On Equilibrium, Disequilibrium, and Rational Expectations

There's been some animated discussion recently on equilibrium analysis in economics, starting with a provocative post by Noah Smith, vigorous responses by Roger Farmer and JW Mason, and some very lively comment threads (see especially the smart and accurate points made by Keshav on the latter posts). This is a topic of particular interest to me, and the debate gives me a welcome opportunity to resume blogging after an unusually lengthy pause.

As Farmer's post makes clear, equilibrium in an intertemporal model requires not only that individuals make plans that are optimal conditional on their beliefs about the future, but also that these plans are mutually consistent. The subjective probability distributions on the basis of which individuals make decisions are presumed to coincide with the objective distribution to which these decisions collectively give rise. This assumption is somewhat obscured by the representative agent construct, which gives macroeconomics the appearance of a decision-theoretic exercise. But the assumption is there nonetheless, hidden in plain sight as it were. Large scale asset revaluations and financial crises, from this perspective, arise only in response to exogenous shocks and not because many individuals come to realize that they have made plans that cannot possibly all be implemented.

Farmer points out, quite correctly, that rational expectations models with multiple equilibrium paths are capable of explaining a much broader range of phenomena than those possessed of a unique equilibrium. His own work demonstrates the truth of this claim: he has managed to develop models of crisis and depression without deviating from the methodology of rational expectations. The equilibrium approach, used flexibly with allowances for indeterminacy of equilibrium paths, is more versatile than many critics imagine.

Nevertheless, there are many routine economic transactions that cannot be reconciled with the hypothesis that individual plans are mutually consistent. For instance, it is commonly argued that hedging by one party usually requires speculation by another, since mutually offsetting exposures are rare. But speculation by one party does not require hedging by another, and an enormous amount of trading activity in markets for currencies, commodities, stock options and credit derivatives involves speculation by both parties to each contract. The same applies on a smaller scale to positions taken in prediction markets such as Intrade. In such transactions, both parties are trading based on a price view, and these views are inconsistent by definition. If one party is buying low planning to sell high, their counterparty is doing just the opposite. At most one of the parties can have subjective beliefs that are consistent with with the objective probability distribution to which their actions (combined with the actions of others) gives rise.

If it were not for fundamental belief heterogeneity of this kind, there could be no speculation. This is a consequence of Aumann's agreement theorem, which states that while individuals with different information can disagree, they cannot agree to disagree as long as their beliefs are derived from a common prior. That is, they cannot persist in disagreeing if their posterior beliefs are themselves common knowledge. The intuition for this is quite straightforward: your willingness to trade with me at current prices reveals that you have different information, which should cause me to revise my beliefs and alter my price view, and should cause you to do the same. Our willingness to transact with each other causes us both to shrink from the transaction if our beliefs are derived from a common prior.

Hence accounting for speculation requires that one depart, at a minimum, from the common prior assumption. But allowing for heterogeneous priors immediately implies mutual inconsistency of individual plans, and there can be no identification of subjective with objective probability distributions.

The development of models that allow for departures from equilibrium expectations is now an active area of research. A conference at Columbia last year (with Farmer in attendance) was devoted entirely to this issue, and Mike Woodford's reply to John Kay on the INET blog is quite explicit about the need for movement in this direction:

The macroeconomics of the future... will have to go beyond conventional late-twentieth-century methodology... by making the formation and revision of expectations an object of analysis in its own right, rather than treating this as something that should already be uniquely determined once the other elements of an economic model (specifications of preferences, technology, market structure, and government policies) have been settled.

There is a growing literature on heterogenous priors that I think could serve as a starting point for the development of such an alternative. However, it is not enough to simply allow for belief heterogeneity; one must also confront the question of how the distribution of (mutually inconsistent) beliefs changes over time. To a first approximation, I would argue that the belief distribution evolves based on differential profitability: successful beliefs proliferate, regardless of whether those holding them were broadly correct or just extremely fortunate. This has to be combined with the possibility that some individuals will invest considerable time and effort and bear significant risk to profit from large mismatches between the existing belief distribution and the objective distribution to which it gives rise. Such contrarian actions may be spectacular successes or miserable failures, but must be accounted for in any theory of expectations that is rich enough to be worthy of the name.

