The "Incomplete Revelation Hypothesis" and financial reporting. (Commentary).

INTRODUCTION

The most common form of the Efficient Markets Hypothesis (EMH) states that market prices fully reflect all publicly available information (Fama 1970). The EMH has been highly influential among academics, but practitioners and regulators appear unconvinced. Investors work

hard to identify mispriced stocks on the basis of public data, or pay others to do so, even though the EMH asserts that such efforts are wasted. Managers seek to boost stock prices by hiding bad news in footnotes, and regulators work hard to defeat such efforts, even though the EMH asserts that information is reflected in prices no matter how obscure its presentation.

Beliefs about inefficiency play a central role in the debate over recognizing expenses for incentive stock options. Opponents of expensing argue that the resulting lower net income will inappropriately reduce market prices, while proponents argue the market does not fully recognize compensation costs reported only in footnotes. In efficient markets, however, expensing these costs has no direct effect on prices, as long as the details of the compensation are included in footnotes. The decision to expense option costs could reduce stock price indirectly, even in efficient markets, by affecting the terms of contracts between the reporting firm and other parties (Watts and Zimmerman 1986). However, few of the parties to the debate appear concerned about these effects.

The academic community is showing increasing dissatisfaction with the EMH, swayed partly by evidence that prices underreact to large earnings changes, ratios of prices to fundamentals, and other statistics derived from fundamental accounting analyses. However, the EMH is still influential because there is no alternative theory that explains why we observe the inefficiencies we do. For example, why should the market underreact to large earnings changes, rather than overreact? Without a theory predicting how and why markets are inefficient, studies showing mispricing can be viewed as statistical flukes resulting from fishing expeditions (Fama 1998; Kothari 2001).

In this paper, I present an alternative to the EMH called the "Incomplete Revelation Hypothesis" (IRH). The IRH asserts that statistics that are more costly to extract from public data are less completely revealed in market prices. The IRH can account for many of the phenomena that are central to financial reporting but inconsistent with the EMH. It predicts that investors devote substantial resources to identifying mispriced stocks on the basis of public data, that managers seek to boost stock prices by hiding bad news in footnotes, and that regulators may wish to defeat such efforts, because information that is hard to extract from financial statements will not be reflected in stock prices. The IRH also provides a number of novel and testable predictions that distinguish it from the EMH.

THE INCOMPLETE REVELATION HYPOTHESIS

The IRH is based on equilibrium outcomes in "noisy rational expectations" models. (1) In these models, rational agents choose whether to collect information about the value of an asset. Those who choose to collect the information then trade the asset in a market that also includes "noise" traders. Noise traders are so named because they trade randomly, in response to liquidity shocks, portfolio rebalancing needs, or even irrational whims. This noise keeps prices in the market from revealing information completely, because traders who observe only price cannot tell whether prices are high because informed traders have good news, or because noise traders happen to be buying heavily. This uncertainty allows the informed traders to profit from their information advantage.

A key result of noisy rational expectation models is that there is an equilibrium in which just enough traders collect information to make their trading gains equal to their collection costs. Assume for simplicity that all traders have the same amount of money to place at risk in the market, and the same limited tolerance for risk. In this case, the more traders who collect information, the more completely prices reveal information, and the lower the gain to collecting information. If too few traders collect information, then more prefer to do so, because the gains from informed trading outweigh the costs of collecting the information. If too many traders collect information, then some will regret this decision, because the gains from informed trading are too small to cover collection costs. The equilibrium outcome therefore requires that some but not all traders incur the costs to collect information. In equilibrium, fewer traders collect more costly information. The greater resulting inefficiency allows tho se who collect the information trading gains sufficient to cover the higher collection costs.

I extend this intuition to financial reporting by distinguishing statistics from data. Data are ink spots on sheets of paper, or bits stored in a computer file. Statistics are the useful facts extracted from that data, such as earnings figures and financial ratios. While public data are often free, it takes time and effort to extract statistics even as widely publicized as earnings growth. Given that thousands of companies report earnings every quarter, extracting the relevant statistics is not a trivial task. Hirshleifer and Teoh (2002) provide an excellent discussion of the causes and effects of "limited attention," which keeps traders from considering all available data in making their trading decisions. Applying this perspective to the equilibrium described above, fewer investors base their trading decisions on statistics that are more costly to extract from public data, and market prices reveal those statistics less completely.

