Discussion of "Specification problemswith infonnation content of eamings:

Revisions and rationality ofexpectations and self-selection bias"*

RAY BALL University of Rochester

This paper comprises three related essays on specifying the relation betweenearnings and prices. The essays share a common data set and a common concemwith the specification problem. Abdel-khalik is to be congratulated for payingclose attention to specification issues in this context, because misspecification,at the level of both theory (e.g., ignoring taxes in the CAPM) and researchdesign (e.g., using trading rules that are not implementable due to features ofthe trading mechanism, or failure to control for correlated omitted variables), isa likely culprit for many of the empirical anomalies we observe.

I propose to interpret the paper as contributing to a debate on these specifi-cation issues, rather than as attempting to provide readers with concrete results.After all, we have been researching the earnings-price relation for more than 20years and we have yet to see the last word. Consequently, I propose to add someadditional observations to, as well as commentary on, Abdel-khalik's (1990)contribution. These observations are intended to be idiosyncratic, in the hopethat they will add to the debate that Abdel-khalik has opened, and in the knowl-edge that Raybum's (1990) companion commentary covers different ground.

Omitted variablesThe first essay compares two regression specifications, both having an 11-dayabnormal retum (centered on the quarterly eamings announcement date) as thedependent variable. Only the first and second quarters' eamings announcementsare considered. One specification has a contemporaneous quarterly eamings fore-cast error as its single independent variable. The other specification also includescontemporaneous revisions of forecasts of (1) eamings for remaining quartersin the fiscal year and (2) eamings in the following two years. Adjusted R^s forthe latter specification are reliably larger than for the former. This result rein-forces the Brown, Foster, and Noreen (1985) finding that the market respondsto forecast revisions of eamings that are at least as far as two years away.* The Managerial Economics Research Center at the Simon School, University of Rochester

and the John M. Olin Foundation provided generous financial support. Comments by AndrewChristie are gratefully acknowledged.

Contemporary Accounting Research Vol. 7 No. 1 pp. 178-184

Discussion of Specification Problems With Information Content of Eamings 179

Discovering that the stock market is not myopically focussed on current eam-ings is an important result. Many critics of markets; or of generally acceptedprinciples for calculating accounting eamings, have asserted that the institutionalstmcture is only short-mn oriented. In spite of the cdtics, the result that the mar-ket is not myopic is intuitively appealing (witness the response of Boeing's sharepdce to new orders, which take several years to flow into its reported eamings).

Without detracting from the importance of this result, it is worth observing thatno clear case has been made that a multiperiod market horizon necessarily givesrise to a specification problem. Whether or not a problem exists depends on thehypothesis being tested and on the predictions of credible altemative hypotheses.One cannot talk meaningfully about potential specification problems arisingfrom omitted variables per se without an underlying theory of the eamings-pricerelation that is being tested. In the absence of a stated theory of the eamings-pricerelation, within whose context the hypothesis testing takes place, there essentiallyis an implied theoretical context. In the present case, the multivariate version (4)implicitly is assumed to be correct, yet questions arise such as: "Why only looktwo years ahead?" and "Why use annual, rather than quarterly, eamings?"' Thiscomment is not meant to imply that I do not prefer the multivariate specificationrelative to the univariate, or that I object to testing the altemative specifications.I merely am observing that it would have been preferable to see some theoryto guide the choice of the tested functional form. Nor do I mean to imply thattheory needs to be in some sense perfect or complete or tme for it to guideresearch design choices.^

Are earnings forecasts rational expectations?Here I do object to the test being conducted. The rationale for the test is givenat the outset: "Market participants should, in efficient capital markets, haveformed rational expectations [for eamings]". Muthian rational expectations aredefined as follows (page 156): "A forecast (or a price) is considered a ratio-nal expectation if it is an informed, conditional expectation using the infor-mation available to forecasting (or trading) agents prior to event realization."Abdel-khalik argues that "all prior empirical work has made this assumption"[i.e., that "analysts' eamings forecasts are rational expectations"]. He thereforetests whether analysts' eamings forecasts incorporate all of the information inprices.

