiscal-spending stimulus.

Also:

The point about the table is that even in the inflation scare scenario, when future short rates rise quite high for a while, the debt burden is lower with monetary stimulus (via maturity transformation) than without it. Of course, one can construct even more extreme scenarios in which that is not true (or in which the debt burden is reduced by high inflation) but I would argue those scenarios are highly unlikely given the state of the economy and the current membership of the Fed’s policy committee.

Some Further Comments on Maturity Choice

In an earlier post, I discussed the issue of maturity choice for new Treasury issues, arguing that it affects not only the cost of financing the debt but also the shape of the yield curve, the extent of private sector maturity transformation, and the value of the currency (for instance if foreign lenders have different preferences over maturities relative to domestic lenders.) In many respects, therefore, the Treasury performs actions that are normally considered to be within the purview of the Federal Reserve. But while Fed policy is subject to extensive debate, as is the size of the deficit, there seems to be very little discussion of the manner in which the debt is financed by the Treasury.

Andy Harless (via Mark Thoma) has recently written a long and thoughtful post that deals with related issues. The post is worth reading in full, but here's the gist of his argument:

The inflation rate is now lower than most economists prefer, and the economy remains extremely weak despite the recent upturn in the business cycle. The burning issue is how to find the most cost-effective and politically feasible way to stimulate the US economy, and conventional monetary policy is not an option.

And today Treasury bills are not just more like money than like other assets; from a portfolio point of view, on the margin of new issuance, Treasury bills are exactly like money. Holders of short-term Treasury bills are willing to hold them without receiving interest. Anyone who is willing to hold them is placing no value whatsoever on any liquidity or safety advantage that might be had from holding those assets in the form of money.

Issuing more short-term Treasury bills will have exactly the same effect as issuing more money, since people are indifferent between the two. For practical purposes, as long as their interest rate remains at zero, short-term Treasury bills are part of the money stock. A Treasury bill is a million-dollar bill in the same sense that a Federal Reserve note with Abraham Lincoln on it is a five-dollar bill. Conventional monetary policy, which exchanges money for Treasury bills, is ineffective because it is no policy at all: it simply exchanges one form of money for another.

To put it another way, since the Treasury can issue bills that are exactly like money, it is now the Treasury that is in charge of monetary policy. And whatever one may think of the policy it chooses to follow, we should be holding the Treasury responsible. If you’re worried about “exit strategy” and the possibility of inflation in the near future, then perhaps you should congratulate the Treasury for its policy of financing more of its debt long-term. If you’re worried (as I am) about the persistence of a weak and potentially deflationary economic environment, then you should be critical of the Treasury’s policy. By increasing its maturities the Treasury is essentially following a tight-money policy exactly when a loose-money policy is needed.

The Treasury, of course, has its reasons. Officials expect interest rates to rise over the next several years and would like to lock in today’s low rates, to limit how much it will cost to service the national debt over a longer horizon. I’m skeptical, however, of the assumptions underlying these reasons.

Are interest rates going to rise over the next several years? Perhaps, but if so, then why are people being foolish enough to hold longer-term Treasury securities when they could be holding bills and waiting for a better deal? If it’s just a matter of the future course of interest rates, then it’s a zero-sum game. If the Treasury wins, bondholders lose – and bondholders usually make a point of trying not to lose. Are Treasury officials so much smarter than bondholders?

You might argue that it’s a matter of risk. When the Treasury locks in today’s low interest rates, it may not end up paying less (since it gives up even lower short-term rates), but it makes the payments more predictable. Even if the Treasury is likely to end up paying more, the hedge is worth the price, because the Treasury receives some insurance for the worst case, where rates rise more than expected.

But are rising interest rates really the worst case? Interest rates will rise when and if the economic recovery gains enough speed and traction to give the Fed and bond markets reasonable confidence in its eventual convergence toward our potential growth path. As an ordinary citizen, that’s not an outcome against which I would feel a need to hedge. I don’t want to buy insurance against good news. I’d rather hedge against the opposite outcome, where the recovery peters out and interest rates fall.