In formulating the Incomplete Revelation Hypothesis, I recognize that traders have varying tolerances for risk and money to place at risk. Instead of referring to the number of traders collecting information, appropriate only if all traders are identical, I refer to the "trading interest" driven by a statistic. Trading interest is defined as the additional shares traders are willing to trade for given deviations of market price from the value indicated by the statistic in question. (2) A statistic can drive more trading interest if more traders collect it, if those who collect it have more money to place at risk, or if those who collect it have greater tolerance for risk.

IRH: Statistics that are more costly to extract from public data are less completely revealed by market prices. This association is driven by the following causal chain:

* Statistics that are more costly to extract from publicly available information drive less trading interest.

* Statistics that drive less trading interest are less completely revealed by market prices.

In addition to having a sound theoretical basis, the IRH is well supported by numerous experiments finding that market prices incompletely reflect information not held by all traders. (3)

Because it is derived from models assuming that investors are rational, the IRH clarifies that informational inefficiency need not imply irrationality. Statistics that are costly to extract from data are not completely revealed by prices precisely because trading on those statistics does not generate profits sufficient to cover the extraction cost. Proponents of efficient markets have long recognized this point, but typically invoke extraction costs only as a last resort, to reinterpret evidence of mispricing to be consistent with rationality (Ball 1992). In contrast, the IRH uses these costs as the foundation for specific and testable predictions about the nature and form of inefficiencies, and their implications for financial reporting research, practice, and regulation. The following section discusses these implications in detail.

IMPLICATIONS OF THE IRH FOR FINANCIAL REPORTING RESEARCH, PRACTICE, AND REGULATION

Linking Price Reactions and Extraction Costs

Some of the most basic implications of the IRH are similar to key implications of the EMH used commonly in accounting research. Event studies use the EMH to predict that prices rise after good news and fall after bad news, and price-association studies use the EMH to infer investors' interpretations of data from observed price responses, pioneered by Ball and Brown (1968). The IRH provides the same qualitative predictions. Because information is at least partly revealed in prices, prices rise after good news is released and fall after bad news is released, and price movements are positively correlated with investor interpretations of public data. Thus, researchers relying on these qualitative predictions of the EMH to conduct event studies or price-association studies lose little by relying on the IRH instead.

The IRH goes beyond the EMH by predicting that prices react more strongly to statistics that are more easily extracted from public data. The EMH makes no such prediction, because it ignores extraction costs. The link between extraction cost and price reaction also requires changes in the inferences drawn from price movements. Assume that a firm's stock price rises by 5 percent (adjusted for risk) in response to a public announcement. Researchers could use the EMH to infer that the announcement suggests a 5 percent increase in value. Under the IRH, a 5 percent price reaction is possible only if investors who trade on the statistics included in the announcement perceive more than a 5 percent increase in value, because price changes reflect those perceptions incompletely. The smaller the trading interest driven by the information, the more it must influence traders' perceptions to create a 5 percent increase in price.

The IRH can alter inferences in another way. Francis et al. (2001) find that reported earnings numbers are more closely associated with prices than cash flows, sales and other financial statement data. Using the EMH, they infer that investors view earnings information as more relevant than the other data. The IRH implies a similar result if more investors analyze earnings data than analyze the other statistics. Thus, researchers need to control for differences in investor attention to the statistics before attributing the short-term price effects solely to the beliefs of investors who choose to analyze the statistics.

Testing the link between extraction costs and price behavior requires good measures of these costs. Different perspectives on the nature of extraction costs lead to different measures. One perspective is that extraction costs reflect the cash costs of identifying, collecting, compiling, printing and processing data, or hiring others to do so. Media dissemination and analyst coverage represent inverse measures of costs of identifying and collecting relevant information. News releases that are more widely disseminated and analyzed in the popular press or through corporate press releases should show greater price reactions. Because more informative statistics tend to be more widely published, controls for information content are studies using such measures.

Another perspective is that extraction costs reflect the cognitive difficulty of extracting information from data that has already been identified and collected. Experiments find that professional analysts often fail to recall and respond appropriately to information in complex financial disclosures, suggesting that these costs are not trivial (Hirst and Hopkins 1998). Maines and McDaniel (2000) provide a framework in which data's placement, labeling, isolation, and degree of aggregation in financial statements all influence the cost of extracting information. Future research could expand on this framework to identify statistics that are more difficult to extract from given reports, or reporting formats that make it more difficult to extract given statistics.