This is a stringent criterion. A priori, I would expect markets to fail it.My objection to the stringent rational expectations criterion is based on Hayek's(1945) seminal defense of markets, relative to state planning, on the very groundsthat they are an efficient solution to the problem of "the utilization of knowledgenot given to anyone in its totality" (page 520). This thesis was later picked upin slightly different terms by Alchian (1950) and Friedman (1953, sec. III). It

1 If the answer lies in data availability problems with quarterly eamings forecasts, then that doesnot alleviate any hypothetical specification problems for (4) relative to a model incorporatingquarterly variables.

2 For related comments, see Christie (1987).

180 R. Ball

implies that if markets are to accomplish their economic function, then they willincorporate in prices the decentralized information possessed by a large numberof individuals—none of whom can be expected to know all of the information inprices. Hayek's thesis implies that markets should fail Abdel-khalik's criterionthat "market participants should, in efficient capital markets have formed rationalexpectations." I personally would prefer to see the stock market failing this test,since that would indicate that the market is performing its Hayekian task ofefficiently utilizing information that is decentralized among individuals and thatis unknown to anyone in its entirety.

It is not surprising to leam the result that Abdel-khalik's test rejects therational expectations hypothesis. He believes this is because "markets updateprices much faster than analysts do" (page 159). This could be interpreted asa version of the Hayekian thesis, assuming that individual analysts update theirforecasts considerably less frequently than the market because they individuallyhave considerably less information than that which is built into prices. He drawsthe correct and interesting conclusion that analysts' forecasts are noisy proxiesfor the eamings-related infonnation reflected in security prices, as one wouldexpect from the Hayekian perspective.

I find it difficult to interpret research on eamings forecasts when we have littleinsight into the economics underlying the forecasting. In particular, I do not seehow we can test hypotheses that are based on the assumption that forecastsare made with a view to eaming abnormal retums from better foresight. Thepredicted abnormal retums simply are too small to detect against backgroundnoise in the retums. Suppose that the annual cost of an average forecaster is$150,000 and the forecaster follows only 25 stocks at any time. If forecastsare revised just once per quarter, then the average cost of a forecast revisionis $1,500. This is one millionth of the market capitalization of a $1.5 billionfirm. Since forecasting is a competitive business, one can predict that the privatebenefits from forecasting are in the order of the costs: that is, that they are atrivial percentage of the market capitalization of a NYSE-AMEX firm or evenof a typical institutional portfolios's shareholding. One might quibble aboutthe above numbers, but they are unlikely to be out by the orders of magnituderequired to upset the conclusion. I doubt that we can observe abnormal retums ofthe predicted magnitude of the benefits from forecasting against the backgroundnoise in the retums, so I doubt that we could even test the basic hypothesis thatanalysts' forecasts are motivated by seeking abnormal retums, or any importantimplications of that hypothesis.

Furthermore, it seems unlikely that typical individual forecasts are sufficientlycostly for them to be fully informed forecasts in a strict rational expectationssense. This recalls the earlier observation, that it is helpful to have theory toguide us in research design issues. I am not sure that we have a credible theoryof why security analysts make repetitive eamings forecasts and release them tothe public. To that end, I propose the following model:

Discussion of Specification Problems With Information Content of Eamings 181

1 Information that generates price changes during any interval (e.g., a quarter) ispartitioned into two mutually exclusive and exhaustive subsets: (1) informationthat will be refiected in the eamings to be reported at the end of the quarter;and (2) information that will not be refiected in current eamings. Examplesare a sale made by Sears Roebuck versus an order placed with Boeing; andinformation about current cash flow from operations versus information aboutmarket-wide expected retums (including changes in interest rates). Denote theformer subset as "current eamings-relevant information."

