Believe those who are seeking the truth. Doubt those who find it. Andre Gide

Friday, December 30, 2011

On Paulo and Bobby, English and Math

I was once told by an English professor that Joseph Conrad preferred to write in English (his third language) because sentence meanings in that language often had a wonderful ambiguity that added an artistic flair to his prose.
Well, I'm not sure if that story is true. But I do know that it is easy to misinterpret what people mean when they try to communicate their economic theories in "plain" English. That is why academic economists, when speaking among themselves, prefer to communicate in a much more precise language--math.

For those among you who do not understand this language, I'm sorry. I'll do my best to translate into English as I go along. What I want to do here is provide a formal (mathematical) framework to evaluate the discussion on Ricardian equivalence these past few days (see my previous two posts).

Before I get started, I want to make a few things clear. I was not trying to defend Lucas' claim that G fully crowds out private spending. I am not a Republican (I am a Canadian). I agree with some of things that Krugman says (just take a look at some recent posts). I am annoyed that Krugman repeatedly attacks Lucas for "not understanding his own theory." Not only was that was a low blow, but that sort of talk just promotes a division that I do not think exists in the profession. Moreover, and more to the point of what motivated my original post, in delivering his low blow, Krugman presented his own muddled view of the role that Ricardian equivalence played in Lucas' argument.

So let me try to clear things up. Note that I do not speak for Lucas here. What follows is one possible interpretation of what he had in mind. More precisely, it is what came to my mind when I was trying to interpret the content of his speech.

The model I have in mind is a simple overlapping generations (OLG) economy. People live for two periods; they are "young" and then "old." The population is constant. For simplicity, the young do not care for consumption. Instead, everybody wants to postpone consumption to old age (this is not a critical assumption).

The young are endowed with a unit of labor that produces output y (the young supply this labor inelastically, so we may treat y as an endowment). The young also possess an storage technology; k units of investment today yields F(k,g) units of output tomorrow, where g denotes government investment spending. I assume that output F(k,g) is increasing in both k (private investment) and g (public investment). For simplicity, assume that all capital depreciates fully after it is used in production.

Consider the following two specifications of F(k,g):

PF1: F(k,g) = f(k+g)
PF2: F(k,g) = A(g)f(k)

In PF1, private and public capital are perfect substitutes in production. What this implies is that an increase in g lowers the marginal product of (the return to) private capital spending. In PF2, private and public investment are complements. What this implies is that an increase in g increases the marginal product of (the return to) private capital spending.

I believe, though I am  not sure, that Lucas had in mind specification PF1. At least, this is an assumption that is consistent with his conclusions. He would have come to a different conclusion if he believed PF2. Note: the choice of PF1 vs PF2 has nothing to do with Ricardian equivalence. 

Let me continue to describe my model economy. There is a government security that earns a gross real rate of return R. In the present economic climate, with nominal interest rates close to zero, R<1 is the inverse of the gross rate of inflation. I treat R here as a policy parameter.

The budget constraints for a young agent in this economy are given by:

k + m = y - t
c = F(k,g) + Rm - T

So here, a young person must take his after tax income (y-t) and make a portfolio allocation choice: how much to invest in private capital k and how much in government money/bonds m. In old age, the agent gets to consume the proceeds of his investments, minus his  future tax obligation T.

Next, we have to specify the government budget constraint. I consider two extreme cases.

GBC1: g = t + T/R
GBC2: g = (1-R)m

Under GBC1, I am assuming that the burden of financing g falls entirely on the young. This assumption (together with my use of lump-sum taxes) is going to generate a Ricardian equivalence result: the young are not going to care whether they are taxed now or later for g. (Note: Ricardian equivalence would not hold if I assume instead that the burden of finance falls on both the young and old--that is, if I assume that current g is financed by the current young and current old--in contrast, here I assume current g is financed by current young and future old).

Under GBC2, I assume that g is financed entirely through money creation (seigniorage revenue).

Finally, I consider two experiments:

E1: a permanent increase in g
E2: a temporary increase in g

OK, now let's investigate some of the properties of this simple model and see how it can be used to make sense of things.


Case 1: PF1, GBC1, either E1 or E2

The key equation is the one that equates the marginal product of private capital investment to its opportunity cost:

[1] f'(k+g) = R

Result: An increase in g fully crowds out k (so future GDP remains unchanged). This is independent of whether the young are taxed now or later.

Does this conclusion rely on Ricardian equivalence? Well, yes and no (assuming distortionary tax finance would imply that an increase in g would decrease future GDP). Consider the next case.

Case 2: PF2, GBC1, either E1 or E2

The key equation now takes the form:

[2] A(g)f'(k) = R

Result: an increase in g stimulates k (so future GDP increases). This is independent of whether the young are taxed now or later.

This is the sense in which I believe Lucas' remarks have nothing to do with Ricardian equivalence (it has to do with his belief of PF1 over PF2). And indeed, what he literally says is "and taxing them later is not going to help." That is, it might even hurt--which can only be true if one departs from Ricardian equivalence (e.g., by assuming that the future tax hit will be distortionary). Again...words, words, words...we need an explicit model to decipher and evaluate what he really meant.

Aside: I often hear people say things like "Well, yes, if the increase in g is permanent, then it will fully crowd out. But this does not hold if the increase in g is temporary." My reply to this is: you are wrong. Take a look at the model above. It is possible for a permanent increase in g to increase GDP permanently. In particular, Cases 1 and 2 remain valid whether or not the increase in g is temporary or permanent (they hold for E1 and E2).

Case 3: PF1, GB2, E1

The key equation here is again given by [1]. A permanent increase in g is financed here by an inflation tax. Increasing g obviously requires increasing inflation (lowering R, the real return on government money). But if R is lowered, then condition [1] implies that k+g increases. That is, individuals substitute out of money and into capital (private or public). Consequently, if the government increases g permanently and finances it with money creation, output expands. (Note: this result need not be welfare improving. Do not confuse GDP with  economic welfare).

Case 4: PF1, GB2, E2

OK, so here we have a one-time increase in g financed by a one-time increase in the money supply. I think that this is what Lucas likely had in mind when he claimed that a money-financed increase in g stimulates.

The analysis here becomes a little more complicated because we have to do "out of steady state" analysis. Let me instead give you the intuition.

