# Life Quality Index

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Life Quality Index

The Life Quality Index (LQI) is a compound social indicator of human welfare that reflects the expected length of life in good health and enhancement of the quality of life through access to income. The Life Quality Index combines two primary social indicators: the expectancy of healthy life at birth, E, and the real gross domestic product per person, G, corrected for purchasing power parity as appropriate. Both are widely available and accurate statistics.

Basic concept

The three components of the Life Quality Index, G, E and K reflect three important human concerns: the creation of wealth, the duration of life in good health and the time available to enjoy life. The amount of life available to enjoy wealth acts as a multiplying factor upon the value of that wealth. Conversely, the amount of income one has to enjoy that available lifetime acts as a multiplier on the expected duration of life.

Unlike the United Nation’s Human Development Index (HDI), the LQI is derived rigorously from the economics of human welfare. Like the HDI it can be used to rank nations in order of human welfare (development). However, more important and unlike the HDI it can also serve as an objective function to be used in setting national or corporate goals for managing risk and to guide effective allocation of society’s scarce resources for the mitigation of risks to life or health. The LQI is a summary indicator of net benefit to society for improving the overall public welfare by reducing risks to life in a cost-effective manner.

In the accounting and assessment of human development, we can view the role of individuals as the principal means, or contributors, to development as well as the ends. For example, the productivity of an individual contributes directly to the aggregate wealth creation in a society. However, the income so generated (to whomsoever it may accrue) increases the capacity of society to provide the necessary means such as the required infrastructure (hospitals, schools, clean water, safe roads and structures). The adequacy of the infrastructure in turn benefits the individual via access to quality health and environment, education and means for cultural expression and enrichment. The LQI enhances our decision-making capacity and helps brings into sharp focus the choices and trade-offs we have to make between extension of life and creation of productive wealth.

Formulation

The mathematical expression for the Life-Quality Index L is:

$L = E^KG$

showing the LQI, L as a power function of E, the health-adjusted life expectancy (HALE) at birth and G, the Gross Domestic Product (GDP) per person. The parameter K is a constant based on time budget studies available for many countries. K is approximately equal to 5.0 for developed nations (Rackwitz 2005, Pandey et al. 2006).

ocietal Capacity to Commit Resources (SCCR)

The LQI has been used to determine an acceptable level of expenditure that can be justifiably incurred on behalf of the public interest in exchange for a small reduction in the risk of death that results in improved life-quality for all. This value can be considered as the Societal Capacity to Commit Resources (SCCR) to sustainable risk reduction. Suppose a portion of GDP, dG, is invested in implementing a program that has an impact on public risk, thus modifying the life expectancy by a small amount dE. There is a net benefit if there is a net increase in LQI, dL. This criterion can be derived from the definition of L as:

$frac\left\{dL\right\}\left\{L\right\} = K frac\left\{dE\right\}\left\{E\right\} + frac\left\{dG\right\}\left\{G\right\} > 0$

from which the Societal Capacity to Commit Resources to sustainable risk reduction follows as:

$SCCR = max \left(frac\left\{dG\right\}\left\{dE\right\}\right) = frac\left\{KG\right\}\left\{E\right\}$

Application

The Life Quality Index is a decision tool serving to promote human development through better allocation of society’s scarce resources by reducing wasteful efforts on inefficient risk-reduction and identifying efficient alternatives.

Given that the Societal Capacity to Commit Resources (SCCR) is limited, the LQI is a powerful indicator of merit amongst competing but desirable goods, such as for example level of resources to be directed at air pollution vs water pollution vs low probability, high consequence risks in the distant future.

Using the Life Quality Index or SCCR to Judge Risk

Risks influence the LQI via the age- and sex-specific mortality, calculated by changes in an actuarial life table. The safety benefit is the gain in health-adjusted life expectancy HALE, or life extension expected upon implementation of the program. The cost impacts must also be evaluated, measured as the impact on the real gross domestic product per person (with refinements that could include correction for purchasing power parity for international comparisons). The net benefit of a program is measured, according to the SCCR, by the resultant increases in real gross domestic product per capita and life expectancy, weighted by K, eq.(3). The Life Quality Index may be thought of as refinement of monetary measures commonly used in cost-benefit analysis.

Net Benefit Criterion for Managing Risk

The objective is to maximize life expectancy subject to society’s capacity to commit resources in light of existing or future constraints. Reducing risk of death and disease translates into longer healthful lives. The length of life extension in good health for a population can be reliably measured as the impact on the gain in life expectancy (dE). Resources and monies (-dG) are required to achieve the gains, or increases, in life expectancy. If the resources are wisely spent, then the gains in life expectancy will be sufficiently large that there is a net increase in the Life Quality Index (LQI). In contrast, if inordinate sums are spent on activities that do not save lives or result in only meagre life extension then there is a net decrease in the LQI.

Life Quality Index as a Tool for Managing Risk

Through case studies and worked examples, it has been shown how the Life Quality Index can be used to assist decision-makers in evaluating the effectiveness of regulations and activities aimed at reducing risk to life, health and the environment. The LQI is a versatile tool that can be used to assess a wide range of risk management problems. The examples of application of LQI include:
* the effectiveness of standards and regulations for health and safety;
* harmonization of structural safety standards and design goals;
* assessment of air pollution standards;
* efficiency of life-saving interventions and estimates of the societal willingness (or capacity) to commit resources for safety.

