The bounds of monetary policy on Planet Earth

I read too much from monetarists and quasimonetarists and progressive monetarists and what not that monetary policy is what we need, that fiscal is unnecessary.

For the moment, let’s put aside the big disputes about whether macro demand-side remedies are a good idea. Let’s stipulate that they are, that increasing aggregate demand or accommodating people’s elevated demand for the medium of exchange or whatever would be a good thing. Woo hoo!

Here’s Bryan Caplan Arnold Kling, stipulating exactly that, despite some skepticism:

Intuitively, the equilibrium effect of a one-shot helicopter drop that doubles the money supply is to permanently double nominal income. If this leads to a stealthy, stable reduction in real wages, then output and employment go up permanently, too. Otherwise the price level doubles. Either way, there’s no reason for nominal income to recede as time goes on.

In short, if you think that boosting nominal income is the cure for recession, here’s yet another reason to prefer monetary to fiscal stimulus. One burst of expansionary monetary policy increases nominal income forever. One burst of expansionary fiscal policy increases nominal income for as long as the extra spending continues. At best.

I’m not sure Caplan is right on the economics here. His post seems to assume a world in which base money and bonds are imperfect substitutes. Some people might say that’s normal, and call the other situation a liquidity trap. But if so, liquidity trap is probably the new normal. The Fed has signaled (ht Aaron Krowne) they may pay interest on reserves at the overnight interest rate indefinitely under a so-called “floor” regime. I wish more economists would update their models for a world in which interest is paid on reserves as a matter of course. Interest on reserves represents a permanent policy shift that had been planned since 2006. It was not an ad hoc crisis response that can be expected to disappear. If interest is paid on reserves at the overnight rate and short-term bond markets are liquid, then short-term bonds and base money are perfect substitutes and a helicopter drop performed by the Tim Geithner dropping bonds from an F-16 would be as effective (or ineffective) as Ben Bernanke dropping dollar bills from his flying lawnmower.

But there is one big difference. Timothy Geithner is legally allowed to give away money for nothing. He does it all the time! He writes checks to Social Security recipients, gives money to welfare recipients and oil companies and big pharma. He even writes checks to me when my accountant or George W. Bush decide I’ve paid too much in taxes! Ben Bernanke, on the other hand, would go to jail for stuff like that. Sure, he has the printing press. “Operationally”, as the MMT-ers like to put it, he is entirely unconstrained. His checks never bounce. Why can’t he devalue the dollar, or use the threat thereof to upgrade inflation expectations? The economic law of supply an demand has not been repealed, but neither has US law. By law, the Federal Reserve can only engage in financial asset swaps. It shoves money out the door in exchange for some financial asset that colorably has the same value as the money it has dished.

Helicopter drops by the Federal Reserve are illegal. Helicopter drops by the Treasury happen all the time. Every law ever passed that overpays for anything, that has some manner of a transfer component, is a helicopter drop. I think all of us, left and right, delightful-smelling and stinky, can come together in a big Kumbaya and agree that most Federal spending has a transfer component, and is therefore a helicopter drop to some degree. It would not be a big deal for Congress to pass some law with even bigger, badder transfer components. They love to outdo themselves.

I think on the technocratic right, monetarists tend to think that helicopter drops by the Fed would be fairer than fiscal policy that launders transfers through expenditures. On the left and hard-crank right are people who don’t see the Fed as very fair at all, and emphasize the institution’s inclination to support certain interest groups when it does find ways of sneaking transfers through its legal shackles. My view is, a pox on both your houses, but it sucks that we are roommates. Macroeconomic policy by fiscal expenditures directed to politically favored groups is awful, unfair, and corrosive of the body politic. Macroeconomic policy by asset swaps that are quietly mispriced is awful, unfair, and corrosive of the body politic.

That’s the way it is here on Planet Earth (or at least on Planet USA, which is arguably at some remove from Planet Earth). Of course, we could change things. We could enact a law that instructed the Fed to engage in fair, perfectly transparent, helicopter drops as an instrument of macroeconomic policy. And boy would I support that! We could, as Matt Yglesias suggests (riffing on the work of Beowolf and the MMT-ers), have the Treasury issue some giant platinum coins and give them out to everyone. The difference between those two policies would be, well, no difference at all.

To the degree that our problem is on the demand-side and stems from private-debt-overhang-induced risk aversion or a desire to hoard money, we know the solution. That problem, if it exists, will go away if we give everyone money. But giving everyone money is not conventional, authorized, monetary policy. It requires new law. Politically, the law it requires would be hard law, because it shifts the distribution of risk in our very unequal polity. If we were to give everyone $20,000 tomorrow, whether it’s Ben or Timothy signing the checks, debt-overhang goes away as a macroeconomic concern. I believe, to some degree, in the demand-side story, so I’d wager that real GDP and employment would rise as well. But we would risk a step up in the price level, and therefore a devaluation in real terms of fixed-income claims and bank equity. Under status quo policy stagnation, near-term macroeconomic risks are borne primarily by the poor and marginally employed. With demand-side stimulus, whether designed by Scott Sumner via the Fed or Matt Yglesias via the Treasury, those risks would shift to financial savers, who in aggregate hold the bulk of their portfolio in the form of fixed-income securities, and who also hold the testicles of members of Congress.

The fiscal vs. monetary policy debate has gotten tiresome and distracting. If you think we need demand-side action, say specifically what you think we should do. If it’s a helicopter drop, whether by Fed or Treasury, then we need new law. Push it, and tell the self-styled realists and pragmatists to fuck off. If you think the Fed’s existing toolkit of running asset swaps and controlling the rate of interest on reserves would be enough if only they set expectations properly, then we still need new law. The Fed is not going to target NGDP or a price level path over any relevant time frame without a change in governance structure or mandate. People on the left and right and especially the technocratic center who like to see the Fed as a loophole through a dysfunctional Congress are kidding themselves. The Fed is a political creature, not some haven for philosopher-economists in togas who will openly consider your ideas. Get over it and get your hands dirty.

Update: Oops! I originally confused one of the excellent bloggers over at Econlog for another, misattributing Bryan Caplan’s post to Arnold Kling. Huge apologies to both, and many thanks to @derridative for pointing out the error.

Update History:

  • 31-Aug-2011, 12:45 a.m. EDT: Added update noting my group-blog dyslexia re Bryan Caplan & Arnold Kling, thanks @derridative! Updated text to Caplan, but left Kling struck through once to emphasize the error. Added ht to Aaron Krowne for Fed “floor” article. Changed “an institional” to “the institution’s”.

Who are this ‘we’ of which you speak, Tyler Cowen?

Tyler Cowen has a tag line he’s been using for a while. Here’s the latest example:

Just to review briefly, I find the most plausible structural interpretations of the recent downturn to be based in the “we thought we were wealthier than we were” mechanism, leading to excess enthusiasm, excess leverage, and an eventual series of painful contractions, both AS and AD-driven, to correct the previous mistakes. I view this hypothesis as the intersection of Fischer Black, Hyman Minsky, and Michael Mandel.

In what sense is it true that “we thought we were wealthier than we were”? It is not obvious, for example, that we have encountered some unexpected scarcity in real factors that has forced us to downgrade our perception of our collective wealth. I don’t think that is what Cowen claims has happened, exactly. So what does he mean? We get some clues from his list of names. Fisher Black, as Cowen has interpreted him, suggests that since investors’ views over the short-term are not independent of one another, patterns of aggregate investment can be systematically mistaken for a while in ways that seem surprisingly obvious in retrospect. Hyman Minsky famously argued that the dynamics of financial capitalism encourage and even require ever more fragile and optimistic means of finance, leading inexorably to crisis. Michael Mandel claims that US productivity measures exaggerate domestic capabilities by failing to distinguish between domestic production efficiencies and gains due to outsourcing and production efficiencies elsewhere.

I’d like to add another name to the list, for Cowen’s consideration. Here’s John Kenneth Galbraith (grateful ht to commenter groucho, long ago):

To the economist embezzlement is the most interesting of crimes. Alone among the various forms of larceny it has a time parameter. Weeks, months, or years may elapse between the commission of the crime and its discovery. (This is a period, incidentally, when the embezzler has his gain and the man who has been embezzled, oddly enough, feels no loss. There is a net increase in psychic wealth.) At any given time there exists an inventory of undiscovered embezzlement in — or more precisely not in — the country’s businesses and banks. This inventory — it should perhaps be called the bezzle — amounts at any moment to many millions of dollars. It also varies in size with the business cycle. In good times, people are relaxed, trusting, and money is plentiful. But even though money is plentiful, there are always people who need more. Under the circumstances the rate of embezzlement grows, the rate of discovery falls off, and the bezzle increases rapidly. In depression, all this is reversed. Money is watched with a narrow, suspicious eye. The man who handles it is assumed to be dishonest until he proves himself otherwise. Audits are penetrating and meticulous. The bezzle shrinks.

In any case, a common thread behind all of these stories is that our “overestimate” of wealth is not a random phenomenon. We did not just have a collective “oops!”. In Galbraith’s version, it is outright embezzlers who contrive to keep our accounts inflated. In Mandel’s, it is well-meaning but mistaken government economists (as well as those who unskeptically rely upon them). In Minsky, it is the interplay of competitive dynamics and financing arrangements. The Black/Cowen account is the least specific, but requires some common signal that causes investors’ judgments to be correlated, so their errors do not cancel.

What has been our actual, lived experience of the past decade or so? What were the common signals that rendered investors decisions to be both correlated and mistaken?