It is known that for OLG models, that money is not generally neutral (despite the fact that prices are completely flexible--indeed, I think that price flexibility is critical for the  non-neutrality result). In this model, a one-time increase in the money supply to finance a temporary increase in g will cause a surprise jump in the price level, which has the effect of reducing the purchasing power of the money brought into the period by the old. (If you are an Austrian, you will complain that the old have had their savings stolen by the surprise inflation policy). The effect is to divert purchasing power away from the old (who want to consume) toward the young (who would rather invest). This money-financed increase in g will stimulate; which is consistent with what Lucas said. Moreover, the result relies on a failure of Ricardian equivalence. (In a model with an infinitely-lived representative agent, the money-financed increase in g would have no effect at all, given PF1).


A reader of mine provided me with this quote (apparently, from Brad DeLong):
I learned this from Andy Abel and Olivier Blanchard before my eyes first opened: increases in government purchases are ineffective only if (a) "Ricardian Equivalence holds and (b) what the government buys (and distributes to households) is exactly what households would buy for themselves. RE by itself doesn't do it."

I think this is a nice way to summarize things. (Keep in mind that "ineffective" in the quote above means "no effect--whether good or bad.")

In conclusion, Lucas' remarks need not be interpreted as his theory relying on RE. Indeed, as I hope to have made clear above, his remarks, when taken together, require a departure from RE. The key assumption he makes, in my view (who really knows?) is the part (b) in DeLong's quote (my PF1). That part has nothing to do with RE.

Happy New Year, everyone!

Postscript Dec. 31, 2011
An economist that I admire once said this:
"...just talking plausibly about economics is not the same as having a real understanding; for that you need crisp, tightly argued models."
In case you missed it, Krugman takes a nice shot at me here: I Like Math. I like the cartoon! Moreover, I agree with what he says: "If you resort to math to justify what looks like a very foolish claim, and you can't find a way to express that justification in plain English, then something is wrong."

By "foolish," I presume he means "logically invalid" and not "empirically implausible." For those who speak the language of math and are familiar with OLG models, I have shown that there is a logic to the Lucas view as expressed in that speech. (I don't personally believe that the view is empirically plausible, but that is beside the point of my original post). I have shown that the logic implies a departure from RE; contrary to Krugman's claim. I have tried to express this logic in plain language here and here. And in keeping with the sentiment of the quote above (yes, by PK), I tried to re-express the logic in mathematical form to complement what I said earlier. If I have failed in any way, it is in my ability to communicate the idea in "plain" English. I am not as talented as Krugman in this regard. The logic of my argument, however, remains sound.

But I think it is now time to stop. Let me end by alerting you to an interesting take on the matter by Henrik Jensen: The Krugman Multiplier is Too Big. (He includes a link to a video of the speech by Lucas.)

Postscript Jan. 2, 2012

I should have linked up to this classic paper by Neil Wallace earlier than this, but better late than never: A Modigliani-Miller Theorem for Open Market Operations. As macroeconomists know, there is a strong connection between RE and MM (they are essentially the same proposition applied in different contexts). The Wallace paper asserts that open market operations "matter" only to the extent that some or all of the assumptions that underlie RE/MM are violated. Lucas believes that monetary policy matters. Ergo, his arguments (whatever they might be) cannot be based on RE alone.

Postscript Jan. 09, 2012

Well, I'm sure this one is going to fly under the radar, but I feel the need to record it here. It seems that Brad DeLong agrees with me (h/t Mark Thoma); see here. (Well, he doesn't mention me by name, but his elaboration squares with what I have been trying to say all along.)

Yes indeed, one may question whether the mix of publicly provided goods and services substitutes more or less well with privately supplied goods and services. It matters for whether how a change in G is likely to impact the economy. Ultimately, it is an empirical question. And it has nothing to do with RE. Krugman was wrong to question Lucas' understanding of his own theory. Instead, he could have legitimately questioned Lucas' parameter estimates governing the substitutability of private and public expenditure. But really now, I suppose that would have been a lot less fun.

Postscript Jan. 11, 2012

Krugman is like your neighbor's annoying little puppy that just won't stop gnawing at your feet. Scott Sumner weighs in here: Nobel Prizes for Alchemy?

Wednesday, December 28, 2011

Ricardian equivalence, for the last time

Ah, controversy. What a great way to end the year!

I want to comment on Mark Thoma's post today about the Ricardian Equivalence Theorem (RET). Linking up to the interview with Barro was a good idea, Mark. Everyone agrees that the theorem has nothing to say about the effectiveness of G, and Barro explains all of this splendidly. Moreover, everyone agrees that since the conditions needed to render the proposition valid are violated in reality, the proposition cannot possibly be expected to make a perfectly accurate prediction of how altering the timing of taxes (holding G fixed) is likely to impact the economy. I guess that this is about where our mutual agreement ends.

What is there left to argue about? It's the holidays--I'm sure we'll find something. Let's start with Mark's opening paragraph:
I haven't said much about the recent flare up over Ricardian equivalence. Why? The answer's simple, the empirical evidence does not support it. Why argue about something when we already know it fails to adequately explain the data? Making the Ricardian equivalence assumption might be okay as a first approximation for some questions--though I'd argue that it mostly isn't--but in any case the theory does not adequately capture economic behavior.
I'm not exactly sure which flare up he is talking about, but I suspect that I may be involved in it somewhere, owing to this post here: Does Krugman Understand the Ricardian Equivalence Theorem?

I want to clear up a few things regarding that post. First, I was not trying to defend Lucas' views on fiscal stimulus. Lucas's view on the matter (insofar as one can gather it from what was clearly an informal and off-the-cuff speech) appears to be that a money-financed increase in G is stimulative, while a tax-financed increase in G is not. Now, there may be several ways to criticize the "rationale" of his argument. But whatever criticism you pick, it most certainly cannot be centered on Lucas' alleged appeal to the Ricardian equivalence theorem. For crying out loud--the man is claiming that the method of financing matters for a given G. This can only be true if the Ricardian proposition fails to hold in reality.

Now, what of Mark's claim that the empirical evidence does not support the RET? Well, as I said above, given that we live in a world of distortionary taxation, borrowing constraints, finite planning horizons, etc., etc., it would indeed be remarkable if the predictions of RET held up exactly in the data.

