UFJF - Universidade Federal de Juiz de Fora

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D.S. in Statistics and Decision Suport (2000): Department of Eletrical Engineering/PUC-Rio (RJ/Brazil)

M.S. in Economics (1989): Department of Economics/PUC-Rio (RJ/Brazil)

B.S. in Economics (1984): Faculty of Economics and Management/UFRJ (RJ/Brazil)

Professor (1993 …): Federal University of Juiz de Fora/Faculty of Economics (MG/Brazil).



Lattes (Portuguese version)


Research Interests

My research interests at the moment lie on econometric time series and its application to energy and technological unemployment forecasts. Whenever possible, I try to integrate different methodological approaches in the development of forecasting tools to enhance policy analysis, policy design, and  decision support.



Papers are available in the portable document file format (.PDF). You can best view them using the latest version of Adobe Acrobat Reader.


Um modelo para análise de impactos da integração interna de mercados regionais de eletricidade no Brasil (2016). Revista Brasileira de Energia, 22(1), pp 74-100. The article develops a methodology to analyze scenarios for the integration of regional electricity markets within Brazil. Use is made of a comprehensive interregional input–output model for the Brazilian economy with 16 sectors and 27 federal units. Once a scenario of integration is set up, the model allows to compute the impacts on total electricity consumption (tec) and to decompose them into structural factors, like electricity intensity, degree of local use, and relative sensibility to the coefficients of local versus inter-regional energy use (delta factor). A scenario of uniform redistribution of local consumption towards other regions is set up and its tec impacts measured. The methodology allowed to identify two patterns of sectors positively impacting tec: a) electro–intensive and b) low–intensive but with highly negative delta–factors. The ability to identify the last sector group is a major contribution of the proposed methodology, which is able yet to be explored in
the analysis of different scenarios and through many possible extensions of the model.

Consequências do uso mais eficiente de eletricidade na economia brasileira: uma análise inter-regional de insumo–produto. To be published in História Econômica e História de Empresas. Energy conservation campaigns and technological advances have reduced electricity intensities (EI)  in many countries. Brazil has been an exception, but once the country’s development matures, a downward reversion of its EI’s behavior is expected. The article presents an interregional input–ouput analysis in which scenarios of EI reduction and their intra– and inter–regional impacts upon electricity consumption and other selected variables are assessed. The analysis was undertaken using an interregional input–output model featured with 16 industries and 27 Brazilian federal units. The results point out that while the electricity consumption shrinks, the remainder of the economy keeps unaffected. A conclusion is that this is desirable for the sake of energy policy, but while the power industry is the only affected, new challenges are posed for planning electricity provision in the long–run and for regulating the electricity business by means of incentives.

Distribuição e desigualdade espaciais das emissões de CO2: uma análise de 158 países no período 1992-2004 (2009). With Eduardo Almeida and Terciane Sabadini Carvalho. 7th Meeting of The Brazilian Regional Science Association. The article analyses the recent spatial behavior of global emissions of CO2. Differently from the approach of other studies, that analyze the phenomenon from the convergence perspective of per capita emissions, this work places focus on the effects upon global warming. To do this, a conceptual distinction is made between spatial distribution and spatial inequality. The first refers to absolute, and the second to relative (per capita or by unit of GDP), distribution of the variable of interest in space. In order to measure empirically these concepts, indicators based on the Kullback and Leibler’s information measure were developed. The methodology was then applied to annual data for 19922004 on CO2 emissions, population, and GDP of 158 countries. The results point out that the global distribution of emissions remains stable, but in the group of developing countries a strong movement of spatial concentration, along with a reduction of the inequality of per capita emissions, is under way. On the basis of relations, much studied in the literature, between income inequality and growth, on the one hand, and between per capita income and per capita CO2 emissions, on the other hand, a conclusion is that the growth potential of future emissions is increasing, making it necessary that efforts toward international agreements to reduce the emissions be continued.