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Some of the issues discussed here are explored at greater length in an essay on market ecology that I presented at a symposium in honor of Duncan Foley last week. Duncan was among the first to see that the rational expectations hypothesis implicitly entailed the assumption of complete futures markets, and would therefore be difficult to "reconcile with the recurring phenomena of financial crisis and asset revaluation that play so large a role in actual capitalist economic life." 

The Countrywide Complaint and the Capitalization of Trust

In December 2011 the Department of Justice filed suit against Countrywide Financial Corporation alleging discrimination on the basis of race and national origin in its mortgage lending operations over the period 2004-2008. The result was a record settlement for $335 million with Bank of America, which had acquired Countrywide in 2008.

The complaint was based on a review of "internal company documents and non-public loan-level data" on more than 2.5 million loans and is worth reading in full. In addition to providing evidence of disparate impact, it describes in detail the set of incentive structures under which loan officers and mortgage brokers were operating. These compensation schemes left considerable room for individual discretion in the setting of fees and rates, and for steering borrowers towards particular loan products. The manner in which this discretion was exercised had significant effects on overall levels of compensation, resulting in strong incentives for brokers and loan officers to act against the interests of borrowers.

But these incentives were formally neutral with respect to race and national origin, which raises the question of why they led to such disparate impact. In the standard economic theory of price discrimination, it is the most affluent customers, or the ones who value the product the most, who pay the highest prices. But in the case of mortgage loans it appears that the highest prices were paid by those who could least afford to do so. One possible reason for this is that this set of borrowers was poorly informed about market rates and alternatives. But this alone is not a satisfactory explanation, because such information can be sought if one considers it to be valuable. It may not be sought, however, if if a borrower trusts his broker to be providing the best available terms. I argue below, based on a very interesting paper by Carolina Reid of the San Francisco Fed, that variations across communities in the level of such trust was a key factor in explaining why the incentive structures in place gave rise to such disparate impact.

But first, the complaint:

As a result of Countrywide's policies and practices, more than 200,000 Hispanic and African-American borrowers paid Countrywide higher loan fees and costs for their home mortgages than non-Hispanic White borrowers, not based on their creditworthiness or other objective criteria related to borrower risk, but because of their race or national origin. 

Additionally... Hispanic and African-American borrowers were placed into subprime loans when similarly-qualified non-Hispanic White borrowers received prime loans. Between 2004 and 2007, more than 10,000 Hispanic and African-American wholesale borrowers received subprime loans, with adverse terms and conditions such as high interest rates, excessive fees, prepayment penalties, and unavoidable future payment hikes, rather than prime loans... not based on their creditworthiness or other objective criteria related to borrower risk, but because of their race or national origin.

But what, exactly, were these policies and practices, and how did they give rise to the alleged disparate impact? The complaint focuses on the discretion given to loan officers and mortgage brokers, and the manner in which their compensation was determined. The process for retail loans was as follows:

Countrywide utilized a two-tier decision-making process to set the interest rates and other terms and conditions of retail loans it originated. The first step involved setting the credit risk-based prices on a daily basis... including interest rates, loan origination fees, and discount points. In this step, Countrywide accounted for numerous objective credit-related characteristics of applicants by setting a variety of prices for each of the different loan products that reflected its assessment of individual applicant creditworthiness, as well as the current market rate of interest and the price it could obtain from the sale of such a loan to investors. These prices, referred to as par or base prices, were communicated through rate sheets... Individual loan applicants did not have access to these rate sheets. 

As the second step in determining the final price it would charge an applicant for a loan, Countrywide allowed its retail mortgage loan officers... to increase the loan price charged to borrowers over the rate sheet prices set by Countrywide, up to certain caps; this pricing increase was labeled an overage. Countrywide also allowed these same employees to decrease the loan price charged to borrowers below the stated rate sheet prices; this pricing decrease was labeled a shortage. Countrywide further allowed those employees to alter the standard fees it charged in connection with processing a loan application and the standard allocation of closing costs between Countrywide and the borrower. Employees made these pricing adjustments in a subjective manner, unrelated to factors associated with an individual applicant's credit risk... 

During the time period at issue, Countrywide loan officer compensation was affected by the loan officers' decisions with respect to pricing overages and shortages, as well as other factors, such as volume of loans originated. Loan officers could obtain increased compensation for overages and could have their total compensation potentially decreased for shortages. Countrywide's compensation policy thus provided an incentive for its loan officers in making pricing adjustments to maximize overages and, when offering shortages, to minimize their amount.

