We study the properties of optimal accounting rules in a setting where an impatient firm needs to sell shares to raise immediate cash. The firm possesses information that cannot be credibly conveyed to the outside investors, resulting in costly signaling via the percentage of shares retained by the firm. However, before observing any private information, the firm can choose to commit to an accounting rule that will provide the outside investors a noisy signal of the private information. We show that, so long as the disclosure cannot perfectly reveal the firm's private information, the uniquely optimal accounting rule always consists of 1) disclosure of a lower bound of the expected firm value and 2) a moment of the posterior belief, which, together with the lower bound, completely determines the expected firm value conditional on the disclosure. This optimal accounting rule can be interpreted as being consistent with certain features of the accounting rules that guide firms in financial reporting. In particular, the disclosure of the lower bound is consistent with the conservatism principle embedded in the accounting rules. Our results provide support for conservatism, arguably one of the most important attributes of accounting, in a setting that is particularly relevant for accounting.
Our study is, to the best of our knowledge, the first study of the optimal qualitative properties of accounting information in a systematic way. Previous studies on accounting conservatism (e.g., Chen et al. (2007), Gigler et al. (2009) and Gao (2013a)) also model conservatism as a qualitative property of accounting information that changes the relative informativeness of favorable versus unfavorable signals. However, because of their focus on the particular attributes of conservatism, their papers do not address the qualitative properties of accounting information in a fairly general way, which is our focus.
In deriving the optimal qualitative properties of accounting information, we adopt the concept of information well established in the information theory. This choice exhibits the virtue of flexibility because it is free to choose any information structure so long as it is Bayes-plausible. As discussed in section 2, we believe that this feature makes it particularly appealing to study accounting rules. Our choice of mutual information also exhibits the virtue of comparability because different information structures can be measured using one number: the reduction of entropy. This measure ensures comparability between arbitrary information structures, which we subsequently use to study optimal accounting rules.
We believe our focus on the qualitative properties of information structure is especially relevant for financial reporting because accounting rules often must trade off between different qualitative properties of information with the impact on the quantitative properties being less straightforward. Conservatism versus aggressiveness is one example, while a principle-based accounting standard versus a rule-based accounting standard is another. From this point of view, our paper can be seen as a first step in a line of future research incorporating more institutional details to generate additional insights related to optimal accounting rules. Specifically, in our model, accounting disclosure is still modelled as a black box. Although we can show that the optimal accounting rule can be interpreted to be consistent with conservatism, we cannot show in more detail how the lower bounds are directly related to accounting conservatism applied to specific accounting measurements. To answer those questions, we need to open the black box of accounting measurement (Gao (2013b)). This seems to be the natural next step in examining the relationship between the accounting rules and the optimal qualitative properties of information systems.