I don’t wish to denigrate Mandel’s work, which I consider useful and insightful. Certainly overestimates of domestic productivity contributed to a general sense of optimism, and as Mandel has argued, probably contributed to policy errors during the crisis as apparent high productivity helped policymakers to mistake a chronic economic crisis for a transient distortion in response to a financial shock. Robust apparent productivity growth might well have helped rationalize consumer and housing credit decisions that now seem questionable.

But I think we know something about the investors of the last decade. There was, as This American Life / Planet Money famously put it a “giant pool of money”, specifically sovereign and institutional money, that was seeking out ultra-safe, “Triple A” investment, and sometimes agitating for yield within that category. We really don’t need to look for subtle information cascades in order to explain investors’ “errors”. The investors in question weren’t, in fact, investors at all in an informational sense. To a first approximation, they paid no attention at all to the real projects in which they were investing. They were simply trying to put money in the bank, and competitively shopping for good rates on investments they could defend as broadly equivalent to a savings account.

But how did this “giant pool of money” come to be? The overestimate of wealth occurred prior to as well as during the investment process, a fact which can’t readily be explained by the Black/Cowen story. There was too much income to be invested, income which took the form not of speculative securities but of money, visible flows of central bank reserves and bank deposits. When ordinary investors make mistakes, however correlated, what we observe is a mere overpricing of questionable securities. Under current institutional arrangements, there is only one kind of investor who can convert investors’ mistakes into cash income growth (holding “velocity”, the reciprocal of peoples’ desire to hold income as cash or bank deposits, roughly constant). Only mistakes by banks can explain the increase of money income. (Note that the relevant income here, for the US, is not NGDP, but US dollar income worldwide, including e.g. income generated from exports by China and oil producers.)

It would be plausible to argue that banks were not at the vanguard of the error, that they were only caught up in a general zeitgeist of malinvestment, if other classes of investors were making the same misjudgment. That roughly describes what happened during the dot-com boom. But during second boom, other classes of investors were, to a first approximation, making no judgments at all. Institutional investors were simply buying the securities that banks were willing to treat as “money good” and reaching nihilistically for yield without a care in the world about how it might be generated.

Even the most careful and independent population of investors is likely to have its aggregate expectation disappointed if those investors’ incomes correspond to a lower quality of real resources than is suggested by the number of dollars that alight in their bank accounts. And any rational investor will choose to forego direct participation in risky real projects if intermediaries offer sufficient yield on securities that banks are willing to monetize at will. The primary mistake of non-bank investors was to fail to foresee that banks would change their willingness to accept as “money good” securities that core institutions were designing for precisely that acceptance. The “overestimate” of wealth from which we are now suffering occurred first as an exaggeration of value within the core financial system and then as a willingness of institutional investors to take values given by core financial intermediaries as durably sound. “We” did not decide we were wealthier than we are. Two groups of people whose economic role is precisely to evaluate the quality of our wealth misjudged, one directly by neglecting risk, the other indirectly by trusting the first when it should have known better. The broad public or taxpayers or the polity erred only and precisely by trusting these professionals.

Why were banks so easily persuaded that, via the magicks of tranching and diversification, lending into obviously questionable real projects was so safe that any downside risk could safely be socialized? The banking sector’s job is to convert a portfolio of real investment into money that is ultimately backed by the state, and its responsibility is to do so in a manner such that the likelihood realized values will in aggregate undershoot funds advanced is negligible, without recourse, directly or indirectly, to any heroic government stabilization. “Mistake” is not a remotely sufficient characterization of what occurred. There were discernible incentives behind the banking sector’s misbehavior. Throughout the securitization chain, conservative valuation practices were entirely inconsistent with maximizing employee and shareholder wealth. And why did institutional money trust bank and rating agency valuations when money managers were not too stupid to understand that high yield and low risk make for a fishy combination? Again, the answer is not some kind of sunspot. Agents were well paid not to question “money center banks”, for whose misjudgments and misrepresentations they could never reasonably be blamed.

The broad public did err, by accepting an absurdly and dangerously arranged financial system. If we want to prevent a recurrence going forward, if (qua Black/Cowen) we want to enter a world where it would even be possible for investors’ judgments to be reasonably independent, we have to undo a financial system designed around the delegation of investment decisions from the broad public through several tiers of professionals to a semi-socialized “money center” core. Yes, we also have to attend to the public sector’s role in generating “money good” securities not-necessarily-backed by reliable value. But that’s an implausible account of the lead-up to 2008, and we should be cognizant of the fact that, absent debt-ceiling own goals, public sector securities fail more gracefully than bank advances against private assets. (The costs of public sector over-issue would be experienced either as inflation or economic depression due to tight monetary policy required to avoid inflation even in the face of underemployment and not, at least initially, as a banking crisis.)

Despite all these errors, we have no reason to believe that, in real terms, we are unable to consume or produce today at levels suggested by the pre-2008 trendline. Yes, we’ve recently experienced price spikes that might suggest scarcity of some commodities. But we experienced large spikes prior to the crisis and kept on growing. Over the longer haul, we may be able to grow around emerging scarcities via technological ingenuity or we might have to redefine growth so that we value less resource-intensive consumption more highly in order to sustain the almighty trendline. But at this moment, we are not discouraged by a physical bottleneck, but by increased uncertainty about the future value of our resources, skills, organizations, and political arrangements. The only coherent way to understand Cowen’s tag line is that we currently believe the future to be less bright than we believed it to be in 2007, and this change in collective expectation has altered our behavior. We are not, today, forced to produce or consume less than we expected to in 2007. We are choosing to do so, perhaps pathologically as a Keynesian output gap, perhaps wisely in order to conserve and regroup given diminished expectations going forward. (Even if you buy the latter story, conservation of human resources implies providing education or employment. No true Austrian would characterize involuntary idleness, misery, and decay as desirable no matter how badly we discover we have malinvested.)

If Cowen is right, it has caused us a great deal of misery that “we thought we were wealthier than we were”. We should attend very carefully to the details of how we came to think what we thought, of who told us we were wealthy when we weren’t. (Shades of Galbraith…) More importantly, if we cannot evaluate the quality of our wealth going forward, we are unlikely to make decisions conducive to sustaining and expanding that wealth. There is something in the tone of Cowen’s tagline that suggests an “oops!”, a shrug of the shoulders. Whether he intends that or not, it’s precisely the wrong response to the events of the last decade. “Our” misjudgments were not some random perturbation spiraled out of control. They were the result of a set of arrangements that systematically bribed gatekeepers to make and accept incautious estimates, and to circumvent control systems intended to keep valuations in check. As of this writing, those arrangements remain largely in place.

Update History:

  • 1-Aug-2011, 1:01 a.m. EEST: Changed misspelling, “hos” to “his”, in Galbraith quote. Changed “specifically seeking” to “seeking out” in order to avoid awkward repetition of “specifically”. Changed “are” to “is” to agree with “population”, the actual subject of the sentence. Removed a superfluous “the”. Changed “really can’t” to “can’t readily”. No substantive changes.

Accounting is destiny

So, unusually, Felix Salmon is wrong:

In order for banks to offer principal reductions, two criteria need to have been met: (a) they came into the mortgages via acquisition, rather than writing them themselves; and (b) they bought the mortgages at a discount… Economically speaking…what the banks are doing here does not make sense. Either writing down option-ARM loans makes sense, from a P&L perspective, or it doesn’t. If it does, then the banks should do so on all their toxic loans, not just the ones they bought at a discount. And if it doesn’t, then they shouldn’t be doing so at all.

It makes perfect sense for banks to reduce principal on loans valued at less than par on their books, and to refuse to do so for other loans.

Let’s suppose we have a loan whose direct value will increase if we offer to reduce the principal owed. That’s not a rare situation. As Salmon writes, “a sensibly modified mortgage is likely to be much more profitable for a bank than forcing a homeowner into a short sale or foreclosure and trying to sell off the home in the current market.” Under these circumstances, one effect of a principal reduction is to increase the expected present value of the cash flows associated with the loan. Ka-ching!

However, there are two offsetting effects. The most widely discussed is moral hazard. Banks worry that borrowers for whom a principal reduction would impair rather than enhance the economic value of the loan will find ways of getting reductions too, by strategic mimicry or due to changing norms and public pressure. That helps to explain why (Salmon again), “principal reductions were being done on many mortgages which were actually current and in good standing, rather than on mortgages which were careening towards foreclosure.” Keeping principal modifications something that is offered only to “our best customers” keeps the practice voluntary. It preserves banks’ freedom to discriminate between profit-making and loss-making modifications.

The second offsetting effect of an otherwise desirable principal reduction is a matter of accounting. If a bank has a loan on its books valued at par, and it offers a principal reduction, it must write down the value of the loan. It takes a hit against its capital position, and experiences an event of nonperformance that even the most sympathetic regulators will have no choice but to tabulate. If a bank has purchased a loan at a discount, however, the loan is on the books at historical cost. The bank can offer a principal reduction down to the discounted value without experiencing any loss of book equity.

Of course this is a matter of mere accounting. Whether or not a bank takes a capital hit has no bearing on whether a principal reduction will increase the realizable cash-flow value of the loan.

But accounting is destiny. The economic value of a bank franchise, both to shareholders and managers, is intimately wound up with its accounting position. A bank whose books are healthy may distribute cash to shareholders and managers, while a bank whose capital position has deteriorated will find itself constrained. A well-capitalized bank is free to take on lucrative, speculative new business, while a troubled bank must remain boringly and unprofitably vanilla. The option to distribute and the option to speculate have extraordinary economic value to bank shareholders and managers.

