by Aride Mazzali
A mother formula for econometric estimation, the issue of parent linear models of best-fit solutions and its dual problem
by Maria Grazia Zoia
The body of econometric estimation theory in linear models must necessarily hinge, as a frame of reference, on Rao’s unified theories of linear estimation and least squares. The mathematical counterpart of the basic statistical setups turns out to be quadratic optimization problems, whose solutions yield the optimal estimators. These solutions rest on the inversion of the fundamental bordered matrix of the first-order conditions for optimality. A recently devised partitioned inversion rule leads to a mother formula for estimators within a linear framework. In addition, this paper casts further light on the link between the best fit approach to estimation and model specifications. Indeed, by
taking least squares as a bridge-head and best unbiasedness as a benchmark, quite a deep insight into parameter inference is gained, whose applicative spin-offs are brought to light by a wide-ranging reappraisal of statistic and econometric estimators.
Keywords: Least squares, Econometric models, Best unbiasedness, Orthogonal complements,Inversion rules.
L’econometria metodologica ha nelle teorie unificate della stima lineare e dei minimi quadrati di
Rao i suoi riscontri naturali. Ai sensi di tali teorie, il problema di stima si riconduce ad un problema
di ottimizzazione matematica che trova nell’inversione della cosiddetta ‘‘matrice orlata fondamentale’’
la chiave per la sua soluzione. Una recente formula di inversione per parti consente di
pervenire ad una formula madre per la classe degli stimatori ottimali nei modelli lineari. Da questa
analisi emergono altresı`interessanti collegamenti col problema del modello di riferimento, per un
dato metodo di stima di accostamento ottimale, e dualmente col problema dei minimi quadrati che
conduce allo stimatore ottimale per una data specificazione lineare. L’articolo fornisce un contributo
chiarificatore, con apporti innovativi, a questi temi di preminente interesse per l’econometria
nelle sue interazioni con la statistica.
Moving extreme ranked set sampling for simple linear regression
by N.A. Al-Odat, T.T. Alodat, Mohd T. Alodat, M. Al-Rawwash
The moving extreme ranked set sampling, introduced by Alodat and Al-Saleh (2001), is a modification of the well known ranked set sampling approach that was proposed by McIntyre (1952). In this paper, we suggest new estimators for the simple linear regression parameters under the moving extreme ranked set sampling scheme. Moreover, we show that the proposed estimators are more efficient than their counterparts using the simple random sampling approach. We illustrate our ideas
and thoughts via simulation and data analysis and conduct a comparison between our approach and the traditional ones.
Keywords: Moving ranked set sampling, Ranked set sampling, Simple linear regression.
A fuzzy clustering approach to improve the accuracy of Italian student data. An experimental procedure to correct the impact of outliers on assessment test scores
by Claudio Quintano, Rosalia Castellano, Sergio Longobardi
The aim of this paper is to introduce a new approach to outlier analysis in which the detection is carried out on data with a hierarchical structure and a complex pattern of variability, e.g. pupils in classes, employees in firms, etc. In particular, we analyze the data collected by the Italian National Evaluation Institute of the Ministry of Education (INVALSI) in which the micro units - students- are nested within classes and schools, with a strong presence of outliers at the second level -class- of hierarchy. By the analysis of within class variability, we have developed a procedure to detect outlier
units at class level combining the factorial analysis with a fuzzy clustering approach. The purpose of this method is to go over the dichotomous logic which classifies each unit as outlier or not outlier (hard clustering), computing an ‘‘outlier level’’ measure for each unit and in such a way calibrating the correction of overstimation of children ability due to the outlier presence.
Keywords: outlier correction, data accuracy, assessment test scores.
Statistical analysis of the internationalisation of Italian small and medium sized enterprises
by Luciana Dalla Valle, Giovanna Nicolini
When the choice of one firm’s internationalisation regards the establishment of a subsidiary in a foreign country, then internationalization is a very complex process involving many variables. Some of them regard the features of the foreign countries in which Italian Small and Medium sized Enterprises (SMEs) formerly established subsidiaries; others regard the consequences of SMEs internationalisation
through their economic performance. Through the joint analysis of two variable sets
(about countries and firms) and through the statistical method (the Bayesian hierarchical mixed logit model) we are going to implement, we will be able to describe both the most significant characteristics of the firms that opened subsidiaries abroad and the characteristics of the country where the opening took place. The analysis concerns about 400 firms that started an internationalisation process before 2004.
Keywords: Internationalisation, Bayesian hierarchical models, Markov Chain Monte Carlo, Bayesian mixed logit model.
Italian household debt over the business cycle (1998-2004)
by Isabella Santini
This paper aims to analyse the socio-economic profile of indebted Italian households and possible changes of such profile occurred in the recession period (2001-2004) with respect to that of expansion (1998 – 2000). In order to pursue this aim, Multiple Correspondence Analysis (MCA) has been applied to the Burt matrix obtained by merging the 1998 and 2000 Surveys on Household Income and Wealth (SHIW) of the Bank of Italy, that is the expansion phase surveys, and setting as supplementary
individuals the rows of the Burt matrix obtained by merging the 2002 and 2004 surveys
(SHIW) of the Bank of Italy, that is the recession phase surveys. Through this double merging, it has been possible to analyse jointly the surveys conducted in two different but homogeneous years as far as macroeconomic trends are concerned. The analysis of the above mentioned data has highlighted that, on the whole, the socio-economic profile of indebted Italian households has undergone, in the recession period with respect to that of expansion, noteworthy changes, partly due to the gradual transformation of instruments used in the payment of instalments on more favourable terms and partly due to the high uncertainty with regard to the general economic perspectives which characterize the recession period.
Keywords: household debt, purchasing behaviour, business cycle, multiple correspondence analysis.
Redistribution and equity of polish personal income tax: measurement using micro data from tax returns
by Marek Kosny, Edyta Mazurek
The redistribution effect of taxation is widely analyzed in literature. General findings could be summarized as follows: actual redistribution depends both on construction of tax schedule and unintended effects, such as reranking of incomes, caused by taxation. To separate both components, several decompositions of redistribution index have been described. In this paper, authors analyze decomposition proposed by Kakwani and Lambert (1998), who describe three principles of tax equity and three related measures of inequity. Authors apply outcomes of this decomposition in quest for the equivalence scale that implicitly results from the construction of tax system. Taking into account
decomposition outcomes and the implicit equivalence scale found, we try to assess inequity of Polish income tax system in the context of its welfare consequences. All analyses are made basing on data from revenue offices and Central Statistical Office.
Keywords: decomposition of redistribution index, welfare, taxation.
Bayesian analysis of change point problem in autoregressive model: a mixture model approach
by P. Arumugam, D. Venkatesan, M. Vijayakumar, M. Gallo
This paper is a generalization of earlier studies by Venkatesan and Arumugam (2007) who considered the changes in the parameters of an autoregressive (AR) time series model in order to make Bayesian inference for the shift points and other parameters of a changing AR model. In this paper, the problem of gradual changes in the parameters of an AR model of pth order, through Bayesian mixture approach is considered. This model incorporates the beginning and end points of the interval of switch. Further, the Bayes estimates of the parameters are illustrated with the data generated from known model.
Keywords: Autoregressive model, Bayesian estimation, Structural change, Mixture model, Numerical integration.