Distribuição e desigualdade espaciais do consumo residencial de eletricidade: uma análise do período 1989-2005 com medidas de informação (2008). With Lourival Batista de Oliveira Júnior, Ricardo da Silva Freguglia e Alexandre Zanini. 6th Meeting of The Brazilian Regional Science Association. This paper analyses the spatial behavior of the residential consumption of electricity (CRE) in Brazil and the implications for the provision of electrical energy in the future. Two indicadors based on the Kullback-Leibler information measure are proposed: one for measuring state distribution of total CRE and the other for state inequality of per capita CRE. Differences and relations between these two concepts are presented and discussed. Using data available from the Brazilian Energy Balance and from IBGE, annual time series of both indicators were constructed for 1989-2005. The results indicate the spatial distribution of total CRE is increasing while the spatial inequality of per capita CRE is decreasing, with the latter movement resulting more from interregional than intraregional factors. These movements, while desirable from the sake of population welfare, bring worrisome implications for energy management in the long-run. They tend to magnify the growth potential of total CRE and thus weigh down the challenges of expanding the subsystems for generating, transmitting, and distributing the electricity needed by the country. Implications for energy policy and strategy, as well as directions for further studies, are presented in the end.

Integração de modelos econométrico e de insumo produto para previsões de longo prazo da demanda de energia no Brasil (2008). With Fernando Perobelli, Weslem Rodrigues, and Eduardo Haddad Estudos Econômicos, v.38, n. 4, p. 675-699. The paper presents an econometric+input-output model for long-run forecasting of energy consumption by sector in Brazil. Yearly forecasts are produced for 2005-2010. The approach integrates a time series econometric model with an input-output model. A relevant result is a connection established between vector autoregressive models with or without error correction mechanisms and closed or open input-output models. Two forecasting scenarios are set-up: an expansionist scenario that predicts a faster economic growth; and a damped scenario that predicts a smoothed growth. In the more likely case of the expansionist scenario, expectations are confirmed that energy shortage will take place from 2009 on, thus before the end of the decade. Directions for further research on methodology improvements are considered at the end.

Interações energéticas entre o Estado de Minas Gerais e o restante do Brasil: uma análise inter-regional de insumo-produto (2007). With Fernando Perobelli and Weslem Rodrigues. Economia Aplicada, v. 11 (1). This paper analyses the interactions between the State of Minas Gerais and the rest of Brazil with regard to energy consumption. A hibryd interregional input-output model, by means of which energy intensity measures are computed, is used to undertake the analysis. The energy measures allow, for instance, to assess the degree in which a sector production in Minas Gerais impacts the energy consumption inside and outside the state. Also, the measures allow to assess the degree in which a sector production in the rest of Brazil (outside Minas Gerais) impacts energy consumption inside and outside the state. The analysis presents disaggregate information for 14 economic sectors, two spatial areas (Minas Gerais and the rest of Brazil), and one kind of energy use (total energy), thus allowing to trace an accurate portrait of interdependence patterns. A conclusion is that the methodology provides relevant information for the state managers/planners in the development of efficient strategies to guarantee energy supply.

External trade and spatial development in Brazil: An exploratory analysis. (2004) With Fernando Perobelli. 3rd Meeting of The Brazilian Regional Science Association.The paper aims to enhance the understanding regarding the interactions between foreign trade and spatial development in Brazil. The study abridges 27 Brazilian states, two blocks of trade partners represented by Mercosur and European Union, and 3 years in the period 1989-2003. The methodology consists of the application of exploratory spatial data analysis (ESDA) and is based on the use of Moran’s I statistic to study the temporal evolution of spatial autocorrelation patterns. Based on this approach, it is possible to verify the existence of clusters of high and low foreign trade states, as well as the changes in these clusters along the period between the end of the 1980s and the beginning of the 21st century. The analysis enabled us to examine the potential consequences for the spatial pattern of states’ foreign trade and economic development produced by relevant economical events of the period. At the end of the paper, perspectives and policy conclusions regarding the Brazilian spatial development are made.

Economic regulation in the Brazilian eletric power supply sector: a methodology for defining produtction efficiency frontier and estimating the X-factor (2003). Co-authorship with Alexandre Zanini and Reinaldo Castro Souza. Annals of the 8th Annual Meeting Lacea. Among the duties of the regulatory agency of the electric power supply sector in Brazil there is the periodical revision of energy prices. Such revisions involve estimating the X Factor applied to update prices so that gains in productivity are shared with consumers. To estimate the X Factor it is necessary to measure efficiency and, for this, two issues are important: the choices of benchmarks and of techniques for productivity measurement. This paper proposes an approach to define frontier efficiency of electric power distribution utilities based on clustering homogeneous utilities using neural networks and estimating the frontiers through econometric techniques.

