Estimating the Kullback–Liebler risk based on multifold cross‐validation

This paper concerns a class of model selection criteria based on cross‐validation techniques and estimative predictive densities. Both the simple or leave‐one‐out and the multifold or leave‐m‐out cross‐validation procedures are considered. These cross‐validation criteria define suitable estimators for the expected Kullback–Liebler risk, which measures the expected discrepancy between the fitted candidate model and the true one. In particular, we shall investigate the potential bias of these estimators, under alternative asymptotic regimes for m. The results are obtained within the general context of independent, but not necessarily identically distributed, observations and by assuming that the candidate model may not contain the true distribution. An application to the class of normal regression models is also presented, and simulation results are obtained in order to gain some further understanding on the behavior of the estimators.     

Half‐panel jackknife fixed‐effects estimation of linear panels with weakly exogenous regressors

This paper considers estimation and inference in linear panel regression models with lagged dependent variables and/or other weakly exogenous regressors when N (the cross‐section dimension) is large relative to T (the time series dimension). It allows for fixed and time effects (FE‐TE) and derives a general formula for the bias of the FE‐TE estimator which generalizes the well‐known Nickell bias formula derived for the pure autoregressive dynamic panel data models. It shows that in the presence of weakly exogenous regressors inference based on the FE‐TE estimator will result in size distortions unless N/T is sufficiently small. To deal with the bias and size distortion of the FE‐TE estimator the use of a half‐panel jackknife FE‐TE estimator is considered and its asymptotic distribution is derived. It is shown that the bias of the half‐panel jackknife FE‐TE estimator is of order T^?2, and for valid inference it is only required that N/T³→0, as N,T→∞ jointly. Extension to unbalanced panel data models is also provided. The theoretical results are illustrated with Monte Carlo evidence. It is shown that the FE‐TE estimator can suffer from large size distortions when N>T, with the half‐panel jackknife FE‐TE estimator showing little size distortions. The use of half‐panel jackknife FE‐TE estimator is illustrated with two empirical applications from the literature.     

Bias Reduction in Dynamic Panel Data Models by Common Recursive Mean Adjustment*

The within‐group estimator (same as the least squares dummy variable estimator) of the dominant root in dynamic panel regression is known to be biased downwards. This article studies recursive mean adjustment (RMA) as a strategy to reduce this bias for AR(p) processes that may exhibit cross‐sectional dependence. Asymptotic properties for N,T→∞ jointly are developed. When ( log ²T)(N/T)→ζ, where ζ is a non‐zero constant, the estimator exhibits nearly negligible inconsistency. Simulation experiments demonstrate that the RMA estimator performs well in terms of reducing bias, variance and mean square error both when error terms are cross‐sectionally independent and when they are not. RMA dominates comparable estimators when T is small and/or when the underlying process is persistent.     

Stratified studies about risk ratios in 2 × 2 tables with structural zero

Incomplete correlated 2 × 2 tables are common in some infectious disease studies and two‐step treatment studies in which one of the comparative measures of interest is the risk ratio (RR). This paper investigates the two‐stage tests of whether K RRs are homogeneous and whether the common RR equals a freewill constant. On the assumption that K RRs are equal, this paper proposes four asymptotic test statistics: the Wald‐type, the logarithmic‐transformation‐based, the score‐type and the likelihood ratio statistics to test whether the common RR equals a prespecified value. Sample size formulae based on hypothesis testing method and confidence interval method are proposed in the second stage of test. Simulation results show that sample sizes based on the score‐type test and the logarithmic‐transformation‐based test are more accurate to achieve the predesigned power than those based on the Wald‐type test. The score‐type test performs best of the four tests in terms of type I error rate. A real example is used to illustrate the proposed methods.     

Selection correction and sensitivity analysis for ordered treatment effect on count response

In estimating the effect of an ordered treatment τ on a count response y with an observational data where τ is self‐selected (not randomized), observed variables x and unobserved variables ε can be unbalanced across the control group (τ = 0) and the treatment groups (τ = 1, …, J). While the imbalance in x causes ‘overt bias’ which can be removed by controlling for x, the imbalance in ε causes ‘covert (hidden or selection) bias’ which cannot be easily removed. This paper makes three contributions. First, a proper counter‐factual causal framework for ordered treatment effect on count response is set up. Second, with no plausible instrument available for τ, a selection correction approach is proposed for the hidden bias. Third, a nonparametric sensitivity analysis is proposed where the treatment effect is nonparametrically estimated under no hidden bias first, and then a sensitivity analysis is conducted to see how sensitive the nonparametric estimate is to the assumption of no hidden bias. The analytic framework is applied to data from the Health and Retirement Study: the treatment is ordered exercise levels in five categories and the response is doctor office visits per year. The selection correction approach yields very large effects, which are however ruled out by the nonparametric sensitivity analysis. This finding suggests a good deal of caution in using selection correction approaches. Copyright © 2004 John Wiley & Sons, Ltd.     