You cannot understand banking at all unless you understand that banks must be valued as portfolios of options. You can value some businesses by estimating the present value of cash flows from firm assets, and then subtracting liabilities. But banks are more complicated than that. The value of a bank is a function not only of expected cash flows, but of the shape of the probability distribution of those cash flows, and of the diverse arrangements that determine how different cash flow realizations will be split among a bank’s many stakeholders. A hit to a bank’s capital position narrows the distribution of future cash flows (by attracting regulatory scrutiny) and diminishes the degree to which cash flows can be appropriated by shareholders and managers rather than other parties. To say that a bank should only be concerned with maximizing the long-horizon value of its loan book is like arguing that the holder of a call option ought not object if her contract is rewritten at a higher strike price, because, after all, changing the strike price doesn’t reduce the economic value of the underlying. A bank’s accounting situation and regulatory environment define the terms of the options that are the main source of value for big-bank shareholders. Accounting changes imply real transfers of wealth.

Now the value of a bank to shareholders and managers is very different from the social value of a bank. If we aggregate the interests of all of a banks’ claimants — shareholders, managers, bondholders, depositors, counterparties, guarantors — there is far less optionality. From a “social perspective”, what we want banks to do is to lend into enterprises whose interest payments reflect real value generation and then maximize the expected value of those cash flows, irrespective of who gets what among bank claimants. If we were serious about that, we would force banks to write down their loan portfolios aggressively, so that going forward shareholders and managers have nothing to lose by offering principal modifications when doing so would maximize the cash flow value of their loans. But if we did force banks to write their loan portfolios down aggressively, the shareholders and managers with nothing to lose would be different people than the current shareholders and managers of large banks, via some resolution process or restructuring. Which is much of why we didn’t do that, when we had the chance, and why bank mismanagement of past loans continues to exert a drag on the real economy as we try and fail to go forward. This very minute, there are homeowners who are nervously hoarding cash, who are leaving factories idle and neighbors unemployed, in order to maximize the option value of the bank franchise to incumbent shareholders, managers, and uninsured creditors.

The debt ceiling and the end of QE2

This is a trivial point, but I haven’t seen it made.

It will be very difficult to tell whether the expiration of QE2 was the end of the world, or whether it will matter very much at all, until the debt ceiling standoff is resolved.

Quantitative easing alarmists tend to take a “flow” view of Treasury bond prices. During QE2, the Federal Reserve was purchasing a substantial fraction of the debt issued by the Treasury, reducing the flow of securities that the private sector was required to absorb. Without the Fed as a megapurchaser, the private sector will have to absorb a larger quantity of debt, and may demand concessions on price (or, equivalently, higher yields) in order to do so.

QE2 has ended, but the net flow of Treasury securities to the private sector has not increased. On the contrary, since mid-May net issuance has ground to a halt, as the Treasury has juggled intragovernmental accounts to fund itself without violating the debt ceiling.

I have no idea whether the QE2 Cassandras are correct or not. But we won’t have a reasonable test of their hypothesis, even by the rough and ready evidentiary standards of a blogfight, until the US Treasury resumes funding its deficit by selling securities to the public at large.

FD: I’m short long-term US Treasuries, and have been for years, for reasons that are in part speculative and in part related to hedging other positions. I have no strong view on the degree to which QE2 or its expiration might affect Treasury prices.

Update History:

  • 6-July-2011, 8:25 p.m. EDT: Added parenthetical “(or, equivalently, higher yields)”.

A question for Greece and elsewhere

Suppose that Greece had never adopted the Euro and the terms of its external borrowing had remained subject to “market discipline”, as it had been in the 1990s. Would Greece today be better off or worse off, in real terms, looking forward?

This does not seem to me an easy question to answer. On the one hand, Greece’s borrowing on easy terms inspired a great deal of real activity, including valuable development in a variety of sectors. On the other hand, it is now clear that indiscriminate credit enabled patterns of behavior that were unsustainable, the adjustment from which will be costly and painful. If foreign capital had been available but discriminating, perhaps some of the real activity and development of the 2000s would have not have occurred. But perhaps the activity that would have occurred would have been channeled in different directions, forming patterns more sustainable and profitable, and less corrupt.

This question isn’t really about the Euro per se. Several Central and Eastern European members of the EU also enjoyed indiscriminate credit booms without formally adopting the common currency. Ultimately, the question is whether market discipline, and the restriction of choice that it implies, is a long-term benefit or a long-term cost to the nations that face it. Does active monitoring by foreign creditors ever actually help nations develop well? Or is that a kind of capitalist pipe dream? And if useful market discipline is an old wives tale, is it better for countries to take whatever money is cheaply on offer in spite of the likelihood of inefficient use, or to restrict external borrowing on the theory that undisciplined cash promotes corruption and boondoggles and ultimately leaves nations hobbled?

These sound like “emerging markets” questions, and they are, but they are more broadly applicable. I find myself asking the same set of questions about the United States, whose external borrowing seems famously immune from market discipline. On net, is that fact a blessing or a curse?

Update History:

  • 3-July-2011, 8:25 p.m. EDT: Removed an unnecessary “the” and an ungrammatical “that would”. No substantive changes.

A license to lie, backdated

In a party-line, 5 to 4 split, the Supreme Court last week severely curtailed investors’ practical ability to hold financial intermediaries accountable for fraud. The case, Janus Capital Group, Inc. v. First Derivative Traders, seems arcane. But for perpetrators of fraudulent securitizations, it is a jubilee. The Supreme Court has eliminated the danger of their being investigated and sued by the people whom they fleeced.

The decision limits the reach of Rule 10b-5:

It shall be unlawful for any person, directly or indirectly, by the use of any means or instrumentality of interstate commerce, or of the mails or of any facility of any national securities exchange,

  • To employ any device, scheme, or artifice to defraud,

  • To make any untrue statement of a material fact or to omit to state a material fact necessary in order to make the statements made, in the light of the circumstances under which they were made, not misleading, or

  • To engage in any act, practice, or course of business which operates or would operate as a fraud or deceit upon any person,

in connection with the purchase or sale of any security.

The case concerned a mutual fund whose prospectus was alleged to contain misleading statements that harmed investors. The question before the Supreme Court was not whether the statements were in fact misleading, but who should be construed as having made the statements. The answer, the Court determined, is perhaps nobody at all. Misleading statements were made, but literally no one can be held accountable.

When an ordinary firm issues securities, the firm itself is the “person” who makes the statements that appear in prospectuses and other disclosures. But with dedicated investment vehicles, things are more complicated. Investment vehicles — mutual funds and ETFs, but also securitizations like RMBS and CDOs — segregate the management and operation of the fund from the legal entity whose securities investors hold. If you “own” a Janus mutual fund, the securities you hold are likely claims against an entity called Janus Investment Fund. But Janus Investment Fund exists mostly on paper. Another company, Janus Capital Management, actually does everything. The human beings who make day-to-day investment decisions, as well as the offices they work in and the equipment they work on, are provided by Janus Capital Management. Communications and legal formalities, including prospectuses, are drafted by employees of Janus Capital Management.

The Supreme Court held is that, even though employees of Janus Capital Management company actually wrote any misleading statements, even though they managed nearly every substantive aspect of the operation of the fund, they cannot be held responsible because they did not “make” the statements. The “person” under law who made the statements was the entity on whose behalf the offending prospectus was issued, the investment fund, which has no capital other than the money it invests for shareholders. Under Janus, the management company is beyond the reach of aggrieved investors.

Then can the fund be meaningfully held accountable? The fund does have an “independent” board of directors, who in theory work for shareholders and “negotiate” the terms of the management contract. In practice, the management company typically organizes the fund and selects its directors. Still, if the investment fund “made the statement”, then surely those directors would be accountable, right? No. The investment fund’s directors supervise the fund at a very high level. In a large “fund family”, the same directors may be responsible for tens or hundreds of different portfolios. They may not have understood that statements in some prospectus were misleading. A violation under Rule 10b-5 must be knowing or reckless to be actionable. So the fund’s directors may prove beyond reach. Outright lies may be told, yet investors may find they have no practical means of holding anyone accountable. Justice Breyer, who dissents from the Court’s decision, writes

The possibility of guilty management and innocent board is the 13th stroke of the new rule’s clock. What is to happen when guilty management writes a prospectus (for the board) containing materially false statements and fools both board and public into believing they are true?

Plausible deniability is the order of the day. Managers can be as nasty as they wanna be. As long as their misbehavior is obscure enough that fund directors can plead ignorance, nobody gets in trouble. (If directors could be held liable, then the management company might be in jeopardy as well, under Section 20(a) of the Securities Exchange Act. But if the directors are innocent, then so are the managers.)

The really high-stakes fraud lately has been in the securitization business. The Janus decision gives CDO arrangers a huge get-out-of-lawsuits-free card. Each asset-backed security or CDOs is its own little investment company, a “special purpose vehicle” with its own notional directors or trustees, often incorporated in the Cayman Islands. Under the reasoning of Janus, any misleading statements in the offering documents for a securitization were made by the SPV, not the investment bank that put together the documents or arranged the deal. The SEC relied in part on Rule 10b-5 in prosecuting Goldman Sachs for its failure to disclose material facts regarding the ABACUS deal. Under Janus, that would no longer be possible. Investors in securitizations can hold literally no one accountable for lies or misstatements in the offering documents. (The directors and trustees of an SPV have little substantive role in managing its operations or controlling its communications, so they would almost certainly be “innocent”.)