Inferência ecológica para recuperação de dados desagregados (2003). With Álvaro Veiga. Revista Brasileira de Estatística, v. 63, n. 219, pp. 29-54. The shortage of disaggregate data is a severe restriction to the development of social studies under spatial perspectives. The problem is of major importance in Brazil because of the shrinkage of IBGE’s Official Statistical System during the 1990’s along with the financial crises of states and municipalities, what prevent them to implement expensive surveys. Techniques of ecological inference (EI) are useful in such instances. Applications of EI include assessment of migration patterns in demography, estimation of traffic flows in transportation planning, and updating of input–output matrixes in economics, among a range of others. The paper presents, discusses and exemplifies the major and most recent methods for EI proposed in the literature, aiming to highlight their applicability to a number of problems that arise in empirical social studies, as well as to present the state of the art in the area with indication of available softwares.

A structured comparison of the Goodman Regression, the truncated normal, and the binomial-beta hierarchical methods for ecological inference (2003). With Álvaro Veiga. In King, G., O. Rosen, and M. Tanner (eds.) Ecological Inference: New Methodological Strategies. New York: Cambridge University Press. The chapter presents an extensive and structured Monte Carlo experiment to compare Goodman Regression, King’s truncated bivariate normal, and the binomial-beta hierarchical methods for ecological inference. The purpose of our research was to assess the predictive performance of these methods and their conformity with standard properties of statistical prediction theory. Thus, the EI problem is regarded as a prediction problem and properties of interest for the evaluation of EI predictors are defined. The experiment is designed based on differences between King’s and the binomial beta hierarchical methods, which are major contributions made recently to the EI literature. The results obtained indicate the Goodman regression is the weakest method, the BBH method has good predictive ability but is a biased point predictor, and King’ method is the best among the three, doing good in predictive performance as well as in statistical properties. Also, the relevance for EI methodology of using Monte Carlo experiments to evaluate and compare EI methods that display aggregation consistency is discussed.

Otimização de entropia: implementação computacional dos princípios MaxEnt e MinxEnt (2002). Portuguese version. Pesquisa Operacional, 22, (1), pp. 37-59. The entropy optimization principles MaxEnt of Jaynes (1957a,b) and MinxEnt of Kullback (1959) can be applied in a variety of scientific fields. Both involve the constrained optimization of entropy measures, which are intrinsically non-linear functions of probabilities. Since each is a non- linear programming problem, their solution depend on iterative search algorithms, and, in addition, the constraints that probabilities are non–negative and sum up to one restrict in a particular way the solution space. The paper presents in detail (with the aid of two flowcharts) a computer efficient implementation of those two principles in the linearly constrained case that makes a prior check for the existence of solution to the optimization problems. The authors also make available easy–to–use Matlab codes. (Click here for an english version of this paper)

The binomial-beta hierarchical model for ecological inference: methodological issues and fast implementation via the ECM algorithm. With Álvaro Veiga.The binomial-beta hierarchical model is a recent contribution to ecological inference. Developed for the 2×2 tables case and from a bayesian perspective, the model is featured by the compounding of binomial and beta distributions into a hierarchical structure. From a sample of aggregate observations, inference with this model can be made regarding values of unobservable disaggregate variables. The paper reviews this EI model with two purposes: First, a faster approach to use it in practice, based on explicit modeling of the disaggregate data generation process along with posterior maximization implemented via the ECM algorithm, is proposed and illustrated with an application to a real dataset; second, limitations concerning the use of marginal posteriors for binomial probabilities as the vehicle of inference (basically, the failure to respect the accounting identity) instead of the predictive distributions for the disaggregate proportions are pointed. In the concluding section, principles for EI model building in general and directions for further research are suggested.