2 It is costless to observe prices and price changes.3 It is not costless to observe current eamings-relevant information, however.

The Hayekian thesis implies that complete knowledge of why individuals act isnot possessed by any single individual. Each individual does or does not makebuy or sell offers in the marketplace, based on that individual's knowledge,tastes and wealth. The extent to which any individual action is based oninformation that will be reflected in this quarter's eamings is not costlesslyknowable by all other individuals. Nor is the market process of aggregatingfrom individual actions to price costlessly knowable by individuals. Hence,the eamings-price function is not costlessly known and no individual cancostlessly invert the function to infer current eamings-relevant informationfrom price.

4 When eamings are announced at the end of the period, individuals act onthe basis of the eamings outcome, the current price and their assessments ofthe current eamings-relevant information already reflected in price. That is,each individual estimates the news in the current eamings outcome. In theextremes, individuals who believe that none (all) of the information in theeamings outcome has already been reflected in price will (will not) view theeamings announcement as revising prices, other things being equal.

5 There thus is a demand for knowledge about the eamings-price function andabout the set of current eamings-relevant information. The accuracy of in-dividuals' assessments of the implications of an eamings outcome is an in-creasing function of the amount of such knowledge. Hence, the efficient in-stitutional stmcture we observe should include cost-efficient technologies forsatisfying the demand for knowledge of the eamings-price function and thusof current eamings-relevant information.

6 Analyst forecasting is proposed as a cost-efficient technology for obtainingknowledge of the eamings-price function and current eamings-relevant infor-mation. Under this thesis, forecasters: (1) collect information from a subsetof individuals, known directly or indirectly by the forecaster, conceming thereasons for their portfolio decisions; (2) partition that information into cur-rent eamings-relevant and other information, to an optimal degree of fineness;(3) express that partitioning by estimating the current eamings implied by the

182 R. Ball

current eamings-relevant information reflected in price; and (4) sell that es-timate as an eamings forecast to clients who might trade on the basis of theeamings outcome when it is announced.^

7 The demand for consensus forecasts then can be interpreted as a demandfor knowledge of the knowledge of a wider subset of individuals than thoseknown by individual forecasters."*

In this simple model, no individual can perfectly infer the current eamings-relevant information from price. Hence, individual forecasters will not continu-ously revise eamings forecasts to incorporate all of the current eamings-relevantinformation in price and will fail the Muthian rational expectations test.

The self-selection/endogeneity issueThe third specification problem addressed by Abdel-khalik involves biases inestimated test statistics when grouping of observations (usually referred to asportfolio formation) prior to estimation is based on the independent variable.Specifically, he addresses a research design in which linear eamings-price rela-tions are estimated separately for "good news" and "bad news" groups. Here,my biases generally are in accord with those expressed in the paper, sinceendogeneity is a pervasive feature of quasi-experimental research designs. Inaddition, a recent working paper by Lo and MacKinlay (1989) has convincedme that grouping on the independent variable leads to "high" probabilities ofrejecting a true null hypothesis in studies of eamings and prices.

Lo and MacKinlay show that if the independent variable (for example, changein eamings yield) exhibits even "small" correlation with the error in observingexpected retums at the individual-security level, then the correlation becomes"large" at the group level. Consequently, the probability of observing apparentabnormal retums that are correlated with the independent variable approachesunity as the group size and the number of groups increase, even when there is nocorrelation with true abnormal retums. Given the large number of observationsused in contemporary studies of eamings and prices (in excess of 50,000), itis misleading in the extreme to use test statistics derived under the assumptionthat no such pregrouping of the data has been performed.'

Several additional features of eamings-price studies exacerbate this problem.First, researchers typically scale eamings by price, perhaps due to the quite validargument in Christie (1987), and thus work with eamings yields. As observedin Ball (1978), eamings yields are likely to be correlated with securities' un-

3 The sale can be "bundled" with commissions.4 We frequently speak of "the market's" earnings forecast, when no such thing exists. I interpret

this phrase as shorthand for an unobservable construct, namely the eamings that would beobtained from price if the eamings-price function could be costlessly inverted. Its unobserv-ability does not make the construct worthless: it can be meaningful way of thinking about therelation between eamings and prices.

