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SALVATORE RENATO - Ricercatore

English version

Afferente a: Dipartimento: Economia e Giurisprudenza

Settore Scientifico Disciplinare: SECS-S/03

Orari di ricevimento: Analisi di Mercato: Nel periodo di chiusura delle sedi universitarie a causa dell'emergenza covid-19, il ricevimento studenti è concordato con il docente. Verrà fissato un appuntamento con gli studenti, seguendo le procedure di connessione remota mediante Google Meet utilizzate anche per le lezioni online. Market analysis: During the time of emergency due to the covid-19, the student reception is scheduled by appointment. The reception will be agreed, following the usual protocol of the lectures (Google Meet).

Recapiti:
E-Mail: rsalvatore@unicas.it

  • Insegnamento Analisi di mercato (91792)

    Primo anno di MANAGEMENT (LM-77), Economia e Diritto per le Professioni
    Crediti Formativi Universitari (CFU): 9,00

    Programma:
    Prima parte: ANALISI DEI DATI DI MERCATO

    Parte introduttiva: le indagini di mercato, i consumi e i comportamenti di acquisto, i questionari e i metodi di rilevazione. L’analisi statistica della domanda. L’impiego dei modelli statistici per l’analisi dei comportamenti di acquisto. La segmentazione del mercato e la scelta del mercato-obiettivo.

    Metodi statistici: richiami di statistica inferenziale: nozioni di base sul campionamento statistico, sulla stima, sulla verifica di ipotesi. Richiami di algebra lineare. Matrici di dati. L’impiego dei modelli lineari per l’analisi della domanda: regressione lineare multipla, regressione multivariata. Modelli non-lineari. Metodi multivariati: analisi in componenti principali, biplots, analisi delle corrispondenze. Segmentazione del mercato: cluster analysis, segmentazione binaria e multipla, alberi di classificazione e regressione. Analisi della varianza (Anova, Ancova, Manova, Mancova). Modelli lineari ad effetti misti: modelli ad effetti fissi, modelli a componenti di varianza, modelli ad effetti casuali, modelli multilevel. Modelli lineari per l’analisi statistica spaziale. Diagnostica dei modelli lineari.

    Applicazioni in laboratorio


    Seconda parte: RILEVAZIONI CAMPIONARIE
    Il disegno di campionamento: popolazione, campione, parametri e stimatori. Errori campionari e non campionari. Spazio campionario e probabilità di inclusione. I principali piani di campionamento: casuale semplice, casuale stratificato, cluster sampling, a due stadi, sistematico, con probabilità variabili. Stima del totale e della media. Stimatori diretti, per quoziente, per regressione. Stima dei parametri nei domini di studio. Dimensione del campione a allocazione delle unità. Piani di campionamento complessi. Dimensionamento delle indagini multiscopo.
    Campionamento stratificato e metodi di allocazione: allocazione proporzionale, allocazione ottima univariata (Neyman), allocazione ottima multivariata (Bethel).
    Stima mediante l’utilizzo di variabili ausiliarie: stimatori GREG. La stima nei mini-domini: stimatori diretti, combinati, indiretti, sintetici, sintetico-regressivi. Stima basata su modelli lineari ad effetti misti. Stima basata su predittori lineari. Stimatori a livello area basati sul modello di Fay-Herriot. Errore quadratico medio predetto nella classe dei predittori lineari.

    Applicazioni in laboratorio

    Testi:
    Testi di riferimento

    a) S. Brasini S., Freo M., Tassinari F.. Tassinari G., Marketing e pubblicità, Il Mulino,Bologna, 2010.
    b) T. Cleff, Applied Statistics and Multivariate Data Analysis for Business and Economics, Springer, 2019
    c) Sarndal C.E., Swensson B., Wretman J., Model Assisted Survey Sampling, Springer, ed. 2003
    d) Rao J.N.K., Molina I., Small Area Estimation, Wiley, 2015

    Valutazione:
    L'esame di fine corso prevede una parte di analisi dei dati, una prova scritta ed una prova orale

  • Insegnamento Analisi di mercato (91792)

    Primo anno di MANAGEMENT (LM-77), Scienze Manageriali
    Crediti Formativi Universitari (CFU): 9,00

    Programma:
    Prima parte: ANALISI DEI DATI DI MERCATO

    Parte introduttiva: le indagini di mercato, i consumi e i comportamenti di acquisto, i questionari e i metodi di rilevazione. L’analisi statistica della domanda. L’impiego dei modelli statistici per l’analisi dei comportamenti di acquisto. La segmentazione del mercato e la scelta del mercato-obiettivo.

    Metodi statistici: richiami di statistica inferenziale: nozioni di base sul campionamento statistico, sulla stima, sulla verifica di ipotesi. Richiami di algebra lineare. Matrici di dati. L’impiego dei modelli lineari per l’analisi della domanda: regressione lineare multipla, regressione multivariata. Modelli non-lineari. Metodi multivariati: analisi in componenti principali, biplots, analisi delle corrispondenze. Segmentazione del mercato: cluster analysis, segmentazione binaria e multipla, alberi di classificazione e regressione. Analisi della varianza (Anova, Ancova, Manova, Mancova). Modelli lineari ad effetti misti: modelli ad effetti fissi, modelli a componenti di varianza, modelli ad effetti casuali, modelli multilevel. Modelli lineari per l’analisi statistica spaziale. Diagnostica dei modelli lineari.

