Protection in numbers? Self-protection as a local public good

Abstract In many contexts with endogenous physical risks - e.g., households, neighbourhood traffic calming, production quality control - risk reduction is a local public good. Risk-reduction incentives then depend on the protected population’s size. Focusing on a household’s physical risks modelled as an i.i.d. Bernoulli trials sequence with endogenous “success” probability, I give sufficient conditions for safety to increase with the number protected via both monotone comparative statics methodology and a “first-order” approach. I utilise a recursive decomposition of a covariance involving a monotonic function of a binomial variable and first-degree stochastic dominance (FSD). Because “protection” problems are generally non-concave, I give a detailed treatment of the second-order condition, again via FSD.

[1]  Massimiliano Amarante,et al.  Conditional expected utility , 2017 .

[2]  Ulrich Schmidt,et al.  Self‐Insurance and Self‐Protection as Public Goods , 2012 .

[3]  Robert M. Schwab,et al.  Disentangling the demand function from the production function for local public services : The case of public safety , 1987 .

[4]  M. Dosemeci,et al.  Urinary biomarker, dermal, and air measurement results for 2,4-D and chlorpyrifos farm applicators in the Agricultural Health Study , 2010, Journal of Exposure Science and Environmental Epidemiology.

[5]  Donald M. Topkis,et al.  Minimizing a Submodular Function on a Lattice , 1978, Oper. Res..

[6]  iv) Note on the Recurrence Formulae for the Moments of the Point Binomial , 1934 .

[7]  J. Shogren.  Endogenous risk and protection premiums , 1991 .

[8]  H. Kunreuther,et al.  Interdependent Security , 2003 .

[9]  K. Mack,et al.  Fatal unintentional injuries in the home in the U.S., 2000-2008. , 2013, American journal of preventive medicine.

[10]  Some recursions for moments of compound distributions , 2003 .

[11]  V. Romanovsky.  Note on the Moments of a Binomial (p + q) n about its Mean , 1923 .

[12]  K. Popper,et al.  The Logic of Scientific Discovery , 1960 .

[13]  Annette Hofmann,et al.  Multivariate Prevention Decisions: Safe Today or Sorry Tomorrow? , 2015 .

[14]  Helen F. Ladd.  Population Growth, Density and the Costs of Providing Public Services , 1992 .

[15]  Clive D. Fraser.  On tort as an implicit insurance system with state-dependent utility: The case of child mortality risk , 1996 .

[16]  Claude Fluet,et al.  The first-order approach when the cost of effort is money , 2012 .

[17]  R S Wilkinson.  Public safety. , 1967, The Medical journal of Australia.

[18]  R. J. Smeed,et al.  Some Statistical Aspects of Road Safety Research , 1949 .

[19]  Robert A. Pollak,et al.  Bargaining and Distribution in Marriage , 1996 .

[20]  Clive D. Fraser.  Income Risk, the Tax-benefit System and the Demand for Children , 2001 .

[21]  W. Allen.  Self-protection against crime: what do schools do? , 2018 .

[22]  Optimal Prevention for Multiple Risks , 2017 .

[23]  Recurrence Formulae for the Moments of the Point Binomial , 1925 .

[24]  M. McElroy,et al.  Nash-bargained household decisions: toward a generalization of the theory of demand , 1981 .

[25]  Carcinogen regulation: risk characteristics and the synthetic risk bias. , 1995, The American economic review.

[26]  J. Laffont,et al.  On moral hazard in general equilibrium theory , 1975 .

[27]  Recurrence Relation and Accurate Value on Inverse Moment of Discrete Distributions , 2015 .

[28]  W. Hamilton.  Geometry for the selfish herd. , 1971, Journal of theoretical biology.

[29]  R. Pollak,et al.  Noncooperative Bargaining Models of Marriage , 1994 .

[30]  M. Manser,et al.  Marriage and Household Decision-Making: A Bargaining Analysis , 1980 .

[31]  P. Jacobsen.  Safety in numbers: more walkers and bicyclists, safer walking and bicycling , 2003, Injury prevention : journal of the International Society for Child and Adolescent Injury Prevention.

[32]  J. Stiglitz,et al.  The Basic Analytics of Moral Hazard , 1988 .

[33]  Marc Lelarge,et al.  Economic Incentives to Increase Security in the Internet: The Case for Insurance , 2009, IEEE INFOCOM 2009.

[34]  D. E. Clark,et al.  HEDONIC PRICES, IDENTIFICATION, AND THE DEMAND FOR PUBLIC SAFETY* , 1990 .

[35]  Howard Kunreuther,et al.  Self-protection and insurance with interdependencies , 2007 .

[36]  Saverio M. Manago,et al.  A Recursive Formula for Moments of a Binomial Distribution , 2005 .

[37]  Gary S. Becker,et al.  Market Insurance, Self-Insurance, and Self-Protection , 1972, Journal of Political Economy.

[38]  J. Riordan.  Moment Recurrence Relations for Binomial, Poisson and Hypergeometric Frequency Distributions , 1937 .