I examine how an internal auditor, called the firm, designs a control system for a strategic employee who conditions his thefts on the amount and types of controls. Society sets minimum testing amounts and fines for detected theft, whereas the firm determines the employee's wages and the amount of monitoring above the minimum. The results fall into three separate cases. When society's minimum testing standards and fines are sufficiently high, the employee never steals in any period. In this case, the firm performs the minimum amount of testing and pays the lowest feasible wage. In the remaining two cases, the testing standard and fines are too low to prevent theft by themselves. In these two cases the firm's control system determines whether there will be theft in the first period. I show that if the firm chooses to prevent all first‐period theft, then it uses only one type of control. She offers a wage premium and monitors the minimum amount. The wage premium substitutes for a tine large enough to prevent all theft. If the firm designs controls that do not prevent all theft, then the firm also uses only one control. In contrast to the no‐theft case, the firm pays the lowest feasible wage and monitors above the minimum. This choice reflects the increasing returns to scale of monitoring in preventing theft.

One of the most common decisions facing an internal auditor is choosing which line items to investigate. An extensive literature (Dworin and Grimlund 1984; Leslie et al. 1980; Menz& fricke 1984; Teitlebaum and Robinson 1975) deals with the statistical and decision-theoretic aspects of his choice. This paper expands on previous work by adding a strategic source of errors: dishonest employees. It addresses the question of how the presence of strategic errors affects the relationship between the auditor's testing strategy and item value. I show that incorporating strategic errors can lead to audit strategies similar to Physical Units and Dollar Units Sampling. I highlight the assumptions driving the results by contrasting a firm's (or internal auditor's) use of an optional test in four stylized models of accounts receivable. The first model examines the firm's behavior when faced with nonstrategic (statistical) billing errors. In this model the accounting system generates random errors that result in over- or underbilling customers. The firm can use a costly, imperfect test to remove errors before the bills are sent out. In this nonstrategic model the firm randomizes and tests an item if and only if the benefit is greater than the cost. Because the amount of billing error is unrelated to the item value, there is no clear link between the firm's testing decision and the value of the line item. The second billing model adds the possible existence of dishonest employees who can steal from line items. A dishonest employee makes two decisions. He decides whether to steal from the line item, and, if he steals, he chooses the amount of the theft. A dishonest employee would steal the entire item if he were certain that the firm would never test that item. The dishonest employee's behavior forces the firm to consider the value of the item in determining the region of untested items. Specifically, low value items are never tested. As in many strategic models, the interaction with dishonest employees may lead to randomization. In particular, the randomized testing strategy can look like Stratified Physical Units Attributes Sampling (Leslie et alt 1980). The firm sorts items into different groups and each item in a group has the same probability of being tested. The third model contains only the statistical errors of incorrectly adding or deleting a sales discount, a percentage of the item value. Since the testing gain is directly related to the value of the line item, the firm's strategy depends on an item's value. The firm always tests high value items, and never tests low value items. The fourth model adds potentially dishonest employees who can pros vide unearned sales discounts to their confederates. In this model the firm stratifies items into three groups. It never investigates small items, always investigates large items, and randomizes over intermediate value items with probabilities roughly proportionate to the value of the item. This procedure is similar to a common audit procedure, Dollar Unit Cell Width Sampling (Leslie et al. 1980).