I urge you to read the whole thing. Regardless of whether or not you accept his prescriptions, the question of maturity choice deserves an airing.

Harless attributes some of his ideas to Benjamin Friedman, with whom he once studied. This reminded me of a paper that Friedman wrote with (a very young) David Laibson, published in a 1989 issue of the Brookings Papers on Economic Activity. This issue also contains an extended commentary by Hyman Minsky, whose work I have discussed previously. Both the paper and Minsky's comments on it are well worth reading, and I hope to post my thoughts on them in due course.

On Mattresses, Ideologues, and Cheerleaders

I suppose one ought to be grateful for small mercies; Bryan Caplan has learned how to spell mattress.  Here he is on December 16:

unless employers are unusually likely to put cash under their matresses...

And here again three days later:

the net effect on AD depends on the marginal propensity to stuff income under one's mattress.

Now it would a a major step forward if he were to discover the existence of bills, bonds, equities, mutual funds of various stripes, and rare stamps and coins, all of which can serve as channels for savings, and none of which automatically create a demand for current production in equal measure to the cost of acquiring them. But, as Winterspeak notes, that would be too much to ask:

Glibertarian Bryan Caplan reveals why microeconomics is just useless at analyzing the economy at a macro scale. If you cannot understand that spending equals income at an economy wide level, you'll spout a lot of two sentence nonsense.

I don't think that microeconomics is at fault. The blame lies with a particularly crude and naive textbook version of microeconomics and its uncritical application by ideologues and their cheerleaders.

Some Progress in the Minimum Wage Debate?

On the blog he shares with Tyler Cowan, Alex Tabarrok writes:

A fall in wages increases the incentive to hire (call this the substitution effect) but it decreases the income of people who already have jobs and this in turn decreases their spending and other people’s income (call this the macro income effect).  In essence, Krugman and others are arguing that the macro income effect can dominate under certain situations.

Yes, but one needs to go a bit further than this. If the macro income effect dominates, then there will be layoffs in other sectors, most immediately in those producing outputs that low wage workers purchase. And these layoffs will not be confined to low wage workers. This means that even if the employment of low wage workers rises, there will be a decline in employment across other segments of the skill distribution. Concede this point and we're done.

Tabarrok doubts the empirical relevance of the macro effect, based as far as I can tell on the perusal of a before-and-after table by Scott Sumner. I will leave the empirical question to the empiricists, except to say that the magnitudes of the various effects will obviously depend on the initial level of the minimum wage and on prevailing economic conditions.

Finally, let me repeat that I agree with Winterspeak, Tyler Cowan, and The Economist that the effects on aggregate demand of changes in the mimimum wage, regardless of their sign, are likely to be small. But it's important to get the reasoning right, because the same methods apply to discussions of flexible wages and prices more generally.

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Update (12/18). As I said in my earlier post on the topic, the aggregate demand consequences of a fall in wages also depend on financial market effects. If the the unspent portion of the rise in employer incomes makes it into the bond market, lower long-term rates could stimulate investment. If it goes into stocks, the resulting asset price appreciation could also conceivably raise investment. Neither of these effects seems likely under current conditions. This is why I have argued that Greg Mankiw's proposal of an investment tax credit is deserving of serious attention.

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Update (12/19). It's worth thinking a bit more closely about what Alex calls the substitution effect. This is presumably what Tyler had in mind when he urged me to shift marginal cost curves down and watch what happens. He was arguing that the firm will lower price and use the additional hires to step up production to meet the increased demand. Now obviously this will not increase market share if one's competitors are doing the same thing, but it could increase the overall consumption of goods and services produced with low wage labor. Even disregarding the macro income effect, this implies a decline in demand for goods and services produced with skilled, high wage labor. In other words, there will be a "substitution effect" in unemployment patterns, more unskilled jobs and less skilled jobs. Add the macro income effect to the analysis and matters become worse. The only way that lower wages can increase aggregate demand is by stimulating private investment through changes in asset prices and interest rates. This is just not going to happen under current conditions (hence my support for this proposal). In any case, a partial equilibrium analysis is totally inadequate for thinking through these questions.