Very similar incentives were in place for mortgage brokers who brought loan applications to Countrywide for origination and funding through its wholesale channel. As in the case of retail loans, rate sheets were made available to brokers on a daily basis with prices specified for different loan products based on borrower characteristics. Brokers were not required to "inform a prospective borrower of all available loan products for which he or she qualified, of the lowest interest rates and fees for a specific loan product, or of specific loan products best designed to serve the interests expressed by the applicant." In fact, the manner in which broker compensation was determined created incentives to actively conceal such information, since they were paid "based on the extent to which the interest rate charged on a loan exceeded the base, or par, rate for that loan to a borrower with particular credit risk characteristics fixed by Countrywide and listed on its rate sheets."

Aside from variation across borrowers in rates and fees for a given product, there was also variation in the types of products towards which borrowers were steered:

It was Countrywide's business practice to allow its mortgage brokers and employees to place a wholesale loan applicant in a subprime loan even when the applicant qualified for a prime loan according to Countrywide's underwriting practices... These underwriting guidelines were intended to be used to determine whether a loan applicant qualified for a prime loan product, an Alt-A loan product, a subprime loan product, or for no Countrywide loan product at all.  Countrywide's compensation policy and practice created a financial incentive for mortgage brokers to submit subprime loans to Countrywide for origination rather than any other type of residential loan product.

The incentives to increase overages, reduce shortages, and steer borrowers towards subprime products even when qualified for prime loans clearly operated against the interests of borrowers. Coupled with the incentives tied to loan volume, this compensation scheme encouraged brokers and loan officers to set terms that varied systematically across borrowers. Applicants who were more sophisticated and knowledgable, and would walk away from riskier or more expensive products, received better terms than those who were more naive. And those who were suspicious of their brokers and aware of the incentives under which they were operating secured better terms than those who were more trusting.

Hence the disparities in rates and fees identified in the complaint could, in principle, have arisen from differences across social groups in the degree to which they trusted those with whom they were transacting. Carolina Reid's paper provides some evidence for this interpretation. Reid argues that "while financial services have gone global... obtaining a mortgage is still a very local process, embedded in local context and social relations." In order to better understand this process, she interviewed homeowners in Oakland and Stockton, two areas that experienced very high rates of subprime lending prior to the crisis and correspondingly elevated rates of foreclosure subsequently. These were also areas in which a disproportionately large share of originations were mediated by mortgage brokers. Here is what she found:

One of the strong themes that emerged from the interviews was the extent to which respondents of color expressed their desire to work with a broker from their own community or background... In this sense, the interviews support Granovetter’s hypothesis that individuals are “less interested in general reputations than in whether a particular other may be expected to deal honestly with them—mainly a function of whether they or their own contacts have had satisfactory past dealings with the other.” (Granovetter 1985, p. 491) In numerous interviews, borrowers said that they turned to their social networks and relations in the neighborhood to identify a local mortgage broker who would be willing to “work with someone like me.” Part of this was driven by a lack of trust in traditional lenders, and several respondents in Oakland noted a historical distrust of banks in the community... More frequently, however, respondents noted that they didn’t think they could obtain or qualify for a loan without help from someone who was ‘like them’ but who knew the system... 

Respondents listed a wide array of ways that they received recommendations for both real estate agents and mortgage brokers: family, neighbors on the block, the local church, their jobs, the park, and parents at their kids’ school...  

The desire to be served by someone from the community was not lost on mortgage brokers, who during this time period actively created the impression that they were part of the community to help promote their business. Strategies ranged from relying on customer referrals to generate new business, to frequenting local churches, social gatherings, and businesses and by adopting local social conventions... The interviews pointed to how the respondents felt immediately connected to these brokers, “he understood my situation”, “he told me that he understands how difficult the paperwork is, especially when you have lots of jobs,” “I liked his ideas for how to brighten the kitchen,” “she seemed to understand why we wanted to move from SF, buy a house, provide for a yard for the kids, a good school.” 

In theory, mortgage brokers are well‐placed to serve as a “bridging tie” and “trusted advisor”, since they have both experience with the lending process and access to information about mortgage products and prices. Empirical research studies, however, have revealed that the during the subprime boom, yield spread premiums coupled with a push for a greater volume of loan originations provided a financial incentive for brokers to work against the interests of the borrower (e.g. Ernst, Bocia and Li 2008). In addition, since there was no statutory employer‐employee relationship between lending institutions and brokers, there were few legal protections to ensure that brokers provide borrowers with fair and balanced information. This aligns with the “trust” that social relations engender... In both Stockton and Oakland, respondents did not seem to be aware of the potential for perverse incentives on the part of brokers, and instead trusted them fully to act in their best interests. 