Optimal risk rate in a functional inverse problem

In this note, we will consider the problem of recovering an unknown input function when the output function is observed in its entirety, blurred with functional error. An estimator is constructed whose risk converges at an optimal rate. In this functional model, convergence rates of order 1/n (n is the sample size) are possible, provided that the error distribution is sufficiently concentrated so as to compensate for the ill‐posedness of the inverse of the model operator.     

Exploiting tail shape biases to discriminate between stable and student t alternatives

The nonnormal stable laws and Student t distributions are used to model the unconditional distribution of financial asset returns, as both models display heavy tails. The relevance of the two models is subject to debate because empirical estimates of the tail shape conditional on either model give conflicting signals. This stems from opposing bias terms. We exploit the biases to discriminate between the two distributions. A sign estimator for the second‐order scale parameter strengthens our results. Tail estimates based on asset return data match the bias induced by finite‐variance unconditional Student t data and the generalized autoregressive conditional heteroscedasticity process.     

THE TRUTHINESS HURTS

This essay applies some of the key insights in Bryan Caplan's The Myth of the Rational Voter. We discuss the relevance of cheap signals in political systems as well as the relevance of ideas in public policy with ‘rationally irrational’ voters. We add a fifth bias, ‘stick‐it‐to‐the‐man bias’, to Caplan's proposed anti‐market, anti‐foreign, make‐work and pessimistic biases, and we apply them all to environmental policy.     

The distortion of information to support an emerging evaluation of risk

A persistent problem in the assessment of the risk of an event is a bias driven by the desirability of different outcomes. However, such a desirability bias should not occur in the absence of prior dispositions toward those outcomes. This assumption is tested in an experiment designed to track the evaluation of information during an emerging evaluation of risk. Results confirm the presence of a substantial desirability bias even when there is no prior disposition toward any outcome. These findings bear implications for the assessment of risk not only in the presence of prior desirability, but also in situations currently considered benign.     

Modelling heterogeneity and dynamics in the volatility of individual wages

This paper presents a model for the heterogeneity and dynamics of the conditional mean and conditional variance of individual wages. A bias‐corrected likelihood approach, which reduces the estimation bias to a term of order 1/T², is used for estimation and inference. The small‐sample performance of the proposed estimator is investigated in a Monte Carlo study. The simulation results show that the bias of the maximum likelihood estimator is substantially corrected for designs calibrated to the data used in the empirical analysis, drawn from the PSID. The empirical results show that it is important to account for individual unobserved heterogeneity and dynamics in the variance, and that the latter is driven by job mobility. The model also explains the non‐normality observed in log‐wage data. Copyright © 2010 John Wiley & Sons, Ltd.     

Simulating non‐normal distributions with specified L‐moments and L‐correlations

This paper derives a procedure for simulating continuous non‐normal distributions with specified L‐moments and L‐correlations in the context of power method polynomials of order three. It is demonstrated that the proposed procedure has computational advantages over the traditional product‐moment procedure in terms of solving for intermediate correlations. Simulation results also demonstrate that the proposed L‐moment‐based procedure is an attractive alternative to the traditional procedure when distributions with more severe departures from normality are considered. Specifically, estimates of L‐skew and L‐kurtosis are superior to the conventional estimates of skew and kurtosis in terms of both relative bias and relative standard error. Further, the L‐correlation also demonstrated to be less biased and more stable than the Pearson correlation. It is also shown how the proposed L‐moment‐based procedure can be extended to the larger class of power method distributions associated with polynomials of order five.     

Decision making under risk in Deal or No Deal

We analyse the choices of 399 contestants in the Australian version of the television game show Deal or No Deal. We calculate risk aversion bounds for each contestant, revealing considerable heterogeneity. We then estimate a structural stochastic choice model that captures the dynamic decision problem faced by contestants. To address individual heterogeneity, we nest the dynamic problem within the settings of both a random effects and a random coefficients probit model. Our structural model produces plausible estimates of risk aversion, confirms the role of individual heterogeneity and suggests that a model of stochastic choice is indeed appropriate. We find mixed evidence of greater risk aversion by females. We also examine generalizations to expected utility theory, finding that the rank‐dependent utility model adds non‐negligible explanatory power and indicates optimism in probability weighting. Finally, we test, but are unable to confirm, the existence of an endowment effect for lotteries. Copyright © 2009 John Wiley & Sons, Ltd.     