[One of the most common decisions facing an internal auditor is choosing which line items to investigate. An extensive literature (Dworin and Grimlund 1984; Leslie et al. 1980; Menzefricke 1984; Teitlebaum and Robinson 1975) deals with the statistical and decision-theoretic aspects of his choice. This paper expands on previous work by adding a strategic source of errors: dishonest employees. It addresses the question of how the presence of strategic errors affects the relationship between the auditor's testing strategy and item value. I show that incorporating strategic errors can lead to audit strategies similar to Physical Units and Dollar Units Sampling. I highlight the assumptions driving the results by contrasting a firm's (or internal auditor's) use of an optional test in four stylized models of accounts receivable. The first model examines the firm's behavior when faced with non-strategic (statistical) billing errors. In this model the accounting system generates random errors that result in over- or underbilling customers. The firm can use a costly, imperfect test to remove errors before the bills are sent out. In this nonstrategic model the firm randomizes and tests an item if and only if the benefit is greater than the cost. Because the amount of billing error is unrelated to the item value, there is no clear link between the firm's testing decision and the value of the line item. The second billing model adds the possible existence of dishonest employees who can steal from line items. A dishonest employee makes two decisions. He decides whether to steal from the line item, and, if he steals, he chooses the amount of the theft. A dishonest employee would steal the entire item if he were certain that the firm would never test that item. The dishonest employee's behavior forces the firm to consider the value of the item in determining the region of untested items. Specifically, low value items are never tested. As in many strategic models, the interaction with dishonest employees may lead to randomization. In particular, the randomized testing strategy can look like Stratified Physical Units Attributes Sampling (Leslie et al. 1980). The firm sorts items into different groups and each item in a group has the same probability of being tested. The third model contains only the statistical errors of incorrectly adding or deleting a sales discount, a percentage of the item value. Since the testing gain is directly related to the value of the line item, the firm's strategy depends on an item's value. The firm always tests high value items, and never tests low value items. The fourth model adds potentially dishonest employees who can provide unearned sales discounts to their confederates. In this model the firm stratifies items into three groups. It never investigates small items, always investigates large items, and randomizes over intermediate value items with probabilities roughly proportionate to the value of the item. This procedure is similar to a common audit procedure, Dollar Unit Cell Width Sampling (Leslie et al. 1980).]

Issues surrounding the allocation of sunk capacity costs to products are among the oldest in managerial accounting. On the one hand, such costs are generally deemed to be irrelevant, but on the other hand, actual accounting systems commonly make these allocations. This paper examines a decision maker who incurs costs to acquire capacity and then uses an opportunity cost to allocate that capacity among a sequence of product proposals. Under specified circumstances, the sunk cost of capacity is shown to approximate the optimal opportunity cost of capacity. As the number of product proposals grows, the expected opportunity loss from using a simple sunk cost based capacity allocation rule goes to zero. The model is extended to consider different types of products and a multiperiod setting. Résumé. Les questions qui entourent la répartition des coûts irrécupérables relatifs à la capacité entre les différents produits comptent parmi les plus vieux problèmes en comptabilité de gestion. D'une part, ces coûts sont généralement réputés n'être pas pertinents, tandis que d'autre part, en réalité, les systèmes de comptabilité assurent couramment ces répartitions. Les auteurs examinent le cas d'un décideur qui engage des frais pour acquérir une certaine capacité et utilise ensuite un coût d'option pour répartir cette capacité entre une série de projets de fabrication de produits. Dans des circonstances données, les auteurs démontrent que les coûts irrécupérables de la capacité acquise se rapprochent du coût d'option optimal de cette capacité. À mesure que croît le nombre de projets de fabrication de produits, la perte d'option prévue, si l'on utilise une règle de répartition simple de la capacité fondée sur les coûts irrécupérables, se rapproche de zéro. Le modèle est élargi de façon à englober différents types de produits et plusieurs périodes.

Accounting research contains two distinct approaches to the interaction between accounting management and the independent auditor. Game theory suggests that the auditor's testing strategy will affect the manager's reporting strategy and that the two strategies form an equilibrium. The game‐theoretic approach views the auditor as active, in that the auditor acknowledges the effect that his or her testing strategy has on the manager's reporting. In contrast, in the decision‐theoretic approach, the auditor tests reports, but ignores the effect that such testing might have on the manager's reporting behavior. Essentially, the decision‐theoretic approach views the auditor as passive, taking the reporting strategy as given when designing tests. We use United Kingdom data to estimate both models and test their validity using nested hypothesis tests. Our results demonstrate that the active, game‐theoretic model better describes the auditor‐manager interaction. This is the first empirical validation of the game‐theoretic model using archival accounting data.