It is ironic that distrust of traditional lending institutions such as commercial banks led some borrowers to seek out brokers from their own communities whom they felt they could trust. But these brokers were operating under high-powered incentives to inflate rates and fees and guide borrowers towards subprime products even when they were eligible for cheaper alternatives. The trust that was placed in the brokers allowed them greater flexibility to respond to these incentives and left borrowers worse off than they would have been if they had been more suspicious or better aware of the incentive structures in place.

Viewed in this manner, the subprime saga has some broader implications. From the point of view of a company operating in multiple local markets with a diverse customer base, the strategy of giving local employees or contractors the discretion to adjust prices can be very profitable. This is especially so if these employees appear trustworthy to their customers, but are not in fact deserving of such trust. As Groucho Marx is reputed to have said:

The secret of life is honesty and fair-dealing. If you can fake that you've got it made. 

For products involving frequent repeat purchases by the same customer, reputation effects and competition can limit the degree of price discrimination. But the purchase of a home is an infrequent transaction for most people, and the complexity of the loan product precludes easy comparison with alternatives on offer. Trust then becomes a key determinant of pricing and transaction volume, especially when strong and hidden incentives for the betrayal of trust are in place.

Betrayal also leads to the erosion of trust over time. It could be argued that trust is one of our most valuable public goods, substantially lowering the costs of transacting. In the complete absence of trust, the volume of resources that would need to be devoted to monitoring would be prohibitively large and many organizations and markets would simply not exist. Trust also comes naturally to most of us, based on simple cues such as those revealed in Reid's interviews. High-powered incentives to secure and then betray such trust are therefore costly not just to the immediate victims, but also to the broader community. This may be one of the less visible consequences of the subprime crisis. 

Returns to Information and Returns to Capital

One of the benefits of maintaining this blog is that it gives me the opportunity to think aloud, expressing half-formed ideas in the hope that the feedback will help me sort through some interesting questions. My last post on double taxation attracted a number of thoughtful (and in some cases skeptical) comments for which I am grateful.

What I was trying to do in that post was to evaluate two incompatible statements: Warren Buffet's declaration that he pays a substantially lower tax rate at 18% than any of his office staff, and Mitt Romney's conflicting claim that his effective tax rate is close to 50%, the sum of the corporate tax rate and the rate on long-term capital gains. I argued that since the corporate tax is capitalized into prices at both the time of purchase and the time of sale, it ought not to be simply added to the capital gains tax to determine an effective rate.

The point may be expressed as follows. Over the past couple of years Romney seems to have paid about 3 million dollars in taxes on income of about 20 million annually, a rate of about 15%. If his effective tax rate is 50% then his "effective" gross income is about twice his current after-tax income, or approximately 34 million. What he is claiming, in effect, is that in the absence of the corporate tax, and with no change in the nature of his economic activities, he would have been able to secure a capital gain of 34 million annually. This does not seem plausible to me. Elimination of the corporate tax would certainly result in a one-time gain to any currently held long positions, but I don't see how it could allow him to generate an extra 14 million, which is 70% greater than his current gross income, on an ongoing basis every year.

Whatever the merits of this argument, I think that most commenters on my earlier post agree with me on two things:

1. The adding-up approach to effective tax rates does not work for short sales and related derivative positions, since it would lead to the absurd conclusion that short sellers were paying a negative effective tax rate on capital gains.
2. Elimination of the corporate tax would result in a sharp rise in equity prices and a windfall gain to current long investors, but would have more modest and uncertain effects on the returns to future investors who enter positions after the lower rate has been capitalized into prices. 

In particular, the following comment from Richard Serlin got me thinking about the nature of capital gains:

With regard to short selling, when the corporate tax first hits (or becomes known to hit), they'll get a windfall, but then their expected returns (of the short sales people actually choose to take) will adjust to the new norm for their risk. It's not like short selling opportunities that pay a fair market risk adjusted return always exist, anyway. When they do, it's largely not a reward for the capital, but for the information that the stock is an overpriced bad deal.