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Update (12/19). Nick Rowe (via Mark Thoma) addresses the "microeconomic miscreants" from a macroeconomic perspective. I personally feel a bit uneasy using models with such high levels of aggregation because they leave out too many things (for instance, the effects of changes in the minimum wage on the skill distribution among the unemployed). But he makes some useful points. 

On the Distribution of Gains from Government Action

Greg Mankiw has written a thoughtful post making the case for an investment tax credit. I was struck in particular by the following passage:

The cash-for-clunkers program is thought by many to have promoted, or at least accelerated, car purchases.  An ITC would be similar, but it would apply to business investment rather than personal cars.  Instead of targeting a very narrow, politically favored industry, it encourages investment broadly.  It should have positive effects on aggregate demand in the short run and positive effects on aggregate supply in the medium and longer run.

The cash-for-clunkers program bothered me not only because it targeted a specific industry but also because it distributed gains among consumers on the basis of criteria that were very arbitrary. For instance, the requirement that eligible trade-in vehicles had to have a combined city/highway fuel economy of at most 18 miles per gallon excluded from participation those who had purchased fuel efficient vehicles in the past. This does not conform to any intuitive notion of fairness.

The biggest recent example of such distributional effects is of course the bailout of AIG counterparties by the Federal Reserve. Earlier this month I attended a speech by Bill Dudley at Columbia University in which he explicitly recognized the anger that such actions can fuel:

The actions taken by the Federal Reserve and others to stabilize the financial system had the effect of rescuing many of the same financial institutions that contributed to this crisis. Many of those financial institutions are now prospering, and many of their employees will be highly compensated. This situation is unfair on its face. But it is even more galling in an environment in which the unemployment rate is 10 percent and many people are struggling to make ends meet.

Later in the speech he returns to the issue:

... it is deeply offensive to Americans, including me, and runs counter to basic notions of justice and fairness, that some of the very same individuals and financial firms that precipitated this crisis have also benefited so directly from the response to the crisis. This has occurred at the same time that many Americans have lost their jobs and hard-earned savings. The public outrage this situation has produced is understandable. In the context of actions taken to support the financial system, the Federal Reserve and other government agencies have provided considerable support to banking organizations and other large systemically important financial institutions. The employees and executives of those institutions have benefitted from our intervention. In a perfect world we would be able to prevent those individuals and institutions from benefitting; we would have a better way to penalize those who acted recklessly. But once the crisis was underway, one goal took precedence: keeping the financial system from collapsing in order to protect the nation from an even deeper and more protracted downturn that would have been more damaging to everyone.

The issue came up again in the question and answer session (which is not transcribed in the published version of the speech).

I don't know whether there were options available at the time that would have secured the goal of maintaining financial stability without such a large redistribution of wealth in favor of those who stood to lose from an AIG bankruptcy. But it seems to me that such fairness concerns are not given enough early attention in the design of government policies.

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Update (12/18). I find Greg Mankiw's case for an investment tax credit quite convincing. He advocated the same policy a few days ago in a New York Times piece, but the substance of the argument there was lost amid the partisan jabs, on which Nate Silver pounced. I discussed the longstanding Mankiw-Silver feud here, concluding that "couching an economic argument in overtly moralistic or political terms can considerably diminish its impact." This is certainly a case in point.

On Partial Equilibrium Models of Demand and Supply

My last post on the aggregate demand effects of changes in nominal wages has attracted some attention, so I'd like to clarify a couple of things.

It was not the point of the post to claim that declines in nominal wages would lower or increase aggregate demand. The point was to argue that the simple partial equilibrium models of demand and supply that were being used by some to address the question were simply not up to the task of answering it. It was a reaction against the view -- expressed by Bryan Caplan and endorsed by Tyler Cowen -- that such effects could easily be deduced from textbook microeconomic theory. And it was a plea to move beyond partial equilibrium analysis in addressing such questions.

