Management by the Numbers: A Formal Approach to Deriving Informational and Distributional Properties of “Unmanaged” Earnings

• Published date: 01 March 2019
• DOI: http://doi.org/10.1111/1475-679X.12249
• Author: THOMAS HEMMER,EVA LABRO
• Date: 01 March 2019

DOI: 10.1111/1475-679X.12249

Journal of Accounting Research

Vol. 57 No. 1 March 2019

Printed in U.S.A.

Management by the Numbers: A

Formal Approach to Deriving

Informational and Distributional

Properties of “Unmanaged”

Earnings

THOMAS HEMMER ∗AND EVA LABRO †

Received 23 September 2016; accepted 8 October 2018

ABSTRACT

We explore the theoretical relation between earnings and market returns

as well as the properties of earnings frequency distributions under the as-

sumption that managers use unbiased accounting information to sequen-

tially decide on real options their firms have and report generated earnings

truthfully, with the market pricing the firm based on those reported earn-

ings. We generate benchmarks against which empirically observed earnings-

returns relations and aggregate earnings distributions can be evaluated. This

parsimonious model shows a coherent set of results: reported losses are less

∗Rice University: †University of North Carolina.

Accepted by Haresh Sapra. Exceptional research assistance by Jim Omartian and Jedson

Pinto is much appreciated. We thank two anonymous referees, Romana Autrey (discussant at

AAA meeting), Jonathan Bonham, Rich Frankel, Mirko Heinle, Brian Mittendorf (discussant

at MAS meeting), Jim Omartian, Richard Saouma, Jack Stecher, Ian Tarrant, Frank Zhou, an

anonymous MAS midyear meeting reviewer, workshop participants at Chicago Booth, HEC

Lausanne, Penn State, University of Iowa, University of Melbourne, University of Minnesota,

University of New South Wales, Washington University in St. Louis, conference attendees at

the 2016 University of Alberta Conference, 2016 Purdue Theory Conference, 2015 Accounting

Research Workshop in Zurich, 2015 American Accounting Association Annual meeting in

Chicago, AnpCONT 2014 in Brazil, and the 2014 Templeconference on convergence between

financial and managerial accounting for comments and suggestions.

5

CUniversity of Chicago on behalf of the Accounting Research Center,2018

6T.HEMMER AND E.LABRO

persistent than reported gains, decision making diminishes the S-shaped mar-

ket response to earnings and earnings relate to returns asymmetrically in the

way documented by Basu [1997]. Furthermore, the implied frequency dis-

tribution of aggregate earnings is neither symmetric nor necessarily single-

peaked. Instead, it may exhibit a kink at zero and look similar to the plots re-

ported by Burgstahler and Dichev [1997]. However, within our model, none

of these phenomena are due to reporting noise, bias, or some undesirable

strategic managerial behavior. They are the natural consequences of using

past earnings as the basis for value increasing managerial decision making

that in turn generates the future earnings on which future decisions will be

based.

JEL codes: D80; G14; M40; M41

Keywords: information for decision making; decision usefulness; precision;

bias; persistence; earnings management; earnings discontinuity

1. Introduction

A significant fraction of the academic accounting literature spanning the

past 50 years has revolved around peculiar empirical patterns of earn-

ings and perceived irregularities in how earnings relate to market prices

and/or returns. Key examples are seemingly low earnings response co-

efficients (ERCs), S-shaped price responses to earnings, a distinct dip at

zero in large sample earnings frequency distributions, and the more (less)

positive relation between returns and earnings for negative (positive) re-

turns. Standard, yet disjoint, explanations offered in the literature include

manipulation of reports by managers, leakage or obfuscation of informa-

tion, and fundamental deficiencies, biases and/or intentional asymmetries

in the accounting rules and principles by which accounting measures are

constructed.1

We do not dispute that all of the above issues can, in principle, con-

tribute to persistent, seemingly surprising, empirical patterns. Instead, we

formally demonstrate that once one assumes that financial reports are not

produced exclusively for the consumption of external users but also to

facilitate frequent internal managerial decisions within the reporting en-

tity (i.e., managerial accounting information is correlated with the infor-

mation summarized periodically in external financial statements; Hemmer

and Labro [2008]), many of these peculiar empirical patterns of earnings,

distributional and informational, naturally arise. Accordingly, what we do

dispute is that these patterns are inconsistent with truthful or unbiased re-

porting and, therefore, that they provide prima facie empirical evidence of

manipulation or biases in accounting rules.

1For example, Watts [2003] lists all explanations for accounting conservatism, while De-

chow, Richardson, and Tuna [2003] go over many of the explanations for the kink in the

earnings frequency distribution.

MANAGEMENT BY THE NUMBERS 7

We provide our insights based on, arguably, the simplest model possible

in which firms each must hire a manager in order to operate. A manager

is an expert decision maker who selects and implements a variety of oppor-

tunities available to a firm. In contrast to much of the accounting litera-

ture, we assume managers are maximizing shareholder value, rather than

their own best interest; they never engage in any strategic decision-making

or reporting behavior. Finally, we argue that, while largely ignored in the

financial accounting literature (e.g., Dechow, Weili, and Schrand [2010],

p. 345), those managerial decisions are first order in determining the prop-

erties of reported earnings.

To model the evolution of real economic earnings over many short pe-

riods where a random uninformed selection of an opportunity produces

zero terminal value in expectation, we rely on a standard binary random

walk. To highlight accounting’s central internal decision facilitating role,

we assume that, while managers do know the overall quality level of their

opportunity set, they cannot tell ex ante the quality of individual choices

in their opportunity set but subsequently will be able to make inference

about the chosen course of action from observed realized (past) accounting

earnings.

In particular, a manager will use the internally reported accounting in-

formation to update his beliefs in the standard Bayesian way. Then, if at

some point in time, based on the accrued evidence, he believes that select-

ing an alternate opportunity will improve firm profitability, he will do so.

Past decisions may be somewhat sticky in terms of profitability (e.g., due to

adjustment costs and the inability to fully undo prior strategy implemen-

tations, impairing funds available for future strategy implementations), so

even when the manager attempts to select a new strategic direction, it may

only result in a new underlying profitability-generating process with some

probability, and the proportion of better and worse earnings-generating

opportunities available may differ from the initial.

Accounting earnings measure real economic earnings without any noise

or bias and are reported internally on a timely basis to the manager as the

earnings process unfolds and updates thus become available. The less fre-

quent periodic financial reports that are provided to market participants

are assumed to be an unperturbed aggregate of the frequent earnings real-

izations that have occurred over the reporting horizon. Market participants

use these reports to update their homogeneous and consistent prior be-

liefs about the value of each firm in a standard Bayesian fashion and price

the firm accordingly. They earn returns equal to the belief revision in ex-

pected terminal value of the firm after the release of the earnings report,

scaled by the expected terminal value of the firm at the start of the horizon.

Because for extreme earnings values the market updates less, returns are

nonlinear.

Our model provides a unified theory of the following empirically ob-

served informational and distributional properties of earnings: decision