But surely that is setting the bar a little too high (not one of us has a theory that can perfectly predict such outcomes). Rather, the question is whether or not the assumptions constitute sufficiently good approximations for the purpose at hand (i.e., for a given policy experiment). Indeed, in the interview posted by Mark, Barro states his view on the matter quite plainly:
As a first-order proposition, it is right that it matters little whether you pay for government spending with taxes today or taxes tomorrow...
So, to Barro it seems that the empirical evidence broadly supports the proposition, at least, to a first-order approximation. If so, that is bad news for me, because I like to work with models where the proposition fails. It would, however, be good news for those promoting an increase in G in the face of large deficits (the size of the deficit should not factor into the debate, if the proposition holds true).

In any case, I'm not sure whether Mark's claim about the empirical evidence not supporting RET is entirely valid. I am reminded of a paper I once saw Emanuela Cardia present: Replicating Ricardian Equivalence Tests With Simulated Series. Here is the abstract:
This paper  replicates standard consumption function  tests of Ricardian equivalence  using series  generated from  a  model which nests Ricardian equivalence within a  non-Ricardian alternative (due  to finite  horizons and/or  distortionary taxation). I show that the estimates of the effects of taxation on consumption are not robust and that standard tests may have weaknesses which can lead to conflicting results, whether Ricardian equivalence holds or not. The simulations also show that no clear conclusions about Ricardian equivalence can be drawn from observing a low correlation between the current account and government budget deficits.
In short, I think that the empirical evidence may be somewhat more mixed than what Mark suggests.

At the end of the day, I think that the key lesson of the RET is not (for example) that "deficit financed tax cuts do not matter." Rather, the lesson should be that "such a policy is likely to be much less stimulative than you would expect if you were to base your thinking on a model that did not incorporate Ricardian forces."

Now who wants to argue with that?

Tuesday, December 27, 2011

Does Krugman Understand Ricardian Equivalence? (Wonkish)

Suppose that the government wants to acquire the resources necessary to implement a new expenditure program G = {g1, g2, g3 ... }, where gt denotes government purchases of goods and services at date t.

Let us take G as given. To begin their evaluation of G, macroeconomists ask the following two questions. First, what are the likely macroeconomic consequences of implementing program G? Second, does the answer to first question depend on how G is financed? (Financing is assumed to take the form of taxes, deficits, and money creation, or some combination thereof).

The Ricardian Equivalence Theorem (RET) is a proposition that helps us answer the second question above. In particular, the RET lays out a set of conditions that must hold for the following proposition to hold: It does not matter how the government finances G

Whether the set of conditions holds in reality is a separate issue that need not concern us here. (You may be interested to read this article from the Economist on the subject page 1 and page 2). For now, let me emphasize what the RET does not say: The RET does not say that G does not matter (it says that the method of financing G does not matter). 

The G is so unimportant in the RET, that it is useful to ignore it completely when teaching the theorem to students for the first time. That is, set G = {0, 0, 0 ...} and then ask whether it matters how G is financed. One way to finance such a program would be to cut taxes today and raise them tomorrow. Since G is fixed (at zero, in this case), this implies running a deficit today, which is matched by a surplus tomorrow. The RET states the conditions under which a deficit-financed tax cut like this does not matter.  A deficit today simply represents a higher future tax bill; and people really don't care whether they are kicked in the a$$ today or tomorrow--it's still an a$$-kicking.

What I have just described is the stuff of elementary macro textbooks. We should all understand now that the RET has nothing to do with G. In particular, we should all know enough never to write a column with the title: A Note on the Ricardian Equivalence Argument Against Stimulus.

The title of Krugman's post shows that it is he who does not understand the Ricardian proposition. There is no "Ricardian Equivalence argument against stimulus." Indeed---the proposition can be used to defend bond-financed stimulus. (In particular, if deficits do not matter, then why not bond finance?)

Now, perhaps you might want to entertain the idea that Paulo knows all this and only chose the title to mock that horrible Bob Lucas fellow. Could be. Except for the fact that Lucas makes no reference to the RET in his informal speech.

In fact--good lord, can it be true--it appears to me that Lucas is making distinctly non-Ricardian arguments in his assessment of fiscal policy. Take a closer look at the passage quoted by Krugman. First, Lucas asserts that a money-financed increase in G will be stimulative; but that the stimulus part comes from the manner in which the spending is financed.  (Because money can be thought of as zero-interest debt, this is virtually the same thing as saying that a deficit-financed increase in G will be stimulative.) Second, Lucas goes on to argue why he thinks a tax-financed increase in G will not be stimulative. In other words, his argument could be interpreted to be mean the method of finance matters. Needless to say, this is not a  Ricardian Equivalence argument against stimulus. 

One may agree or disagree with what Lucas has to say on any given issue (certainly, I do at times). But to come out and publicly declare the man to be ignorant of high-school economics--repeatedly--and on the basis of an informal speech--from a fellow Nobel-prize winner--who is himself is guilty of the charge leveled against his own colleague in the profession---well---holy cow, I don't know what else to say.

PS. A couple of related blog posts on this subject:
Responding to Krugman on Ricardian Equivalence (Andrew Lilico, The Telegraph)
Ricardian Equivalence Redux (Stephen Williamson)

Addendum (Dec 29, 2011)
And in my defense:
On what is and is not an argument about Ricardian equivalence (Andrew Lilico)
Ricardian equivalence heat (Steve Williamson)
In PK's defense:
The great Ricardian equivalence throwdown! (Noahopinion)

Note: I am surprised that no one picked up on the following. If some "conservatives" are claiming that increasing G is "a wash" by whatever mechanism they have in mind, then does it not follow that increasing G further is innocuous? And indeed, decreasing G must be a wash too, if this is indeed what they believe. 

Monday, December 19, 2011

The China Factor

The sovereign debt crisis in Europe has garnered most of our attention as of late. But should Europe really be our main concern? For several months now, many economists (including myself) have been casting a nervous eye over to China. Paul Krugman summarizes these concerns nicely in his NYT article today: Will China Break? Mark Gongloff earlier asked the million dollar question here: China's Shadow Banking System: The Next Subprime?  Hmm...

