The first step in estimating the value of life is, generally, to estimate the tradeoff individuals are willing to make between the risk of death and compensation. In wage-risk studies the estimate of the trade-off takes the form of a slope coefficient on the risk of death variable from regression analysis. The estimated slope coefficient is then used to estimate the value of life. This paper addresses two separate but related issues that affect the calculated value of life. One issue is how the estimate of the slope coefficient may vary depending on the base amount of risk in the observations used for its estimate. This issue is addressed by determining the shape of the indifference curve between compensation and the risk of death. The other issue is the definition of the value of life. Two proofs are presented. One proof shows that the calculated value of life will vary according to the base amount of risk involved in the study. The other shows how the calculated value varies according to how the value of life is defined. An economist who uses the value of life studies should be aware of these influences.

In wage-risk studies the observations used to estimate the slope coefficient on the risk of death are usually gathered in an area where the absolute amount of risk is, say, from .01 % to .1 %. This amount of risk is small considering that the risk of death spans from 0.0% to 100%. Thus, it is certainly possible that the slope coefficient (and therefore the estimated value of life) would be significantly different if the observations used to estimate it came from a different area of the risk spectrum. This paper contains a proof which shows that for a risk averse individual, the slope coefficient will increase as the base amount of risk increases. The proof is accomplished by determining the shape of the indifference curve between compensation and the risk of death and is supported by evidence found in the literature.

The second issue is the definition of the value of life. The first definition considers how much a person would willingly sacrifice in order to avoid a 100% risk of death. The value of life is estimated by combining the estimated slope coefficient with the indifference curve between compensation and the risk of death. The results of this paper show that assuming the indifference curve is linear, which is the same as assuming the slope coefficient remains constant, leads to a conservative estimate of the amount an individual would sacrifice to avoid a 100% risk of death.

The value of life can also be defined as the amount an individual would pay to eliminate the risk of death. The amount is estimated by using the estimated slope coefficient and the utility of risk avoidance. The proofs show that the two methods, the indifference curve method and the utility of risk avoidance method, result in vastly different estimated values of life. A discussion of the reasoning implied by each method follows the proofs.

Section II begins by placing the discussion of the slope coefficient in terms of an indifference curve between the risk of death and compensation. Section II also contains empirical evidence found in the literature concerning the shape of the indifference curve. The section concludes with a proof of the shape of the indifference curve. Section III discusses alternate definitions of the value of life and their effect on the calculated value of life. Section IV contains the conclusions.

#### II. The Estimate of the Slope Coefficient

Dr. Gary R. Albrecht has more than 25 years of experience specializing in Economic Forecasting and Forensic Economics. The Director of Econometric Modeling at the University of Kansas, his research has been published in the Journal of Forensic Economics, Journal of Legal Economics, Trial Briefs, and The Earnings Analyst.