It is certainly true, as Richard points out, that profits to short positions are rewards for information, broadly interpreted to include the processing and analysis of information. They are not returns to capital in any meaningful sense, although one requires capital to enter a short position. But the same is true for at least some portion of the profits to long positions. In fact, the essence of Buffet's investment strategy is to identify underpriced companies in which to take long (and long-term) positions on which capital gains are then realized.

If capital gains are viewed largely as a return to capital, then the double taxation argument makes some sense. But viewed as a return to information and analysis, it is not clear why capital gains should be given preferential tax treatment relative to the income generated, for instance, by doctors or teachers.

I suspect that Warren Buffet views his income as being generated largely by information and judgment, and does not believe that his opportunities for ongoing capital gain would be substantially increased if the corporate tax were eliminated. He does not therefore see the tax as a significant burden, and does not consider his effective gross income to be substantially greater than that which he declares on his tax returns. Whether Romney himself feels the same way is impossible to know, since political expediency currently compels him to take a very different position. 

Double Taxation

The release of Mitt Romney's tax returns has drawn attention yet again to the disparity between the rates paid on ordinary income and those paid on capital gains. It is being argued in some quarters that the 15% rate on capital gains vastly underestimates the effective tax rate paid by those whose income comes largely from financial investments, on the grounds that corporations pay a rate of 35% on profits. Were it not for this tax, it is argued, dividends and capital gains would be higher, and so would the after-tax receipts of those who derive the bulk of their income from such sources.

Romney himself has made this argument recently, claiming that his effective tax rate is closer to 50%:

One of the reasons why we have a lower tax rate on capital gains is because capital gains are also being taxed at the corporate level. So as businesses earn profits, that's taxed at 35 percent. Then as they distribute those profits in dividends, that's taxed at 15 percent more. So all total, the tax rate is really closer to 45 or 50 percent.

The absurdity of this claim is clearly revealed if one considers capital gains that accrue to short sellers, who pay rather than receive dividends while their positions are open. Following the logic of the argument, one would be forced to conclude that short sellers are taxed at an effective rate of negative 20%, thereby receiving a significant subsidy due to the existence of the corporate tax. The flaw in this reasoning is apparent when one recognizes that asset prices are lower (relative to the zero corporate tax benchmark) not only when a short position is covered, but also when it is entered.

There is no doubt that the presence of the corporate tax depresses the price of equities, but it does so both at the time of purchase and at the time of sale. If there were no corporate tax, dividends and capital gains per share would certainly be higher, but an investor would have paid substantially more per share to acquire his assets in the first place. As a result he would be holding fewer shares for any given initial outlay, and his after-tax income (holding constant the rate paid on capital gains) would not be substantially different.

To see why, it is useful to think about what determines the price of equities. Three factors are especially important: the current earnings of a firm (after payment of interest and taxes), the rate at which these earnings are expected to grow, and the riskiness of the security, which itself is linked to the degree to which the firm's earnings are correlated with broader market movements. Securities that are riskier in this latter sense tend to appreciate faster on average because investors would otherwise avoid them, depressing their prices and raising their expected returns until such returns are viewed as adequate compensation for the greater risk of holding them. This risk is routinely expressed as a market capitalization rate, interpreted as the expected return that investors require in order to hold the security. Airline and automobile stocks, for instance, have higher market capitalization rates than do shares in utilities.

The manner in which these factors interact to influence prices may be illustrated by considering the simplest possible case of a firm with constant expected earnings growth and a fixed dividend payout ratio. In this case, for reasons discussed in any introductory finance textbook, the fundamental value of the security is given by the simple formula D/(k-g), where D is the current dividend forecast (a constant share of the earnings forecast), g is its expected rate of growth, and k is the market capitalization rate. Shares in a debt-free firm that pays 20% of its earnings as dividends, is currently earning $10 per share annually, is expected to grow at 10%, and has a market capitalization rate of 12% would then have a share price of $100. After a year (assuming no change in these parameters) the share price would be $110 and the dividend payout $2. An investor would have made $12 on a $100 investment, a percentage return precisely equal to the market capitalization rate. All this is with no corporate tax.

Now suppose that a 35% corporate tax is in place, so after-tax earnings per share are $6.50 instead, with no change in other specifications. Dividends are then $1.30 per share and the initial share price is $65. After a year this rises to $71.50. Adding dividends and capital gains, an investor makes $7.80 for each share purchased at $65, again earning precisely 12%. Each share results in lower revenues to the investor, but since more shares can be purchased at the outset, aggregate income is no different.