P.S. And what's with these stories I keep hearing about China's missing bosses? (e.g., China's Vanishing Factory Bosses). Sounds ominous, if true. We truly do live in interesting times. 

Monday, December 12, 2011

Beveridge Curves for 36 U.S. Cities (updated)

On October 9, 2010, I posted some regional vacancy-unemployment data for the United States; see: Beveridge Curves for 36 U.S. Cities.

My measure of vacancies was the Conference Board's help-wanted index (HWI).  A colleague of  mine (Silvio Contessi) pointed me to a paper by Regis Barnichon (EL 2010) that identifies a major flaw in this data series. Barnichon summarizes the problem here:
The traditional measure of vacancy posting is the Conference Board Help-Wanted Index (HWI) that measures the number of help-wanted advertisements in 51 major newspapers. However, since the mid-1990s, this “print” measure of vacancy posting has become increasingly unrepresentative as advertising over the internet has become more prevalent. Instead, economists increasingly rely on the Job Openings and Labor Turnover Survey (JOLTS) measure of job openings. However, this measure is only available since December 2000 and cannot be used to contrast current labor market situations with past experiences.
In this paper, I build a vacancy posting index that captures the behavior of total—“print” and “online”—help-wanted advertising, by combining the print HWI with the online Help-Wanted Index published by the Conference Board since 2005. 
Here is how Barnichon's correction looks for the aggregate data.

That is, the secular decline (blue line) in the original HWI series is estimated to be entirely the consequence of a substitution away from print to electronic forms of job advertising.

With this in mind, I asked my tireless research assistant (Constanza Liborio) to recalculate our regional Beveridge curves using Barnichon's correction (for those interested, I can email you a file describing the exact procedure employed).

The regional vacancy data was purchased from the Conference Board (their Help Wanted Online data series), so unfortunately, I cannot make it available to you without their permission. I have permission to display the data, however. Here is what we get.

Addendum: Dec. 13, 2011

As I have stressed in an earlier post, one should be careful in using these raw correlations to identify the source of disturbance; see: Interpreting the Beveridge Curve.

A reader points out that the Monster Employment Index (available since 2004) might be of some use for measuring regional employment opportunities. 

Thursday, December 1, 2011

On Bagehot's Penalty Rate

What principles should govern the way a lender-of-last-resort (LLR) operates during a financial crisis? On this question, one is frequently referred to two key principles, attributed to Walter Bagehot in his book Lombard Street. The two principles are usually summarized as "lend freely and at a penalty rate." What does this mean?

In "normal times," firms regularly borrow cash on a short-term basis (say, to meet payroll). These loans are usually collateralized with a host of assets (e.g., accounts receivable, property, securities). The dictum "lend freely" in this context means to extend cash loans freely against the collateral that is normally put up to secure short-term lending arrangements.

The rationale commonly offered for the LLR is that during a crisis, "perfectly good" collateral assets are either no longer accepted as security for short term loans, or that if they are, they are heavily discounted (e.g., a creditor will only lend 75 cents for every dollar in collateral, instead of the usual 99 cents). Whatever the ultimate cause, this type of "liquidity crisis" creates havoc in the payments system. This havoc can be avoided, or at least mitigated, by a LLR that stands ready to replace the "missing" lending activity. (Or so the story goes.)

Let's say that the normal discount rate on high grade collateral is 0 < d < 1. So if a creditor offers to lend $99 for every $100 in collateral, d = 0.01 (one percent discount). Let's suppose that during a crisis, the discount rate rises to c > d. (If c = 0.5, then there is a 50% discount or "haircut" on collateral.) One issue that the LLR must address is the discount rate it should offer on an emergency loan. Let me call this discount rate p.

Now, if the LLR sets p = c, then what is the point of having an LLR? So clearly, if the LLR is to influence lending activity in any manner, it must  set p < c. Opponents of LLR activity like to label p < c a "bailout." (This term is rarely defined precisely; it appears to be a label to attach to programs that one does not like.)

At the other extreme, the LLR could set p = d. In this case, the LLR is discounting collateral in the same way that the market does during "normal" times. If the LLR instead set p > d, it is charging a "penalty rate." (Note: I do not think that Bagehot ever used this term.) How should the LLR set this penalty rate and why? Here is Bagehot:
First. That these loans should only be made at a very high rate of interest. This will operate as a heavy fine on unreasonable timidity, and will prevent the greatest number of applications by persons who did not require it. The rate should be raised early in the panic, so that the fine may be paid early; that no one may borrow out of idle precaution without paying well for it; that the Banking reserve may be protected as far as possible. (emphasis, my own)
Well, O.K., so he does not appear to answer the question of what discount rate to apply; only that it should be "very high." But I am less interested here in the precise penalty rate as to the rationale for why a penalty rate is necessary. A colleague of mine (who appears to have done a great deal of reading in the area) suggests that the rationale was primarily to ensure that the Bank of England did not run out of reserves (an event that would have led to its failure, and the subsequent end of civilization in the minds of many at the time).

Of course, the Federal Reserve Bank of the United States does not face the prospect of running out of cash reserves, the way that the Bank of England did back then. This is because "cash" back then took the form of specie (gold and silver coin). "Cash" today takes the form of small denomination paper notes (and electronic digits in reserve accounts) that the Fed can issue "out of thin air." In light of our modern institutional structure, I wonder whether Bagehot, living in today's world, might not have dropped his "penalty rate" dictum?

Is there any good reason left for the penalty rate? Perhaps there is. But it is clearly of second-order importance during a financial crisis. First, lend freely. It is probably not the time to worry about this penalty rate or that penalty rate in the depths of a liquidity crisis. If an institution is deemed, after the fact, to have benefited "unfairly" at the expense of society during an emergency lending episode, then a "fee for service" (i.e., tax) could be applied after the crisis has passed.

P.S. Would be interested to hear from historians on this subject.

Postcript: January 30, 2012
I would like to thank Josh Hendrickson for sending me the link to this paper:

Turning Bagehot on his Head.
Abstract: Ever since Bagehot’s (1873) pioneering work, it is a widely accepted wisdom that in order to alleviate (ex ante) bank moral hazard, a lender of last resort should lend at penalty rates only. In a model in which banks are subject to shocks but can exert effort to affect the likelihood of these shocks, we show that the validity of this argument crucially relies on banks always remaining solvent. The reason is that when banks become insolvent, Bagehot’s prescription dictates to let them fail. Penalty rates charged when banks are illiquid (but solvent) then reduce banks’ incentives to avoid insolvency ex ante and thus increase bank moral hazard. We derive a condition which shows precisely when this effect on ex ante incentives outweighs the traditional one and show that it is fulfilled under plausible scenarios.

