John C. Fellingham

Contracts without memory in multiperiod agency models

Abstract Settings are considered in which optimal multiperiod contracts can have no memory, i.e., where second period payments do not need to depend on first period outcomes. If contracts have no memory, a repeated agency game can be played myopically; there are no gains to long-term relationships. Conditions on preferences for a no memory contract are presented. In an agency game with moral hazard on the act selection, preference separability and domain additivity imply the existence of a no memory contract. In a setting without moral hazard but with asymmetric information on the outcome, domain additivity implies no memory.

Models of Capital Investments with Private Information and Incentives: a Selective Review

The purpose of this paper is to selectively review research that addresses capital budgeting decisions in settings characterized by dispersed information and incentive problems. The papers are theoretical; they formulate and analyze models that vary in the number of periods considered, the number of economic actors involved, and the number of alternative projects available. The aims of the review are to describe some of the formulations that have been studied, to highlight their key economic and mathematical properties, to reveal their common economic forces, and to collect and organize their basic results. Copyright Blackwell Publishers Ltd 1997.

Ex Ante Randomization in Agency Models

We consider how a principal can use randomized strategies in designing optimal contracts in agency settings. We distinguish between ex post randomization (over fee schedules following act selection by the agent) and ex ante randomization (over fee schedules before act selection). We show that ex ante randomization may be efficient in both full information and private information settings under certain assumptions regarding preferences and the production technology. It is particularly significant that additive separability and concavity of the agents utility function as well as concavity of the production function do not rule out efficient ex ante randomized contracts in private information settings, although, as is known, they rule out ex post randomization.

Inferring Transactions from Financial Statements

In this paper, we embed the double entry accounting structure in a simple belief revision (estimation) problem. We ask the following question: Presented with a set of financial statements (and priors), what is the reader’s “best guess” of the underlying transactions that generated these statements? Two properties of accounting information facilitate a particularly simple closed form solution to this estimation problem. First, accounting information is the outcome of a linear aggregation process. Second, the aggregation rule is double entry.

Reconciling Financial Information at Varied Levels of Aggregation

Financial statements summarize a firm’s fiscal position using only a limited number of accounts. Readers often interpret financial statements in conjunction with other information, some of which may be aggregated in a different way (or not at all). This paper exploits properties of the double-entry accounting system to provide a systematic approach to reconciling diverse financial data. The key is the ability to represent the double-entry system by network flows and, thereby, access well-recognized network optimization techniques. Two specific uses are investigated: the reconciliation of audit evidence with management-prepared financial statements, and the creation of transaction-level financial ratios.

Preference representation and randomization in principal-agent contracts

Abstract Conditions on an agents preferences that induce a demand for ex ante randomization are derived. When the agent has constant absolute risk aversion in wealth but additive-separable preferences in wealth and effort, optimal contracts often require randomization. Under additive separability, the principal can use randomization to exploit the interaction between incentive considerations and the agents outside opportunities. However, when the agent has constant absolute risk aversion in wealth but multiplicative-separable preferences, participation and incentive considerations separate; hence, optimal contracts do not exhibit ex ante randomization.

Synergy, Quantum Probabilities, and Cost of Control

A standard control problem is analyzed using quantum probabilities. There are some advantages of conducting the analysis using the axiomatic structure of quantum probabilities: (1) there is synergy associated with bundling activities together, and, hence, a demand for the firm; (2) information occupies a central place in the analysis; (3) accounting information questions can be related to other information sciences. The main result is that control costs decline when aggregate performance measures are used; aggregation arises naturally. An implication is that the common practice of acquiring individual measures may be misguided in an environment where synergy is a first order effect. Also, double entry accounting appears well suited for processing information in a synergistic context.

On the Role of Receivables in Managing Salesforce Incentives

ABSTRACT Despite the obvious problems associated with collections, firms routinely sell on credit. Conventional wisdom suggests offering credit is a necessary evil when dealing with insistent cash-constrained customers. This paper provides a more positive view of trade credit. We find that offering credit can enhance the efficiency of incentive contracts with sales personnel. In effect, with a credit sale, a client gets a second chance to generate enough cash. The clients second chance gives the sales agent another opportunity to demonstrate his past diligence to the firm. Moreover, to limit the risk associated with the fact that even a high-quality client may fail to eventually come up with funds, the firm relies on the accrual system. In particular, the agents (discretionary and early) choice of the bad debt allowance conveys his private information regarding client quality; the payments associated with subsequent collections/default keep such reporting in check.

Depreciation in a model of probabilistic investment

A pervasive theme in both accounting and statistics is aggregation. However, in contrast to statistics, a customary standard for determining the best aggregation rule in accounting is unavailable or, at least, not explicitly defined. Also, most accounting procedures follow a well-specified recursive algorithm of updating a summarized history number (a beginning balance sheet number) by the current periods activities (changes). In this paper, we present a setting in which the best accounting aggregation rule arises naturally, resembles observed depreciation schedules, and proceeds recursively in a manner analogous to the above outlined stock-flow updating process. Our main results are (1) in every period, the performance of the BLU estimate based on active investments can be replicated by the periods depreciation amount and (2) in every period, the performance of the BLU estimate based on the entire history of investments can be replicated by a recursive procedure that updates the BLU estimate of the previous period with the current periodas investment realization. Depreciation successfully satisfies multiple objectives – it serves as a periodic allocation of realized investment amounts and as a statistic for the unknown investment population mean. Depreciation schedules commonly used in practice, straight-line, accelerated and declining balance, are shown to be best in particular settings.

Discussion of Optimal Contracts with Costly Conditional Auditing

Professor Evans has presented some interesting characteristics of an optimal contract in an environment in which both the action and outcome (both real-valued) are unobservable to the principal. The main result is that for any action, an audit will occur over a lower region of outcomes. The optimal contract is specific to the strucure of the game being played; the important feature of the game in this case is that the agent triggers the audit after observing the outcome. In this discussion, I consider the robustness of this game structure by contrasting it with another structure, in particular, one in which a random investigation strategy is committed to by the principal at the time of contracting. First, focus on the game as presented in the paper under discussion, in which the agent triggers the audits. There are two key characteristics of the optimal contract for this game structure: (1) Over the nonaudit region, that is, where no audit is performed to reveal act and outcome to the principal, the contract specifies a constant transfer to the principal. Since outcome and action are unobservable, they cannot be used as a basis for contracting, and hence, the only possible contract is a constant transfer from the agent. (2) Over the audit region of outcomes, where it is in the best interest of the agent to trigger an audit, the contract specifies a constant transfer to the agent, and hence constant consumption. Under the conditions of an audit everything is observable by everyone so a first, best solution is achievable (ignoring audit costs). Optimal risk sharing requires that the risk-neutral principal assumes all the risk (hence the constant transfer to the agent). Consider a numerical example to illustrate the existence of these costs