Using Beveridge curve dynamics to identify cyclical and structural shocks

I recently gave a short presentation to the Board of Directors of the Louisville branch of the St. Louis Fed. Following my presentation (which stimulated a lively discussion), I had the opportunity to listen to each member report on local economic conditions from different parts of Kentucky. Two themes stood out. The first was how "an air of uncertainty" along a variety of dimensions had "frozen" investment plans (with the apparent exception of younger entrepreneurs, who probably do not know any better-jk). The second was the unfilled demand for highly skilled, specialized workers (primarily in manufacturing).

I want to focus on the second theme here. In some sense, it is really amazing that firms are struggling to find qualified workers in an era of 8% unemployment. The Financial Times recently ran a piece on the subject: Skills Gap Hobbles US Employers, and I have to say that Mr. Greenblatt below would have fit right in at my BOD meeting:

Drew Greenblatt has been looking for more than a year for three sheet-metal set-up operators to work day, night or weekend shifts. 

The president of Marlin Steel Wire Products, a company in Baltimore with 30 employees, Mr. Greenblatt says his inability to find qualified workers is hampering his business' growth. "If I could fill those positions, I could raise our annual revenues from $5m to $7m," he says.  

He is offering a salary of more than $80,000 with overtime, including health and pension benefits. Yet in spite of extensive advertising,  he has had no qualified applicants. He is trying to train some of his unskilled staff but says none has the ability or the drive to complete the training. 

This quote identifies two problems. The first is what economists call "skills mismatch" caused by a "structural" shock. The second, that some workers are unwilling and/or unable to upgrade their skills is another matter that deserves attention, but is something that I will leave aside here. 

  
Apart from anecdotal evidence, how does one go about measuring "skills mismatch caused by structural shock?" One idea, initially proposed by Abraham and Katz (JPE, 1986), is to use the comovement to in vacancy and unemployment rates to identify "cyclical" and "structural" shocks. 

I put those terms in quotes because there are no set definitions for them. I like to think of a cyclical shock as an event that makes it more or less profitable to find the same kind of worker for the same kind of job. And I like to think of a structural shock as an event that makes it more or less profitable to find a different kind of worker for a different kind of job. 

Anyway, the Abraham and Katz idea is that one would expect cyclical shocks to trace out a stable, negatively-sloped Beveridge curve. That is, one would expect the job-vacancy rate and the unemployment rate to move in opposite directions.  A structural shock, by contrast, is expected to move vacancy and unemployment rates in the same direction. The idea here is that it is now more difficult to find the right kind of worker, so that even greater levels of recruiting intensity is likely to be associated with higher unemployment rates. 

The FT article cited above uses this idea in the diagram to the right (together with the results of a Kaufman poll of entrepreneurs) to suggest that the high U.S. unemployment rate is primarily the consequence of "structural" factors. 

Here is what the U.S. Beveridge curve looks like from May 2005 - November 2011 (The vacancy rate is computed from the Conference Board's help-wanted-online data, which is available from 2005 only).

As the HWOL measure of job vacancies is available at the city level, Constanza Liborio and I thought it might be interesting to see how job availability varies across major U.S. metropolitan areas and how job vacancy rates correlate with regional unemployment rates before and after the beginning of the most recent recession.

Specifically, the exercise we perform is as follows. Consider a major U.S. metropolitan area. Compute the average job vacancy rate and unemployment rate for this metropolitan area over the prerecession period May 2005 – November 2007. Recalculate these averages since the beginning of the last recession, December 2007 – November 2011. Next, compute the change in the vacancy rate and unemployment rate across these periods. Perform this exercise for a set of the largest metropolitan areas in the U.S. 

The results are displayed in the following figure.

Not surprisingly, we see that the unemployment rate in all these metropolitan areas went up since the recession began.  However, the same is not true of job vacancy rates (that is, not all vacancy rates went down, as one might have expected). Specifically, while we observe the typical Beveridge curve dynamic in many jurisdictions (suggesting that cyclical factors are dominant), we also observe vacancy rates remaining relatively stable, or even rising, in several others (suggesting that structural factors are dominant). 

So the tentative conclusion here is that the relative importance of cyclical vs. structural factors appears to vary across regions. To the extent that monetary policy is an effective stabilization tool, it cannot be expected to impact all regions of the country equally. In many regions, localized fiscal policies (education and training subsidies, etc.) may prove to be a more direct and effective tool.
Related story:
More Workers Moving for Out-of-State Jobs

Alien Employers or: How I Learned to Stop Worrying and let the World Run a Current Account Surplus

Meet your new boss.

Back when the Greek crisis was just breaking, I remember having my morning coffee, still half asleep, TV turned on in the background, when I heard a news reporter ask an interesting question. I put my coffee down and turned to the TV. The Parthenon was in the background, communist banners were draped about, and small smokey fires burning here and there. And the reporter, standing excitedly in the middle of all this, rather earnestly asked what I thought was a very good question: Why should Germany even consider bailing out Greece? 

Then, with hardly a pause, he breathlessly began to explain why. His answer went something like this...

"Why?! Let me tell you why, people..." [turns head to the left] "As I look over here, I see and Audi and a BMW..." [turns head to the right] "...and as I look over there, I see a Mercedes and a Volkswagen!" [turns to camera--big light bulb flashing over his head] "Greece is an extremely important export market for Germany!"

Well, as the following diagram shows, this certainly does appear to be the case (source):

So as far as I can gather, what the fellow is trying to tell us is this. The Germans should forgive Greeks their debts because, well, how else will the Greeks continue to afford importing German-made cars? After all, it is the Greek consumer that is selflessly keeping the German autoworker employed. Moreover, it has been a fine recipe for keeping German unemployment low, and growing German wealth. Yes, that's right...wealth in the form of...well, you know...grade A assets, like Greek government bonds.

