Do former athletes make better managers? Evidence from a partially adaptive grouped-data regression model

The goal of this paper is to introduce a partially adaptive estimator for the grouped-data regression model based on an error structure described by a mixture of two normal distributions. The model we introduce is easily estimated by maximum likelihood using the EM algorithm adapted from the work of Bartolucci and Scaccia (Comput Stat Data Anal 48:821–834, 2005). The partially adaptive estimator is applied to data used by Long and Caudill (Rev Econ Stat 73:525–531, 1991) to examine the impact of intercollegiate athletics on income. We estimate a variation of the original regression model and find that there is a considerable financial advantage for those male athletes now working in business management. This finding is consistent with the idea that athletes acquire team-building and organizational skills that are helpful in business.

[1]  Brenton R. Clarke,et al.  Comment on "Estimating mixtures of normal distributions and switching regressions" by Quandt and Ramsey , 1978 .

[2]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  Steven B. Caudill,et al.  The Impact of Participation in Intercollegiate Athletics on Income and Graduation , 1991 .

[5]  J. B. Ramsey,et al.  Estimating Mixtures of Normal Distributions and Switching Regressions , 1978 .

[6]  James B. McDonald,et al.  An application and comparison of some flexible parametric and semi-parametric qualitative response models , 1996 .

[7]  P. Bickel.  On Adaptive Estimation , 1982 .

[8]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[9]  S. Sclove.  Application of model-selection criteria to some problems in multivariate analysis , 1987 .

[10]  Thanasis Stengos,et al.  Partially Adaptive Estimation Via the Maximum Entropy Densities , 2005 .

[11]  Bronwyn H Hall,et al.  Estimation and Inference in Nonlinear Structural Models , 1974 .

[12]  Robert F. Phillips.  Partially adaptive estimation via a normal mixture , 1994 .

[13]  James B. McDonald,et al.  A comparison of semi-parametric and partially adaptive estimators of the censored regression model with possibly skewed and leptokurtic error distributions , 1996 .

[14]  Richard E. Quandt,et al.  The Econometrics Of Disequilibrium , 1988 .

[15]  Michael J. Hartley,et al.  Estimating Mixtures of Normal Distributions and Switching Regressions: Comment , 1978 .

[16]  K. D. Kumar,et al.  Comment on “Estimating Mixtures of Normal Distributions and Switching Regressions” , 1979 .

[17]  Francesco Bartolucci,et al.  The use of mixtures for dealing with non-normal regression errors , 2004, Comput. Stat. Data Anal..

[18]  Alain Monfort,et al.  Pricing and Inference with Mixtures of Conditionally Normal Processes , 2007 .

[19]  Richard J. Butler,et al.  Robust and Partially Adaptive Estimation of Regression Models , 1990 .

[20]  Jeffrey S. Racine,et al.  Nonparametric estimation of regression functions with both categorical and continuous data , 2004 .

[21]  James B. McDonald,et al.  A comparison of some robust, adaptive, and partially adaptive estimators of regression models , 1993 .

[22]  C. Stein.  Efficient Nonparametric Testing and Estimation , 1956 .

[23]  Tue Gørgens,et al.  Semiparametric Estimation of Single-Index Hazard Functions Without Proportional Hazards , 2006 .

[24]  Rudolf Beran,et al.  Asymptotically Efficient Adaptive Rank Estimates in Location Models , 1974 .

[25]  Robert F. Phillips.  A note on testing for switching regressions , 1991 .

[26]  James B. McDonald,et al.  A Comparison of Partially Adaptive and Reweighted Least Squares Estimation , 2003 .

[27]  Charles F. Manski,et al.  Adaptive estimation of non–linear regression models , 1984 .

[28]  James B. McDonald,et al.  Partially Adaptive Estimation of Regression Models via the Generalized T Distribution , 1988, Econometric Theory.

[29]  Steven B. Caudill,et al.  Estimating a mixture of stochastic frontier regression models via the em algorithm: A multiproduct cost function application , 2003 .

[30]  Marko Sarstedt,et al.  Sample- and segment-size specific Model Selection in Mixture Regression Analysis , 2006 .

[31]  C. J. Stone,et al.  Adaptive Maximum Likelihood Estimators of a Location Parameter , 1975 .

[32]  James V. Hansen,et al.  Partially adaptive robust estimation of regression models and applications , 2006, Eur. J. Oper. Res..

[33]  Jeffrey S. Racine,et al.  CROSS-VALIDATED LOCAL LINEAR NONPARAMETRIC REGRESSION , 2004 .

[34]  D. Henderson,et al.  Do Former College Athletes Earn More at Work? , 2005, The Journal of Human Resources.

[35]  Mark B. Stewart,et al.  On Least Squares Estimation when the Dependent Variable is Grouped , 1982 .

[36]  H. Bozdogan.  Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions , 1987 .