Development of the Life Quality Index

The concept of the Life Quality Index was first initiated at the Institute for Risk Research [http://www.irr-neram.ca/] , University of Waterloo, Waterloo, Ontario, Canada in the early 1990s The two primary publications were:

# Lind, N.C., Nathwani, J.S. and Siddal, E. (1992). Managing Risks in the Public Interest, Institute of Risk Research, University of Waterloo Press, Waterloo, ON, Canada and
# Nathwani, J.S., Lind, N.C., and Pandey, M.D. (1997). Affordable Safety by Choice: The Life Quality Method. Institute for Risk Research, University of Waterloo Press,Waterloo, ON, Canada, pp 230.

The principal investigators involved in the development of the Life Quality Index have been Professors Niels Lind, Jatin Nathwani and Mahesh Pandey.

References

# Allen, R.G.D. (1935). A note on the determinateness of the utility function. The Reviewof Economic Studies, 2(2), 155-158.
# Beckerman, W. (1968). An Introduction to National Income Analysis. Weidenfeld and Nicolson, London, UK
# Hicks, J.R. (1939). Value and Capital. Clarendon Press, USA.
# Hicks, J.R. (1939). The foundation of welfare economics. The Economic Journal, 49(196), 696-712.
# Hicks, J.R. (1940). Valuation of social income. Economica, No. 26.
# Hicks, J.R. (1958). The measurement of real income. Oxford Economics Paper.
# Hicks, J.R. (1975). The scope and status of welfare economics. Oxford Economics Paper 27(3), 307-326.
# Kubler, O. and Faber, M.H. (2005). LQI: On the correlation between life expectancy and the gross domestic product per capita. Proceedings of ICOSSAR 2005, Rome, Italy.
# Lind, N.C. (2002). Social and economic criteria of acceptable risk. Reliability Engineering and System Safety, 78(1), 21-26.
# Lind, N.C. (2005). Turning Life into Life Expectancy: The Efficiency of Life-Saving Interventions. To Appear in Int. Journal of Risk Assessment and Management.
# Maes, M.A., Pandey, M.D. and Nathwani, J.S. (2003). Harmonizing Structural Safety Levels with Life Quality Objectives. Canadian J. of Civil Engineering, 30(3), 500-510.
# Nathwani, J.S., Pandey, M.D. and Lind, N.C. A standard for determination of optimal safety in engineering practice. Proc. IFIP Conference, pp.1-8. May 23-25, Aalborg, Denmark, 2005.
# Nathwani, J.S. (2004) Strategic Principles for Managing Risk, Keynote Lecture, Proceedings.of the 11th IFIP Conference Reliability and Optimization of Structural Systems, (eds.) Maes, M.A. and Huyse, L., 13-22.
# Nathwani, J.S. and Narveson, J. (1995) “Three Principles for Managing Risk in the Public Interest,” Int J.Risk Analysis, vol. 15, No.6, pp 615-626, 1995.
# Organization of Economic Development and Cooperation (OECD). www.oecd.org/statistics.
# Pandey, M.D. and Nathwani, J.S. (2003). Life-Quality Index for the estimation of societal willingness-to-pay for safety. J. Structural Safety, 26(2), 181-199.
# Pandey, M.D. and Nathwani, J.S. (2003). Canada Wide Standard for Particulate Matter and Ozone: Cost-Benefit Analysis using a Life-Quality Index. Int. J. Risk Analysis, 23(1), 55-67.
# Pandey, M.D. and Nathwani, J.S. (2004). Discounting Models and the Life-Quality Index for the Estimation of Estimation of Societal Willingness-to-Pay for Safety. Proc. 11th IFIP Conference Reliability and Optimization of Structural Systems, (eds.) Maes, M.A. and Huyse, L., pp.87-94.
# Pandey, M.D. Nathwani, J.S.and Lind, N.C. (2006). The Derivation and Calibration of the Life-Quality Index. from Economic Principles. J. Structural Safety, 28 (1-2), 341-360.
# Pandey, M.D. and Nathwani, J.S. Foundational Principles of Welfare Economics Underlying the Life Quality Index for Efficient Risk Management, Int. J. Risk Assessment and Management, February 2005.
# Rabl, A., Nathwani, J., Pandey, M.D. and Hurley, F. (2003) Tools and Strategies for Improving Policy Responses to the Risk of Air Pollution, Int. Conf. Strategies for Clean Air and Health. 5-7 November, Rome, Italy.
# Pandey, M.D. and Nathwani, J.S. A Reinterpretation of Life-Quality Index for Cost-Benefit Analysis of Safety Programs. Proc. Int. Conf. Application of Statistics and Probability in Civil Engineering (ICASP 03), Der Kiureghian A., Madanat, S. and Pestana, J.M. (eds.), Vol.1, 711-717. San Francisco, CA, July 6-9, 2003.
# Pandey, M.D. and Nathwani, J.S. (2003) A Conceptual Approach to the Estimation of Societal Willingness-to-Pay for Nuclear Safety Programs. Int. J. Nuclear Engineering and Design, 224(1), 65-77.
# M.D. Pandey and J.S. Nathwani. (1997) Measurement of Socio-economic inequality using the life quality index, Social Indicators Research, vol 39, 187-202.
# UNDP, United Nations Human Development Reports, 1991, 1993, 1995, 2000.

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