استخراج و کالیبراسیون شاخص کیفیت زندگی (LQI) از اصول اقتصادی

The life-quality index (LQI) is a versatile tool to support the effective implementation of programs and practices for managing risk to life safety. The LQI allows a transparent and consistent basis for determination of the net benefit arising from projects, programs, standards and policies undertaken at some cost to improve safety or enhance the quality of life. The paper shows that the LQI model is in harmony with well-established principles of economics, utility theory and recent developments to quantify the progress of nations through indicators of human development. The initial calibration of the LQI was based on a simplifying assumption of a linear relation between the GDP and work time. In this paper, we modify the calibration using empirical data for GDP and work time and link the LQI model to well-established economic principles and theory of production. The proposed improvements to the model eliminate a systematic bias associated with estimation of societal willingness to pay for safety. In addition, it provides a rigorous basis for program evaluation to assist decision-makers in directing expenditures where they may most effective.

1.1. Background Efficient management of risks to life safety involves the search for a balance between the overall potential for harm and good outcomes. In recent years several acceptability criteria with quantitative rationale have been derived from compound social indicators ([12], [15], [10] and [23]) to support evaluation of broad program outcomes. A prominent and recent example of this is the Human Development Index (HDI). Developed under the auspices of the United Nations Development Program to compare internationally the level of social development of nations. The HDI combines three social indicators, the gross domestic product per person per year (GDP), life expectancy at birth (LE) and education, and ranks nations accordingly. The UNDP approach does not provide any guidance about how such an index could be used to help guide practical decisions around funding or programs and choices. Lind et al. [12] recognized that risk management is not only about engineering and economic efficiency of investment but, more importantly, it is about improving the overall public welfare by reducing risk to life in a cost-effective manner. They proposed the use of two key social indicators, real GDP per capita and life expectancy (LE) (already identified in the UN Human Development Project) for judging the effectiveness of decisions about risk and life safety. The concept was expanded by Nathwani et al. [15] who further developed the life-quality index (LQI) to establish a test of efficiency for programs and regulations to manage risks. Using a social indicator to derive an objective value of acceptable risk places risk mitigation in the context of national goals implicit in the indicator. The HDI aims to reflect how well a nation enables its citizens to live long, healthy and enriched lives. The HDI reflects a set of values that focuses on human development and measures progress of nations in achieving them through fine tuning the GDP, corrected for purchasing power parity (Lind, 2004). The HDI and the LQI rank developed nations quite similarly (Lind, 2003). The LQI is simpler and based on better-defined component indices weighted to reflect peoples’ revealed preference for the work/non-work time ratio and productivity. It allows an explicit valuation of a project’s effectiveness for life extension. Although the use of social indicators to track progress of nations is a recent development, the philosophical foundations of welfare economics was established earlier by Pigou [22] and Hicks [4] and [5], and these ideas continue to influence the development of social and economic policies centered around the concept of human welfare. The LQI is an innovation that builds on the concept of a social indicator that is a function of mortality and economic production and places an implicit value on reduction of life risk. The implied value is the increase in wealth production (i.e., real GDP per person) required to neutralize a small unit increase in mortality ([12], [15], [10] and [23], Lind, 2003, 2004). Use of LQI based on key social indicators offers the great advantage in that it provides a criterion of acceptable risk that harmonizes with national social and development objectives reflected in the social indicator. The basis for the derivation and calibration of the LQI parameters has engendered discussion in the analytical community and further elaboration of the LQI framework will assist practitioners in implanting the concept in decision making. The purpose of the paper is to present an analytical approach to the derivation and calibration that is consistent with established principles of economic sciences. The proposed LQI calibration is based on the concepts of production economics utilizing available economic data, thereby, removing a simplifying assumption used in the original study. 