Vita e Pensiero

The paper deals with the estimation of the attitude to risk of a group of people, the Board of the Foundation for the Saving Bank of Florence. A specific method is used: the so-called trade-off method, both with the outward and the inward procedure. In a previous study Bacci and Chiandotto (2002) presented the data, holding that the risk attitude for the Board implies propensity to risk when low levels of income and utility are concerned, and risk aversion for higher values of income/utility. Different theoretical utility functions are estimated in this paper: very simple ones, like the power utility function, and more complex ones, including the specification used in Bacci and Chiandotto (2003). Our results imply either risk neutrality (aversion), when so-called outward trade-off procedure (inward trade-off procedure) data alone are used or, perhaps, risk aversion (propensity) when low (high) values for income/utility are considered.

This work remarks the need to carefully evaluate the real importance of each variable used in a multivariate analysis context, with particular regard to cases when an overall performance ranking is the main final purpose. In particular, both a preliminary transformation of variables – aimed at reducing asymmetry and variability of their variation ranges – and the evaluation of their intrinsic explicative power – through redundancy analysis and weighting methods – are proposed. Theoretical and empirical considerations are developed in the frame of quality of life evaluation, carried out at the Italian provinces level on the basis of a yearly survey managed by the Italian economic newspaper ‘‘Il Sole24ore’’. A particular emphasis is given to some normalisation criteria and the case when original variables are grouped ‘‘a priori’’ into logical blocks. A final comparison between the actual ranking method and a series of alternatives is proposed as well.

Since first formulated, orthogonal Procrustes analysis has been mainly related to the biometrical study of shapes (shape analysis) based on landmarks. Essentially, this is a method to superimpose two configurations of points by means of a similarity – a combination of a translation term, an isotropic change of scale and an orthogonal transformation – in order to produce an optimal fit, in a least-squares sense. And among them, the problem of finding the best orthogonal transformation has its own particular interest from a biological point of view and it is known as the Procrustes rotation (PR) problem. In morphometrics, the presence of a particular type of symmetry often constrains the search of the PR to be either a determinant 1 or a determinant -1 orthogonal matrix. While the analytical solution to the first problem is well known, a formal proof of the solution to the latter is still required. A common-analytical proof of the solution for both constrained PR problems is given in this work, based on the standard (and unique) singular-value descomposition.

Being temporarily not at home can often cause the impossibility to give out a questionnaire to each selected unit of a sample; moreover, a high percentage of nonrespondents can strongly affect the quality of estimates. In order to solve this problem the ‘‘not at home’’ are usually called back until they become available; however, this methodology highly increases the costs of a survey. The main idea of this paper traces back to an estimation method early proposed by Politz and Simmons; in particular, a new estimator, based on the regression method, is proposed, so that the auxiliary information about the number of evenings spent at home by the units of the target population can be used. The proposed estimator is shown to be unbiased and more efficient than the one based only on the responses of the units being at home when first contacted. Moreover, unlike from the Politz-Simmons estimator, the variance of the proposed estimator can be easily determined and computed. Finally, in order to discuss the asymptotic properties of the regression estimator, the results of some simulations are reported; both the proposed estimator and the Politz-Simmons one turn out to be asymptotically unbiased; however, the regression estimator still proves to be more efficient.

This paper illustrates a method for estimating equivalence scales, that is, the income required by one household to reach the same standard of living as another one. The original method considered in the present study was introduced by Kot in 2002, whereas here we formulate a different procedure based on the quantiles of the Dagum distribution. We estimate the scale parameter through the maximum likelihood method based on the results of the survey carried out by the Banca d’Italia on the household income and wealth in 2002. The reason for the chosen method is based on the fact that the Dagum distribution fits the Italian income distribution well. Finally, two ways for finding the confidence interval for the elasticity of the equivalence scale are considered.

The key implication of the life cycle (LCH – Modigliani and Brumberg, 1954) and of the permanent income (PIH – Friedman, 1957) theories is that transitory variations in income, such as those arising from business cycle fluctuations, do not modify the purchasing behaviour of households which sustain, eventually, consumption either by running down assets and/or by incurring debt. Nevertheless, several empirical studies have shown that, due to capital market imperfections, during business cycle recession households, especially those with a severe overall economic situation, are, actually, forced to reduce the level of consumption of goods with more elastic demand. However, some questions still need an answer as far as Italian context is concerned: during the business cycle recession, do households modify their purchasing behaviour varying, apart from the expenditure level, the share of overall consumption devoted to each category of goods and services? That is, to what extent are household purchasing decisions concerning the share of overall consumption devoted to each category of goods and services consistent with the economic theories on the inter-temporal allocation of resources developed by Modigliani and Brumberg (1954) and by Friedman (1957)? With this objective in mind, it will be highlighted if and how much the composition of Italian household expenditures according to the COICOP divisions changed in the recession phase (2001-2004) with respect to that of expansion (1997-2000), applying, to the data from Italian Household Expenditure Surveys, the Correspondence Analysis for three-way tables (Escofier and Drouet, 1983).

The fundamental problem with the classical coefficient of kurtosis β2 is that it is not clear what it exactly measures. We here investigate whether β2 has a simple interpretation according to Zenga’s kurtosis diagram. Our answer is negative, even in the symmetric case. We therefore suggest an alternative standardization of the fourth moment which is easily interpreted as a kurtosis parameter for general distributions.

This paper proposes, for ordinal variables, an index of asymmetry based on the cumulative and retrocumulative frequencies. The paper shows that this new index has a connection with the bipolar mean, recently introduced by Maffenini and Zenga (2006). An application to a real case is presented to show how the asymmetry index works.