Estimation of Insurance Deductible Demand Under Endogenous Premium Rates

• DOI: http://doi.org/10.1111/jori.12260
• Published date: 01 June 2020
• Author: Jing Yi,Joshua D. Woodard
• Date: 01 June 2020

ESTIMATION OF INSURANCE DEDUCTIBLE DEMAND UNDER

ENDOGENOUS PREMIUM RATES

Joshua D. Woodard

Jing Yi

ABSTRACT

Government-subsidized insurance is ubiquitous, yet estimation of demand

in such markets remains challenging. The premium charged for a given

deductible is determined by actuarial construction; thus, observed choice-

pairs are endogenous leading to biased estimation under standard

econometric approaches. A theoretical model and simulation study are

developed, and a new identification strategy proposed. An empirical

application using Federal Crop Insurance Program—a $100 billion/year

program—data reveals that demand is quite elastic after accounting for this

endogeneity. Mistreatment of such endogeneity is likely partly responsible

for pervasive faulty findings of inelastic insurance demand in related

applications. Policy implications are also discussed.

INTRODUCTION

Government subsidization of insurance is commonplace in many insurance markets,

including health, flood, terrorism, deposit, agriculture, among others (Brown,

Kroszner, and Jenn, 2002; Brown et al., 2004; Ziebarth, 2010; Michel-Kerjan and

Kunreuther, 2011; Woodard et al., 2012; Aron-Dine, Einav, and Finkelstein, 2013;

Dickstein et al., 2015; Jaspersen and Richter, 2015), and comes in both supply-

This is an open access article under the terms of the Creative Commons Attribution License,

which permits use, distribution, and reproduction in any medium, provided the original work

is properly cited.

Joshua D. Woodard is an associate professor and the Zaitz Family Sesquicentennial

Faculty Fellow in Agribusiness and Finance in the Dyson School of Applied Economics

and Management at Cornell University. Woodard can be contacted via e-mail:

woodardjoshua@gmail.com. Jing Yi is a postdoctoral research associate at the Dyson School

of Applied Economics and Management, Cornell University. Yi can be contacted via

e-mail: jy348@cornell.edu [Correction added on 17 August 2018, after first online publication:

The email address of Jing Yi has been corrected.]. Acknowledgment is given to our funders who

supported parts of this work, including the Zaitz Family Sesquicentennial Faculty Fellowship

and National Crop Insurance Services Grant No. 1218405. None of the funders wereinvolved in

the preparation or design of the manuscript or work. All errors and omissions are our own.

©2018 The Authors. Journal of Risk and Insurance published by Wiley Periodicals, Inc. on behalf of

American Risk and Insurance Association. Vol. 9999, No. 9999, 1–24 (2018).

DOI: 10.1111/jori.12260

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Vol. 87, No. 2, 477–500 (2020).

and demand-enhancing forms including explicit premium subsidies, mandatory

coverage, and favorable government reinsurance. The analysis of consumer

responses to subsidization is central to evaluating, budgeting, and designing these

programs. Such interventions are often argued on the premise that they either

complete a missing market and/or reduce some externality to society, though there

are many arguments against such interventions as well (e.g., Priest, 1996). Often, the

large administrative databases maintained by the government on actual purchases

are the primary source of data for evaluating and predicting market responses to

changes in policy or subsidy rates. Understanding how to answer such questions

using transactional data is thus of great importance but presents challenges related to

endogeneity and complexity of product and program structures.

In the United States, the Federal Crop Insurance Program (FCIP) is a foundational

agricultural support program, with around $100 billion in liabilities annually. In fact,

the FCIP is the largest directagricultural subsidy program in the United States, and the

single largestagricultural insurance program globally and historically.Internationally,

subsidized agricultural insurance has also gained a foothold as a preferred mode of

interventionto complete missing risk management markets in the presence of systemic

risk, including large programs in China,India, and in many African countries (Mahul

and Stutley, 2010; Takahashia et al., 2016; Woodard, Shee, and Mude, 2016).

Having sound demand elasticity estimates is of upmost policy importance. For

example, the U.S. Government Accountability Office (GAO) recently released a

report that concluded—based on elasticity estimates in the literature—that

demand for crop insurance in the United States is inelastic, and then subsequently

inferred that subsidization could be cut, and insured paid rates increased

substantially without significantly affecting program participation (U.S. Govern-

ment Accountability Office, 2014). However, the findings in the literature cited in

that report are somewhat puzzling prima facie given the large uptake in the last

decades observed in the FCIP in response to increased subsidization. The price of

insurance (premium rate) for a given deductible (quantity) or coverage level

chosen by the insured is determined according to a convex actuarial premium

menu (typically referred to as the “rate curve”). Insurance coverage quantities

and prices in observed data are ultimately generated from such actuarial

schedules, and thus observed data are endogenously determined. We show that

when multiple deductible (i.e., coverage) levels are available, the near universal

approach of estimating demand elasticities with observed coverage on premium

rates via ordinary least squares (OLS) will thus result in severely biased demand

elasticities. This fundamental specification aspect regarding the endogeneity of

the premium schedule in deductible level has received no treatment in the

economic literature on insurance demand.

To our knowledge no cohesive strategy has been developed, or theoretical or

econometric basis articulated, to address this despite the broad appeal in a wide

universe of insurance markets. Premium rate endogeneity considerations have been

found to be important in related contexts though. For example, Weiss, Tennyson, and

Regan (2010) find that accounting for rate endogeneity resulting from regulations can

have profound empirical impacts when evaluating incentive distortions in insurance

2THE AUTHORS.JOURNAL OF RISK AND INSURANCE PUBLISHED BY WILEY PERIODICALS,INC.ON BEHALF OF

AMERICAN RISK AND INSURANCE ASSOCIATION

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