None of this should be in the least bit surprising. Note, however, that if the corporate tax were to be eliminated today, there would be a sharp rise in the price of equities and current asset holders would enjoy a windfall gain. Similar issues arise with respect to the mortgage interest deduction: eliminating this would result in an immediate decline in home values, severely punishing those who purchased recently at prices that reflected the anticipated tax savings over the duration of the mortgage.

This does not necessarily mean that eliminating the corporate tax while simultaneously raising the rate on capital gains is necessarily a bad idea, or that elimination of the mortgage interest deduction is necessarily bad policy. A case could be made for both initiatives. The corporate tax is not uniformly applied due to the broad range of loopholes and exemptions, and the mortgage deduction is regressive and inhibits both neighborhood integration and labor mobility. But any such changes will have major distributional effects that must be taken into account in any comprehensive evaluation of the policy. Doing so properly requires a clear distinction between stocks and flows, and an analysis that goes a little deeper than simple arithmetic.

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Update: Follow-up post here.

Self-Fulfilling Prophecies and the Iowa Caucus

A few days ago Nate Silver made the following intriguing comments on the Iowa Caucus (emphasis added):

There are extremely strong incentives for supporters of Mrs. Bachmann, Mr. Santorum and Mr. Perry to behave tactically, throwing their weight behind whichever one appears to have the best chance of finishing in the top two. What that means is that if any of these candidates appear to have any momentum at all during the final week of the campaign, their support could grow quite quickly as other voters jump on the bandwagon.

This is also a case in which the polling may actually influence voter behavior. In particular, if one of these candidates does well in the highly influential Des Moines Register poll that should be published on New Year’s Eve or thereabouts, that candidate might be a pretty good bet to overperform polling as voters use that as a cue on caucus night to determine which one is most viable...

I’m not sure that this theory actually makes any sense... But it may not matter if the theory is true. If voters are looking for anything to break the logjam between these candidates, mere speculation that one of them has momentum could prove to be a self-fulfilling prophecy.

What's most interesting about this is the possibility that even a methodologically flawed or misleading poll, provided that it is given credence, could coordinate expectations on one of these three candidates and result in a surge of support.

In fact, this seems to be precisely what has happened. A CNN/Time poll covering the period December 21-27 revealed Santorum to be in third place with 16% of the vote. This was an outlier at the time, and was sharply criticized by Tom Jensen of PPP and by Nate himself for surveying only registered Republicans:

What’s wrong with using a list of Republican voters for a Republican caucus poll? The answer is that it’s extremely easy for independent and Democratic voters to register or re-register as Republicans at the caucus site. Historically, a fair number of independent voters do this.

According to entrance polls in Iowa in 2008, for instance, about 15 percent of participants in the Republican caucus identified themselves as independents or Democrats on the way into the caucus site... Most other pollsters are making some attempt to account for these voters. They are anticipating that the fraction of independents and Democrats will be at least as high as it was in 2008 if not a little higher, which would make sense since Republicans do not have a competitive Democratic caucus to compete with this year.

The recent Public Policy Polling survey, for instance, estimated that 24 percent of Iowa caucus participants are currently registered as independents or Democrats and will re-register as Republicans at the caucuses. This month’s Washington Post/ABC News poll put the fraction at 18 percent. There is room to debate what the right number is but it will certainly not be zero, as the CNN poll assumes.

Since few independents and Democrats are inclined to vote for Santorum, the CNN/Time poll very likely exaggerated the level of support he enjoyed at the time. But despite this, it contributed to expectations of a surge which seem to have become self-fulfilling. The Des Moines Register poll released last night confirms this, with Santorum rising sharply from 10% on the 27th all the way to 22% four days later. This survey, conducted by the highly regarded Ann Selzer, has historically been among the most reliable of Iowa polls.

Did a misleading poll based on an unsound sample shift expectations in such a manner as to fulfill it's own flawed forecast? Tom Jensen certainly appears to think so:

Selzer had Santorum at 9% Tu-W. We had him at 10% M-Tu. Surge quite possibly generated by CNN poll that was quite possibly wrong... If CNN had shown Perry at 15% and he got all the momentum stories, the buzz in Iowa might be all about him this weekend.

The CNN/Time poll may also have given Romney an expectational boost at the expense of Paul by excluding independents from the survey. As Tom Jensen noted in his response, Romney was ahead of Paul in the restricted sample of the PPP poll, but quite clearly behind overall on December 27. It's an interesting example of how a seemingly innocuous methodological decision on a single primary poll could end up having major ramifications for the direction of the country.