    Applicazioni in laboratorio


    Seconda parte: RILEVAZIONI CAMPIONARIE
    Il disegno di campionamento: popolazione, campione, parametri e stimatori. Errori campionari e non campionari. Spazio campionario e probabilità di inclusione. I principali piani di campionamento: casuale semplice, casuale stratificato, cluster sampling, a due stadi, sistematico, con probabilità variabili. Stima del totale e della media. Stimatori diretti, per quoziente, per regressione. Stima dei parametri nei domini di studio. Dimensione del campione a allocazione delle unità. Piani di campionamento complessi. Dimensionamento delle indagini multiscopo.
    Campionamento stratificato e metodi di allocazione: allocazione proporzionale, allocazione ottima univariata (Neyman), allocazione ottima multivariata (Bethel).
    Stima mediante l’utilizzo di variabili ausiliarie: stimatori GREG. La stima nei mini-domini: stimatori diretti, combinati, indiretti, sintetici, sintetico-regressivi. Stima basata su modelli lineari ad effetti misti. Stima basata su predittori lineari. Stimatori a livello area basati sul modello di Fay-Herriot. Errore quadratico medio predetto nella classe dei predittori lineari.

    Applicazioni in laboratorio

    Testi:
    Testi di riferimento

    a) S. Brasini S., Freo M., Tassinari F.. Tassinari G., Marketing e pubblicità, Il Mulino,Bologna, 2010.
    b) T. Cleff, Applied Statistics and Multivariate Data Analysis for Business and Economics, Springer, 2019
    c) Sarndal C.E., Swensson B., Wretman J., Model Assisted Survey Sampling, Springer, ed. 2003
    d) Rao J.N.K., Molina I., Small Area Estimation, Wiley, 2015

    Valutazione:
    L'esame di fine corso prevede una parte di analisi dei dati, una prova scritta ed una prova orale

  • Insegnamento Market analysis (91995)

    Terzo anno di Economia e commercio (L-33), Economics and business
    Crediti Formativi Universitari (CFU): 6,00

    Programma:
    The course joins together statistical theory and practice by exploring market surveys data. The focus is on the assessment of the consumers behavior and the market segmentation. An introductory part is devoted to draw up the market survey, by working on the questionnaire and the design of the data collection. Subsequently, the analysis of the data will be performed with statistical methods. Linear regression, analysis of variance, non-linear and explorative multivariate methods will be used in order to figure out the consumers attitudes. Some main applications will be held in the computer lab.

    Il corso è basato sull’acquisizione teorica e pratica dei metodi statistici per l’analisi dei dati di mercato. In particolare l’attenzione è rivolta al comportamento del consumatore e alla segmentazione di mercato. La parte introduttiva del corso si concentra sulla preparazione dell’indagine di mercato, sulla messa a punto del questionario e del disegno di campionamento. Per esaminare in modo più approfondito le preferenze e le scelte del consumatore, l’analisi dei dati provenienti dall’indagine viene condotta con metodi statistici quali la regressione lineare, l’analisi della varianza, i modelli non lineari e le tecniche esplorative multivariate. Il corso prevede delle esercitazioni sui diversi metodi di analisi dei dati in laboratorio informatico.

    Testi:
    Reference book - Testo di riferimento

    T. Cleff, Applied Statistics and Multivariate Data Analysis for Business and Economics, Springer, 2019

    Valutazione:
    At the end of the course, it is mandatory to prepare an homework based on a data analysis. The exam consists of a written and an oral examination.

    L'esame di fine corso prevede una parte di analisi dei dati, una prova scritta ed una prova orale

Prenotazione appello

E' possibile prenotarsi ad un appello d'esame, collegandosi al portale studenti.

Elenco appelli d'esame disponibili

  • Denominazione insegnamento: 91995 Market analysis - Economia e commercio - (2019/2020)
    Data e ora appello: 26/06/2020, ore 11:00
    Luogo: Exam in telematic mode through Google Meet: meet.google.com/wwq-mnnp-jgr
    Tipo prova: prova scritta
    Prenotabile: dal 05/05/2020 al 19/06/2020 (prenota l'appello)
  • Denominazione insegnamento: 10695 ANALISI DI MERCATO - ECONOMIA, MANAGEMENT E FINANZA D'IMPRESA 10695 ANALISI DI MERCATO - ECONOMIA E DIRITTO D'IMPRESA 10695 ANALISI DI MERCATO - Economia 90376 ANALISI DI MERCATO - Management 90376 ANALISI DI MERCATO - ECONOMIA E DIRITTO D'IMPRESA 90376 ANALISI DI MERCATO - MANAGEMENT 90376 ANALISI DI MERCATO NESSUNA CANALIZZAZIONE - ECONOMIA E DIRITTO D'IMPRESA 91792 Analisi di mercato - ECONOMIA E DIRITTO D'IMPRESA - Via Sant'Angelo Campus Folcara 03043 90552 Analisi di Mercato - Manifesto per Carriera speciale - corsi singoli e crediti extracurriculari 91792 Analisi di mercato - MANAGEMENT 91268 Statistica Economica - Manifesto per Carriera speciale - corsi singoli e crediti extracurriculari 91792 Analisi di mercato - ECONOMIA E DIRITTO D'IMPRESA CASSINO - Via Sant'Angelo Campus Folcara 03043 92944 Statistica economica - Manifesto per Carriera speciale - corsi singoli e crediti extracurriculari - (2019/2020)
    Data e ora appello: 01/07/2020, ore 09:00
    Luogo: Esame scritto in modalità telematica tramite Google Meet: meet.google.com/miv-bfnt-anr
    Tipo prova: prova scritta
    Prenotabile: dal 07/01/2020 al 01/06/2020 (prenota l'appello)