Friday, November 25, 2011

A bridge over the macroeconomic divide

No one can deny that Paul Krugman is a gifted expositor of economic ideas. His column today, "Death by Hawkery," constitutes a fine example of this skill in action.

What I found most interesting in this column is something that would have almost surely escaped his average reader. In particular, I noticed that in telling his basic story, he appealed to a mathematically explicit model of credit cycles written by Nobu Kiyotaki and John Moore (JPE 1997).

Why do I find this interesting?

Well, first of all, I notice that at the time, Kiyotaki was affiliated with that great "freshwater macro" department at the University of Minnesota. You will also notice that the arch-devil Ed Prescott is thanked (among others) for his "thoughtful comments and help" on the paper.

I mention this because I think that Krugman has in the past overemphasized the disagreement that exists among the newer cohorts of macroeconomists (one could make the case that disagreement was much greater in the past); see, for example, here: Disagreement Among Economists. On this matter, I side with Steve Williamson, who I think has rightly taken Krugman to task on this issue; see here and here.

Secondly, I find it interesting that the mechanism highlighted by Kiyotaki and Moore in no way relies on nominal or real price rigidities. It is, in fact, a real business cycle model. Yes, you heard me correctly: Paul Krugman is appealing to an RBC model to help him account for recent events. (Granted, it is an RBC model that incorporates limited commitment, a friction that plays a prominent role in all modern macro theory; see my post here: Asset Shortages and Price Bubbles: A New Monetarist Perspective).

I think this constitutes evidence that the great macroeconomic divide is not as great as it is sometimes portrayed. Most of the disagreement I am aware of is of the gentlemanly "let us agree to disagree" type. But there is no fundamental disagreement in basic macroeconomic methodology among most academic macroeconomists. (There are, of course, healthy and welcome challenges from the fringes of the profession.)

Now for some comments on the economic ideas.

As you may have gathered from my previous post, I am generally sympathetic to the idea of expanding the supply of U.S. treasury debt at this time (with a commitment to unwind in the future, if and when economic conditions improve). Of course, a big question is what to do with the funds acquired in this manner. I'm with Krugman in that heck, we may as well use it to build physical capital (public infrastructure). Financing a corporate tax cut to stimulate domestic private capital spending might be a good idea too (not so politically popular though).

These provisional policy recommendations suggest themselves to me by way of a class of "new monetarist" models that I like to use to organize my thinking about things. But I should say, however, that I'm still not sure just how seriously to take these models (at least, their current incarnations). I'm still a little sketchy about how one might plausibly generate negative real rates of interest in these models; that is, models that take seriously the intertemporal production capabilities of actual economies (you will note that Krugman abstracts from physical capital in telling his little story).

I can't help but note that this same class of models might be used instead to support "conservative" policies. In particular, one force that can potentially drive the expected marginal product of capital (real interest rate) lower is the rational (or irrational) expectation of a future regulatory/tax burden paid for by capital accumulators of all types (including human capital).

If (and I emphasize the if) this is the (or a significant part of the) fundamental problem (and how do we really know that it is not?), then it is hard to see how treasury debt expansion and/or inflationary policy is going to solve it. Fixing the problem in this case means providing an environment that rewards private investment. Death by Dovery is also a possibility. 

Wednesday, November 23, 2011

Not enough U.S. debt?

One way to measure the ability to service debt is to compute a debt-to-income ratio. Suppose, for example, that your income is $50K per year, that your home is worth $200K, and that you have a $150K mortgage. Then your debt-to-income ratio is 150/50 = 3; or 300%.

Similarly, one way to measure the ability of a country to service its national debt is to compute debt-to-GDP (a measure of domestic income) ratio. The ratio of U.S. federal debt to GDP is currently close to 100%.

Of course, what has a lot of people worried is not the level, but the trajectory, of this ratio. Clearly, the debt-to-GDP ratio cannot rise forever.

No, but on the other hand, there is some evidence to suggest that it can feasibly go much higher. (Whether it should be permitted to do so is a different question, of course.)

Before I go on, I want to clear up a misguided analogy that I frequently hear repeated. The misguided analogy is the idea of the government behaving like a household running up a massive amount of credit card debt.

If this is the way you like to think about things, let me ask you this: Which of your credit cards charge you 0% interest? I ask because that is the interest rate creditors around the world are willing to lend to the U.S. federal government. And what sort of credit card company starts to reduce the interest it charges on your debt as you become progressively more indebted (see the figure above)?

In fact, the terms are even much better than 0%. The real cost of borrowing is measured by the real (inflation adjusted) interest rate. As the figure above shows, the real cost of borrowing has plummeted over the last decade for the U.S. government. As the following figure shows, the U.S. government can now borrow funds for 10 years at close to zero real interest. It can borrow funds for 5 years at a negative real interest.

Now, a negative real rate of interest is a pretty cool deal. Imagine importing 100 bottles of beer from China today, and having to return only 99 bottles next year. If the interest rate remains unchanged one year from now, you can rollover your debt and make a profit. For example, you could borrow another 100 bottles of beer from China, use 99 of these bottles to pay off your maturing obligation, and then drink the remaining beer for free. (Of course, domestic beer brewers would become upset at the lack of demand for their own product, but maybe they can be bribed with free Chinese beer?)

Before we get too carried away, however, I explain here why these very low real rates constitute bad news.

Why are real rates so low?

My own view is that this phenomenon, at its root, has little to do with Federal Reserve or Treasury policy. I believe that the decline in real rates on U.S. treasuries reflects a steady change in how agents and agencies around the world want to structure their wealth portfolios. There has been a massive substitution away from many asset classes into U.S. treasuries; and it is this fundamental market force that is driving real interest rates lower.