Insuring against the shortfall risk associated with real options

We would like to insure against the risk that a geometric Brownian motion, correlated with the price process of a certain traded asset, is in a set E at time T. In this paper it is shown that the best action one can take to insure against this risk is to buy a binary option on the traded asset. We give explicit formulas in the case that E is an infinite interval. The setting of all our investigations is the Black-Scholes model. Mathematics Subject Classification (2000): 91B28, 60J65, 62P05, 91B30, 62F03 Journal of Economic Literature Classification: G31     

Subperfect Game: Profitable Biases of NBA Referees

This paper empirically investigates three hypotheses regarding biases of National Basketball Association referees. Identification of basketball referee bias is typically difficult as changes in observed statistics may be caused by either changes in referee bias or player behavior. We identify bias by exploiting the fact that referees have varying degrees of discretion over different types of a particular statistic‐turnovers. This allows us to conduct a treatment and control‐style analysis, using the less discretionary turnovers as the player behavior control. The results provide evidence that referees favor home teams, teams losing during games, and teams losing in playoff series. All three biases are likely to increase consumer demand.     

Testing for Flexible Nonlinear Trends with an Integrated or Stationary Noise Component

This paper proposes a new test for the presence of a nonlinear deterministic trend approximated by a Fourier expansion in a univariate time series for which there is no prior knowledge as to whether the noise component is stationary or contains an autoregressive unit root. Our approach builds on the work of Perron and Yabu ( 2009a ) and is based on a Feasible Generalized Least Squares procedure that uses a super‐efficient estimator of the sum of the autoregressive coefficients α when α = 1. The resulting Wald test statistic asymptotically follows a chi‐square distribution in both the I(0) and I(1) cases. To improve the finite sample properties of the test, we use a bias‐corrected version of the OLS estimator of α proposed by Roy and Fuller ( 2001 ). We show that our procedure is substantially more powerful than currently available alternatives. We illustrate the usefulness of our method via an application to modelling the trend of global and hemispheric temperatures.     

Cartel dating

The begin and end dates of cartels are often ambiguous, despite competition authorities stating them with precision. The legally established infringement period(s) from documentary evidence need not coincide with the period(s) of actual cartel effects. In this paper, we show that misdating cartel effects leads to a (weak) overestimation of but‐for prices and an underestimation of overcharges. Total overcharges based on comparing but‐for prices to actual prices are a (weak) underestimation of the true amount overcharged, irrespective of the type and size of the misdating. The bias in antitrust damage estimation based on predicted cartel prices can have either sign. We extend the before‐during‐and‐after method with an empirical cartel dating procedure, which infers structural breaks of unknown number and dates that mark the actual begin and end dates of the collusive effects. Empirical findings in the European Sodium Chlorate cartel corroborate our theoretical results.     

SOCIAL SECURITY AND RETIREMENT DECISION: A POSITIVE AND NORMATIVE APPROACH*

Abstract Social insurance for the elderly is judged responsible for the widely observed trend towards early retirement. In a world of laissez‐faire or in a first‐best setting, there would be no such trend. However, when first‐best instruments are not available, because health and productivity are not observable, the optimal social insurance policy may imply a distortion on the retirement decision. The main point we make is that while there is no doubt that retirement systems induce an excessive bias towards early retirement in many countries, a complete elimination of this bias (i.e. a switch to an actuarially fair system) is not the right answer for two reasons. First, some distortions are second‐best optimal. This is the normative argument. Second, and on the positive side, the elimination of the bias might be problematic from a political perspective. Depending on the political process, either it may not be feasible or alternatively it may tend to undermine the political support for the pension system itself.     

‘I Like How You Think’: Similarity as an Interaction Bias in the Investor–Entrepreneur Dyad

Investigating the factors that influence venture capital decision‐making has a long tradition in the management and entrepreneurship literatures. However, few studies have considered the factors that might bias an investment decision in a way that is idiosyncratic to a given investor–entrepreneur dyad. We do so in this study. Specifically, we build from the literature on the ‘similarity effect’ to investigate the extent to which decision‐making process similarity (shared between the investor and the entrepreneur) might bias or otherwise impact the investor's evaluation of a new venture investment opportunity. Our findings suggest venture capitalists evaluate more favourably opportunities represented by entrepreneurs who ‘think’ in ways similar to their own. Moreover, in the presence of decision‐making process similarity, the impacts of other factors that inform the investment decision actually change in counter‐intuitive ways.     

Real Asset Valuation under Imperfect Competition: Can We Forget About Market Fundamentals?

Real assets are usually valued by computing the stream of profits they can bring to a price‐taking firm in a liquid market. This method ignores market fundamentals by assuming that all the relevant information is included in the spot price. Our article analyses the bias resulting from such an approach when the market is imperfectly competitive. We propose a stylised two‐period model of the natural gas market with no uncertainty, focusing on strategic interactions between two types of oligopolistic players—pure traders and suppliers with downstream customers—who have access to storage. We show that the true value of storage capacity is not the same for traders and for suppliers. Comparing the latter value with the traditional price‐taking valuation reveals a systematic bias that tends to induce underinvestment.