Notizie generali

• Ricercatore universitario nel S.S.D. SECS-S/03 Statistica economica, in servizio presso il Dipartimento di Economia e Giurisprudenza dell’Università degli Studi di Cassino e del Lazio meridionale dal 01.10.2002
• E’ membro dell'International Association of Survey Statisticians (ISI-IASS)
• E’ socio ordinario della Società Italiana di Statistica
• E’ membro dell’European Working Group on Small Area Estimation

• E’ referee delle riviste "Journal of Statistical Computation and Simulation" (Taylor and Francis), "Statistical Methods and Applications" (Springer), "Agricultural and Food Economics" (Springer)
• A partire dall'a.a. 2006/2007 e fino all’a.a. 2009/2010 è stato coordinatore del Dottorato di Ricerca in Metodi Quantitativi per l’Economia e il Territorio dell’Università degli Studi di Cassino
• E’ stato presidente del Comitato Organizzatore del Convegno "L'Informazione Statistica e le Politiche Agricole" (ISPA 2004)”, Cassino, 2004
• E’ stato presidente del Comitato Organizzatore del Convegno "Le statistiche agricole verso il Censimento del 2010: valutazioni e prospettive", Cassino, 2006


Attività didattica

• E’ docente di Analisi di mercato presso l’Università degli Studi di Cassino e del Lazio Meridionale dall’a.a. 2004/2005.
• E’ stato docente di Statistica aziendale presso l’Università degli Studi di Cassino e del Lazio meridionale dall’a.a. 2004/2005 all'a.a. 2012/2013.
• E’ stato docente di Statistica economica presso l’Università degli Studi di Cassino dall’a.a. 2003/2004 all’a.a. 2007/2008.
• E’ stato docente di Rilevazioni campionarie presso il Dottorato di Ricerca in Metodi Quantitativi per l’Economia e il Territorio dell’Università degli Studi di Cassino e del Lazio Meridionale dall’a.a. 2005/2006 all'a.a. 2009/2010
• E’ stato docente di Analisi multivariata applicata presso il Dottorato di Ricerca in Istituzioni e Metodi di Analisi dei Sistemi Territoriali dell’Università degli Studi di Cassino e del Lazio Meridionale.
• E’ stato docente di Analisi multivariata presso il Dottorato di Ricerca in Economia Agraria dell’Università “Parthenope” di Napoli dal 2000 al 2003.
• E’ stato docente di Strumenti Quantitativi 3 presso il Master in Economia e Finanza della Piccola e Media Impresa dell’Università degli Studi di Cassino e del Lazio Meridionale (a.a. 2005/2006).


Attività di supporto nel Dipartimento di appartenenza:

• relatore di Tesi di Laurea e di Dottorato
• Attività di orientamento
• componente di Commissione Orari, Commissione Statuto e Commissione Didattica dal 2003 al 2007

Attività di ricerca

• Interessi di ricerca: modelli utilizzati nell’ambito del campionamento statistico, analisi statistica multivariata per le applicazioni in campo economico.
• E’ attualmente coordinatore scientifico della Ricerca “Analisi dei dati del VI Censimento Generale dell’Agricoltura della Campania”, accordo di ricerca stipulato tra la Regione Campania e l’Università degli Studi di Cassino e del Lazio meridionale.
• E’ stato coordinatore scientifico della ricerca “Analisi della realtà agricola della Regione Lazio”, ricerca stipulata in convenzione con l’Arsial (Regione Lazio).
• Ha partecipato a diversi Progetti di Ricerca di Interesse Nazionale cofinanziati dal Ministero dell’Università e della Ricerca (PRIN 2003, PRIN 2005 e PRIN 2007), aventi come oggetto metodologie e applicazioni di metodi e modelli per le indagini campionarie in campo economico.

Progetti di ricerca in partecipazione:

a) Partecipazione (in qualità di coordinatore) nell’Accordo di Ricerca “Analisi dei dati del VI Censimento Generale dell’Agricoltura della Campania”, stipulato tra la Regione Campania e l’Università degli Studi di Cassino e del Lazio meridionale (2012).

b) Partecipazione (in qualità di coordinatore) nella Convenzione di Ricerca “Analisi della realtà agricola della Regione Lazio”, ricerca stipulata in convenzione con l’Arsial (Regione Lazio) (2008).

c) Partecipazione al progetto “Il riposizionamento funzionale dell’agricoltura e il rinnovato ruolo dei servizi di sviluppo agricolo”, coordinata dal prof. De Rosa dell’Univ. Di Cassino. I compiti sono relativi all’effettuazione del piano di campionamento delle aziende italiane (2011-2012).

d) Partecipazione al progetto PRIN 2007, finanziato dal MIUR, dal titolo “L’utilizzo delle informazioni ausiliarie nelle indagini campionarie complesse: la produzione di statistiche in tema di sviluppo economico delle aree rurali ” (progetto presentato con le Università di Firenze, Perugia, Pisa, Trieste, e l’ISTAT)

e) Partecipazione al progetto PRIN 2005, finanziato dal MIUR, dal titolo “L'universo di riferimento per il sistema delle statistiche agricole: criteri di definizione e organizzazione della rilevazione delle aziende agricole ” (progetto presentato con le Università di Firenze, Perugia, Pisa, Trieste, e l’ISTAT)

f) Partecipazione al progetto PRIN 2003, finanziato dal MIUR, dal titolo “Le statistiche agro-ambientali fra economia globale e sviluppo rurale” (progetto presentato con le Università di Firenze, Pisa, Trieste, e l’ISTAT)

Diagnostics and influence analysis for small area models
Salvatore R. (Univ. Cassino), Morales D. (Univ. Elche, Spain), Pagliarella M.C. (Univ. Siena)