The phenomenon began in the early 1990s, with the collapse of the Japanese stock market. Then Mexico in 1994, the Asian crisis 1997-98, Russia in 1998, and Brazil in 1999; see Bernanke (2005). Investors became rationally pessimistic about the returns to investing in these countries, as well as similar countries that had not yet experienced crisis. The natural effect of this would be capital outflows from these countries into relative safe havens, like the United States.

The basic thesis here is very much related to what Ricardo Caballero calls a "global asset shortage." See his discussion here and here; and my own discussion here and here.

The global investment collapse associated with the recent recession has pushed already low real rates lower still. There has been a flight to U.S. treasuries not only by foreigners, but this time by Americans too. Evidently, the perceived return to domestic capital spending remains low. (Some basic theory available here.)


Given this pessimistic outlook, it seems unclear what monetary policy can do (the Fed is largely limited to swapping low interest currency for low interest treasuries).

I do, however, believe that there may be a role for the U.S. treasury (in principle, at least). In particular, given the huge worldwide appetite for U.S. treasury debt (as reflected by absurdly low yields), this is the time to start accommodating this demand. Failure to do so at this time will only drive real rates lower. For a world economy that is reasonably expected to grow, negative real interest rates imply a dynamic inefficiency. In short, this is the time to start raising real rates, not lowering them (real rates theoretically rise when new debt crowds out private capital, but note that new debt can also be used to finance corporate tax cuts to stimulate investment, if so desired).

Of course, what theory also tells us is that the government should also be prepared to reverse this recommended debt expansion (assuming that tax rates remain unchanged) once the domestic and world economy return to normal. One may legitimately question whether the government can be expected to make these cuts at the appropriate time. If the government lacks credibility along this dimension (or if future governments cannot be expected to abide by policies put in place by previous governments), then political forces may emerge to block an otherwise socially desirable debt expansion. Perhaps this is one way to interpret recent events.

Friday, November 11, 2011

Keystone Kops and Deficient Demand

Don't worry Sir...we'll find a way to stop those Canadians!
Domestic capital spending has been very slow to recover in the U.S. following the official end of the previous recession. Why is this the case?

Deficient demand, that's why. People are pessimistic. Their pessimism leads them to cut back on spending. And because everyone cuts back on spending, there is little incentive to hire new workers or start new capital projects. This means lower incomes for workers, which leads them to cut back even more on spending. Fear has become a self-fulfilling prophecy.

That's right -- all you people in the private sector out there -- you're a bunch of scaredy cats. That's why the government needs to take your money and spend it for you. You'll be the richer for it.

The problem with this "scardey cat" hypothesis is that there seems to be plenty of evidence suggesting that the private sector would love to start spending, if only the government would let it.

James Hamilton lists a few examples here highlighting some of the impediments to capital spending in the U.S. energy sector: Making Jobs Priority One.

Here is Hamilton describing the Keystone Gulf Coast Expansion Project in greater detail. He summarizes nicely here (in Shovel Ready):
And TransCanada wants to spend $7 billion of its own currency (no federal dollars asked for at all) to build exactly what we need in the form of the Keystone Gulf Coast Expansion Project. The pipeline would add capacity to transport another 500,000 barrels each day from Canada, North Dakota, and other regions in the U.S. to refiners on the Gulf Coast. At a price differential of more than $20/barrel, that wold generate over ten million dollars in new wealth every day. Beneficiaries of that wealth creation include the estimated 20,000 Americans who would work on construction of the pipeline and the $5 billion in estimated new property tax revenue for state and local government over the pipeline's lifetime.
Evidently, this project has been "shovel ready" for at least three years now. The project is being held up because of environmental concerns; see here and here (although, see Mark Perry). In fact, just yesterday, the Obama administration once again postponed the critical permitting decision until 2013; see here. Among other things, the following is highlighted:
The delay pushes a decision on the contentious proposal well beyond the 2012 presidential election in November, allowing President Obama to avoid a politically fractious determination in the midst of his reelection bid.
The political calculus is obvious here. And sadly, it's probably a good political calculation. But I do not wish to criticize the politics behind this (and several other related) decision(s). Not here, at least.

What I should instead like to stress is this: Whatever the merits of the cases made against these large private capital expenditure plans, their effect is to depress private domestic capital spending. This depressive is not some psychologically induced "animal spirit" that so many commentators and policymakers appear fond of ascribing to private sector behavior. It constitutes a real "tax" on private economic activity. And while it may be hard to quantify precisely how much this "regulatory tax" is holding back the recovery in domestic capital spending, the evidence from the Keystone project alone suggests that it is not insignificant. 

Thursday, November 10, 2011

Fiscal multipliers: another caveat

James Hamilton reminds us of what all Econ 101 students learn (or are supposed to learn) about the peculiarities of national income and product accounting and the caveats that need to be kept in mind when equating the measured GDP to true economic activity. The lesson is hammered home by Yoshiyasu Ono in this paper The Keynesian Multiplier Effect Reconsidered published earlier this year. Here is Hamilton's nice summary of the paper:
According to traditional Keynesian models, even for the case of a completely useless government project, if we were to raise private-sector taxes by just the amount needed to pay the salaries of the hole-diggers, GDP would increase, with a balanced-budget multiplier of one. Yet, Professor Ono asks, how could paying the crew a salary to dig a useless hole possibly lead to an improvement in welfare relative to simply handing them a direct transfer and allowing them to spend more time safely and comfortably at home with the family? And, to make things very simple, if the source of funds for paying the workers was in fact a tax levied on those same individuals, how could we possibly conclude that the enterprise has increased total national income?  
The answer is, we include government spending, even on useless projects, in the definition of GDP, and assume that the value of what is produced is the dollar sum that the government paid for it. The reason even useless government spending has a balanced-budget multiplier of one is that we now have a filled-in hole that we didn't have before. So we have more goods and services (in the form of a newly filled-in hole) than we used to, and impute the value of this new extra stuff as added income for the nation as a whole.
To understand what underlies this phenomenon, we have to revisit the definition of GDP. The Gross Domestic Product is defined as the market-value of all final goods and services produced by domestic factors of production over some specified time period.

It is also useful to keep the following in mind. All production is, by definition, sold (inventory accumulation is treated as a capital expenditure). Therefore, total output equals total expenditure. Moreover, as any expenditure on one side of a transaction constitutes income on the other side, it follows that total expenditure equals total income. To summarize:
 Output (GDP) is equivalent to Expenditure is equivalent to Income
Just to be clear, this is not a theory. It is an accounting identity (something that is true by definition). Now let me work through a series of examples.