Appropriate research designs can sidestep the most difficult problems in measuring extraction costs. The most effective research designs examine how differences in extraction costs are associated with differences in price reactions or other aspects of market behavior. For example, a researcher might examine whether markets react more strongly to a dollar of incentive stock option costs included in earnings than the same dollar of costs buried in a complex footnote. Evidence of such a difference would support the IRH, even though the research design does not measure the actual cost of extracting the information from either type of disclosure.

Research designs can also simplify measurement issues by tying market behavior to the dissemination of information among investors. The IRH links extraction costs to market behavior because extraction costs influence dissemination. Survey methods may be effective at determining how many investors base their trading strategies on particular statistics such as earnings growth or footnotes about off-balance-sheet financing. Evidence that statistics driving more trading interest are revealed more completely in stock prices provides strong support for a key prediction of the IRH without measuring extraction costs.

Return Predictability (Drift)

The most common way to demonstrate informational inefficiency is to form good-news and bad-news portfolios based on whether a particular statistic is favorable or unfavorable. Researchers then test whether risk-adjusted returns for the two portfolios "drift" apart after the market has an opportunity to react to the news. Such drift indicates a failure of the market price to reveal the statistic completely when the data in question are first released. Prices drift predictably as the information is revealed more completely, either through the cumulative effect of trades based on that information, or through the ultimate resolution of the events that the statistic is able to predict.

The IRH predicts greater drift for statistics that are more costly to extract. Sloan (1996) provides support for this prediction that is particularly relevant to financial reporting. He finds that prices incompletely reveal financial statement ratios indicating the proportion of earnings driven by accruals. These ratios are presumably more costly to extract than total earnings. The IRH also predicts systematic underreaction to information contained in footnotes and statistics derived through fundamental analysis, with larger underreactions to footnotes that are more complex or to statistics that require more complex analyses.

The IRH can also potentially account for underreactions to large earnings changes (Bernard and Thomas 1990). It may seem unlikely that the costs of extracting statistics about earnings surprises are high enough to generate measurable returns. However, prices in noisy rational expectations models react completely to a statistic only if all market participants base their trading strategies on that statistic. While the out-of-pocket costs of collecting earnings statistics may be small, the costs of collecting information include opportunity costs. Most investors base their trading strategies on only a subset of available information. Thus, as long as opportunity costs keep some investors from basing trading decisions on earnings, perhaps because they trade on statistics reflecting market share, industry power, or technological advances, the IRH predicts that markets will incompletely reveal earnings information. Researchers might test whether earnings drift and other forms of drift are larger for firms for which earnings information is less widely disseminated, or for which information collection is generally more costly, perhaps due to limited analyst coverage. (4) Earnings drift may also be larger in industries in which non-earnings information is more relevant, increasing the opportunity cost of extracting earnings-based statistics.

The IRH places limits on the form of inefficiencies, because it predicts underreactions to statistics, rather than overreactions. I discuss overreactions in a later section of the paper.

Financial Analysis and Investment Practice

The EMH presents a paradoxical view of the demand for financial analysis: perfectly efficient markets reveal information so completely that no one will bother collecting it, but if no one collects it, then the information is not revealed. (5) The IRH uses the insights of rational expectations models to make explicit the relationship between the degree of inefficiency and the demand for costly information. It measures the demand for information in terms of the trading interest that information drives, and predicts that demand declines as the costs of extracting information rises. A number of theoretical papers, including Lundholm (1991), use noisy rational expectations models to explore demand for costly private information. The IRH suggests that similar models could shed light on decisions to extract costly statistics from public data.

Assuming that all investors have identical wealth and risk aversion, and face identical analysis costs, as in Grossman and Stiglitz (1980), the IRH implies that fewer investors collect more costly information. Market features that reduce extraction costs--such as the presence of analysts or an active financial press--tend to increase information collection. Variation across investors also yields some interesting predictions. Information held by investors with more capital to put at risk or less risk aversion drives more trading interest; such investors can benefit more from information, and should be more willing to devote resources to analysis. This suggests that information tends to be concentrated in the hands of those managing large portfolios.