Small area estimation is generally recognized as the pool of methodologies designed for indirect estimation of the population parameters in small domains. Data collected form some well-organized sample surveys, can be effectively utilized to derive direct estimates for large areas, such as administrative districts or regions in national territories. Sample sizes in the small domains of interest are typically reduced by the survey design itself, if the objective is to provide accurate estimates at higher level of aggregation than that of small areas. In any case, direct estimates in specific areas are not reliable, because the smallness of sample sizes in that areas can drive to unacceptably large standard errors (Rao, 2003). The small area estimation methods deal with a “model-based” estimation strategy, and the kind of models that are mainly utilized in literature are those from the linear and generalized linear mixed effects models theory (Demidenko, 2004). If some important question in the applications are connected with the selection of covariates, and the estimation of the mean squared error of the estimates after the model fitting, some methodologically relevant aspects can be find when we try to assess the impact that some data or clusters have on the model estimation itself (Demidenko and Stukel, 2005). As we know, potential outliers, or data with high-leverage values, can influence dramatically the model parameters estimates, and in that way they can affect the global performance of the model, in terms of the survey population parameters estimates (Battese et al., 1988). Some important features of the small area models are connected with the evaluation on the data structure, concerning: a) their impact on the estimation of fixed and random effects, and on the covariance parameters estimates, and b), on the estimation of predicted values by the model, namely the survey parameters estimates, and finally on the estimation of the mean squared error of the area estimates (MSE, Prasad and Rao, 1990). The evaluation of the influence on covariance parameters estimates is also a relevant question, because their estimates can specify correctly their own weight on the regression-synthetic estimation component in the small area model-based estimators (Rao, 2003). The general evaluation of the measures of statistical influence on small area estimates, together with the small area model diagnostics, represent the main topics of our research. The methodological starting point will be the specification, the deepening and the assessment of the usefulness of diagnostic methods in the context of the linear and generalized linear mixed effects models theory.
The researchers intend to deepen some aspects related to the model diagnostics and influence analysis in linear and generalized linear mixed models, like the area-level and unit-level models, also for multivariate small area estimation and following the two-level approach in defining the model covariates. These research methods will be dedicated initially to the definition of the leverage matrix in the context of the Fay-Herriot model and the unit-level models, when we estimate the covariance parameters with the residual maximum likelihood method or the methods of moments. In fact, the last estimation methods, were the first of them requires the normality of the distribution of the errors and of the random effects, while the second is a distribution-free quadratic estimation method, are the more efficient (Demidenko, 2004) in estimating the model covariance parameters. Particular attention will be dedicated to the computing of the leverage effects of the observed data, that in the case of the area-level models are represented by area direct estimates. In the estimation of the fixed effects in linear mixed models, the general least squares estimator is function of the model covariance matrix, that is function itself of the covariance matrix of the random-area effects.
The linear and nonlinear mixed models utilized in the model-based approach to the indirect estimation in the small domains of interest, have some different features respect to the traditional linear and generalized linear mixed models. For example, in the Fay-Herriot area-level model, a balanced model that considers only one observation unit at each area, one of the two covariance parameters it is assumed equal to the estimate delivered by the direct estimator in the small domain of reference, varying form area to area. Further it is fundamental to test the fitting of the model in analyzing the influence of the observations, the domains, and of the model characteristics respect to some model parameters and small area statistics based on those parameters. The last, in fact, can drive to the effective estimation of the population survey parameters for the small domains themselves. In the context of the linear (mixed) models-based small area estimation, the component of the Eblup estimate of the survey parameter (the total or the mean), that is due to the indirect estimation, depends on the efficiency of the local areas direct (the design) estimates (in the area-level models), while in the context of the unit-level model estimation depends on the contribution of the “model-assisted” survey regression estimator component. When the direct survey estimators have relevant sampling variances, as well as when the estimated intra-cluster variance(s) is the prevalent part of the model variance (respect to the estimation of the variance of the random-area effects), the Eblup estimator attaches more weight on its regression-synthetic component.
For these reasons, the ratio (weight) based on these estimated variance components in the area-level and unit-level models, will represent a fundamental target of the present research. Further, this weight, attached on the model-based indirect component of the Eblup estimator, together with the estimation of the conditional expectation of the fixed effects estimates, is able to specify the amount of the bias of the Eblup regression estimator. This will be another specific feature in the model influence and diagnostics analysis in small area estimation addressed by the research. Another crucial aspect in the context of small area statistics, is connected with the so-called benchmarking property. This property is satisfied by the Eblup area-level model estimator, and refers to the design-consistency of the estimates delivered by the unit-level models. As we know, in the standard unit-level model-based estimation, the data are considered without specifying their survey sampling weights. When we deal with small domains of relevant sampling size, the question of the design-consistency draws attention. In lack of the benchmarking property, the estimates of the population parameters at higher level in the planned survey domains, delivered by the direct estimator, can differ substantially from the result of the aggregation by the areas of the small area model estimates. In the unit-level models, design-consistent estimators can be defined through the so-called pseudo-Eblup estimators. Starting from the weighting of the model at the unit level by the design sampling weights, the first step is on the estimation of the variance components of the weighted unit-level model. Then, the solution of the design-weighted estimating equations, respect to the model fixed effects estimates, leads to the desired property. So, the influence analysis gathered by the observation data on the variance components estimates, and on the composite effect due to the interaction of the design weights among areas and the fixed effects estimates, can be considered as a methodologically relevant question. In fact, the influence of the single observed units in the specification of the model parameters estimates, that lead to the pseudo-Eblup estimates, can be dramatically different. This because the design sampling weights can have drastic different values in some small domains of interest, i.e. not planned by the survey design.
The estimates obtained from the restricted maximum likelihood and moment methods, will be the starting points for the analysis of the influence on the predicted values, on fixed and random effects (random area effects), and on the estimation of the mean squared error of the empirical estimators (Eblup estimators). In fact, a component of the leverage effect or of the other influence measures, is due to the estimation of the covariance matrix of the random effects, because the observed data (or groups of them) may result influential on the model outcomes through the model parameters estimates considering fixed the model covariance matrix, and also varying from the observed data the covariance parameters estimates itself. Generally speaking, the model diagnostics and the influence analysis on the model parameters consists on the specification of certain matrices that contain influential values, leverages, or simply not well-explained by the estimated model, substituting the model covariance matrix with an empirical estimate of it, obtained also with the above mentioned estimation methods. It is possible that an important part of the influence effect on the model is due to the estimation of that matrix. In practice, it can be useful to know what part of the measures of influence is due to the estimation of the model covariance matrix, respect to the evaluation of the survey estimates, and of other statistics delivered by the models.
Another important part of the research will focus on the influence analysis on the estimation of the survey parameters. One of the crucial aspects of employing the mixed models in context of small area estimation, is the estimation the random effects (random-area effects). Another relevant question is how the observed data or model specifications can affect the estimation of the mean squared error of the Eblup estimators. The research unit will plays an important part of its activity on diagnostics and influence analysis methods for the mean squared error estimation. The influence analysis on the mean squared error of the empirical predictors will concern the impact on its components: the variability due to the direct estimates at area level, the variability due to the regression parameters, and to the estimation of the “empirical” covariance parameters.
When we utilize small area estimation methods with economic and territorial data, the researchers are interested to identify statistical units or territories that can influence the parameters estimates of the mixed model adopted, and also the estimates of the model covariance matrix of that models. Further, it is important the model diagnostics and the influence on the variability of the estimators at territorial level. The research project will focus, by an applicative point of view, on the leverage analysis and the cluster deletion diagnostics in the context of economic and territorial studies. Further, the research work will address the question related to the evaluation of the sensitivity of the model respect to “territorial” perturbations, that can be very useful in the economic analysis of the district of production.
The specification of local areas that are homogenous with respect to the demand for policy is a current research topic and the condition for effective policy planning (Mipaaf, 2009). The recent evolution of the common agricultural policy, changing from market intervention to rural development measures, deeply affected the public demand for information in agriculture (OECD, 2009). The set of relations between farms and the surrounding socio-economic environment becomes a key, yet hardly explored, topic (Banks et al., 2002, Storti, 2000). The wealth of information offered by the official statistics can be used to overcome the limitations of the current mappings. Using farm-level data, it is possible to study the farm sector using a multidimensional matrix at the local level.
The small area models that will be utilized for this study will be the area-level and the unit-level models. In particular, following the two-level approach, the influence analysis will be conducted evaluating units and territorial characteristics at the same time in that models.