Tyler Cowan responded to this with yet another partial equilibrium model of supply and demand:

Graph a monopolist and shift the marginal cost curve down. Watch what happens. The first main paragraph of Sethi simply doesn't consider this mechanism but rather it assumes that changes at the margin don't matter.

That was in the comments section of Mark Thoma's blog. A similar claim now appears on his own page:

There is a simple story here.  Lower the minimum wage and firms with market power will in general hire more labor.  (Sethi's critique refuses to consider that mechanism but simply shift the MC curve and watch it happen.)

By all means, shift the MC curve and watch what happens. But please keep in mind not a single firm but a population of firms, some of which do not pay minimum wage at all. And be sure to shift the demand functions for all firms producing goods and services that minimum wage workers currently purchase. And now tell me whether it is self-evident that aggregate demand will rise in response to a decline in nominal wages.

It is not self-evident. In order to address the question it is necessary at a minimum to work with a model with multiple firms, in which the expenditure patterns from wage and capital income are properly specified, and some alternatives to immediate consumption (such as financial assets) exist. Simulate this model on a computer if you like, and watch what happens. I would be interested to know. But please don't make definitive claims about aggregate demand effects of changes in nominal wages based on an introductory textbook model that is simply incapable of carrying the weight.

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Update (12/17). Andrew Gelman is (understandably) puzzled by the fact that there is a debate going on about a policy that has no chance of being implemented. Mark Thoma provides some explanation, and I hope to post my own thoughts on this soon. Paul Krugman has more. 

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Update (12/19). Some possible signs of progress in this debate.

Some Further Comments on Nominal Wage Flexibility

Tyler Cowan thinks that we should cut the minimum wage, and links to Bryan Caplan for an explanation. And Caplan thinks that it's all quite elementary:

Cutting wages increases the quantity of labor demanded.  If labor demand is elastic, total labor income rises as a result of wage cuts.

Even if labor demand is inelastic, moreover, wage cuts reduce labor income by raising employers' income.  So unless employers are unusually likely to put cash under their matresses, wage cuts still boost aggregate demand.

Let's take this step by step. First, consider the claim that cutting wages increases the quantity of labor demanded. Through what mechanism does this occur? Consider a firm (McDonald's, say) that can now pay its workers less. It will certainly do so. But will it increase the size of its workforce? Not unless it can sell more burgers and fries. Otherwise its newly expanded workforce will produce a surplus of happy meals that will (unhappily) remain unsold. And this will not only waste the expense of hiring and training new workers, it will also waste significant quantities of meat, potatoes and cooking oil. So the firm will make do with its existing workforce until it sees an uptick in demand. And no cut in the minimum wage will automatically provide such an increase in demand. As a result, the immediate effect of a cut in the minimum wage will be a decline in total labor income.

Employer income, of course, will rise. Some of this will be spent on consumption, but less than would have been spent if the same income had been received by low wage earners. The net effect here is lower aggregate demand. But wait, what will happen to the remainder of the increase in employer income? It will not be placed under mattresses, on this point I agree with Caplan. It will be used to accumulate assets. If these are bonds, then long rates will decline, and this might induce increases in private investment. Then again, it might not, unless firms believe that additions to productive capacity will be utilized. And right now they do not: private investment is not being held down by high rates of interest on long-term debt.

Finally, what if employers use the unspent portion of their augmented income to buy shares? We would have a run up in stock prices not unlike that we have seen in recent months. Note that this would not be a speculative bubble: the higher prices would be warranted given that firms have lower labor costs. But would this asset price appreciation stimulate private investment in capital goods? Again, not unless the additional capacity is expected to be utilized.

Mark Thoma has more on this, as does Paul Krugman. I discussed the opposing views of Becker and Tobin in an earlier post. What I cannot understand is why people of considerable intelligence persist in conducting a partial equilibrium Walrasian analysis of the labor market, as if we were dealing with the market for oranges. Please stop it.