We develop results for the use of LASSO and Post-LASSO methods to form firststage predictions and estimate optimal instruments in linear instrumental variables (IV) models with many instruments, p, that apply even when p is much larger than the sample size, n.We rigorously develop asymptotic distribution and inference theory for the resulting IV estimators and provide conditions under which these estimators are asymptotically oracle-efficient.In simulation experiments, the LASSO-based IV estimator with a data-driven penalty performs well compared to recently advocated many-instrument-robust procedures.In an empirical example dealing with the effect of judicial eminent domain decisions on economic outcomes, the LASSObased IV estimator substantially reduces estimated standard errors allowing one to draw much more precise conclusions about the economic effects of these decisions.Optimal instruments are conditional expectations; and in developing the IV results, we also establish a series of new results for LASSO and Post-LASSO estimators of non-parametric conditional expectation functions which are of independent theoretical and practical interest.Specifically, we develop the asymptotic theory for these estimators that allows for non-Gaussian, heteroscedastic disturbances, which is important for econometric applications.By innovatively using moderate deviation theory for self-normalized sums, we provide convergence rates for these estimators that are as sharp as in the homoscedastic Gaussian case under the weak condition that log p = o(n 1/3 ).Moreover, as a practical innovation, we provide a fully data-driven method for choosing the user-specified penalty that must be provided in obtaining LASSO and Post-LASSO estimates and establish its asymptotic validity under non-Gaussian, heteroscedastic disturbances.

We propose robust methods for inference about the effect of a treatment variable on a scalar outcome in the presence of very many regressors in a model with possibly non-Gaussian and heteroscedastic disturbances. We allow for the number of regressors to be larger than the sample size. To make informative inference feasible, we require the model to be approximately sparse; that is, we require that the effect of confounding factors can be controlled for up to a small approximation error by including a relatively small number of variables whose identities are unknown. The latter condition makes it possible to estimate the treatment effect by selecting approximately the right set of regressors. We develop a novel estimation and uniformly valid inference method for the treatment effect in this setting, called the “post-double-selection†method. The main attractive feature of our method is that it allows for imperfect selection of the controls and provides confidence intervals that are valid uniformly across a large class of models. In contrast, standard post-model selection estimators fail to provide uniform inference even in simple cases with a small, fixed number of controls. Thus, our method resolves the problem of uniform inference after model selection for a large, interesting class of models. We also present a generalization of our method to a fully heterogeneous model with a binary treatment variable. We illustrate the use of the developed methods with numerical simulations and an application that considers the effect of abortion on crime rates.

The accepted manuscript version (last revised 5 Jan 2018 (v8)) has 118 pages, 3 tables, 11 figures, and includes supplementary appendix. This version corrects some typos in Example 2 of the published version. This supplement contains 11 appendices with additional results and some omitted proofs. Appendices F-J include additional results for Sections 2-7, respectively. Appendix K gathers auxiliary results on algebra of covering entropies. Appendices L and M contain the proofs of Sections 4 and 5 omitted from the main text. Appendix N contains the proofs of Sections 6 omitted from the main text, together with the proofs of the additional results for Section 6 in Appendix I. Appendix O reports the results of a simulation experiment.

ABSTRACT Our study is motivated by the theory of credence goods in the auditing setting. We propose that audit committee accounting expertise should reduce information asymmetries between the auditor and the client, thereby limiting auditors' ability to over-audit and under-audit. Consistent with this notion, our results indicate that when audit committees have accounting expertise, clients (1) pay lower fees when changes in standards decrease required audit effort; (2) pay a smaller fee premium in the presence of remediated material weaknesses; and (3) have a reduced likelihood of restatement when audit market competition is high. Our findings in the under-auditing setting generally are strongest among non-Big 4 engagements, consistent with non-Big 4 auditors being less sensitive to market-wide disciplining mechanisms such as reputation, legal liability, and professional regulation. We also provide evidence that the nature of audit committee members' accounting expertise differentially impacts the committee's ability to curtail over- and under-auditing. JEL Classifications: M40; M41; M42.