Consistency of technical efficiency estimators in linear mixed effects stochastic production frontier models
Salvatore R. (Univ. Cassino)

The influence of external factors on the measure of technical efficiency of firms is a relevant question, because the analysis of that impact on different levels of production has two main features. Firstly, it allows to measure the efficiency rate of the production units that share the same level of the external factors, and, secondly, to recognize relevant factors that affect the efficiency in production itself.
Mixed model stochastic frontier production functions were introduced by Salvatore and Viviani (2009). The model considers firms efficiency by capturing the portion of model variability due to the presence of inefficient firms in the sample data. Measures of firm-specific efficiency rates are delivered by predictions on marginal and conditional residuals. This work highlights consistency of technical efficiency estimates in that model. Different levels of technical efficiency of firms are evaluated by distribution-free quadratic estimators. The model parameters estimates can be attained by an iterative unbiased variance least squares estimation procedure.
The introduction of the stochastic frontier model is due to the simultaneously and independent works by Aigner et al. (1977) and Meeusen and van den Broeck (1977). The models proposed reflect the endeavour of describe the situation in which available data can effectively estimate production functions at smaller level than that attributed to technical inefficiency. In that models, the estimation of production function was made specifying production inputs and two error terms, the first representend by technical inefficiency, the residual by the statistical noise. The stochastic production frontier model consider technical inefficiency independent with inputs and statistical noise, and the estimation of the technical inefficiency component of the global error requires specific assumptions in terms of the inefficiency distribution. Firstly, it is necessary to consider a one-sided distribution, and further it is required to specify its distribution function, such as half-normal, gamma, exponential, truncated-normal. Aigner et al. (1977) underline that the proposed density parametrization of the global error term permits to identify the relative weight of the technical inefficiency variability. Further, the empirical applications reported highlights that technical inefficiency represents the minor part of the total estimated variability. Parameter estimates slightly differ from models that account for the only two-sided noise error term. Meeusen and van den Broeck (1977) came to similar results using exponential distribution for the one-sided inefficiency error term. Further works by Jondrow et al. (1982), Waldman (1984), Greene (2000), also discuss developments in identifying individual technical efficiency estimates in analyzing joint residuals from the stochastic production frontier model. Battese and Coelli (1988) suggest some technical efficiency point estimators, but estimates are not consistent, due to the circumstance that the variability of the conditional distribution of the technical efficiency is independent of the individual observations.
Pitt and Lee (1981), Bauer and Hancock (1993), Simar et al. (1994), Kumbhakar and Lovell (2000), discuss models that account also for exogenous variables as non-neutral firms characteristics, in order to analyze direct influences of external factors in the estimation of the frontier production function. Ali and Flinn (1989) and Kalirayan (1990) proposed two-stage models in which exogenous factors influence production outputs indirectly on the efficiency of the firm production. Berger and Mester (1997) and Wang and Schmidt (2002) employed Monte Carlo simulations in order to highlight underestimation of the influence of parameters related to exogenous factors on the technical efficiency term in the two-stage model. Kumbhakar et al. (1991), Reifschneider and Stevenson (1991), Huang and Liu (1994), Battese and Coelli (1995), underline the relevance of non-neutral firms characteristics in estimating production frontiers, and proposed to estimate jointly technical efficiency and the exogenous variables effects at the same time. Technical efficiency is evaluated through the impact of exogenous model parameters with one-sided error term, as residual part in the inputs production frontier model with a two-sided statistical noise. In particular, Huang and Liu discuss a model that accounts for interactions between external firm-specific factors and production inputs. Caudill and Ford (1993), Caudill et al. (1995), studied influences of external factors on the production frontier function estimation through the heteroscedasticity of the one-sided efficiency term, as function of firm characteristics. The approach is also useful in testing models with constant variance of the technical efficiency. All the previous models deal with a nonnegative error term, and efficiency estimators have all distributions related to the strong distributional assumption of the one-sided technical inefficiency.
Since the stochastic frontier production functions models was intended for cross-sectional data, the recent literature considers data model developments and applications in the context of panel data (Viviani et al., 1999). The recent literature in stochastic frontier models for panel data shows that the assumptions related to the distribution of the technical efficiency is widely relaxed. Pitt and Lee (1981), Schmidt and Sickles (1984), are the first that modeled production function frontiers for panel data without any assumption on the distribution of technical efficiency. Cornwell et al. (1990), Kumbhakar (1990), Battese and Coelli (1992), Lee and Schmidt (1993), proposed models in a similar way, and in addition shows that the time-invariant technical efficiency could be relaxed. Kumbhakar, Battese and Coelli assumed specific distribution for technical efficiency and estimate methods as Maximum Likelihood (ML), whereas Cornwell et al., Lee and Schmidt estimate models through panel data frameworks without distributional assumptions on technical efficiency, starting from incorrelation between inefficiency and inputs. Recently, Lee (2006) proposed a model that allows group-specific patterns of temporal change in technical inefficiency, as a generalization of the model by Lee and Schmidt (1993).
