Demetris Christodoulou

The Double Entry Constraint, Structural Modeling and Econometric Estimation†

The key proposition of the paper lies in the treatment of financial statements as a matrix of endogenous information codetermined by double entry. To account for the highly structured information set in econometric estimation, we develop a generalised structural system for use with accounting variables, within which the deterministic relationships governing financial statement articulation are clearly defined. The framework is used to formulate fully identified models that are consistent with the underlying duality that characterises the generating process of accounting data. To demonstrate the efficacy of the approach, we consider the model of equity pricing in Penman and Yehuda (2009), and the model of investment sensitivity to operating cash flow in Fazzari, Hubbart and Petersen (1988) and Kaplan and Zingales (1997). By comparison with the more traditional estimation methods, the structural system is shown to yield estimates with increased precision that adhere to double entry rules.

A Structural Accounting Framework for Estimating the Expected Rate of Return on Equity

This paper shows how the expected rate of return (ERR) on equity may be estimated using only published accounting results, based on the information dynamics of reported earnings. As accounting-based valuation models conditional upon financial statement articulation lead to a rank deficient system of estimating equations, the paper introduces a nonlinear constraint on the articulation that allows the information system simultaneously to produce an estimate for the ERR by iteration, together with predictions for the key clean surplus forecasts of net earnings, net dividend, and the book value of equity. Further decomposition produces estimates of expected capital gain, expected earnings, and the expected change in equity book value, and by rearrangement, the expected change in unrecorded goodwill. The clean surplus relation is maintained in the forecast variables. Exploratory data methods are used to examine the nonlinear relationship between components of the accounting-based ERR and realized stock returns. Findings show that realized returns are higher (lower) than estimated ERR in expansionary (recessionary) periods, with evidence of a stronger returns impact in recessionary periods. For the large majority of firms, realized returns revert to the estimated ERR, and the time-varying accounting components are strongly related to future realized stock returns, consistent with time variation in the ERR around a long-run average. Predicted earnings and dividends provide useful additional information on short-run variations in the ERR.

Bounded variation and the asymmetric distribution of scaled earnings

Abstract This paper proposes a finite limits distribution for scaled accounting earnings. The probability density function of earnings has been the subject of a great deal of attention, indicating an apparent ‘observational discontinuity’ at zero. Paradoxically, the customary research design used in such studies is built on the implied assumption that the distribution of scaled accounting earnings should approximate a continuous normal variable at the population level. This paper shows that such assumptions may be unfounded, and, using large samples from both the US and the EU, the study provides alternative evidence of a consistently asymmetric frequency of profits and losses. This casts further doubt on the interpretation of the observed discontinuity in the distribution of earnings as prima facie evidence of earnings management. A particular innovation in this paper is to scale the earnings variable by the magnitude of its own components, restricting the standardised range to [–1,1]. Nonparametric descriptions are provided that improve upon the simple histogram, together with non‐normal parametric probability estimates that are consistent with the scalar that is proposed. A notable advantage of this approach is that it avoids some of the statistical shortcomings of commonly used scalars, such as influential outliers and infinite variances.

The accounting identity trap: identification under stock-and-flow rank deficiency

ABSTRACT Empirical research relying on inputs from published company financial statements ignore the fact that the observed accounting data matrix has been purposefully designed to be rank deficient by means of articulation between stocks and flows. This inherent feature of the data-generating process suggests structural non-identification when both stocks and flows appear in the design matrix and a constraint is required to identify parameters. Much financial research has fallen into this ‘accounting identity trap’ and routinely employs implicit constraints to enable estimation, albeit without acknowledgement of the constraints hence the misleading inferences. This article elucidates the problem of parameter identification under stock-and-flow rank deficiency using existing applications on equity pricing. The focus is on the interpretation of slope coefficients that must be anchored on economically defensible parameter constraints.