We develop a model of the relation between accounting and economic incomes that incorporates realistic and intuitive assumptions about how accounting rules and practices incorporate different types of information about economic value into accounting income, depending on properties of the information. In subsequent sections, we use this model as a framework to analyze the validity of Basu regression measures of asymmetrically timely recognition of economic gains and losses.
2.1 A Model of Accounting Income Recognition
The origins of the following model can be traced back to Ball and Brown , Beaver, Lambert, and Morse , Fama , Kothari and Sloan , Basu , Kothari , Beaver and Ryan , Roychowdhury and Watts , and others. We begin by assuming that capital markets are informationally efficient.6 We focus on shocks to firm value, ignoring variation in expected returns, with the implicit assumption being that variation in expected returns either does not occur or is controlled for as discussed in Ball, Kothari, and Nikolaev .
While informationally efficient returns reflect all publicly available information in a timely fashion, we assume that accounting rules and practices emphasize verifiability, objectivity, and conservatism, as reflected, for example, in the historical cost principle and revenue recognition rules, and hence accounting income in any period incorporates some but not all the information that becomes publicly available during the period. The consequence is that accounting income incorporates some information with a lag: that is, “prices lead earnings.”7
Information in our model can be made public via earnings or any other information channel. We do not implicitly or explicitly assume that accounting systems and earnings announcements have no role in price formation. We assume only that, to the extent the market responds to reported earnings, it understands its components. In particular, the market distinguishes the components that reflect information made public in prior periods from those that reflect current-period information.
In line with the above assumptions, the total revision in security price (i.e., stock return) comprises three components, which are incorporated in accounting income differently:
where the subscripts t and t – 1 refer to time periods, and
- Rt = total unexpected security return;8
- xt = portion of the total unexpected return Rt that invariably is contemporaneously captured in accounting income, It;
- yt = portion of the total unexpected return Rt that is not contemporaneously captured in It unless required by conservative accounting;
- gt = portion of the total unexpected return Rt that never is contemporaneously captured in It, but always is incorporated with a lag;
- It = accounting income;
- wt = an indicator variable that takes the value of one when conservative accounting rules and practices lead to recognition of y in the current period; and
- ɛt = “noise” in accounting earnings that reverses in the next period.
The unexpected return components xt, yt, and gt are stationary and time-independent random variables (Bachelier , Samuelson , Fama , Campbell, Lo, and MacKinlay ) whose variances are denoted by σx2, σy2, and σg2, respectively, and:
Accounting-induced noise ɛt has variance σɛ2 and is assumed independent of return components.
To keep the analysis tractable, we make the following linearity assumption. We assume that the information components x, y, and g can be expressed as linear functions of each other (e.g., where f(., .) is linear and e is an uncorrelated residual), which we operationalize by assuming that the variance–covariance matrix of x, y, and g is independent of the sign of news. This implies that ; or more generally, and , so that .9 This assumption allows us to focus on the effect of conservatism and ignore other potential sources of nonlinearity in the returns–earnings relation, such as an arbitrary nonlinear relation between the information components x and y or between x and g.10 To the extent that such nonlinearities are present, they comprise a confounding factor (akin to an omitted variables problem) that needs to be understood and controlled for when estimating conditional conservatism.
In practice, the distribution of returns is skewed, which often indicates nonlinearity in the data. Conditional conservatism implies a particular source of nonlinearity and hence calls for a particular functional form, which the Basu  regression accommodates. If other sources of nonlinearity are present, the specification can be augmented accordingly to measure the separate effect of conservatism. As in all empirical work, it is important to use a specification that controls for the confounding effects of any economic forces other than conservatism when parsing out its effect on the returns–earnings relation. This issue is addressed in more detail in Ball, Kothari, and Nikolaev . In this paper, we ignore skew in returns in order to focus on the effects of accounting rules and practices per se.
2.2 An Interpretation of The Model in Terms of Accounting Practices
In this model, financial reporting rules and practices lead to accounting income always contemporaneously incorporating the information component xt, regardless of its sign or magnitude (i.e., without conditional conservatism). The intuition is that this component represents the least costly source of information to verify, and thus it invariably is recognized in the same period as it affects returns. This type of information could include current-period news about current-period cash flow, such as learning the actual cash realizations of current-period revenues and expenses in comparison with their expectations. It also could include news about future cash flows that is verifiable at low cost, and that is incorporated symmetrically in accounting income via working capital accruals. Symmetrically, low-cost verification typically applies to current operating-cycle information, such as cash receipts and payments, and the quantities of accounts receivable, accounts payable, and inventories. For example, accruals are used to adjust current-period cash flow for both increases and decreases in the quantity of closing inventory relative to opening inventory, because they are approximately equally low in cost to verify. Similarly, cash collections from customers are adjusted for both increases and decreases in accounts receivable. These working capital accruals incorporate into accounting income current information about future cash flows. For example, other things equal, an increase in closing inventory is information that less cash will be spent on purchasing inventory in future periods, and it is verifiable at low cost regardless of its sign. In some limited circumstances, symmetrically low-cost verification can apply to long-cycle information as well, an example being index funds, in which gains and losses on long-term investments in traded stocks are symmetrically low cost to verify and, in practice, are both accounted on a daily basis.