The mechanisms at work here have some broader implications. They reveal the potential value to candidates (or their supporters) of manipulating prices in prediction markets such as Intrade, which have come to be closely monitored indicators of candidate viability. And they appear in all sorts of other contexts, from sovereign debt crises to speculative currency attacks.

In fact, any borrower who has financed long-dated assets with short term liabilities needs to periodically roll over debt, and the willingness of investors to facilitate this depends on their beliefs about whether other investors will continue to facilitate it in the future. These expectations are subject to capricious change, often as a result of small and seemingly unimportant triggers. The Iowa caucus illustrates the phenomenon, and the Eurozone debt crisis demonstrates its broader relevance.

Price Coherence on Intrade

A couple of days ago, Richard Thaler tweeted this:

Intrade prices seem incoherent. How can Newt nomination price soar but Obama win stay at 50%?

Here's what Thaler is talking about. Over the past couple of weeks, the price of a contract that pays $10 in the event that Gingrich is nominated has risen sharply from about a dollar to above $3.50:

Over the same period a contract that pays $10 if Obama is reelected has remained within a narrow window, trading within a ten cent band a shade above $5:

Thaler considers this pattern to be incoherent because Gingrich is widely believed to be a weaker general election candidate than Romney. For instance, in head-to-head poll averages Obama currently leads Gingrich by 5.7%, but leads Romney by the much smaller margin of 1.5%.

But even if Gingrich really is the weaker candidate against Obama under any set of conditions that might prevail on election day, it does not follow (as a point of logic) that a rise in the Gingrich nomination price must be associated with a rise in the Obama reelection price. For instance, a belief among voters that Obama is more vulnerable would ordinarily result in a decline in his likelihood of reelection, but this could be offset if the same belief also leads to the nomination by the GOP of a more conservative but less electable candidate.

This reasoning is consistent with the so-called Buckley Rule, which urges a vote for the most conservative candidate who is also electable. As perceptions about the electability of the incumbent shift, so does the perceived viability of more ideologically extreme members of the opposition. These countervailing effects can dampen fluctuations in the electability of the incumbent. Hence the market data alone cannot decisively settle the question of price coherence. 

Notes on a Worldly Philosopher

The very first book on economics that I remember reading was Robert Heilbroner's majesterial history of thought The Worldly Philosophers. I'm sure that I'm not the only person who was drawn to the study of economics by that wonderfully lucid work. Heilbroner managed to convey the complexity of the subject matter, the depth of the great ideas, and the enormous social value that the discipline at its best is capable of generating.

I was reminded of Heilbroner's book by Robert Solow's review of Sylvia Nasar's Grand Pursuit: The Story of Economic Genius. Solow begins by arguing that the book does not quite deliver on the promise of its subtitle, and then goes on to fill the gap by providing his own encapsulated history of ideas. Like Heilbroner before him, he manages to convey with great lucidity the essence of some pathbreaking contributions. I was especially struck by the following passages on Keynes:

He was not without antecedents, of course, but he provided the first workable intellectual apparatus for thinking about what determines the level of “output as a whole.” A generation of economists found his ideas the only available handle with which to grasp the events of the Great Depression of the time... Back then, serious thinking about the general state of the economy was dominated by the notion that prices moved, market by market, to make supply equal to demand. Every act of production, anywhere, generates income and potential demand somewhere, and the price system would sort it all out so that supply and demand for every good would balance. Make no mistake: this is a very deep and valuable idea. Many excellent minds have worked to refine it. Much of the time it gives a good account of economic life. But Keynes saw that there would be occasions, in a complicated industrial capitalist economy, when this account of how things work would break down.

The breakdown might come merely because prices in some important markets are too inflexible to do their job adequately; that thought had already occurred to others. It seemed a little implausible that the Great Depression of the 1930s should be explicable along those lines. Or the reason might be more fundamental, and apparently less fixable. To take the most important example: we all know that families (and other institutions) set aside part of their incomes as saving. They do not buy any currently produced goods or services with that part. Something, then, has to replace that missing demand. There is in fact a natural counterpart: saving today presumably implies some intention to spend in the future, so the “missing” demand should come from real capital investment, the building of new productive capacity to satisfy that future spending. But Keynes pointed out that there is no market or other mechanism to express when that future spending will come or what form it will take... The prospect of uncertain demand at some unknown time may not be an adequately powerful incentive for businesses to make risky investments today. It is asking too much of the skittery capital market. Keynes was quite aware that occasionally a wave of unbridled optimism might actually be too powerful an incentive, but anyone in 1936 would take the opposite case to be more likely.