Following the parametric approach to the estimation of production functions and firm's specific technical efficiency, Aigner et al. (1977) show that frontier paramaters are very close with the OLS estimates delivered by the average production function estimation (Nisticò and Viviani, 1987), in which there is the only presence of a measurement error. The parameter estimates are quite different from those of the deterministic frontier approach (Timmer, 1971). The work of Aigner et al. (1977), in the proposed case studies, allow to deduce that the model symmetric error overcomes the one-sided error component due to the technical efficiency. In other words the observed variability beneath the frontier is negligible. In the same way, the work of Meeusen and van den Broeck (1997), in which the one-sided error term follows the exponential distribution, shows the susbstantial equality between the stochastic frontier model parameter estimates and the traditional OLS estimates. In the context of the stochastic frontier approach, the measurement of the individual efficiency respect to the maximum value of production is a crucial point. Some difficulties rise from the problem of the direct observation the efficiency error term, since residuals from the model represent the aggregate measurement of efficiency and error terms. Materov (1981), Jondrow et al. (1982), focused their work on the estimation of the conditional distribution of the efficiency error term, specifying point estimates based on expected values of that conditional distribution. Battese and Coelli (1988) suggest the application of an alternative form of that technical efficiency point estimator. Unfortunately, as mentioned above, the technical efficiency estimates are not consistent (Kumbhakar and Lovell, 2000).
The model discussed in the present research is a rather different attempt to the problem of estimating production frontier functions. Two starting points are stated beforehand: a) the model is designed for including production technology as inputs in terms of continuous variables, and various sources of inefficiency in terms of exogenous categorical variables firms group-specific classification (cross-sectional data), as well as for repeated measurement of firms characteristics over time (panel data); b) the model works without specific distributional assumptions related to technical inefficiency. The purpose of the framework is to exploit all resources from random effects linear mixed models theory (Demidenko, 2004), and, to do this, all model error terms must be symmetric. Random effects models are actually extensively employed in the context of panel data stochastic frontier research (Greene, 2005a, 2005b, Gori et al., 2002, Grassetti et al., 2005), preserving the one-sided technical efficiency nuisance term. The linear mixed effects (LME) model here presented can be used as a kind of framework, on which basis we can derive the population average production function estimate, as well as firms group-specific average production functions. Further, the model explains the presence of inefficiency as a portion of the model variance, based on the covariance matrices of random effects and residual.
If the variability due to specific efficiency parameters in the model is estimated to be negligible or zero, the model reduces to a standard linear mixed effects model with two sources of variation, related to the standard matrix of covariance parameters of random effects and of the measurement errors. This research is planned in different parts: after the description of the model presented and its basic assumptions, we discuss about the measures of global and group-specific inefficiency. After this, an empirical analysis is presented, and, finally, conclusions and future developments are discussed. The application is based on Italian National Statistics Institute Farm Structure Survey's wheat production data, related to the Lazio Administrative Region in Italy.
This study develops a stochastic frontier production model as a framework in analyzing both cross-sectional and panel firms production data. Various sources of inefficiency in terms of exogenous categorical variables in cross-sectional data, as well as repeated measurement of firms characteristics over time can be studied. Starting from the specification of a standard linear mixed effects model with between-groups and subject-specific measurement errors as technology frontier model, we introduce technical inefficiency as extra-variability parameters in the original linear mixed model setup. Technical efficiency parameters explain the portion of variability due to the presence of inefficient firms, through the parts of conditional and marginal model residuals that justify firms position respect to the average population and group-specific production functions.A two-stage parameter estimation is required: a first estimation of covariance matrix parameters of random effects and of residual, and then the further minimization of a model variance least squares objective function due to the technical efficiency parameters. We apply the model in analizyng wheat production in Italy, where groups are identified as some provinces of the Lazio Region.

