GUILTY CONSCIENCE AND INCENTIVES WITH PERFORMANCE ASSESSMENT ERRORS

This study examines the effects of guilty conscience on incentive in the situation where an agent performance assessment has errors. There are two types of assessment error: undervaluation and overvaluation. In overvaluation, agents will not correct the assessment because their wages would then decrease. Although agents will want their undervaluation corrected, principals will not correct the error due to increased wage cost. Hence, correcting errors is complicated. However, this type of selfish behavior by agents and principals produces feelings of guilt, particularly when others trust them. In this situation, a high incentive is desirable for conscientious people with a strong sense of guilt or for nonconscientious people who do not feel guilt, but it is undesirable for intermediate‐type people who are conscientious only to a certain extent. (JEL D03, D82, J41)     

A class of local likelihood methods and near-parametric asymptotics

The local maximum likelihood estimate θ^ _t of a parameter in a statistical model f ( x , θ) is defined by maximizing a weighted version of the likelihood function which gives more weight to observations in the neighbourhood of t . The paper studies the sense in which f ( t , θ^ _t ) is closer to the true distribution g ( t ) than the usual estimate f ( t , θ^) is. Asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the sample size tends to ∞. In this setting, the relative entropy risk of the local method is better than that of maximum likelihood. The form of optimum weights for the local likelihood is obtained and illustrated for the normal distribution.     

Local model uncertainty and incomplete-data bias (with discussion)

Summary.  Problems of the analysis of data with incomplete observations are all too familiar in statistics. They are doubly difficult if we are also uncertain about the choice of model. We propose a general formulation for the discussion of such problems and develop approximations to the resulting bias of maximum likelihood estimates on the assumption that model departures are small. Loss of efficiency in parameter estimation due to incompleteness in the data has a dual interpretation: the increase in variance when an assumed model is correct; the bias in estimation when the model is incorrect. Examples include non-ignorable missing data, hidden confounders in observational studies and publication bias in meta-analysis. Doubling variances before calculating confidence intervals or test statistics is suggested as a crude way of addressing the possibility of undetectably small departures from the model. The problem of assessing the risk of lung cancer from passive smoking is used as a motivating example.     

Asymptotical improvement of maximum likelihood estimators on Kullback–Leibler loss

We discuss the general form of a first-order correction to the maximum likelihood estimator which is expressed in terms of the gradient of a function, which could for example be the logarithm of a prior density function. In terms of Kullback–Leibler divergence, the correction gives an asymptotic improvement over maximum likelihood under rather general conditions. The theory is illustrated for Bayes estimators with conjugate priors. The optimal choice of hyper-parameter to improve the maximum likelihood estimator is discussed. The results based on Kullback–Leibler risk are extended to a wide class of risk functions.     

Minimum Wages and Trainers' Dilemma

This paper examines how a minimum wage, viewed as an incentive to trainers, would affect the informal help provided through on‐the‐job training. In the work environment, experienced employees play a significant role in training new employees. However, the more help they provide to trainees, the less likely that the trainers themselves will be promoted. This is the trainer's dilemma: help trainees or work for promotion. We show that a minimum wage alleviates the trainer's dilemma, as it increases the earnings of non‐promoted workers and reduces the net benefit of promotion for experienced employees. Hence, minimum wage regulation encourages informal help and enhances welfare, although it reduces the firm's profit.     

Local sensitivity approximations for selectivity bias

Observational data analysis is often based on tacit assumptions of ignorability or randomness. The paper develops a general approach to local sensitivity analysis for selectivity bias, which aims to study the sensitivity of inference to small departures from such assumptions. If M is a model assuming ignorability, we surround M by a small neighbourhood N defined in the sense of Kullback–Leibler divergence and then compare the inference for models in N with that for M . Interpretable bounds for such differences are developed. Applications to missing data and to observational comparisons are discussed. Local approximations to sensitivity analysis are model robust and can be applied to a wide range of statistical problems.