In theory, Rule 10b-5 is not investors’ only redress against securities fraud. Mutual fund operators and arrangers of securitizations are underwriters as well as managers. Underwriting is fraught with conflicts of interest, so Sections 11 and 12 of the Securities Act of 1933 give investors the right to sue when misleading statements come to light. These sections offer powerful tools to investors in public offerings of ordinary shares. But they are not so useful to buyers of mutual funds or securitization deals.

When material mistruths about an ordinary firm are exposed, its share price typically drops. This provides a measure of the loss “caused” by the misstatement. The value of mutual fund shares, however, is computed according to the NAV of the fund’s assets, and so is not usually affected by a revelation. Sections 11 and 12 of the Securities Act specify that investors are to recover losses “resulting from” the misstatement. Showing that any losses are due to some other cause is an affirmative defense. So mutual fund managers argue, often successfully, that the proximate cause of investor losses are declines in the value of portfolio assets, declines which are unrelated to any misstatement on their part. Rule 10b-5, on the other hand, doesn’t provide for such a defense. In Rule 10b-5 actions, courts can take into account “transaction causation” (“but for the lie, I wouldn’t have invested!”) and consider investor losses more flexibly.

Securitizations are often organized so as to avoid US registration requirements. For an unregistered security, Section 11, which creates liability for false registration statements, obviously doesn’t apply. According to Thomas Lee Hazen and David Ratner, a 1995 Supreme Court decision

…which surprised almost everyone [held that] 1933 Act §12(a)(2)…does not…apply…unless [offerings] are made publicly by means of a statutory prospectus… [I]t appears that there will be no liability under any provision of the 1933 Act for written or oral misstatements in offerings which are exempt from that Act’s registration requirements, and that persons making such misstatements can only be sued under 1934 Act Rule 10b-5

So, until last week, the only effective remedy that investors in both mutual funds and securitizations had against misleading statements in prospectuses was Rule 10b-5. Now investors have no practical remedy whatsoever. [*] The government can still hold these vehicles accountable, under Section 17 of the Securities Act. But investors are not permitted to sue under that section, and regulators may be reluctant to pursue powerful or politically favored firms.

The Supreme Court’s decision in Janus is a license to lie. And it is backdated. The statute of limitations on Rule 10b-5 actions is five years. Perhaps naively, I had hoped that some of the egregious fraud of the securitization boom would be punished by investors, despite the “let’s look forward”, see-no-evil attitude of the regulatory community. Thanks to Janus, lawsuits-in-progress may be disappearing as we speak. Lawsuits regarding the particularly rancid 2006 / 2007 vintage of securitizations may never be filed. Going forward, if you are considering an investment in a mutual fund or ETF, you should understand that you will have little recourse if information provided in the prospectus turns out to be misleading or incomplete, even outright fraudulent. Perhaps you are comfortable relying solely upon your fund managers’ reputation, perhaps not. If you have a say in how a pension fund or endowment or bank invests its money, I can’t imagine why you’d permit investment in any sort of securitization while you have no meaningful assurance that what is being sold to you is actually what you are buying, even or perhaps especially if the deal is being offered by a big, famous, “deep-pocketed” bank. Much of my own savings is invested in various ETFs. I am significantly more nervous about that than I was a week ago.

Update: Jennifer Taub, who wrote a wonderfully detailed eight-post series on the Janus case in January (1, 2, 3, 4, 5, 6, 7, 8, followup), points out that in the case just decided, it was not mutual fund investors who were suing, but shareholders in the parent of the management company, Janus Capital Group, whose stock lost value when when the misstatements and related misconduct were exposed. This was the mutual fund “market timing” scandal, which received a great deal of press when it broke in 2003. In this very prominent instance, the SEC pursued and reached a settlement with the management company on behalf of fund investors, so no private action was necessary. However, the reasoning of the Janus decision creates a very large barrier for investors in general when, for whatever reason, the SEC declines to act as their champion.

[*] Justice Breyer, in his dissent, notes another potential remedy, to which he suggests the majority opinion hints obliquely. But pursuit of that remedy — liability based on the provisions of Section 20(b) of the Securities Exchange Act — would be at best a speculative enterprise. Justice Breyer points out, “‘There is a dearth of authority construing Section 20(b),’ which has been thought largely ‘superfluous in 10b–5 cases.’ 5B A. Jacobs, Disclosure and Remedies Under the Securities Law §11–8, p. 11–72 (2011)”

Update History:

  • 20-June-2011, 8:25 a.m. EDT: Added parenthetical about indirect liability under 20(a).
  • 20-June-2011, 10:40 a.m. EDT: Added bold update, clarifying, per Jennifer Taub’s comment, that Janus Capital Group, Inc. v. First Derivative Traders involved investors in the parent of the management fund, not investors in the mutual funds themselves.
  • 21-June-2011, 12:35 a.m. EDT: Removed a superfluous “as well”. In the bold update, changed “8 post” to “eight-post”, un-parenthesized a parenthetical and changed a “that” to a “, which”. No substantive changes.

Private participation

So, Greece is the word today.

If I understand the current impasse, much of the trouble is about how to engineer “private participation” in the losses that lenders to Greece and other debtors must eventually bear. The Eurocrats have decided they cannot allow Greece simply to default and impose haircuts on all of its creditors, and they cannot prevent a default by covering Greece’s solvency gap with public sector transfers alone. Despite European leaders’ best efforts to obfuscate and obscure transfers, creditor-state publics know they will be saddled with the lion’s share of these losses. They demand that private sector lenders bear at least a portion of the costs. Yet, there is no way to force a private bondholder to accept anything less than payment in full and on-time without that act constituting a default, thereby triggering the legal controversies and dangerous precedents that the Eurocrats are struggling to avoid.

Suppose the EU were to organize a debt forgiveness fund. This would be a public sector entity whose purpose would be to help Greece and other troubled states retire their unpayable debt. Initially it would be financed by loans from EU member states. With the fund’s help, Greece would make all payments on time and in full. The fund’s contributions would constitute outright transfers. Greece would have eliminated, not postponed its obligations.

However, the fund would repay its loans to member states with income from a dedicated tax. The tax would attach to interest and principal payments on Greek debt, and to capital gains on sales of that debt. This would not constitute a default by Greece and its successors. The troubled sovereigns would make their payments. It would not bind all holders of any class of bond: public-sector and conventionally tax-exempt holders would be unaffected, so it should not constitute a formal credit event (ht @Alea_, @dsquareddigest). For even greater assurance that the EU-wide tax would not constitute a default, it could attach to the debt of all Eurozone states, but at rates computed as a function of various state solvency criteria. Greece, Portugal, and Ireland needn’t be named at all in the law defining the tax, but Greek bondholders might find themselves paying 30% of interest and principal receipts to the, um, “Unity Fund”, while German bondholders pay less than 1%. The rates and total receipts, ultimately the share of the solvency gap that will be borne by the private sector, becomes a political decision within the EU rather than a technical question of smoke and mirrors. Given the discount at which PIIGS debt currently trades, the EU could impose large taxes without further depressing prices, as long as the market is persuaded that the tax scheme eliminates the possibility of default.

To avoid moral hazard, assistance to a particular state could be calibrated to tax receipts from that state’s bonds. (The modest quantity of funds collected from currently solvent states might be held as a form of overcollateralization.) Or there could be some burden-sharing among private bondholders. Again, that’s a political choice.

I don’t necessarily love this plan. But it does seem like it could work, and I haven’t seen the option discussed. So, for your consideration.

Note: An oddity about the Eurocrats apparent determination to impose haircuts without a formal default is that by avoiding a CDS credit event, they impose losses on European bondholders that would otherwise fall to American banks. The scheme above shares that deficiency, but apparently the EU’s leaders prefer paying off American banks to the difficulties that would attend a “hard” default.

Bank bailouts and the rentier class

Robert Kuttner has a great column about the “rentier class” and the struggle between “between the claims of the past and the potential of the future”. See responses by Adam Levitin, Mike Konczal, Paul Krugman, Yves Smith and Matt Yglesias.

I want to make an obvious political economy point. The most organized and active agents of the rentier class are, of course, banks. As Konczal points out

[Financial sector] profits are based off milking the bad debts of the housing and credit bubbles while Americans struggling under a crushing debt load. Instead of sharing the losses, the financial sector has locked itself into the profit stream and left the real economy to deal with the mess.

Financial sector lobbying plays an outsized role in tilting policy away from risk-and-loss-sharing arrangements and towards an alchemy of blood from turnips.

But it didn’t have to be this way. Banks, after all, are not only creditors. They are also the economy’s biggest debtors. In theory, bank loyalties ought to be mixed. On the one hand, banks prefer deflationary, zero-forgiveness tight-money policies, to maximize the real value of their assets and of the lending spread from which they draw profits and bonuses. On the other hand, troubled banks are very happy to support loose money and expansionary policy, even at risk of inflation. For bank managers and shareholders, it is bad to have the value of past loans eroded by inflation. But it is much worse to lose their franchises entirely, to have their wealth, prestige, and freedom put at risk in the aftermath of an explicit bank failure. When banks are in trouble, they are perfectly happy to support all manner of expansionary policy, as long as short-term interest rates are kept low. Even a broad-based inflation helps troubled banks twice over, by increasing borrowers incomes and by steepening the yield curve. Increased incomes ensure that loans will be repaid in nominal terms, preventing insolvency due to credit losses. A steep yield curve permits banks to recapitalize themselves via maturity transformation, using deposits to purchase Treasury notes while the central bank promises to hold short rates low for a few years.

