Indirect likelihood inference

Given a sample from a fully specified parametric model, let Zn be a given finite-dimensional statistic - for example, an initial estimator or a set of sample moments. We propose to (re-)estimate the parameters of the model by maximizing the likelihood of Zn. We call this the maximum indirect likelihood (MIL) estimator. We also propose a computationally tractable Bayesian version of the estimator which we refer to as a Bayesian Indirect Likelihood (BIL) estimator. In most cases, the density of the statistic will be of unknown form, and we develop simulated versions of the MIL and BIL estimators. We show that the indirect likelihood estimators are consistent and asymptotically normally distributed, with the same asymptotic variance as that of the corresponding efficient two-step GMM estimator based on the same statistic. However, our likelihood-based estimators, by taking into account the full finite-sample distribution of the statistic, are higher order efficient relative to GMM-type estimators. Furthermore, in many cases they enjoy a bias reduction property similar to that of the indirect inference estimator. Monte Carlo results for a number of applications including dynamic and nonlinear panel data models, a structural auction model and two DSGE models show that the proposed estimators indeed have attractive finite sample properties.

Indirect likelihood inference (revised)

Standard indirect Inference (II) estimators take a given finite-dimensional statistic, Z_{n} , and then estimate the parameters by matching the sample statistic with the model-implied population moment. We here propose a novel estimation method that utilizes all available information contained in the distribution of Z_{n} , not just its first moment. This is done by computing the likelihood of Z_{n}, and then estimating the parameters by either maximizing the likelihood or computing the posterior mean for a given prior of the parameters. These are referred to as the maximum indirect likelihood (MIL) and Bayesian Indirect Likelihood (BIL) estimators, respectively. We show that the IL estimators are first-order equivalent to the corresponding moment-based II estimator that employs the optimal weighting matrix. However, due to higher-order features of Z_{n} , the IL estimators are higher order efficient relative to the standard II estimator. The likelihood of Z_{n} will in general be unknown and so simulated versions of IL estimators are developed. Monte Carlo results for a structural auction model and a DSGE model show that the proposed estimators indeed have attractive finite sample properties.

Essays in macroeconomy and dynamic term-structure models

This thesis is composed of three articles with the subjects of macroeconomics and - nance. Each article corresponds to a chapter and is done in paper format. In the rst article, which was done with Axel Simonsen, we model and estimate a small open economy for the Canadian economy in a two country General Equilibrium (DSGE) framework. We show that it is important to account for the correlation between Domestic and Foreign shocks and for the Incomplete Pass-Through. In the second chapter-paper, which was done with Hedibert Freitas Lopes, we estimate a Regime-switching Macro-Finance model for the term-structure of interest rates to study the US post-World War II (WWII) joint behavior of macro-variables and the yield-curve. We show that our model tracks well the US NBER cycles, the addition of changes of regime are important to explain the Expectation Theory of the term structure, and macro-variables have increasing importance in recessions to explain the variability of the yield curve. We also present a novel sequential Monte-Carlo algorithm to learn about the parameters and the latent states of the Economy. In the third chapter, I present a Gaussian A ne Term Structure Model (ATSM) with latent jumps in order to address two questions: (1) what are the implications of incorporating jumps in an ATSM for Asian option pricing, in the particular case of the Brazilian DI Index (IDI) option, and (2) how jumps and options a ect the bond risk-premia dynamics. I show that jump risk-premia is negative in a scenario of decreasing interest rates (my sample period) and is important to explain the level of yields, and that gaussian models without jumps and with constant intensity jumps are good to price Asian options.

Análise do comportamento das expectativas de inflação no Brasil sob uma regra de aprendizado

Os estudos sobre as expectativas de inflação no Brasil rejeitam a hipótese de racionalidade. Essa rejeição se dá por meio de testes estatísticos que identificam a existência de um viés sistemático quando comparamos a expectativa de inflação e a inflação realizada. Atualizamos alguns destes testes com o tamanho de amostra disponível atualmente. No presente trabalho, realizamos um experimento de Monte Carlo que simula o comportamento da inflação e da sua expectativa em um modelo DSGE. Esse modelo inclui uma regra monetária sujeita a choques transitórios e permanentes (que representam uma mudança de regime). A partir das séries simuladas com esses modelos, realizamos testes estatísticos para verificar se os resultados são semelhantes aos observados na prática. O exercício de simulação realizado não foi capaz de gerar séries com essas mesmas características, não trazendo evidência que esse mecanismo de aprendizado possa explicar o viés encontrado nas expectativas de inflação.