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Update (12/16). Thanks to Mark for reposting this, and to Paul Krugman for following up. Tyler responds as follows on Mark's page:

Graph a monopolist and shift the marginal cost curve down. Watch what happens. The first main paragraph of Sethi simply doesn't consider this mechanism but rather it assumes that changes at the margin don't matter.

To which I have replied as follows:

Tyler, a fall in wages won't just shift the marginal cost curve down, it will also shift down the demand curve and hence marginal revenue. This will happen for all firms who produce stuff that minimum wage workers consume, regardless of whether or not they themselves pay minimum wage. Now we may disagree about what the eventual outcome will be (I think there will be debt deflation, as described in Fisher 1933, and so admirably summarized recently on your blog). You may disagree. But we can't settle this with partial equilibrium models of monopolists and their cost curves.

I'm sure that this debate will continue. My only hope is the we get beyond partial equilibrium models from introductory microeconomics in discussing these terribly important questions.  

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Update (12/17). The Economist points out (quite sensibly) that even demand constrained firms may increase hiring with lower wages in order to improve product quality: "If a firm can produce a particular number of burgers with either 5 workers earning $7 an hour or 6 workers earning $6 an hour it won't necessarily prefer the 5 worker set-up." True enough, but this is not the appropriate comparison: if the wage drops, employment will rise only if 6 workers earning $6 an hour are preferred to 5 workers earning $6 (not $7) an hour. In other words, the choice is between improving quality or pocketing the difference in wages.

I do not doubt, by the way, that a lower minimum wage could raise employment in some firms. But unless the aggregate wage bill rises, some other firms will experience declining demand, and may respond by laying off workers across a much broader range of skills. My point is simply that in order to capture these effects, it is essential that one move beyond the partial equilibrium framework. More here.

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Update (12/18). Winterspeak adds:

Any discussion of the minimum wage turns into a Rorschach test for the ideology of the commenter.

This is unfortunately true, and ideology does seem to be clouding judgment and analytical clarity on the issue. My focus has remained on the methods one uses to reason about the effects of changes in the minimum wage, rather than on the magnitude or sign of these changes. I agree with Winterspeak, Tyler Cowan, and The Economist that the effects of such changes on aggregate demand, regardless of their sign, will likely be small. But it's important to get the reasoning right, because the same methods apply to discussions of flexible wages and prices more generally. To answer Andrew Gelman, this is why I think the debate is important. Hence the title of this post, and the content of the earlier post to which it refers.

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Update (12/19). Perhaps some signs of progress in this debate. Alex Tabarrok writes:

A fall in wages increases the incentive to hire (call this the substitution effect) but it decreases the income of people who already have jobs and this in turn decreases their spending and other people’s income (call this the macro income effect).  In essence, Krugman and others are arguing that the macro income effect can dominate under certain situations.

My response:

Yes, but one needs to go a bit further than this. If the macro income effect dominates, then there will be layoffs in other sectors, most immediately in those producing outputs that low wage workers purchase. And these layoffs will not be confined to low wage workers. This means that even if the employment of low wage workers rises, there will be a decline in employment across other segments of the skill distribution. Concede this point and we're done. 

Furthermore:

It's worth thinking a bit more closely about what Alex calls the substitution effect. This is presumably what Tyler had in mind when he urged me to shift marginal cost curves down and watch what happens. He was arguing that the firm will lower price and use the additional hires to step up production to meet the increased demand. Now obviously this will not increase market share if one's competitors are doing the same thing, but it could increase the overall consumption of goods and services produced with low wage labor. Even disregarding the macro income effect, this implies a decline in demand for goods and services produced with skilled, high wage labor. In other words, there will be a "substitution effect" in unemployment patterns, more unskilled jobs and less skilled jobs. Add the macro income effect to the analysis and matters become worse. The only way that lower wages can increase aggregate demand is by stimulating private investment through changes in asset prices and interest rates. This is just not going to happen under current conditions (hence my support for this proposal). In any case, a partial equilibrium analysis is totally inadequate for thinking through these questions.