But banks’ interests are aligned with those of debtors only to the degree that banks, like debtors, are at risk of real insolvency. When we committed to a policy of “no more Lehmans”, when we made clear via TARP and TGLP and the Fed’s alphabet soup that big banks would have funding on demand and on easy terms, when we modified accounting standards to eliminate the risk that bad loans on the books would translate to failures, when we funded their recapitalization on the sly, we changed banks. We transformed them from nervous debtors into pure rentiers, who see a lot more upside in squeezing borrowers than in eliminating a crippling debt overhang. And since banks are, shall we say, not entirely disenfranchised among policymakers, we increased the difficulty of making policy that includes accommodations between creditors and debtors, accommodations that permit the economy to move forward rather than stare back over its shoulder, nervously and greedily, at a gigantic pile of old debt.

Our problem is not that our banks are still weak, our financial system too fragile. Our problem is that we have made our banks strong and cocky, so they needn’t care about abstractions like lives disrupted, production foregone, human capacities undeveloped. We’d have better policy if banks themselves were at risk of foreclosure when Joe Sixpack still can’t find a job. We should work to put them in that position.

Should we be scandalized by IPO pops?

So, I’m late to this. There’s a big link parade at the end of the post.

LinkedIn had an IPO on May 19, priced at $45 per share. The stock briefly sold in the $120s that day, and closed at $94.25. In the lingo, there was a big “pop”.

From a certain perspective, IPO pops are puzzling, even scandalous, events. Here is the theory of the outraged:

  • Shares are assets with real economic value that professional investment bankers, after communicating with “the investor community”, are capable of discerning.
  • The price at which those shares will trade in public markets, on the first day and thereafter, is a reasonable approximation of real economic value, because stock markets are efficient.
  • Therefore, if investment banks (who, in consultation with the issuer, set the IPO price) sell the shares for substantially less than the price at which the shares trade on the open market, they have screwed their client. The issuing firm and its original investors have “left money on the table” by failing to extract the full value their shares. Meanwhile, someone, some flipper, will have purchased shares at the IPO price and resold them after the pop, taking profits that might have gone to the issuer.
  • So issuers really ought to be upset about IPO pops (even though they mostly aren’t). “I don’t understand why competitive forces don’t drive this kind of egregious underpricing out of the system,” a finance professor tells the Financial Times.

Puzzle, puzzle, toil and trouble. Here’s a tidbit to taunt the good professor: In the 1990s and especially during the tech bubble, pops tended to be larger for IPOs led by “top tier“, high market-share investment banks than when shares were offered via midlevel underwriters. It’s a topsy turvy world, apparently. During hot IPO cycles, when underpricing is especially pronounced, “competitive forces” seem actively to favor underpricers.

Pretty much every premise of the case against IPO pops is false. Shares of all but the most staid firms do not have known, predictable economic values that highly trained professionals can predict ex ante. Further, share prices are autocorrelated, which is a fancy way of saying that if a stock trades for $100 today, it is more likely to trade above $100 three months from now than a stock that trades today for $50. There are lots of ways to interpret share price autocorrelation. Perhaps markets are efficient, so that a high price today is indicative of durable economic value. Perhaps markets are not so efficient, but investors nevertheless use yesterday’s price to determine the price at which shares will trade today.

Regardless of which story you believe, consider the situation of insiders and early investors in IPO firms. These investors face a “lock-up” period of three to six months after the IPO, during which they cannot sell. (This is intended as a kind of guarantee to new buyers that the shares are not total lemons.) If you hold a share of stock that you cannot sell for several months, you are better off, in a statistical sense, if the shares that you hold trade for $100 today than if they trade for $50 today. Sure, even after a pop, share prices could wither to worthlessness by the time the lock-up period ends. And sometimes that happens. But overall, if you are a preexisting investor in an IPO firm, the expected future value of your shares is substantially higher if your shares trade at $100 now than if they trade at $50.

So, if you are an early investor in a firm now making its debut, an IPO pop is mixed news. On the one hand, discovering that the shares you continue to own are very valuable is good news. On the other hand, if it is true that you could have sold the shares that you did sell for this much higher price, you’ve been screwed. On balance, how should a rational shareholder evaluate these conflicting signals? Should she be glad or disappointed? Should she fire her shoddy investment bank or celebrate its success?

If you are sure that stock markets are completely efficient and so share prices are independent of all the schmoozing and marketing done by your underwriter, then you should be outraged. You would have learned the same good news had you gone with a different investment bank, and your underwriter, if it were more competent or less corrupt, could have set a higher price and made you a great deal more money. But if you think that the stuff investment banks do when they underwrite an IPO actually does affect the price at which shares eventually trade, you might not be so angry. You might consider the “money left on the table” to be part of the fee you pay in order to be made as rich as possible.

IPOs are not all alike. In the lingo, they are sometimes “financing events” and they are sometimes “pricing events”. When IPOs are financing events, insiders are selling substantial fractions of their firms, trying to to divest their holdings or raise large sums for corporate purposes. When they are “pricing events” insiders are selling a small fraction of their shares in order to gain various benefits that come with being a public firm. In a “financing event”, when insiders are selling a lot of stock, the money left on the table from an IPO pop might amount to a substantial fraction of total equity value, too much money to be treated as a transaction cost. But in a “pricing event”, the money left on the table in a pop — the “opportunity cost of issuance” — may not be so large.

A very good predictor of how much an IPO will pop is “overhang”, the ratio of shares retained by insiders to shares sold during an IPO. IPOs with high overhang — that is, IPOs where insiders are selling only a small fraction of the firm — are much more likely to pop than IPOs in which investors are selling a lot of their shares. (This is true even controlling for the absolute value of shares sold, so it is unlikely to be just an artifact of scarcity.) To my mind, the explanation for this regularity is simple. Investment banks behave differently for high overhang IPOs (“pricing events”) than for low overhang IPOs (“financing events”).

For low overhang IPOs, in which much of the firm is being sold, underwriters go for accuracy. Investment banks do not want clients to spread word that they lost half the value of their firm to flippers on the big day. So bankers work to keep the IPO price and the immediate market price aligned. They try to set a reasonable price in the first place, they place shares with investors likely to sell pops and buy dips, they stabilize prices directly via their own activity in the market. (Underwriters have a partial exemption from market manipulation rules that allows them to “stabilize” new issues.)

But for high overhang IPOs, investment banks, in consultation with their clients, go for broke. The “book-building” process, often described as an anodyne sounding of investor interest, becomes an occasion to market the hell out of the issue. Investment banker activity, proxied by changes (even downward changes) to the planned issue price are predictors of IPO pops. For high overhang IPOs, underwriters and their clients agree that everything that can be done should be done to get the shares trading at the highest valuation possible, despite a necessarily conservative issue price.

When only a small fraction of a firm is being sold, issuers quite rationally permit investment banks to underprice their IPOs, because doing so aligns underwriters interests with their own. Issuers want their firms to be highly valued. An issuer who makes it clear that she will hold her underwriter accountable for underpricing is behaving foolishly, threatening to punish an outcome she desires. A smart issuer understands perfectly well that money left on the table will be used as kickbacks to favored clients of the investment bank. But why should she mind? She views that money as performance pay, a transaction expense. Given the small fraction of shares sold, it represents a modest cost. Further, she understands that the reason she chose her market-leading, high reputation underwriter is precisely because of the bank’s relationships with institutional investors, the bank’s ability to persuade people in its rolodex to take up and hold (not flip) new issues. If the issuer is not naive, she knows that the underwriter’s ability to place shares comes from plum deals the bank frequently offers the people in its rolodex. With the money she leaves on the table, the issuer is paying for exactly what she is trying to buy.

Efficient markets proponents will blanche at this whole scenario. How can underwriters affect share values? Surely, investment banks can’t “fool” the market over a six month lock-up period?! But nobody is fooling anybody, exactly. Nobody — not Warren Buffett, not the firm’s CEO, not even your psychic friend at Goldman Sachs — knows the “true value” of a speculative firm. A small rejiggering of earnings growth assumptions or the appropriate discount rate can double or halve estimates of “economic value”. The dirty little secret of fundamental analysis is that it can never tell you the correct price of a stock. Fundamental analysis can indicate that a price is wrong, that it is deeply below or outrageously above any reasonable valuation. But an independent analysis (one that ignores the market and estimates value based on a discount rate and expected cash flows) will very rarely approximate actual share prices (unless the analyst cheats, and reverse engineers the market). What issuers believe a good investment bank can do, with its marketing and its reputation, is get the shares trading on the optimistic end of the range of reasonable valuations. And that, to preexisting shareholders, can be much, much more valuable than a bit of money left on the table from underpricing.

So, is there any scandal here at all? I think so, but it’s not about investment banks screwing underwriting clients. On the contrary, I think investment banks usually serve both their underwriting clients and their favored investors pretty well. The scandal, I think, is that the IPO process offers issuers, underwriters, and favored investors too much and the rest of us too little. After the first day pop, IPOs tend to underperform other issues over the long term. Not by enough to reverse the first-day pop over the lock-up period. On average, new IPOs don’t underperform the market very much in the first six months after the pop. (During the 2000s, IPOs did perform poorly even in the first six months, but that is probably because the tech bubble crashed within 6 months of many IPOs.) IPOs get optimistically priced on their first day, and whoever winds up holding the shares from the end of the lock-up period and out several years pays for that. In general, buying IPOs at the issue price is a great deal, while buying IPOs on the secondary market is hazardous even a year or two after the offering. The IPO process ends up being a boon to insiders (the issuer, its underwriter, and favored investors), which is paid for over time by less connected investors who fail to demand a sufficient premium to hold recently IPO-ed shares.