• Di Pasquale, J., Nannoni, E., Sardi, L., Rubini, G., Salvatore, R., Bartoli, L., Adinolfi, F., and Martelli, G., Towards the Abandonment of Surgical Castration in Pigs: How is Immunocastration Perceived by Italian Consumers?, Animals, 9, 198, 2019
• Bartoli L., Pagliarella M.C., Russo C., Salvatore R., Small Area Estimation in the Presence of Area-Level Correlated Responses, Mathematical Population Studies, 25(1), 20-40, 2018
• Bianchi M., Parisi V., Salvatore R., Female entrepreneurs: motivations and constraints. An Italian regional study, International Journal of Gender and Entrepreneurship, 8, 3, 198 - 220, 2016
• Cappuccio F., Salvatore R., Spatial temporal multivariate small area estimation, Proceedings of the 48th Meeting of the Italian Statistical Society, Salerno, Italy, 2016
• Pagliarella M. C., Salvatore R., Spatio-Temporal Unit Level Models, In: Pratesi M. (Ed.), Analysis of Poverty Data by Small Area Estimation, Wiley, 2016
• Morales D., Pagliarella M. C., Salvatore R., Small Area Estimation of Poverty Indicators under Partitioned Area-Level Time Models, Statistics and Operations Research Transactions, 39(1), 19-34, 2015
• De Rosa M., Adinolfi F., Capitanio F., Salvatore R., Impact of Agricultural Extension Services on Innovation Adoption in Italy, Journal of Extension Systems, 30(2), 71-92, 2014
• R. Salvatore, M.C. Pagliarella, Spatio-temporal time-variyng effects models and state-space models with spatial structure: an assessment of their efficiency in small area estimation, The Small Area Estimation International Conference, Poland, 2014
• D. Morales, M.C. Pagliarella, R. Salvatore, Partitioned area-level time models for estimating poverty indicators, The Small Area Estimation International Conference, Poland, 2014 - relazione invitata
• R. Salvatore, M. C. Pagliarella, Diagnostics and influence analysis in the multivariate Fay-Herriot model, Proceedings of the Third Italian Conference on Survey Methodology (ITACOSM2013), Milan, 2013
• Bartoli L., Bartoli V., Palombo L., Salvatore R. (2013). Le dinamiche demografiche territoriali e le misure dell'invecchiamento in Agricoltura. RIVISTA ITALIANA DI ECONOMIA, DEMOGRAFIA E STATISTICA, vol LXVII –N., ISSN:0035-6832.
• Bartoli L., Bartoli V., Palombo L., Salvatore R. (2013). L'evoluzione di lungo periodo delle eta' "soglia" di vecchiaia e dei conseguenti livelli di invecchiamento demografico in Italia. RIVISTA ITALIANA DI ECONOMIA, DEMOGRAFIA E STATISTICA, vol LXVII –N., ISSN:0035-6832.
• R. Salvatore, M. C. Pagliarella, The diagnostics of the mean squared error of the Eblup in small area estimation models, Proceedings of the 46th Meeting of the Italian Statistical Society, Rome, 2012
• R. Salvatore, D. Morales, M. C. Pagliarella, Some diagnostics and influence analysis tools for small area estimation models, The SAE 2011 Conference on Small Area Estimation, Germany, 2011
• R. Salvatore, C. Russo, M. Sabbatini, A mixed-model frontier approach in efficiency analysis, Survey Research Methods and Applications, Proceedings of the Second Italian Conference on Survey Methodology, Pisa, Italy, 2011
• R. Salvatore, C. Russo, Small area estimation models diagnostics and business decisions, Survey Research Methods and Applications, Proceedings of the Second Italian Conference on Survey Methodology, Pisa, Italy, 2011
• R. Salvatore, Technical efficiency estimators in linear mixed effects stochastic production frontier models, Proceedings of the 45th Meeting of the Italian Statistical Society, Padova, 2010, Cleup – Relazione invitata
• R. Salvatore, L. Bartoli, V. Bartoli, L. Palombo, Un'analisi comparativa delle scelte occupazionali di immigrati ed autoctoni mediante modelli non lineari ad effetti misti, Rivista Italiana di Economia Demografia e Statistica, LXIV, 4, 2010
• R. Salvatore, D. Morales, M.C. Pagliarella, Influence analysis in small area estimation, Proceedings of the 45th Meeting of the Italian Statistical Society, Padova, 2010, Cleup
• R. Salvatore, Piano di campionamento, in: Sabbatini M. (a cura di), Evoluzione e prospettive dell'agricoltura del Lazio - Statistiche ufficiali e informazioni ausiliarie al 2007. p. 143-169, Milano, Franco Angeli, 2009
• R. Salvatore, L. Bartoli, M. C. Pagliarella, L. Palombo, Comparing native versus immigrant occupational choices of Italian labour forces: a generalized linear mixed model approach, Proceedings of the International Conference "Challenge for Analysis of the Economy, the Businesses, and Social Progress", Hungary, 2009
• R. Salvatore, A. Viviani, A mixed model approach to the estimation of stochastic production frontiers, The XI European Workshop on Efficiency and Productivity Analysis, Pisa, Italy, 2009
• R. Salvatore, C. Russo, M. C. Pagliarella, Pseudo-EBLUP estimation in assessing stochastic production frontier models, The ITACOSM 09 Conference in Survey Methodology, Siena, Italy, 2009