So a modern economy can find itself in a situation in which it is held back from full employment and prosperity not by its limited capacity to produce, but by a lack of willing buyers for what it could in fact produce. The result is unemployment and idle factories. Falling prices may not help, because falling prices mean falling incomes and still weaker demand, which is not an atmosphere likely to revive private investment. There are some forces tending to push the economy back to full utilization, but they may sometimes be too weak to do the job in a tolerable interval of time. But if the shortfall of aggregate private demand persists, the government can replace it through direct public spending, or can try to stimulate additional private spending through tax reduction or lower interest rates. (The recipe can be reversed if private demand is excessive, as in wartime.) This was Keynes’s case for conscious corrective fiscal and monetary policy. Its relevance for today should be obvious. It is a vulgar error to characterize Keynes as an advocate of “big government” and a chronic budget deficit. His goal was to stabilize the private economy at a generally prosperous level of activity.

This is as clear and concise a description of the fundamental contribution of the General Theory that I have ever read. And it reveals just how far from the original vision of Keynes the so-called Keynesian economics of our textbooks has come. The downward inflexibility of wages and prices is viewed in many quarters today to be the hallmark of the Keynesian theory, and yet the opposite is closer to the truth. The key problem for Keynes is the mutual inconsistency of individual plans: the inability of those who defer consumption to communicate their demand for future goods and services to those who would invest in the means to produce them.

The place where this idea gets buried in modern models is in the hypothesis of "rational expectations." A generation of graduate students has come to equate this hypothesis with the much more innocent claim that individual behavior is "forward looking." But the rational expectations hypothesis is considerably more stringent than that: it requires that the subjective probability distributions on the basis of which individual decisions are made correspond to the objective distributions that these decisions then give rise to. It is an equilibrium hypothesis, and not a behavioral one. And it amounts to assuming that the plans made by millions of individuals in a decentralized economy are mutually consistent. As Duncan Foley recognized a long time ago, this is nothing more than "a disguised form of the assumption of the existence of complete futures and contingencies markets."

It is gratifying, therefore, to see increasing attention being focused on developing models that take expectation revision and calculation seriously. A conference at Columbia earlier this year was devoted entirely to such lines of work. And here is Mike Woodford on the INET blog, making a case for this research agenda:

This postulate of “rational expectations,” as it is commonly though rather misleadingly known... is often presented as if it were a simple consequence of an aspiration to internal consistency in one’s model and/or explanation of people’s choices in terms of individual rationality, but in fact it is not a necessary implication of these methodological commitments. It does not follow from the fact that one believes in the validity of one’s own model and that one believes that people can be assumed to make rational choices that they must be assumed to make the choices that would be seen to be correct by someone who (like the economist) believes in the validity of the predictions of that model. Still less would it follow, if the economist herself accepts the necessity of entertaining the possibility of a variety of possible models, that the only models that she should consider are ones in each of which everyone in the economy is assumed to understand the correctness of that particular model, rather than entertaining beliefs that might (for example) be consistent with one of the other models in the set that she herself regards as possibly correct...

The macroeconomics of the future, I believe, will still make use of general-equilibrium models in which the behavior of households and firms is derived from considerations of intertemporal optimality, but in which the optimization is relative to the evolving beliefs of those actors about the future, which need not perfectly coincide with the predictions of the economist’s model. It will therefore build upon the modeling advances of the past several decades, rather than declaring them to have been a mistaken detour. But it will have to go beyond conventional late-twentieth-century methodology as well, by making the formation and revision of expectations an object of analysis in its own right, rather than treating this as something that should already be uniquely determined once the other elements of an economic model (specifications of preferences, technology, market structure, and government policies) have been settled.

I think that the vigorous pursuit of this research agenda could lead to a revival of interest in theories of economic fluctuations that have long been neglected because they could not be reformulated in ways that were methodologically acceptable to the professional mainstream. I am thinking, in particular, of nonlinear models of business cycles such as those of Kaldor, Goodwin, Tobin and Foley, which do not depend on exogenous shocks to account for departures from steady growth. This would be an interesting, ironic, and welcome twist in the tangled history of the worldly philosophy.