Now where on earth might a fellow get an idea so bizarre as this? Well, how about here: Germans and Aliens (Paul Krugman):

But the Germans believe that their own experience shows that austerity works: they went through some tough times a decade ago, but they tightened their belts, and all was well in the end. Not that it will do any good, but it's worth emphasizing that Germany's experience can only be generalized if we find some space aliens to trade with, fast. Why? Because the key to German economic affairs this past decade has been a truly massive shift from current account deficit to surplus. 

Now, other countries within Europe could emulate Germany's past if Germany herself were willing to let its current account surplus vanish. But it isn't, of course. So the German demand is that everyone run a current account surplus, just like they do -- something that would only be possible if we can find someone or something else to buy our exports. It remains remarkable to see with how little wisdom the world is governed.

Now, I'm not sure whether any German really has made an explicit demand for all countries to run current account surpluses. But if anyone did, it would clearly be silly. The current accounts of all countries must necessarily sum to zero; at least, in the absence intergalactic trade.

But then, that sort of gave me an idea. Why not a world current account surplus?  What is an account, anyway? It's just a book-entry object. Let's give the account owner a proper name. And what's in a name? May as well call the account holder "Space Alien," with a "local" delivery address, say, the Pacific Ocean.

Next step. Contract some agency to print up Space Alien bonds, rate them AAA, then use them to acquire goods from all over the world, including ocean vessels. That should lower world unemployment. Then load the vessels with the newly purchased cargo, sail them out to their delivery point (the mid Pacific, say), and sink them all. (This last step is absolutely necessary, as sending the goods to any country on earth will mean job-killing imports for that country, jeopardizing their current account surplus).  Alas, the Space Aliens will ultimately have to default on its debt but, you know, who really cares? Just means more work is needed to replenish our lost wealth.

Now, if you think this sounds a little loopy, let me direct you to this: Fake Alien Invasion Would End Economic Slump.

Of course, this is all just a variation of the old Keynesian prescription of employing people to dig up holes and fill them up again. And, contrary to what you may be thinking, the purpose of this post is not to argue against the ability of such a program to increase net employment. What I want to question instead is why running a current account surplus is necessary for all this hocus pocus to work? 

Here's an idea. Instead of exporting vehicles to Greece, why don't German car manufacturers ship their cars to domestic German residents instead? The domestic purchasers could pay for the cars by issuing fake paper, just like their foreign counterparts. And when the time comes to default, well, at least all the BMWs, Audis, Mercedes, and Volkswagens will be residing on German soil. 

The regional dispersion in U.S. vacancy and unemployment rates

Since I happen to have handy some regional data on the help-wanted index (HWI) for the U.S., I thought it might be interesting to see whether U.S. vacancy and unemployment dynamics in a cross-section display any interesting patterns. (I would like to thank Kyle Herkenhoff for suggesting this exercise to me).

The regional HWI data is from the Conference Board. I explain here how the data was corrected for the recent substitution from print to electronic media in job advertising activities. That data was constructed for 36 U.S. cities.  I construct a "vacancy rate" measure by dividing the HWI by the labor force and normalizing to 10  in 1990:1. Here is what the aggregate data looks like:

As one would expect, there is a strong negative correlation between vacancies and unemployment; this is the so-called Beveridge Curve.

Labor economists sometimes like to gauge labor market conditions by constructing a "labor market tightness" variable--the ratio of vacancies to unemployment, or the v/u ratio. The v/u ratio plays a prominent role equilibrium unemployment theory; see Diamond, Mortensen and Pissarides. As the following diagram shows, labor-market-tightness is highly procyclical.

Regional Patterns

The following diagram plots the unemployment rates for 36 metropolitan areas in the U.S. The solid black line is a population-weighted average (it corresponds to the national unemployment rate).

The figure shows that there is significant disparity in regional unemployment rates at all points in the business cycle. As the U.S. economy emerged from the recession in the early 1990s, regional variation in unemployment rates seems to have declined for the rest of that decade. Nothing much changed until the most recent recession, where we see a dramatic increase in both the average unemployment rate and its in its dispersion across regions.

Next, let's take a look at regional "vacancy rates" (the city-based HWI divided by regional labor force).

The dispersion in regional vacancy rates appears to be very, very large (measurement error?). Using my eyeball metric, it appears that the dispersion in vacancy rates is somewhat procyclical. In particular, look at how the dispersion appears to increase throughout the 1990s expansion--at the same time, the dispersion in unemployment rates is declining. This suggests that the dispersion in labor-market-tightness is procyclical; and indeed, the following diagram shows this to be the case.

It would be interesting to know what might be behind these regional differences in labor market tightness, and why this regional dispersion varies over the business cycle.

First, what accounts for the dispersion? In a basic Mortensen-Pissarides labor market search model, extended to incorporate regions, I think that the labor-market-tightness variable is likely to equate across regions (at least, allowing for factor mobility). Regional differences in tax rates, etc., might account for some of the disparity. But the measured disparity is huge.

Second, what accounts for the cyclical properties of the dispersion? Is it simply the case that some regions are populated by industries that are more cyclically sensitive to aggregate shocks? Or is it the case that the shocks themselves are concentrated in certain regions, with the effects propagating to other regions of the country?

If anyone would like to see this data plotted in a different way, or see some statistics reported, feel free to let me know. (Thanks to Constanza Liborio for preparing these graphs.)

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.

Analysis

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).

Conclusion

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?

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?

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 g_t 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. 

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.