An Ordered-Response Income Adequacy Model

An Ordered-Response Income Adequacy Model Individual and social well-being are central to analysis of equity and social progress. It is natural that the measurement of well-being is a point of convergence for economics and other social sciences. Interest currently exists in using subjective data to estimate welfare or utility functions for individuals. There is corresponding interest in the comparison of welfare functions across households. Analyses of the theoretical potential for improvements in welfare, the incidence of poverty, and the formation of preferences can use such estimates and comparisons. The "Leyden model," so known for its place of origin, dominates work on measuring welfare levels of individuals from subjective data.(1) Analysis using the Leyden model (LM) have worked on specifying poverty lines, measuring economic progress, testing for optimal income distributions, and estimating the value of social service benefits and environmental improvements. This study introduces a new approach to estimating individual welfare levels from subjective data. It also deals with comparing welfare measures across individuals. The types of data used are plentiful in secondary sources. The approach does not require some of the assumptions of the LM that are objectionable to many economists.(2) The basic tools of the approach developed here, ordinal response models and random utility theory, are not new. The way they are combined is new, as is their use with introspective data on welfare. The neoclassical economists' equivalent and compensating variations follow from the model. In mathematical form, these measures are very similar to measures used in more ad hoc fashion in the LM literature. the approach is a bridge between neoclassical economic welfare measures and LM in the type of data with which it starts and in the form of welfare computations. This paper assumes familiarity with neoclassical economic welfare measures. It also assumes familiarity with the philosophical underpinnings of ordinal utility and revealed preference and with various approaches to estimating family equivalence scales. The proper provides a brief overview of the LM. There are excellent and inclusive review articles on the LM for the interested reader. THE LEYDEN MODEL The Leyden model is the most rigorous previous work in economics using subjective assessments of income adequacy. This section gives the model's specification, assumptions, and results, so that they can be compared with those of the ordered-response model. The model starts with a survey question: Taking into account my (our) condition of living, I would consider a net family income per week/per month/per year as excellant if it were above _____, and good if it were between _____ and _____. There is a similar question for amply sufficient, sufficient, barely sufficient, insufficient, very insufficient, bad, and very bad (open-ended category). For each household, the verbal descriptions evaluate hypothetical incomes, denoted by [Y.sub.h] can be a representative income for the interval. For instance, [Y.sub.h] may be the midpoint for the income interval associated with "good." The next step is to associate a numerical utility score with each verbal description. In general, scores depend on the number of questions and assign equal intervals between any two adjacent questions. The result of this step is a set of incomes and corresponding utility numbers for each household. The LM postulates that utility numbers and incomes for any household follow the log-normal cumulative distribution function, U([Y.sub.h]) = N[(In Y.sub.h - m)/s]. The utility function for each household has partners m and s. U([Y.sub.h]) maps from income to utility on a zero-one continous scale. Parameter m is the log of income associated U([Y.sub.h]) = 0.5. It is the log of income at which the cumulative normal distribution function that describes utility has its inflection point. …