8. Materiales y métodos
8.19.8. Elaboración de dummy-módulo
Happiness economics—the term apparently coined by Clark and Oswald (1994), with predecessors in van Praag (1971), Easterlin (1974), and the so-called Leyden School—is diametrically opposed to mainstream neo- classical economics in that it does not assume beforehand that individu- als optimize their utility by situating themselves in a point of tangency between an indifference curve and the budget curve.3 Instead, the happi- ness or LS approach starts empirically by asking individuals how satisfied they are with their life or how happy they are.4 The rationale for this approach is empirical evidence that individuals are able to evaluate their
an urban quality of life index: theory and methods 71
satisfaction with life as a whole. Such evaluation may take the form of verbal categories, such as “bad,” “adequate,” and “good”; or it may use a numerical scale on which, for instance, 0 stands for the worst conceivable situation and 10 stands for the best conceivable situation. It has been dem- onstrated that these measurements are well correlated with various aspects of behavior associated with happiness, such as frequency of laughter in moments of social interaction. People who are happy according to such measurements also are considered happy by their friends and families; such individuals express positive emotions more frequently and are more optimistic, sociable, and extrovert.
No uniformity so far exists on how to phrase satisfaction questions. Respondents may be asked, generally speaking, How happy are you with your life? or How satisfied are you with your life? Possible responses include selections from a list of four verbal levels (for example, “bad,” “insufficient,” “sufficient,” or “good”) or from a numerical scale of 0 to 10, depending on the questionnaire design. Respondents also may be asked to evaluate other aspects of their lives (called life domains), such as their health, financial situation, and housing. In spite of the fact that there are different wordings of satisfaction questions, in practice the results are fairly well comparable.
Given the LS question as described above, it may be assumed that life evaluation depends on a set of variables describing the individual situa- tion, such as income, age, marital status, number of working hours, health situation, family size, travel distance to work, and type of work—in short, a vector x of k different variables x1, . . . , xk. These can be called aspects
or dimensions of one’s life situation. Some of these aspects or dimensions, like the number of working hours or travel time to work, can be influenced by the respondents themselves; others, like age, cannot be changed by the individual. These dimensions also may include urban and environmental features, like safety, cleanliness, or climate variables.
Figure 3.1 presents three curves, representing three satisfaction levels (W). In this example, life satisfaction depends on only two aspects or dimensions, x1 and x2. The higher the curve, the higher the satisfaction level. By construction, these are satisfaction indifference curves. In prac- tice, the number of response categories is finite—say, 0, 1, 2, . . . , up to 10. It follows that a dense and continuous map of indifference curves cannot be observed; but it is possible to observe 11 of them, corresponding to the response categories 0,1, . . . , 10. It is surprising that simply question- ing individuals enables the construction of indifference curves, without assuming optimizing behavior or functional specifications. In fact, the identifying power of neoclassical marginal conditions is not needed.
A question of terminology should be clarified before this discussion continues. The term indifference curve traditionally is derived from the analysis of consumer behavior, where the individual ranks commodity bundles according to preferences. In the present context, the term has a
wider meaning in which the space of alternatives consists of different life situations. A life situation is described by a vector x of relevant charac- teristics, such as age, income, housing situation, and street safety. Some of those characteristics involve market goods that can be purchased, and others do not.
It can be assumed that each indifference curve is described by the equa- tion f(x1,x2, . . . , xk) = W (constant), where the value of W indicates the level
of the indifference curve. If two situations—
(
x x11, 12, . . . ,xk1)
=x(1) and x x12, 22, . . . ,xk2 x(2)(
)
= where W (1) < W (2)—are compared, then x(2) is pre- ferred over x(1). In that case, the individual’s perceived trade-off ratio may be defined as the subjective trade-off ratio between any two dimensions. The ratio is defined as the required compensation in dimension x2 when the quantity of dimension x1 is reduced by one unit, such that there is no change in the indifference curve level. This trade-off ratio is called “subjec- tive” because it is defined by the subjective satisfaction measure. However, here the trade-off ratios between urban aspects are not derived by observa- tion of purchase behavior (for example, purchase of houses), but by direct observation of how urban features affect satisfaction with life as a whole or with urban dimensions in particular.The trade-off ratio is found by solving for Δx2 in the equation f(x1 + Δx1, x2 + Δx2, x3 . . . , xk) = f(x1, x2, ..., xk), (3.4) W = 1 W = 2 W = 3 x2 x1
Figure 3.1 Satisfaction Indifference Curves
an urban quality of life index: theory and methods 73
taking Δx1 as given. If the function f(.) is differentiable, this yields as a limiting value the slope coefficient of the indifference curve at x, which is
lim ,
1 0
2 1 1 2
Δ →x
(
Δx Δx)
= −f f also known as the substitution rate or trade-offratio, where fi stands for the partial derivative with respect to xi.
If the satisfaction indifference curve is linear in x for a specific level C, then the equation of the curve will be
a1x1 + a2x2+ . . . + akxk = C; (3.5)
and then the trade-off ratio between x1 and x2 is constant all along the indifference curve and equal to −a1/a2. If all indifference curves are paral- lel lines, there is one common trade-off ratio equal to –a1/a2.