The equilibrium models underlying the IRH imply that traders will extract statistics more actively in markets with more noise trade, because the greater noise allows informed traders to profit more from their information. However, noise should not affect the level of efficiency, which will always equate trading gains with the cost of information collection.

Managers' Financial Reporting Behavior

Managers usually prefer high stock prices and high returns for the firms they manage. High prices and returns can increase the value of their stock options and stock holding, increase cash compensation, and improve their chances of retaining their current jobs or landing positions with other firms. Consistent with the IRH, managers make many decisions motivated, at least partly, by a desire to make it harder for investors to uncover information that the managers do not want to affect their firms' stock prices:

* Managers choose and lobby for accounting methods that improve highly visible statistics, such as earnings-per-share and debt-equity ratios, and conceal expenses and liabilities in less-visible footnote disclosures.

* Managers classify arguably ongoing expenses as nonrecurring or extraordinary items, while reporting arguably unusual gains as part of operating income.

* Managers develop "cookie jar" reserves to maintain the capacity for positive accruals to boost earnings in the future (Nelson et al. 2002).

* Managers announce pro forma earnings numbers that emphasize improvements relative to their own strategically chosen benchmarks, while making it more difficult for investors to observe other measures of performance (Schrand and Walther 2000; Krische 2001).

Proponents of the EMH argue these actions affect stock prices only because they alter the information provided to the market or alter the terms of stated contracts, such as debt covenants or earnings-based compensation contracts. However, evidence for these alternative explanations is not always apparent. The IRH predicts that such behavior has the greatest effects on market prices when information is most costly to extract, or when trading interest is relatively low, for example, because a stock is not particularly liquid.

The IRH also implies that decisions to conceal information can signal information about management. Because making bad news hard to extract inflates market prices only temporarily, investors can infer that managers who do so have a greater need for an immediate stock price boost. If less competent managers tend to be more impatient, perhaps because they believe poor stock price performance will trigger investigations into their competence, then investors can use reporting choices to infer managerial competence (Bloomfield and Kadiyali 2000).

Financial Reporting Regulation

Many accounting regulations can be viewed as governing the cost of extracting key statistics from financial data. For example, SFAS No. 130 permits firms to report the components of "Other Comprehensive Income," such as unrealized gains and losses on certain investments, in a Comprehensive Income Statement, instead of reporting these components only in the Statement of Changes in Stockholders Equity. Inefficient markets, such a change is important only if it conveys different information about the content of items. For example, investors might infer that a gain reported on the income statement has greater economic meaning than one simply passed through the owners' equity accounts. However, such changes also alter the ease with which investors can extract that statistic (Hirst and Hopkins 1998), thereby affecting market prices.

Regulations affecting extraction costs also affect investor welfare, because not all traders choose to extract costly statistics. Traders who face relatively low extraction costs, perhaps because they have access to investment professionals or information services, tend to benefit from regulations that increase the difficulty of extraction.

In the models underlying the IRH, informed traders recoup extraction costs in transactions with noise traders who seek liquidity, need to rebalance their portfolios, or trade for any reason other than a rational response to information. Regulators can protect noise traders with regulations that place relevant information in the hands of more investors, as argued by Lev (1988). The more completely prices reflect information, the smaller the losses of the noise traders. However, regulators who wish to protect noise traders must recognize that doing so reduces the potential gains of extracting information, which in turn may limit the development of novel forms of financial analysis. The social benefits of improved financial analysis may outweigh the social benefits of alleviating noise trader losses.

RATIONALITY, IRRATIONALITY, AND THE IRH

Many discussions of inefficiency pit rationalists who assume that investors behave rationally, against behavioralists, who assume that investors behave in systematically irrational ways. The IRH accommodates both perspectives. From a rationalist perspective, the noise trading that drives inefficiency reflects the random activities of rational investors who trade for noninformational purposes, such as needs to balance their portfolios. Traders rationally choose not to extract all statistics from public data because the costs of doing so exceed the benefits. The internal consistency of this perspective, drawn from the rational expectation models underlying the IRH, clarifies that informational inefficiency need not indicate investor irrationality. From a behavioralist perspective, noise trade is driven by investors' irrational and unpredictable changes in sentiment. (6) Collection costs are simply convenient ways to represent the bounded abilities of investors to interpret information. Managers' incentives to exploit incomplete revelation do not depend on its cause. Thus, whether the IRH is given a rational or behavioral interpretation does not affect the nature or importance of its predictions about price or reporting behavior.