5 The relevance of Lo and MacKinlay (1989) to eamings-price studies was pointed out to me byTom Lys.

Discussion of Specification Problems With Information Content of Eamings 183

observable expected retums and thus with the error in our imperfect attemptto control for expected retums. Hence, eamings-price studies seem particularlylikely to encounter the Lo and MacKinlay test-statistic bias. Second, followingBall and Brown (1968), researchers typically difference the eamings variablebefore grouping. Hence, there is the added difficulty of controlling for changesin expected retums. The Lo and MacKinlay argument would imply a "large"induced correlation between the eamings change for the group (or the portfoliorank) and estimated abnormal retums, due to the difficulty in controlling for notonly the level but now also the induced change in the latter. Third, researcherstypically concentrate on extreme eamings-change groups, thus magnifying theproblem of controlling for changes in expected retums even further. Fourth,extreme eamings-change (scaled by price) portfolios are dominated by small-capitalization stocks, for which the CAPM is a notoriously poorly specifiedmodel of expected retums.

I regard it as ironic in the extreme that the studies that appear most eager toconclude that eamings (and other accounting data) are correlated with postan-nouncement abnonnal retums are those that must rely most absolutely on aparticular model of security pricing (the CAPM) and on empirical proxies forsecurity retums and market indexes. The model is so simple that it does noteven incorporate personal taxes, which could easily be correlated with eamingsyields and expected retums.

Such research is valuable in magnifying, to the extreme, the deficienciesin our models of securities' expected retums. In pointing us to the statisticalproblems involved in grouping on the independent variable, Abdel-khalik hasperformed a valuable service.

SummaryAbdel-khalik observes, during this relatively mature phase of the literature on theeamings-price relation, it is sensible to address attention to issues of specifyingthe form of that relation for testing purpose. The paper addresses three suchissues, thus fulfilling the valuable role of bringing the attention of the literatureto these and related specification issues.

ReferencesAbdel-khalik, A.R., "Specification Problems with Infonnation Content of Eamings:

Revisions and Rationality of Expectations, and Self-Selection Bias," ContemporaryAccounting Research (Fall, 1990) pp. 142-172.

Alchian, A. A., "Uncertainty, Evolution, and Economic Theory," Journal of PoliticalEconomy (June 1950) pp. 211-21.

Ball, R., "Anomalies in Relationships Between Securities' Yields and Yield-Surrogates," Journal of Financial Economics (June 1978) pp. 103-26.

Ball, R. and P. Brown, "An Empirical Evaluation of Accounting Income Numbers,"Journal of Accounting Research (Autumn 1968) pp. 159-178.

Brown, P., G. Foster, and E. Noreen, Security Analyst Multi-year Eamings Forecastsand the Capital Market (Sarasota, Fl: American Accounting Association, 1985).

184 R. Ball

Christie, A., "On Cross-Sectional Analysis in Accounting Research,'7o«ma/ of Ac-counting and Economics (December 1987) pp. 231-258.

Friedman, M., "The Methodology of Positive Economics" in M. Friedman (ed.).Essays in Positive Economics (Chicago: University of Chicago Press, 1953).

Hayek, F., "The Use of Knowledge in Society," American Economic Review (Septem-ber 1945) pp. 519-530.

Lo, A.W. and A.C. MacKinlay, "Data-snooping Biases in Tests of Financial AssetPricing Models," Sloan School of Management, M.I.T. (October 1989).

Raybum, J., "Discussion of 'Specification Problems with Infonnation Content ofEamings: Revisions and Rationality of Expectations, and Self-Selection Bias,'"Contemporary Accounting Research (Fall, 1990) pp. 173-177.