1.2. The life-quality index Originally the LQI was presented as a function of the real GDP (G $/person/year) and life expectancy (E years/person) [15] as follows: where c is a constant, denoting the annual fraction of work time per person required for producing G. The LQI was derived on the basis of a differential equation of LQI with some restrictions placed on its coefficients. The differential equation approach is considered less intuitive and there is a need to provide a fuller explanation of for the wider use by decision-makers. Subsequently, Pandey and Nathwani [18], [19] and [20] presented a derivation of LQI using the concept of a lifetime utility function and improved its technical foundation. In this formulation, the LQI turns out to be (1 − c)th root of the original index given in Eq. (1): This derivation provides a richer explanation of the underlying concepts and it links the LQI to concepts generally understood by practitioners in decision analysis, economic modelling, cost-benefit analysis and risk assessment. One important goal in managing risks to life safety is to determine an acceptable level of expenditure that can be justifiably incurred on behalf of the public in exchange for a small reduction in the risk of death without comprising the life-quality. This value can be considered as a fair estimate of the Societal Willingness to Pay (SWTP) for safety. Suppose a small proportion of GDP, dG, is invested in implementing a project, program or regulation that affects the public risk and modifies the life expectancy by a small amount dE. The net benefit criterion requires that there should be a net increase in LQI, which can be derived from Eqs. (1) and (2) as Rackwitz [23] and [24] expanded the LQI framework and applied it for the first time to determine optimal safety levels in civil engineering infrastructures. Rackwitz [25] also presented an extensive analysis of economic data to support the rationale behind the LQI. Maes et al. [13] applied LQI for optimizing the life-cycle cost of structures. The LQI model has also been applied to the cost-benefit analysis of air quality standards and nuclear safety design practices [18], [19] and [20]. 1.3. Applications of LQI As the LQI model began to be applied for judging the effectiveness of risk management programs, practitioners have raised questions about the form of the model and its calibration. Specific issues are as outlined below: (i) It has been noted in the literature that there are two independent methods of deriving LQI, namely, the differential equation method and the utility function method, and it may create confusion for the practitioner. In this paper, we show that the two methods are conceptually identical and that they are related to the concepts of ordinal utility function and the utility indifference curve. (ii) The validity of using a utility function in the derivation of LQI has been criticized [3]. Here, we clarify the issue and note the classic conundrum of utility being viewed as a cardinal or an ordinal concept. (iii) The calibration of LQI in terms of the work-time fraction along with labour-leisure tradeoff has also been criticized. The original calibration was based on a linear relation between the GDP and the work time. In this paper, the revised calibration of LQI removes a systematic bias associated with the estimation of societal willingness to pay (SWTP). The LQI comprises two essential components of life quality, real GDP per capita and life expectancy. A fuller discussion of the components of GDP and what it represents in the context of social income and welfare, as described below, help clarify the foundational basis of the LQI.

The LQI is derived using the concepts of economics sciences and a lifetime utility function as where C and q are constants that depend on the economic structure of a society in terms of the coefficient of labour share in the gross-domestic product (GDP) and the annual work-time fraction. Using Canadian and the US economic data, and average value of q = 0.2 is proposed for LQI-based analysis life-safety projects. The coefficient C is not relevant to the estimation of societal willingness to pay (SWTP). Given that many economists, regulators and decision-makers are more familiar with concepts of economics and utility theory, this should promote communication to a wider audience. The key conclusions of the paper are as follows. There is a unified basis of deriving the LQI in the context of ordinal utility theory. Earlier derivations utilizing a differential equation format are implicitly based on the utility indifference curve derived from a power utility function under some restrictive conditions. A key parameter is the marginal rate of substitution between the national income and life expectancy, and it is unaffected by a monotonic transformation of the utility function. The assumption of a linear relation between the GDP and work time, used in previous LQI calibration, is modified to provide an improved basis for estimating the societal willingness to pay based on an empirically valid theory of economic production functions in which the GDP is a power function of the work time. The paper clearly illustrates the process of deriving all LQI parameters specific to a country through the economic data analysis.