Desagregação de dados com inferência ecológica: implementações de modelos baseados na normal truncada e na binomial-beta via Algoritmo EM (2000). Doctoral Dissertation (Portuguese Version). Ecological inference comprises the set of statistical procedures for the prediction of disaggregate data when data are available only in aggregate form. Two recently proposed approaches have been motivating new developments in the field: the model based on a truncated bivariate normal (MNBT) and the hierarchical binomial–beta model (MHBB). The thesis reevaluates these approaches and explores more efficient computational implementations via the EM Algorithm and one of its extensions, the ECM Algorithm. As compared to quasi–Newton algorithms, a stable yet slower version is obtained for the implementation of the MNBT, and a stable and faster version is obtained for the MHBB. The methodologies are compared in predictive terms by means of an extensive Monte Carlo experiment and of the application to real datasets. The superiority of the MNBT is evident in the majority of cases. Modeling mistakes of the MHBB are corrected and an asymptotic restriction of the predictions made with this model is pointed.

Estimating King’s ecological inference normal model via the EM algorithm (2000). With Álvaro Veiga, Paper presented at the Midwest Political Science Association Annual Meeting. Chicago: April. Recently, King (1997) introduced a new model for ecological inference (EI), based on a truncated bivariate normal, which he estimates by maximum probability and uses to simulate the predictive densities of the disaggregate data. This paper reviews King’s model and its assumption of truncated normality, with the aim to implement maximum probability estimation of his model and disaggregate data prediction in an alternative fashion via the EM Algorithm. In addition, we highlight and discuss important modeling issues related to the chance of non–existence of maximum likelihood estimates, and to the degree that corrections for this non–existence by means of suitably chosen priors are effective. At the end, a Monte Carlo simulation study is run in order to compare the two approaches.

Methods of ecological inference for disaggregation problems in operations research (1999). Paper presented at the XXXI Simposio Brasileiro de Pesquisa Operacional, held in the city of Juiz de Fora, MG, Brazil: October. Operations research techniques are widely used in business projects planning. Usually, a preliminary task of project planners is to assess the potential market for a business project, which involves defining the target population and evaluating its size. As the potential market is part of a larger aggregate of consumers, techniques for disaggregate data estimation (DDE) are often needed, and for long entropy optimization techniques have been used with this purpose. However, a line of research on DDE techniques displaying promising developments is Ecological Inference (EI). The paper presents a brief review of the recent literature on EI techniques, aiming at diffusing them among operations research analysts, and also a new method proposed by the author to make EI via the statistical technique known as EM Algorithm.

Modelos bayesianos de previsão aplicados à análise do comportamento da produção industrial de Minas Gerais (1998). Texto para Discussão NUPE/FEA no. 05. The paper presents some results of a research where the bayesian forecasting methodology was used to analyse and predict the short run behavior of industrial production in Minas Gerais. The indicator used was the monthly series of industrial production computed by FIBGE covering the period January 1981 to November 1996. From the graphical analysis of the series and the knowledge of events with relevant macroeconomic repercussion, as the various stabilization plans, a base of external prior information was combined with the data in the development of descriptive and predictive models for the indicator’s behaviour. The restrospective (descriptive) analysis, undertaken on the estimated series level (i.e., after seasonality was extracted) pointed different patterns for the short run dynamics of Minas Gerais’ industry in the period of study, with phases of linear growth alternating with phases of unstable oscillations: the most detached one occurring during the Collor Government. The predictive analysis indicated that the models which are less adaptative to short run oscillations perform better in a forecasting system then the more adaptative ones.



Function codes, written in the Matlab language from MathWorks, Inc., that implement the methods developed in my Doctoral Dissertation and other papers are available here for download.

maxent.m – Implements Jayne’s MAXENT principle, say, maximizes Shannon’s measure of entropy subject to linear constraints (get these with the paper in portuguese in the file po_entropia.zip (For an english version of the paper, click here)

minxent.m – Implements Kullback’s MINXENT principle, say, minimizes Kullbacks measure of cross-entropy subject to linear constraints (idem).

phase1.m – checks whether the system of linear constraints has an admissible solution by runing phase 1 of the simplex algorithm; it is(necessary for use with functions maxent.m and minxent.m (idem).

bbh1.zip – A set of Matlab codes to implement the binomial beta model for ecological inference via the ECM algorithm, developed within my Doctoral Dissertation. (Get these with the paper “The binomial-beta hierarchical model for ecological inference: methodological issues and fast implementation via the ECM algorithm (2001)“, with Álvaro Veiga, and also available at the Polmeth Paper Archive)


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Professor – Rogério Silva de Mattos