First, suppose that a firm pays a worker $1 to produce an object that has a market value of $2. What is the contribution to GDP? The answer is $2. There are two ways to see this. First, the market-value of what has been produced/sold is $2. Second, total income has increased by $2. (Labor income has increased by $1 and profit income has increased by $1).

Now, suppose that a firm pays a worker $1 to produce an object that has a market value of $0. What is the contribution to GDP? The answer is zero. Again, there are two ways to see this. First, the market-value of what has been produced is zero. Second, while it is true that the income of the worker has increased by $1, this income gain is offset exactly by a $1 income loss for the firm. All that has happened in this example is a transfer of purchasing power from the firm to the worker. This is redistribution, not production.

Next, suppose that the government pays a worker $1 to produce an object that has a market value of $0. What is the contribution to GDP? The true contribution is zero. But that's not how the contribution will be measured in the NIPA. The NIPA assumes that the market value of the object produced by (or on behalf of) the government is $1. All that has happened in this example is a transfer of purchasing power from the taxpayer to the worker. This is redistribution, not production. But it will nevertheless be measured as production.

Why does this happen? Is someone trying to pull the wool over our eyes? No. As it turns out, many of the government services produced by government workers are provided for "free" and are hard to value at market prices (national defense is a classic example). When this is the case, it does not seem unreasonable to impute the market-value of a non-priced service by the cost of production.

Having said this, the lesson here is that one should nevertheless use caution in interpreting the estimated multiplier effects of fiscal stimulus programs using historical data as indicators of the likely impact of contemporaneous spending measures on true (as opposed to measured) GDP. The estimates are surely biased upward, although by how much likely depends on the exact nature of the expenditure.

What I have just described is a caveat for those who are inclined to perform cost-benefit exercises using "Keynesian" multiplier analysis. This type of analysis emerged out of a static model (the Keynesian Cross), where the benefit of a $1 expenditure by the government had to exist contemporaneously (there is no explicit future in a static model), which explains why the existence of multipliers greater than unity are so important in this way of thinking about things.

There is a better way of evaluating the net benefit of a government stimulus program. This involves estimating the expected net present value of the program (easier said than done, of course). With the real return on U.S. Treasuries so low (see my previous post), with U.S. infrastructure reportedly in a sorry state, and with so many unemployed construction workers, I would be surprised to learn that there are few positive NPV infrastructure projects currently available.

Unfortunately, political shenanigans (from all sides) sometimes make a mockery out the attempt to estimate NPV in a systematic and unbiased manner. We appear to be living in such times.

Thursday, November 3, 2011

Negative real interest rates

The nominal interest rate is a relative price. It is the price of a dollar today measured in units of (the promise of) future dollars. For example, if the risk-free annual interest rate on a U.S. treasury is currently 5%, then one dollar today is valued at 1.05 future (one year from now) dollars.

Current dollars usually trade at a premium relative to future dollars; the degree of this "impatience" is reflected in the nominal interest rate. The higher the nominal interest rate, the more money is valued today vis-a-vis future money. A high nominal interest rate reflects the market's strong desire to have you part with your money today (in exchange for a promise of future money). Conversely, a low nominal interest rate reflects the market's ambivalence about where to allocate dollars across time. A zero nominal interest rate means that the market values current and future dollars equally. To the extent that it is costless to store cash over time, the nominal interest rate is bounded below by zero. This "fact" is sometimes referred to as the zero lower bound.

In macroeconomic theory, the nominal interest rate plays second-fiddle to the so-called real interest rate. The real rate of interest is also a relative price. It is the price of output today measured in units of future output (think of "output" as consisting of an expenditure-weighted basket of commonly purchased consumer goods and services.) So, if the risk-free annual interest rate on an inflation-indexed U.S. treasury is 2%, then one unit of output today is valued at 1.02 units of output in the future.

In the same way that the nominal interest rate measures the relative scarcity of money across time, one can think of the real interest rate as reflecting the relative scarcity of output across time. Economists typically focus on the real interest rate because people presumably care about output and not money (they care about money only to the extent that it may be used to purchase output).

Current output usually trades at a premium relative to future output; that is, the real interest rate is usually positive. The higher the real interest rate, the more output is valued today vis-a-vis future output. A high real interest rate reflects the market's strong desire to have you part with your output today (in exchange for a promise of future output). Unlike the nominal interest rate, however, there is nothing that naturally prevents the real interest rate from becoming negative; see Nick Rowe. And indeed, this appears to have happened recently in the U.S. The following diagram plots the real interest rate as measured by the n-year treasury inflation-indexed security (constant maturity) for n = 5, 10, 20; see FRED.

Prior to the Great Recession, real interest rates are hovering around 2% p.a. and the yield curve is upward sloping (long rates higher than short rates), at least until early 2006 (when it flattens). Following the violent spike up in real interest rates (associated with the Lehman event), real interest rates have for the most part declined steadily since then. The 20 year rate is below 1%, the 10 year rate is basically zero, and the 5 year rate is significantly negative. What does this mean?

The decline in real rates that has taken place, especially since the beginning of 2011, is a troubling sign. A negative 5-year rate implies that current output is now less valuable than future (5 year) output. In other words, (claims to) future output are now trading at a premium. This premium may be signalling an expected scarcity of future output. If so, then this is a bearish signal.

The decline in market real interest rates is consistent with a collapse (and anemic recovery) of investment spending (broadly defined to include investments in job recruiting). For whatever reason, the future does not look as bright as it normally does at the end of a recession. To some observers, this looks like a "deficient aggregate demand" phenomenon. To others, it is the outcome of a rational pessimism reflecting a flow of new regulatory burdens and a potentially punitive tax regime. Both  hypotheses are consistent with the observed "flight to safety" phenomenon and the consequent decline in real treasury yields.

Unfortunately, the two hypotheses yield very different policy implications. The former calls for increased government purchases to "stimulate demand," while the latter calls for removing whatever barriers are inhibiting private investment expenditure. There seems to be room for compromise though. Surely there are public infrastructure projects that can be expected to yield a real return higher than zero? This is a great time for the U.S. treasury to borrow (assuming that borrowed funds are not squandered, of course).

