EVALUATING THE EXPECTED WELFARE GAIN FROM INSURANCE

• Date: 01 January 2016
• Author: Glenn W. Harrison,Jia Min Ng
• DOI: http://doi.org/10.1111/jori.12142
• Published date: 01 January 2016

EVALUATING THE EXPECTED WELFARE GAIN FROM

INSURANCE

Glenn W. Harrison

Jia Min Ng

ABSTRACT

Economic theory tells us how to evaluate the expected welfare gain from

insurance products on offer to individuals. If we know the risk preferences of

the individual, and subjective beliefs about loss contingencies and likelihood

of payout, there is a certainty equivalent of the risky insurance policy that can

be compared to the certain insurance premium. This simple logic extends to

nonstandard models of risk preferences, such as those in which individuals

exhibit “optimism” or “pessimism” about loss contingencies in their

evaluation of the risky insurance policy. We illustrate the application of

these basic ideas about the welfare evaluation of insurance policies in a

controlled laboratory experiment. We estimate the risk preferences of

individuals from one task, and separately present the individual with a

number of insurance policies in which loss contingencies are objective. We

then estimate the expected consumer surplus gained or foregone from

observed take-up decisions. There is striking evidence of foregone expected

consumer surplus from incorrect take-up decisions. Indeed, the metric of

take-up itself, widely used in welfare evaluations of insurance products,

provides a qualitatively incorrect guide to the expected welfare effects of

insurance.

Consider the humble question of the welfare valuation of some new insurance

product, such as the “micro-insurance” products being offered and promoted in

developing countries. In general, these policies currently are evaluated by the metric

Glenn W. Harrison is at the Department of Risk Management & Insurance and Center for the

Economic Analysis of Risk, Robinson College of Business, Georgia State University. Jia Min Ng

is at the Department of Risk Management & Insurance, Robinson College of Business, Georgia

State University. Harrison is also affiliated with the School of Economics, University of Cape

Town and IZA—Institute for the Study of Labor. The authors can be reached via e-mail:

gharrison@gsu.edu and jng4@gsu.edu. We are grateful for helpful comments from reviewers

and seminar participants at the RMI Department of Georgia State University. Details of

procedures and the literature are available in CEAR Working Paper 2015–10 at http://cear.gsu.

edu.

© 2016 The Journal of Risk and Insurance. Vol. 83, No. 1, 91–120 (2016).

DOI: 10.1111/jori.12142

91

of product take-up.

1

Although take-up is easy to measure, it does not automatically

reflect the existence or size of the welfare gain of the insurance product to the insured.

An insurance product usually involves the individual

2

giving up a certain amount of

money ex ante some event in the expectation of being given some money in the future

if something unfortunate occurs. Welfare evaluation, therefore, generally requires

that one knows risk and time preferences of the individual, since the benefits of the

product are risky, and in the future, while the costs are normally

3

certain and up front.

We must also know the subjective beliefs that the individual used to evaluate possible

losses.

4

Of course, there is a “revealed preference” argument that if the product is (not) taken

up it was perceived to be a positive (negative) net benefit. But that is only the starting

point of any serious welfare evaluation, particularly if one wants to quantify the size of

the welfare effect. What if the subjective beliefs were biased, in the sense that the

individual would revise them if given certain information? What if the evaluation of

the product used some criteria other that Expected Utility Theory (EUT)? What if the

individual simply made a mistaken decision, given beliefs and risk preferences?

Invoking this revealed preference argument implies that one could never find a

negative welfare from any insurance decision!

Instead of making a priori assumptions about those preferences that are likely to be

wrong, we can use controlled experiments to estimate individual preferences,

1

Many recent field experiments that evaluate alternative insurance products focus exclusively

on take-up as a proxy for welfare: for example, see Gin

e, Townsend, and Vickrey (2007, 2008),

Cole et al. (2013), Dercon et al. (2014), Cole, Stein, and Tobacman (2014), Banerjee, Duflo, and

Hornbeck (2014), and Cai et al. (2015). Virtually no attempt is made to design products that

reflect the risk preferences of individuals. One example of the casual nature of judgments in

this area comes from Gin

e, Townsend, and Vickrey (2008, p. 544), describing how the premium

was set: “The policy premium was initially benchmarked on projected payouts using historical

rainfall data (at least 25 years of data for each rain gauge were used). The premium was

calculated as the sum of the expected payout, 25 percent of its standard deviation, 1 percent of

the maximum sum insured in a year, plus a 25 percent administrative charge and 10.2 percent

government service tax. In some cases the premium dictated by this formula was then

reduced, because it was believed to exceed farmers’ willingness to pay.” After all of the formal

actuarial arithmetic, we scratch our heads and just change things based on some hunch. To

justify being puzzled by low take-up, Banerjee, Duflo, and Hornbeck (2014, p. 292) refer to

“evidence of a strong need for health insurance,” but by this all they mean is evidence that

average health expenditures exceed the typical premium by a factor of 8.9 ¼4670/525. Such

expenditures always exhibit significant skewness, with many at zero, affecting the welfare

evaluation of the insurance product. An online appendix details the various welfare metrics

used in applied evaluation of insurance products.

2

One could extend this approach to consider the social welfare evaluation of insurance

products for groups of individuals, such as households, villages, or even nations.

3

Some insurance products in developing countries spread the premium payments over the life

of the contract.

4

There is an unfortunate tendency in many academic evaluations of insurance purchase to

assume that individuals somehow know the probabilities that are estimated or guessed at by

actuaries.

92 THE JOURNAL OF RISK AND INSURANCE