Portfolio efficiency tests with conditioning information using empirical likelihood estimation

We evaluate the use of Generalized Empirical Likelihood (GEL) estimators in portfolios efficiency tests for asset pricing models in the presence of conditional information. Estimators from GEL family presents some optimal statistical properties, such as robustness to misspecification and better properties in finite samples. Unlike GMM, the bias for GEL estimators do not increase as more moment conditions are included, which is expected in conditional efficiency analysis. We found some evidences that estimators from GEL class really performs differently in small samples, where efficiency tests using GEL generate lower estimates compared to tests using the standard approach with GMM. With Monte Carlo experiments we see that GEL has better performance when distortions are present in data, especially under heavy tails and Gaussian shocks.

Long-term Prospects For The Environmental Profile Of Advanced Sugar Cane Ethanol.

This work assessed the environmental impacts of the production and use of 1 MJ of hydrous ethanol (E100) in Brazil in prospective scenarios (2020-2030), considering the deployment of technologies currently under development and better agricultural practices. The life cycle assessment technique was employed using the CML method for the life cycle impact assessment and the Monte Carlo method for the uncertainty analysis. Abiotic depletion, global warming, human toxicity, ecotoxicity, photochemical oxidation, acidification, and eutrophication were the environmental impacts categories analyzed. Results indicate that the proposed improvements (especially no-til farming-scenarios s2 and s4) would lead to environmental benefits in prospective scenarios compared to the current ethanol production (scenario s0). Combined first and second generation ethanol production (scenarios s3 and s4) would require less agricultural land but would not perform better than the projected first generation ethanol, although the uncertainties are relatively high. The best use of 1 ha of sugar cane was also assessed, considering the displacement of the conventional products by ethanol and electricity. No-til practices combined with the production of first generation ethanol and electricity (scenario s2) would lead to the largest mitigation effects for global warming and abiotic depletion. For the remaining categories, emissions would not be mitigated with the utilization of the sugar cane products. However, this conclusion is sensitive to the displaced electricity sources.

Augmented Mixed Models For Clustered Proportion Data.

Often in biomedical research, we deal with continuous (clustered) proportion responses ranging between zero and one quantifying the disease status of the cluster units. Interestingly, the study population might also consist of relatively disease-free as well as highly diseased subjects, contributing to proportion values in the interval [0, 1]. Regression on a variety of parametric densities with support lying in (0, 1), such as beta regression, can assess important covariate effects. However, they are deemed inappropriate due to the presence of zeros and/or ones. To evade this, we introduce a class of general proportion density, and further augment the probabilities of zero and one to this general proportion density, controlling for the clustering. Our approach is Bayesian and presents a computationally convenient framework amenable to available freeware. Bayesian case-deletion influence diagnostics based on q-divergence measures are automatic from the Markov chain Monte Carlo output. The methodology is illustrated using both simulation studies and application to a real dataset from a clinical periodontology study.

Resolvendo a equação de Schrödinger utilizando procedimentos numéricos fundamentais

A combination of the variational principle, expectation value and Quantum Monte Carlo method is used to solve the Schrödinger equation for some simple systems. The results are accurate and the simplicity of this version of the Variational Quantum Monte Carlo method provides a powerful tool to teach alternative procedures and fundamental concepts in quantum chemistry courses. Some numerical procedures are described in order to control accuracy and computational efficiency. The method was applied to the ground state energies and a first attempt to obtain excited states is described.

Modelos de volatilidade estocástica em séries financeiras: uma aplicação para o IBOVESPA

Neste artigo apresentamos uma análise Bayesiana para o modelo de volatilidade estocástica (SV) e uma forma generalizada deste, cujo objetivo é estimar a volatilidade de séries temporais financeiras. Considerando alguns casos especiais dos modelos SV usamos algoritmos de Monte Carlo em Cadeias de Markov e o software WinBugs para obter sumários a posteriori para as diferentes formas de modelos SV. Introduzimos algumas técnicas Bayesianas de discriminação para a escolha do melhor modelo a ser usado para estimar as volatilidades e fazer previsões de séries financeiras. Um exemplo empírico de aplicação da metodologia é introduzido com a série financeira do IBOVESPA.