In the scheme of things, this is pretty small beans. Caveat emptor and all of that. Still, a practice that taxes investors broadly in order to reward people for systematically mispricing securities does deserve some tut-tutting.

P.S. The academic literature on IPO underpricing is all about kickbacks. I prefer my conspiracy theories to be fringe, but this is all pretty mainstream. Famous explanations describe underpricing as a kickback necessary to induce uninformed investors to participate, or to induce informed investors to reveal what they know during the book-building process. For a real conspiracy theory, check out spinning, which has investment banks offering kickbacks to managers so that they’ll tolerate underpricing that screws their own firms’ shareholders.

Update History:

  • 4-June-2011, 4:25 p.m. EDT: Changed an “and” to a “so”, so it’d read better. Also change “And sometimes that does happen” to “”And sometimes that happens”.
  • 11-July-2011, 11:30 p.m. EDT: Replaced a “they” with “shares”, the intended but missing antecedent. Removed an ungrammatical “to”. No substantive changes.

Visualizing Keynesian & Monetarist recessions

So this will be an unusual post, more picture book than essay. Plus, it’s interactive! If you are willing to install the Mathematica plug-in, you can be the central banker / fiscal authority of your very own graphical economy!

As readers may have noticed, I’ve been thinking lately about Keynesian and monetarist business cycle theories. I don’t mean to wholly endorse these theories. I’ve some sympathy for Austrian-ish or “recalculationist” ideas too. But I do think there’s merit in the idea that recessions frequently occur because aggregate expenditure is, for whatever reason, inadequate. I’ve been frustrated by all the squabbles, between self-styled Keynesians and post-Keynesians, academic defenders of mainstream central banking and the more risqué internet “quasimonetarists”. My view is that these groups are more alike than different in their economic ideas, but that they manufacture controversies to signal political affiliations and institutional preferences regarding how and by whom policy decisions should be made.

So, I’ve been trying to understand the ways in which these theories are alike and different, and organize my own thinking about how to evaluate different policy proposals. I’m a pretty visual thinker, but for a variety of reasons, I’ve never found the most common ways to diagram Keynesian ideas — IS/LM and AS/AD — especially helpful. In my mind, I found myself falling back on Econ 101 style supply and demand graphs, where the commodity of interest, whose “price” and quantity is to be determined, is nominal expenditure. I’m sure this is not a novel approach, but I’ve gotten a lot of mileage out of it. Perhaps you won’t find it entirely useless.

The hardest part is to make sense of the basic set-up, so let’s talk it through.

The Basics

Below is a diagram of an economy in which demand shortfalls do not lead to output losses and money is neutral, because there are no price rigidities.

The downward-sloping yellow line is a demand curve, and the upward-sloping green line is a supply curve. Hopefully that seems familiar. However, we’re in a bit of a mirror universe, because we are graphing the supply and demand of expenditure. So the “expenditure suppliers”, represented by the green curve, are economic consumers. They supply dollars, for a “price”, which is some quantity of real goods and services. The “expenditure demanders” are economic producers. They demand dollars, but are only willing to offer so many goods and services for a buck. The equilibrium, the point where the two lines intersect, shows the price of a dollar, in real goods and services, that equalizes producers’ demand for money and consumers willingness to supply it.

For example, suppose that, at equilibrium, you can buy two widgets for a dollar. So the price of a widget is 50¢. But the price of a dollar is two widgets! Note the relationship — the dollar price of widgets is


This relationship is reflected on the axes if the graph. The left axis shows the price of money in real goods. If money is “expensive”, if you have to offer a lot of real stuff to get a dollar, that corresponds to a low price level, think deflation. Conversely, if money is “cheap” — if the equilibrium falls towards the bottom of the graph — then that means goods and services are expensive, think inflation. The right-hand axis shows the conventional price level, which rises as you travel vertically down the graph. As the price of money in real goods and services falls to 0, so you’d give up a dollar for next to nothing, the price level on the right-hand axis rises to infinity.

The X or quantity axis of the graph indicates how many dollars will be spent at the equilibrium. This has a very natural interpretation as nominal GDP. So, from the equilibrium point on the graph, we can read the price level (on the right axis) and the nominal GDP directly.

Real GDP is represented by the area of the bluish rectangle in the bottom left corner of the graph. To understand why, recall that real GDP is just


But the Y axis of the graph is


So the area of the bluish rectangle is


So what determines the shape of the expenditure supply and demand curves? Let’s start with demand. Suppose the economy produces at capacity and there are no “rigidities” to prevent the sale of all output. Producers will always accept however many dollars are on offer and sell the maximum achievable RGDP. Then


Since the inverse price level is our Y axis, and NGDP is our X axis, the function that describes our no-rigidity demand curve is just

Y = (MAX_RGDP / X)

which is the graph of a grade-school hyperbola. We’ll modify this shape a bit, when we start thinking about price rigidity. But let’s hold off on that.

What determines the shape of expenditure supply? That’s where all of the action is in terms of fiscal and monetary policy, and we’ll graph lots of funky shapes below. But fundamentally, the answer to this question is easy. Imagine a world of consumers, each of whom must decide how much to spend now and how much to save for the future. Suppose we can characterize consumers’ “intertemporal preferences” with a utility function. Then we can compute how much each consumer will spend. Naturally, that utility function will take into account the current price level, among other parameters. If we hold other parameters constant, we can compute how expenditure varies with the current level of prices. We add up all consumers’s expnditures and plot them on the X axis, against (1 / PRICE_LEVEL) on the Y axis. That gives us our expenditure supply curve.

Immaculate Deflation

In the graph above, everything has been normalized to one. The graph shows one unit of real goods “buying” one dollar of expenditures, for a price level of one. Suppose that consumers become more reluctant to spend money, that is, they perceive the marginal opportunity cost of parting with money as increasing. The result would be an “immaculate deflation”, in that expenditure would fall, but so would the price level, so that the reduced expenditure would still purchase all the economy’s real product, and RGDP would not fall at all. Here’s the graph:

Note expenditures have fallen, but the quantity of goods offered for each dollar has risen. Real GDP — the area of the bluish rectangle — has not changed.

Price Rigidity

In the real world, when nominal expenditures fall, the quantity of goods offered for a dollar doesn’t rise enough to compensate. The quantity of goods purchased actually decreases. Let’s graph that:

The expenditure supply curve is identical to that in the previous graph. However, the shape of the expenditure demand curve has changed. There is now a “kink”, that begins (as I’ve drawn it) just under the original equilibrium expenditure of one. Our steepened expenditure supply hits the kinked region, forcing that the quantity of goods offered for a dollar to be lower — or the price level to be higher — than in the previous graph, with its unkinked, flexible-price expenditure demand curve. This means that, given the reduced level of expenditure (caused, as before, by the steepening of the expenditure supply curve), the quantity of goods consumers purchase is less than the economy’s capacity. We observe a fall in real GDP and a recession.

As before, the area of the bluish rectangle represents Real GDP. The dotted white line shows the flexible-price expenditure demand curve, while the yellow line is the expenditure demand curve that actually obtains, with its kink and price rigidity. The reddish rectangle represents the output gap: the area that should have formed part of GDP, but does not because of the price rigidity.

In this example, the price level has from 1 to 0.96 (a 4% deflation), and real GDP has fallen by 10%. Note that in the previous example, with the same steepened expenditure supply curve but flexible prices, the price level fell even farther (to 0.88, a 12% deflation), but RGDP was unaffected. There’s an important bit of intuition here. We often imagine that deflation causes recessions, and indeed in our graph, we can see that deflation is associated with recessions. We would only see an output gap when the equilibrium fell before the kink in the curve, which is always a price level lower than our original price level. But under flexible pricing, the deflation would have been more severe, without harming RGDP. It is not too much deflation that creates the output gap, but too little deflation given the fall in expenditures! Tepid deflation is a marker of recessions, but it is the decline in nominal expenditure, in NGDP, that drives the show.

If you are wondering where the shape of the sticky-price expenditure demand curve comes from, see my earlier post on sticky prices. Basically, to generate the expenditure demand curve with price rigidity, I assume that industry leverage is uniformly distributed over some range, that firms in industries set minimum prices based in their degree of leverage, and that firms’ capacity is constrained in the short term. If you don’t buy that story, but agree that prices are sticky downward but not so sticky upward, then you can take the shape as an arbitrary qualitative depiction of that.

The Expenditure Supply Curve

Expenditure supply is where the action is in making sense of Keynesian and monetarist interventions. The nice thing about this framework is one can posit any intertemporal utility function you like for agents in your economy and then compute the shape of the expenditure supply curve as you vary parameters.

For the purpose of this exercise, I’ll adopt an unrealistic but illustrative utility function presumed to be shared by all consumers. Consumers will face a two period, rather than infinite horizon optimization problem. Their behavior will be based upon a number of factors, all of which are treated as exogenous parameters:

  • An interest rate ri which determines the Period 2 value of money not spent in Period 1.
  • An current wage w1, in nominal dollars.
  • An expected future wage μw2, in nominal dollars.
  • Variance of the distribution of future wages, σw22
  • Skewness of the distribution of future wages, skeww2
  • A current price level P1
  • An expected future price level E[P2]. (Oddly, the current price level is what we are trying do determine. The expected future price level is known, and helps to pin the present price level.)
  • A current taxes-and-transfers surplus S1.
  • An expected future taxes-and-transfers surplus E[S2].
  • A discount rate rd, which is the rate at which consumers discount future utility.