The IRH does not permit every form of irrationality that behavioralists can imagine. It permits only forms of irrationality that capture information-processing costs. A behavioral model consistent with the noisy rational expectations models must assume that traders rationally interpret the statistics they collect, although they might ignore important data, even when placed before them. It must also assume that traders trade rationally given their interpretations. These restrictions prohibit the IRH from explaining overreactions to public data.

The IRH can accommodate some phenomena commonly referred to as overreactions, because they are more appropriately viewed as underreactions. For example, extreme ratios of price-to-earnings or price-to-book value tend to revert over time to more moderate levels. Extreme long-term returns revert to long-term averages in a similar way. These predictable price movements imply that high prices are too high and low prices are too low. However, such an interpretation does not specify the information to which the market is supposedly overreacting. As a result, these errors are better viewed as underreactions to the statistics used to identify the price errors--prices fail to reveal the news indicated by extreme prices relative to earnings or book value, or by extreme returns relative to average returns. In general, researchers should view deviations of price from the values indicated by fundamentals as underreactions to the fundamentals, whenever they are unable to identify the statistics driving those deviations. I n this case, the IRH accommodates the deviations as the effects of noise trading, which may be rational or irrational.

Under-and overreactions can also be difficult to distinguish when a widely disseminated statistic is contradicted or qualified by a statistic that is less widely disseminated. For example, one could use the evidence in Sloan (1996) to argue that markets overreact to the transitory accrual component of earnings. However, another interpretation is that only some investors decompose earnings into accruals and cash flows, causing the market to underreact to this information. Hand (1990) also provides evidence open to multiple interpretations. Hand (1990) finds that market prices react to the component of earnings reflecting a previously announced debt-equity swap. Because the gain from the swap was public data when the swap was first announced, the EMH predicts no price reaction to this component of income when total earnings are announced. This reaction to old information can therefore be interpreted as an overreaction. However, another interpretation is that not all investors are aware of the initial swap anno uncement, causing the market to underreact to the information that a component of earnings is old news. (7)

It may be possible to interpret all evidence of overreaction to one statistic as an underreaction to another contradictory statistic, rendering the overreaction consistent with the IRH. Such interpretations seem appropriate when one can identify the specific information to which investors are underreacting, as in the case of Sloan (1996) and Hand (1990). However, it is more difficult to reinterpret the evidence of DeBondt and Thaler (1987), who find that prices overreact to persistent trends in earnings. In this case, there is no obvious statistic that investors are ignoring. Rather, they appear to be overestimating the persistence of earnings trends.

As an alternative to reinterpreting overreactions as underreactions to unidentified statistics, researchers should consider extending the IRH to incorporate pervasive forms of irrationality that would allow the IRH to predict overreactions, as well as underreactions. Experimental research suggests that three forms of irrationality seem particularly useful as a basis for understanding overreactions:

* Overreliance on unreliable data. Many experiments find that people tend to react too strongly to statistics that have little information content, because their reactions are determined by how salient the information is and how strongly it is emphasized, rather than by its statistical validity. (8) Markets might overreact to persistent earnings trends because the older earnings numbers have very little power to predict future earnings, but are very salient to investors. Similarly, markets might overreact to repeated publication of interesting but relatively uninformative evidence, such as income from debt-equity swaps, pro farina earnings announcements, or analysts' projections. A special case of this error arises when investors fail to completely account for the incentives of the reporters to distort their information. For example, Forsythe et al. (1999) find that buyers in a laboratory market take sellers' reports at face value, even though the sellers systematically inflate their reports. Recent investiga tions into the influence of misleading and self-interested analyst reports suggest that such a lack of skepticism may have played a part in the overpricing of Internet stocks.

* Aggressive Trading by Less-Informed Investors. Markets might overreact because investors who collect little information fail to recognize their informational disadvantage in the market. This error, found in countless experiments, causes relatively uninformed traders to trade too aggressively and influence prices too much. This behavior, in turn, causes market prices to overreact to statistics that are collected by relatively uninformed investors who collect little other information (9)

* Inappropriate In formation Collection. The models underlying the IRH assume that each trader balances the costs and benefits of the statistics they extract information, given what other traders collect. However, the benefits depend on how many other traders collect the statistics, and traders choose what statistics to collect without knowing other traders' decisions. Economic models assume that traders can predict others' decisions accurately, but experimental tests of similar settings find that they often have trouble doing so (Bloomfield 1991). If traders underestimate how many others collect highly publicized statistics, then they will trade too aggressively on those statistics, causing market overreactions. Future experiments could test this possibility.