In the event of an impasse, can the Fed save the day? It is hard to see how. The Fed's influence on real economic activity is usually thought to flow through the influence it has (or is supposed to have) on the real interest rate. One could make the case that real interest rates are presently low in part owing to the Fed's easing policies. But this would be ignoring the fact that the Fed's easing policies were/are largely driven by the collapse in investment spending. (I am suggesting that in a world without the Fed, these real interest rates would be behaving in more or less the same way.)

In any case, real interest rates are already unusually low. How much lower should they go? Is it really the case that our economic ills, even some of them, might be solved in any significant manner by driving these real rates any lower? My own view is probably not. If there is something the Fed can do, it is likely to operate through some other mechanism. The problem is not that real interest rates are too high. The problem is that they are not high enough (the robust economic prospects that push real rates higher appear to be absent).

Most Fed types probably hold the view that the main goal of monetary policy is to keep inflation low and stable so as to "anchor" inflation expectations; see James Hamilton on Ben Bernanke's 2007 inflation expectations speech. Bernanke defines well-anchored inflation expectations as being "relatively insensitive to incoming data."

We can compute a market-based measure of inflation expectations using a no-arbitrage-condition which states the the real rate of return on nominal and inflation-indexed treasuries should be roughly equal (the Fisher equation). The relevant nominal interest rates are plotted here:

Next, take the nominal interest rate above (at a given horizon) and subtract the corresponding real interest rate from the first diagram to get:

According to this data, the sharp spike up in real interest rates in the depths of the financial crisis stemmed entirely from a precipitous decline in longer-horizon inflation expectations. While inflation expectations appear to have rebounded to their more normal range of 2-3%, they continue to be more volatile than before the recession.

On the other hand, there is no evidence to suggest that inflation expectations are whirling out of control, one way or the other. I'm not sure to what extent this constitutes success. At the very least it is not utter failure.

Am off to Vancouver now for the 25th Annual CMSG

Wednesday, November 2, 2011

What went wrong at MF Global

Here is a nice quick summary of what went wrong: CNBC video (short, sweet, and to the point.)

It's the same old song. Big financial firm makes a big bet. Information flows relating to probable payoffs suddenly signal higher risk. Rating agencies move in to downgrade firm's liabilities. A "run" ensues (widespread redemptions) leading to...a liquidity event? or a solvency event? (only time will tell, I suppose.)

Why does MF Global matter? One reason is that the institution was added to the Fed's list of 22 primary dealer banks just 8 months ago. See WSJ article below.

Fed Takes Collateral Damage in MF Global Meltdown
Tue, 1 Nov 2011
698 words
By Min Zeng
November 1, 2011, 10:16 AM ET

The Federal Reserve is among those feeling the pinch from the collapse of MF Global Holdings Ltd., which only eight months ago was added to the Fed’s list of 22 primary dealer banks.

MF Global’s spectacular downfall seems unlikely to pose a systemic financial risk to either the U.S. economy or the Fed, in sharp contrast to the fallout from Lehman Brothers in 2008. But it’s possible it will make the selection procedure tougher for primary dealers, an elite group of institutions with which the New York Fed conducts monetary policy and which are obligated to participate in U.S. Treasury debt auctions.

MF Global’s fortunes quickly went downhill over the past week amid concerns over its exposure to the euro zone’s sovereign debt. In this way, its travails underscore the potential contagion risks to the U.S. financial system via the primary dealer network. Besides MF Global, several primary dealers are owned by big European banks, including France’s BNP Paribas SA and Societe Generale SA, whose shares sold off in September due to concerns about their exposure to debts in Greece and other heavily indebted euro-zone sovereigns.

“At the very least these applications will undergo a much more stringent vetting procedure,” said Chris Rupkey, senior financial economist at Bank of Tokyo-Mitsubishi UFJ Ltd. in New York. “The lesson of history after these sudden financial bankruptcies is that regulators come down harder than ever. They don’t want to see another MF Global again on their watch.”

The Fed may need to increase the standards of its scenario analysis when determining the balance-sheet strength of the primary dealers, said Adrian K. Miller, senior fixed income strategist at Miller Tabak Roberts Securities LLC in New York.

A spokesman from the New York Fed declined to comment Monday afternoon.

The Fed had already tightened conditions for selecting dealers. The latest revision came in January 2010, which included an increase in capital requirements from $50 million to $150 million.

On that basis, some believe the Fed can’t be faulted for having one of its dealers go bankrupt.

“No one can hold the Fed responsible for the risk of the firm,” said Michael Franzese, head of Treasury trading at Wunderlich Securities in New York. “You try and put adequate procedures in place so it doesn’t happen but you have to trust people to do the right thing.”

Firms that have been seeking to join the primary dealer list include Toronto-Dominion Bank, the second-largest bank in Canada, and CRT Capital, a Connecticut-based broker dealer.

Membership has proven profitable at time when Treasury volumes have increased and demand for Treasury bonds has been fueled by the more conservative strategies of investors spooked by the euro-zone crisis and by the Fed’s support for the market.

After naming MF Global and Societe Generale to the list in February, earlier this month the Fed added BMO Capital Markets Corp. and Bank of Nova Scotia, both of Canada, boosting the dealer number to 22.

Now, with MF Global’s exit leaving a space open, other prospective dealers could campaign for entry, knowing that the central bank needs an enlarged pool to facilitate the giant bond transactions it undertakes to channel monetary stimulus into the economy, according to market analysts.

The Fed at the start of this month launched “Operation Twist” — a $400 billion operation to run until mid-2012 through which it will sell short-dated Treasurys and buy those with maturities of between six years and 30 years. Those transactions will be carried out via primary dealers.

Primary dealers will also be needed once the Fed starts to withdraw the cash it pumped into the banking system over the past few years, a strategy that has swollen the central bank’s balance sheet to beyond $2 trillion from less than $900 billion shortly before the 2008 financial crisis.

The Treasury Department has an interest in sustaining a large membership list for primary dealers, too. It needs these institutions to underwrite government bond sales as it continues to announce giant auctions to fund the fiscal deficit. If the auctions don’t go smoothly, the Treasury’s borrowing costs will rise.