The second component of stock return, yt, is incorporated in accounting income either contemporaneously or with a lag, depending on the accounting operator wt. The intuition here is that yt represents information that is costly to verify, and more cost is incurred in verifying negative than positive news. Consequently, the verification threshold is lower for negative news (Basu , p. 4), and this information component is incorporated asymmetrically. Such information could include the current-period revision in the expectation of unrealized future-period cash flows from “booked” assets, including long-term assets in place and purchased intangible assets, such as patents and goodwill. It could include information about the marketability of current assets, such as inventory. This component also could include news about the present value of future-period cash outflows, such as lawsuit settlements. Using accrual accounting to bring forward shocks to expected future cash flows is known as timely gain and loss recognition. Conditional conservatism implies that wt is more likely to be triggered by bad news (adverse shocks to expected future cash flows) than good news, and hence that loss recognition generally is timelier than gain recognition.
In the event that timely recognition is not triggered and thus the return component yt is not contemporaneously incorporated in income, it is incorporated with a lag, the intuition being that some revisions in expectations of future cash flows are not reflected in accounting income until the actual cash flow realizations occur. Conditional conservatism implies that incorporation with a lag is more likely for good news than bad. The effect of asymmetrically delayed incorporation of information is that, in a two-period model, the total effect on current-period income is wt yt + (1 – wt–1)yt–1.
In practice, the extent of the timely recognition asymmetry is determined by a number of factors. An extensive literature studies determinants that include economic incentives, debt and compensation contracting, governance, GAAP, regulation, and taxes. Since our objective is not to provide an equilibrium model of the extent of conditional conservatism, but rather to investigate the validity of the Basu  measure used in this literature, our model takes the extent of the asymmetry as an exogenous given, and studies the properties of its measurement. In our setting, timely recognition is triggered when yt is below an exogenous threshold c.11
The third component of stock return, gt–1, invariably is incorporated in accounting income with a lag. One source of this return component is revisions in the value of growth options or unbooked intangibles (Beaver and Ryan ). This information component is similar in nature to “rents” in Roychowdhury and Watts . Because growth options by definition are not “booked” as assets on balance sheets, these shocks to firm value are symmetrically incorporated in earnings with a lag, when the associated cash flows are (or are not) realized.
The model also has accounting income incorporating uncorrelated “noise” that reverses over time. An important source of this earnings component would be imperfect accounting accruals. For example, miscounting inventory affects current and future earnings with opposing signs. Other examples are errors in estimating uncollectible accounts receivable, errors in forecasting deferred tax liabilities, the effects of using historical cost interest rates on debt, and errors in estimating assets’ useful lives. Because accounting errors reverse over time, in our two-period model the error term is reversed out in the following period. For tractability we assume accounting error is uncorrelated with return components, and thus we ignore nonrandom “earnings management,” including “smoothing,” that plausibly is negatively correlated with returns.12
In this formulation, yt–1 and gt–1 are the two sources of delayed recognition. They generate the anticipated or stale component of earnings whose value consequences were previously reflected in returns. They therefore are uncorrelated with current-period return Rt, which is influenced only by information arriving contemporaneously. We view this lagged recognition of some components of stock return as a natural feature of the income recognition process in accounting, which can be measured and investigated (e.g., as a function of firm characteristics, managers’ incentives, or countries’ economic and political institutions).
While yt–1 and gt–1 are assumed to be uncorrelated with xt, yt, and gt, and, therefore, with Rt, there are economic reasons to expect a positive correlation among xt, yt, and gt. Recall that all three components are a consequence of economic news affecting investors’ cash flow expectations. However, only the news generating the stock price growth rate component xt, and possibly also yt (i.e., when wt = 1), is incorporated in accounting income contemporaneously, whereas news generating the return component gt finds its way into accounting income in the following period.
The earnings process modeled in equation (2) is intended to capture the important properties of asymmetric accounting recognition rules and practices, and their effect on how new information is incorporated in reported earnings. We next use this framework to investigate the properties of the Basu measure and develop empirical implications.