CONCLUSIONS

Those who believe markets are inefficient rarely provide a coherent and refutable alternative to the Efficiency Markets Hypothesis. This paper presents the Incomplete Revelation Hypothesis (IRH) as such an alternative, and describes its implications for financial reporting research, practice, and regulation.

The IRH assumes that the costs of extracting useful statistics from public data keep markets from fully revealing the meaning of those statistics. This assumption runs counter to the common assertion that accounting data are so widely analyzed that analysis costs could not possibly account for observed inefficiencies. However, no statistic is relied upon by all traders, not even an earnings announcement. As long as some traders ignore a statistic, perhaps in favor of other statistics, traditional models of financial markets predict that prices will reveal the statistic incompletely. In addition, this concern focuses on the realism of the assumptions underlying the IRH, rather than focusing on the validity of its predictions. As Friedman (1953) argues, all useful theories rely on unrealistic assumptions because they seek simplicity. The EMH has been successful largely because its simple assumptions account so well for financial market behavior. Research will establish the usefulness of the IRH by testing its predictions, not by questioning its assumptions.

The IRH extends the EMH by explicitly recognizing the costs of extracting statistics from public data. This extension does not alter the key qualitative predictions of the EMH that most accounting researchers rely on in event studies and price-association studies. However, it converts many phenomena that are "anomalies" from the perspective of the EMH into natural predictions of the IRH. Unlike the EMH, the IRH predicts that investors devote resources to predicting price changes from public data and are able to do so successfully, that managers attempt to manipulate market prices by emphasizing good news and tucking bad news in footnotes, and that regulators attempt to thwart such behavior. Its ability to account for such behavior, while also providing a number of novel testable predictions, gives the IRH great potential as a foundation for financial reporting research, practice, and regulation.

Submitted: August 2001

Accepted: April 2002

(1.) See, in particular, Grossman and Stiglltz (1980).

(2.) In most rational expectation models, traders enter a linear demand function of the form "Demand = b(market price-reservation price)," where the reservation price indicates the value the trader places on the asset, given his or her information. The slope of this line, b, measures the trader's trading interest.

(3.) See, for example, Bloomfield (1996). Libby et al. (2002) provide a review of this literature. Interestingly, little experimental research examines the link between the degree of efficiency and the cost of information collection. See Sunder (1992) for a rare example.

(4.) Bhushan (1994) provides evidence consistent with these assertions.

(5.) This paradox is a major motivation of Grossman and Stiglitz (1980). Lee (2001) discusses the importance of the paradox to those teaching future investment professionals.

(6.) Black (1989) discusses how to interpret the role and nature of noise traders in financial markets.

(7.) Another possibility is that prices react incompletely to the fact that the swap occurred at all, even though the swap is an event that may convey information. Then the re-announcement in earnings makes the reaction more complete by allowing more investors to react to the information. However, Hand (1989) finds that an initial announcement of a larger gain leads to a more negative price response, suggesting that investors view swap gains as bad news. Thus, the positive reaction to the re-announcement does not seem like a completion of the initial negative reaction to the swap's occurrence.

(8.) Griffin and Tversky (1992) and Bloomfield et al. (2002) discuss this evidence.

(9.) Kagel (1995) provides a broad review of this trading error, which is known as the "winner's curse." Bloorufield et al. (1999) provide evidence that such errors can influence market pricin, and cause less-well-informed traders to transfer wealth to more-inforined investors.

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This paper in an outgrowth of presentations at the 2001 P. D. Leake Lectures at Oxford University, the 2001 AAA Doctoral Consortium, the 2001 Conference on Experimental Methods at Harvard University, and Cornell University. Thanks to Paul E. Fischer, John Hand, David Hirshleifer, Mark Nelson, Maureen O'Hara, and Tom Dyckman for helpful comments.

Corresponding author: Robert J. Bloomfield

Email: rjb9@cornell.edu

Robert J. Bloomfield is an Associate Professor at Cornell University.