A “real” model wouldn’t treat all these parameters as free. For example, perhaps the expected price level is dependent upon current interest rates, or fiscal policy. My goal here isn’t to present a falsifiable model of consumer behavior, but to illustrate what proponents of various interventions are claiming, and explore under what circumstances they would or wouldn’t work. We will find, for example, that, running a Period 1 taxes-and-transfers deficit while holding interest rates constant increases Period 1 expenditures. However, this effect will be mostly undone if the Period 1 deficit must be balanced by a Period 2 surplus. We don’t wish to take a position here in the “Ricardian equivalence” debate. Allowing the two deficit parameters to vary freely, rather than enforcing some hypothesized relationship, permits us to illustrate the claims of partisans on both sides.

The utility function I’m using to compute the expenditure supply function is shown below.

Our variable x represents nominal dollar expenditures.

There are a bunch of things about this utility function that are crappy, but I think it’s good enough to show how changes in parameters might affect a expenditure supply curve, and offer some intuition about how various interventions might work.

Although I’m using just one utility function here, a nice thing about this framework is that it need not rely on a representative agent. What we will derive, after all, is a Marshallian supply curve. We can define populations of agents with different parameters or preferences and combine the supply curves by “horizontal addition”.

Visualizing Changes in Expenditure Supply

Let’s start with a graph of an economy characterized by price rigidity, but which is currently at “full employment equilibrium”. (The scare quotes are because I am not explicitly modeling labor, so by full employment I just mean that the economy is producing at capacity.)

Now, suppose that for whatever reason, uncertainty surrounding future wages increases:

The expenditure supply curve steepens. Consumers become more reluctant to part with dollars, as they have been made worse off in the future and prefer to save. Unfortunately, after this steepening, the expenditure supply curve now intersects with the sticky-prices region of the expenditure demand curve. The resulting equilibrium is recessionary; the economy experiences a 5% output gap.

What kind of interventions might we try to fix this? Conventionally, our first resort is to discourage financial saving and promote current expenditures by reducing interest rates:

Dropping interest rates to zero helps, but it turns out to be insufficient, a 3% output gap remains. We have entered the liquidity trap, if you believe in such a thing.

But we are certainly not out of potential of interventions. Suppose we believe that the central bank is very, very good at setting expectations. Okay, if it were really great at that, it could just reverse the shock to consumers’ expectations of wage uncertainty and we’d never leave our initial equilibrium. But suppose the central bank can’t do that, but it can manage expectations of the price level. Then…

That worked! Yay monetary policy, still potent at the zero bound! But, we should be careful. We’ve assumed the central bank could set price level expectations. That’s much less sure than assuming it can set interest rates. Plus, perhaps engineering an uptick in inflation expectations is hazardous. Perhaps the central bank cannot set expectations precisely, so that there is a hazard of overshooting and generating inflation rather than just restoring equilibrium. Perhaps there is value to keeping inflation expectations “anchored”, and the change in expectations required to restore equilibrium would upset that anchoring. So, it’s worth considering alternatives.

Let’s go back to our original disequilibrium, and let the MMT-ers have their way. Suppose that to counter the 5% output gap, the government reduced taxes and/or increased transfers, to run a deficit. Could that work? Absolutely.

However, there’s a catch. My two period setup is pretty Ricardian. Encouraging private spending through a taxes and transfers deficit in Period 1 only works if that deficit is not repaid by running a surplus in Period 2.

However, in the real world, deficits needn’t be repaid via prompt surpluses, and economies (measured in nominal dollars) often grow faster than the interest rate paid on public debt. In this case, debt effectively repays itself over time, without ever requiring surpluses. The core new debate over MMT as well as a very old debate over “Ricardian equivalence” turn on the degree to which people have (or by tax policy can be made to have) a special willingness to hold currency and government securities even when doing so implies an opportunity cost relative to a hypothetical asset that matches the economy’s growth rate. I think the case is very strong that, under many circumstances, people are willing to bear that cost, not least because a hypothetical asset that earns the economy’s growth rate with little risk does not exist, and most people are more concerned with managing risk than with maximizing return.

(Note: If you think transfers that will never be paid for in taxes must increase the expected future price level, then in the immediate term, all that does is to reduce the scale of the program necessary to eliminate the output gap! An increase future price level expectations, like the unfinanced transfer itself, renders the expenditure supply curve shallower, helping carry our equilibrium out of the recession region. Of course, we are observing a one period snapshot of the economy, and there may be long-term bad consequences to “unanchoring” the price level. That’s beyond the scope of our little visualization, but that doesn’t mean we shouldn’t worry about it.)

My little experiment is not so friendly to a taxes-and-transfers-based “hard Keynesianism“, which prescribes prompt surpluses to offset cyclical deficits. In my toy model, a reduction of expected future income is very much like a reduction of present income, as agents can borrow and save at “the” interest rate. But this is not realistic: real humans pay more to save than to borrow, and may face outright credit rationing.

I give lip service to uncertainty by calling the future surplus “expected”, but I don’t actually model it as uncertain, as wages are the only random variable in my toy utility function. If I had, the cost of future surpluses to consumers would be even greater, and it would make “hard Keynesianism” look even worse. So implemented in terms of taxes and transfers, ignoring the wedge between saving and borrowing costs, and holding wealth distribution constant, it’s hard to see how one could ease a recession by running deficits which are expected to be balanced by prompt surpluses. Of course, these assumptions needn’t hold. We do not have to restrict ourselves to taxes and transfers, but can have government deficit-spend on real goods and services directly. Savers do, in fact, face liquidity and borrowing constraints that “hard Keynesianism” can overcome by effectively using the government’s balance sheet to borrow on behalf of consumers. And when we tax-and-transfer, we can also redistribute.

I yet haven’t tried to model consumers facing borrowing constraints. But I have played with variations in which government spends, rather than transfers its deficit, and with redistribution. So let’s look at those.

Stimulus Via Direct Government Expenditure

The economy’s true “expenditure supply” includes the inclination of government to directly purchase goods and services. Thus far we’ve ignored that. If we hold government’s propensity to spend invariant to the parameters of our toy model, ignoring government purchases doesn’t much hurt our analysis. But is that a realistic assumption?

It would be hard to model how government’s inclination to spend varies, and upon what parameters that variation depends. However, governments do sometimes respond to recessions by adopting stimulus programs, which in rough approximation we can model very easily.

Here’s how we’ll do it. We’ll imagine that the government first chooses the quantity of dollars it will spend on real goods and services, and then chooses what it will purchase. That sounds unobjectionable, but it’s really very sneaky, because it means that stimulus spending is not a function of the quantity of real goods and services offered for the money. So the expenditure supply curve due to stimulus is vertical. Including expenditure due to government stimulus simply shifts the expenditure supply curve to the right by the quantity of nominal dollars appropriated!

Let’s see, in the simplest case, how a stimulus program that is not expected to be paid for from an increase in taxes can combat a recession. The dotted green represents the expenditure supply curve in our 5% output gap recession, and the solid green line illustrates the intervention.

Note that the expenditure supply curve in this graph is different from all of our previous graphs. For ordinary consumers, the quantity of expenditure supplied always goes to zero as the price of a dollar in terms of goods and services falls to zero. The curve bottoms out at the origin of the graph. To put things in more familiar terms, if the price level today is infinite — you get literally nothing for a dollar spent — and the price level tomorrow is expected to be finite, you’d spend precisely nothing today. With stimulus via direct spending, the government commits to current-period expenditure regardless of the price level. The expenditure supply curve now bottoms out to the right of the origin.

Unlike a taxes-and-transfers deficit, stimulus via direct spending “works” under our toy model even if it is paid for via a fiscal surplus. It doesn’t matter, under our model, whether the spending is paid for out of current period taxation or future taxation. That is, our model suggests that it might be possible for a government to balance its budget in the teeth of a recession and still stimulate its way out of the recession!

There is a hitch, of course. Our balanced budget is stimulative if and only if spending is increased and balance is accomplished by increasing current taxes. Cutting spending to balance the budget would be contractionary under our framework, while increasing taxes to fund spending is expansionary.

The intuition is pretty straightforward: Consumers divide current wealth between spending and saving. If consumer saving decisions compose to insufficient current spending to avoid recession, the government can preempt those choices by taxing current wealth and spending the entirety of the proceeds.

A few issues and caveats —

  • Compare the graph above to the previous graph, where the stimulus spending is not funded by taxes. The X intercepts show how large the government’s spending program must be to eliminate the output gap. Unsurprisingly, government must commit to a great deal more spending to render a funded stimulus effective than it would need to for an unfunded stimulus.
  • If the spending program were funded by future period taxes rather than current period taxes, the graph would look nearly identical, given the near-perfect substitutability of present and future money in our model. However, as we discussed above, in the real world, consumers find it expensive or impossible to borrow from the future in recessions, so transferring wealth to current consumers and taxing in the near future to pay for it may be directly expansionary. If that is so, then the scale of government spending required to cover the output gap would be smaller if the spending is paid for out of future taxes rather than out of present taxes.
  • If a government commits to large nominal expenditures irrespective of what is to be purchased, indiscriminate spending decisions might degrade the quality and value of current output. If so, effect of the increase on current expenditures might be undone, partially or completely or worse than completely, by a supply-side losses. See “supply and technology shocks” below for an example.

Distributional Effects

Part of my motivation in developing this framework was to come up with a way of conveniently analyzing distributional effects. We can compute different expenditure supply curves for subpopulations of different wealth levels, and “horizontally add” those curves to get the economy-wide expenditure supply. I thought I would easily be able to define some very rough distribution parameter, and show how redistribution affects expenditure supply.

