STATISTICA & APPLICAZIONI - 2007 - 2

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).

In the applied econometrics, the availability of ultra high-frequency databases is having an important impact on the research market microstructure theory. The ultra high-frequency databases contain detailed reports of all the financial market activity information which is available. However, ultra high-frequency databases cannot be directly used. On one hand recording mistakes can be present, on the other hand missing information has to be inferred from the available data. In this paper, we propose a simple method in order to clean up the ultra high-frequency data from possible errors and we examine the method efficacy when we analyze data by using an autoregressive conditional duration (ACD) model.

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.

In the present paper some properties of the arithmetic mean have been employed to determine the parameters of the least squares line, plane and hyper plane, without using partial derivatives and solving the equations of the normal system. It is in fact known that when the criterion of least squares is used to identify an interpolating function, the solution to the problem is obtained via the search for the minimum of a function; therefore the use of partial derivatives becomes inevitable. Instead, the method here suggested allows the interpolating model - which is common to many economic and social subjects - to be presented to university students including those without any knowledge of partial derivatives.