• R. Salvatore, C. Russo, M. C. Pagliarella, Selection of covariates in Small Area Estimation with multilevel models. In: Wywial J. L., Zadlo T., Survey Sampling in Economic and Social Research. p. 76-87, The University of Economics in Katowice Publisher, Poland, 2009
• D. Cimillo, M. C. Pagliarella, R. Salvatore, Two-level model small domain estimation using reduction of dimensionality, Proceedings of the 7th International Conference on Social Science Methodology, 2008
• R. Salvatore, C. Russo, Data reduction in small area estimation, Proceedings of the XLIV Scientific Meeting of the Italian Statistics Society, 2008
• C. Russo, R. Salvatore, Censuses and rural development: analysis of connections between farms and territory, Proceedings of the Conference ”The Agricultural Statistics towards the 2010 Census: assessments and prospects”, ISTAT, 2008 – Relazione invitata
• M. Pratesi, N. Salvati, R. Salvatore, Multivariate methods in small area estimation: an assessment of potential applications in agriculture, Proceedings of the Conference ”The Agricultural Statistics towards the 2010 Census: assessments and prospects”, The Italian National Statistical Institute publisher - ISTAT, 2008
• C. Russo, R. Salvatore, Clustered data in small area estimation: an analysis of rural local economies, The IASS Satellite Conference on Small Area Estimation, Pisa, 2007
• C. Russo, R. Salvatore, Effetti dell'adozione di soglie dimensionali sulla rappresentazione dei fenomeni socio-economici, Workshop intermedio PRIN 2005 "L'informazione statistica in Agricoltura", Trieste, 2007
• C. Russo, R. Salvatore, Optimal design for area crop insurance: a model-based area estimation approach, Atti della Riunione Intermedia della Società Italiana di Statistica "Rischio e Previsione", Venezia, 2007, 73-82 – Relazione invitata
• R. Salvatore, Metodi di ottimizzazione per la valutazione della multifunzionalità delle aziende agricole, Atti del Convegno "Verso un nuovo sistema di statistiche agricole" (AGRISTAT), Firenze, 2006, 331-342
• Grassi, R. Salvatore, Multivariate statistical indicators in assessing farms multifunctionality, Atti del Convegno "Metodi d'Indagine e di Analisi per le Politiche Agricole" (MIAPA), Pisa, 2005, 123-135
• R. Salvatore, Modelli di allocazione multivariata per le indagini sulle aziende agricole, Atti del Convegno "L'Informazione Statistica e le Politiche Agricole" (ISPA 2004), Cassino, 2004, 373-385
• C. Russo, M. Sabbatini, R. Salvatore, General linear models in small area estimation: an assessment in agricultural surveys, The Third International Conference on Agricultural Statistics (MEXSAI), Mexico, 2004
• R. Salvatore, The use of Correspondence Analysis for stratification, Proceedings of the Sixth International Conference on Social Science Methodology "Recent Developments and Applications in Social Research Methodology", The Netherlands, 2004
• R. Salvatore, C. Russo, The environmental impact of Italian farming activities: testing group membership in surveys through multidimensional data analysis, The International Conference on Correspondence Analysis and Related Methods (CARME 2003), Spain, 2003
• R. Salvatore, C. Russo, Collecting agri-environmental data in farm structure sample surveys: a multivariate allocation model, The Sixth Conference on Statistics in Public Resources and Utilities, and in Care of the Environment (SPRUCE VI), Sweden, 2003 (www.maths.lth.se/conferences/spruceVI)
• G. Innocenzi, R. Salvatore, The implementation of the DPSIR model in the italian agri-environmental statistic system: methodology issues rising from the 1998 FSS experience, Proceedings of the EUROSTAT International Conference on the Agricultural Statistics in the new Millennium (ARIADNE 2002), Greece, 2003, 81-100
• L. Bartoli, N. Gargano, M. Sabbatini, R. Salvatore, L’offerta informativa nella definizione delle politiche agrarie, in “Verso i Censimenti del 2000”, Atti del Convegno della Società Italiana di Statistica (SIS ’99), Udine, 2000, Vol. I, 137-166 – Relazione invitata
• M. Ballin, R. Benedetti, R. Salvatore, La stratificazione nelle indagini Istat: metodologie a confronto, Collana ISTAT – Argomenti, n. 16, Istituto Nazionale di Statistica, 1999, 275-292
• R. Salvatore, Su un test distribution-free per piccoli campioni, Working Paper del Dipartimento Economia e Territorio dell’Università degli Studi di Cassino, Serie Statistica Metodologica ed applicativa, n. 3, 1999
• R. Salvatore, Funzioni caratteristiche di variabili aleatorie su uno spazio di Hilbert, Working Paper del Dipartimento Economia e Territorio dell’Università degli Studi di Cassino, serie Matematica e Informatica, n. 2, 1999


Curatele:
• A. Viviani, M. Sabbatini, R. Salvatore, Atti del Convegno "L'Informazione Statistica e le Politiche Agricole" (ISPA 2004), Cassino, 2005
• A. Mancini, M. Sabbatini, R, Salvatore, Atti del Convegno "Le statistiche agricole verso il Censimento del 2010: valutazioni e prospettive", ISTAT, 2008

[Ultima modifica: mercoledì 30 novembre 2016]