I began with a very strong prior: I believed, and still believe, that the poor are much more likely to spend out of current income than the rich, so that redistribution from rich to poor would increase current expenditures (that is, render the slope of the expenditure supply curve more shallow). To get a quick and dirty take on distribution, I compared two economies, one in which all the wealth was held by a single individual, and a second in which the wealth was equally distributed among many individuals. I expected a shallower curve in the second case.

But that is not what I found, under the utility function above. In fact, it is easy to show that, holding total real wealth (both current and expected future) constant, the expenditure supply curves are identical if the economy contains just one spender (while everyone else starves) or a perfectly equal distribution of wealth. So have I revised my priors?

No, not at all. Instead, I’ve understood deficiencies in my utility function, deficiencies that I think are shared with most utility functions used to build macro models. Why is expenditure supply constant, regardless of distribution? It’s pretty simple really. Under the terms of the model, agents are perfectly forward-looking and all wealth must be spent eventually. Intuitively, we think poor people will spend money today if we put it in their hands because the absolute cost of not spending — going hungry, for example — is large. But, given the structure of my and most macro models, agents don’t evaluate current expenditure against absolute gains in present utility, but against opportunity costs in future utility. If an agent is poor, sure, not eating today has a large cost. But eating today exacts a similarly large cost from the still-poor-me of tomorrow. A rich agent gains little by eating a bit more today, but her cost in future consumption for that benefit is similarly low. Under my utility function, as long as the two agents discount future utility identically, they will make precisely the same tradeoff between expenditures today and expenditures tomorrow. So a poor person, despite starvation, will be just as disinclined to spend current wealth as a rich person. The poor person will balance starvation tomorrow against hunger today, and save some fraction of her wealth. The rich person will balance the pleasures of a bon bon tomorrow against a cookie today, and save precisely the same fraction.

I think this is entirely unrealistic, but what’s interesting is to articulate why. Let’s think about it. In my model, all agents live for precisely two periods, no matter how much or how little they consume. In the real world, insufficient consumption today implies death and zero consumption in the future, regardless of how much a person might have saved. So a realistic model needs some concept of subsistence, such that as present consumption falls and the probability of death increases, the value of future savings is increasingly discounted. More generally and less drastically, future wages in my model are stochastic, but independent of present consumption. But that makes no sense. My ability to earn future wages depends upon my current expenditures. My distribution of future wages is dramatically different if I have a home, decent clothing, a telephone, or an education, than if I do not have these things. Ultimately, I need to add to my consumers’ utility function some notion of investment expenditure that impacts future wealth, rather than restricting the choices to pure consumption and financial savings for interest. And there should not be a single, economy-wide investment return, but each individual’s returns should (usually) be diminishing in wealth. My first dollar of expenditure buys me the ability to survive into tomorrow and enjoy potential future wages; its return is very high. Direct investment of my millionth current dollar might buy me an additional nice suit or make some marginal contribution to a business, but its effect on my future wealth is likely to be small. If I include this sort of direct investment in my model, I think I’d generate the expected relationship between poverty and a bias towards current expenditure. But that’s an exercise I’ve not yet done.

Technology and Real Supply Shocks

The supply side of our economy is graphical represented by the yellow expenditure demand curve. That curve is based on a hyperbola, whose numerator is the capacity of the economy in units of real output. A negative real supply or technology shock yields a recession, without any change in consumers’ willingness to spend:

Note that the output gap is 5%, just like demand-shock recession we’ve illustrated in previous graphs. However, this recession is actually much worse. The real output of our economy has fallen by 13%, not by 5%. The negative supply shock eliminated almost 9% from our potential output. Plus, even though the expenditure supply curve has not changed at all, the shift in the expenditure demand curve pushed the equilibrium onto that curve’s rigid price region, generating an output gap of 5% of our diminished potential output (about 4% of our original output) in addition to the loss of real capacity. In response to a negative supply shock, increasing consumers’ willingness to spend can eliminate the loss of output due to price rigidity, but cannot affect the loss of real capacity:

It’s worth commenting on how the shape of the expenditure demand curve as it shifts in response to a supply shock. By hypothesis, the “kink” in the curve is a function of nominal indebtedness. A firm that requires a dollar of revenue to service its debts doesn’t reduce the price of its total output below a dollar, even if a technology shock diminishes the quantity or quality of that output. So the kink stays where it began, at nominal expenditure of 1.

Yet consumers’ willingness to spend is a depends on the value of real output provided. Holding constant expectations about the future, consumers are less willing to provide that dollar of current expenditure for less or worse stuff. So despite a higher current price level — which you might think would ease the burden of servicing on nominal debt — the diminishment of nominal expenditure occasioned by transiently higher prices (the left-shift of the equilibrium) means that firms have a significantly harder time servicing their debts.

Note that, perhaps counterintuitively, our output gap arises because consumers are optimistic that the real supply shock is temporary. If consumers expect the supply shock were permanent, and therefore that the future price level would rise along with the present price level, a demand effect offsets the supply effect, and the output gap disappears. Consumers become more willing to supply expenditures now because they no longer expect tomorrow’s money to be more valuable than today’s. (The shift in the yellow expenditure demand curve is the real supply shock. The shift in the green expenditure supply curve shows the increase in current spending due to expectations of future high prices.)

“Stagflation” comes from any sort of negative real supply or technology shock, but is magnified when consumers believe the shock to be temporary!

This is an important difference between demand and real supply side shocks. If consumers’ inflation expectations are “adaptive”, that is, if we learn from experience to predict the future, then for supply shock, changes in expectations help stabilize the current price level and eliminate any output gap. For a demand shock, adaptive expectations about prices are destabilizing. If a demand-driven deflation means we expect future deflation, that diminishes our willingness to spend, which renders our current output gap and deflation even worse. Supply shocks self-heal, demand shocks self-destruct. (Remember, “supply shocks” are shifts in the the expenditure demand curve of our framework; “demand shocks” are shifts in expenditure supply!)

Of course, even if consumers do believe a real shock to be temporary, the output gap can be eliminated by expansionary monetary or fiscal policy. However, no amount of monetary or fiscal policy can undo the real shock. If potential real GDP has fallen by 10%, encouraging people to spend can eliminate the output gap due to price rigidity, but cannot (in a static sense, at least) bring back the lost potential output.

Until the last graph, we’ve considered changes ceteris paribus, adjusting one or two parameters and imagining that all the rest can be held constant. But of course, most of the controversy surrounding proposed policy interventions is about the way in which various changes are interrelated. So, for example, earlier we showed a graph in which stimulus spending eliminated the output gap from a demand shock. However, those who oppose stimulus often argue that poorly targeted government spending will reduce the quality of real output delivered by the economy. Thus, a demand-side remedies will provoke a reduction of real supply. Let’s illustrate that claim:

Point A on the graph represents a demand-driven recession, the same recession we graphed in Figure 5. If we left it alone, the economy would face a 5% output gap. That sucks, so we try fiscal stimulus, exactly as we did in Figure 9. Unfortunately, although we successfully shift the expenditure supply curve, poorly targeted government spending leads to suboptimal real production. The expenditure demand curve shifts downward. We end up in a different recession, a worse recession in this example, at Point B.

So what does our analysis say? If we use stimulus spending to counter a recession, will it lead us towards the happy outcome diagrammed in Figure 5 or the terrible outcome diagrammed above? I don’t know. As we said at the outset, our toy model is designed to illustrate possibilities, not to choose among them. But he have learned something about how to consider the question. If government spending is of sufficiently high quality that it doesn’t much reduce the value of aggregate output, then it likely can counter demand-shock recessions. If government spending is of such poor quality that the value of aggregate output is impaired by its psychotic purchaser, than stimulus spending may prove badly counterproductive. People’s views on the quality of government expenditures tend to correlate with tiresome political affiliations. My own view is that we have free will, collectively as well as individually, that governments sometimes do deploy resources wisely, but sometimes they make choices that are awful and corrupt. Our work is not to estimate the odds, but to shape the context in which government acts so that it is likely to act well.

If you think this story argue for monetary expansion as opposed to fiscal stimulus, think again. We can tell almost exactly the same story. Expansionary monetary policy, like government spending, increases our aggregate propensity to spend. But who says it has no effect on the production side of the economy? My own view, with the Austrians and other cranks, is that stimulating demand via low interest rates does cripple real supply over time, in part by favoring producers of durable goods, but more insidiously by altering the incentives of holders of financial assets, who diversify to capture monetary policy subsidies rather than discriminate between worthy and unworthy enterprises. I would rather take my chances with more transparent (if transparently corrupt) fiscal policy than with status quo monetary policy.

But that’s just me. The framework we’ve set up can illustrate happy and tragic stories, for both monetary and fiscal interventions. Further, if we come up with models that specify relationships between the parameters, or between the demand side and the production side of the economy, we can illustrate those models with the same sort of graphs we’ve shown here.

We’ve been working with a discrete, two period toy model. However, that’s limiting. For example, if poor government spending harms the supply side of the economy, the effect may not be simultaneous. We’ve crammed several non-instantaneous effects into “Period 1″. But we can draw graphs like this as “snapshots” of models that evolve over time. We can even combine graphs into annoying little movies to watch the economy evolve under various scenarios.

This has been a long exercise, and I’m grateful to readers who’ve made it this far. I’ve learned a lot from playing around with these graphs, but I’ve no idea whether doing so will help others. I hope so!

If you haven’t yet, do try playing around with the interactive graphs here. (You’ll need to install the Mathematica plug-in.)

Update History:

  • 28-May-2011, 8:00 a.m. EDT: Many thanks to JKH, fixed the explanation of Figure 1, which confusingly referred to the Y axis as the X axis.