Assessing influence in survival data with a cure fraction and covariates

Diagnostic methods have been an important tool in regression analysis to detect anomalies, such as departures from error assumptions and the presence of outliers and influential observations with the fitted models. Assuming censored data, we considered a classical analysis and Bayesian analysis assuming no informative priors for the parameters of the model with a cure fraction. A Bayesian approach was considered by using Markov Chain Monte Carlo Methods with Metropolis-Hasting algorithms steps to obtain the posterior summaries of interest. Some influence methods, such as the local influence, total local influence of an individual, local influence on predictions and generalized leverage were derived, analyzed and discussed in survival data with a cure fraction and covariates. The relevance of the approach was illustrated with a real data set, where it is shown that, by removing the most influential observations, the decision about which model best fits the data is changed.

Polyelectrolyte-protein complexation driven by charge regulation

The interplay between the biocolloidal characteristics (especially size and charge), pH, salt concentration and the thermal energy results in a unique collection of mesoscopic forces of importance to the molecular organization and function in biological systems. By means of Monte Carlo simulations and semi-quantitative analysis in terms of perturbation theory, we describe a general electrostatic mechanism that gives attraction at low electrolyte concentrations. This charge regulation mechanism due to titrating amino acid residues is discussed in a purely electrostatic framework. The complexation data reported here for interaction between a polyelectrolyte chain and the proteins albumin, goat and bovine alpha-lactalbumin, beta-lactoglobulin, insulin, k-casein, lysozyme and pectin methylesterase illustrate the importance of the charge regulation mechanism. Special attention is given to pH congruent to pI where ion-dipole and charge regulation interactions could overcome the repulsive ion-ion interaction. By means of protein mutations, we confirm the importance of the charge regulation mechanism, and quantify when the complexation is dominated either by charge regulation or by the ion-dipole term.

Allosteric Control of Gating Mechanisms Revisited: The Large Conductance Ca(2+)-Activated K(+) Channel

Large-conductance Ca(2+)-activated K(+) channels (BK) play a fundamental role in modulating membrane potential in many cell types. The gating of BK channels and its modulation by Ca(2+) and voltage has been the subject of intensive research over almost three decades, yielding several of the most complicated kinetic mechanisms ever proposed. A large number of open and closed states disposed, respectively, in two planes, named tiers, characterize these mechanisms. Transitions between states in the same plane are cooperative and modulated by Ca(2+). Transitions across planes are highly concerted and voltage-dependent. Here we reexamine the validity of the two-tiered hypothesis by restricting attention to the modulation by Ca(2+). Large single channel data sets at five Ca(2+) concentrations were simultaneously analyzed from a Bayesian perspective by using hidden Markov models and Markov-chain Monte Carlo stochastic integration techniques. Our results support a dramatic reduction in model complexity, favoring a simple mechanism derived from the Monod-Wyman-Changeux allosteric model for homotetramers, able to explain the Ca(2+) modulation of the gating process. This model differs from the standard Monod-Wyman-Changeux scheme in that one distinguishes when two Ca(2+) ions are bound to adjacent or diagonal subunits of the tetramer.

Distribution of hepatitis c virus (hcv) genotypes in patients with chronic infection from Rondonia, Brazil

Background: Hepatitis C virus (HCV) is an important human pathogen affecting around 3% of the human population. In Brazil, it is estimated that there are approximately 2 to 3 million HCV chronic carriers. There are few reports of HCV prevalence in Rondonia State (RO), but it was estimated in 9.7% from 1999 to 2005. The aim of this study was to characterize HCV genotypes in 58 chronic HCV infected patients from Porto Velho, Rondonia (RO), Brazil. Methods: A fragment of 380 bp of NS5B region was amplified by nested PCR for genotyping analysis. Viral sequences were characterized by phylogenetic analysis using reference sequences obtained from the GenBank (n = 173). Sequences were aligned using Muscle software and edited in the SE-AL software. Phylogenetic analyses were conducted using Bayesian Markov chain Monte Carlo simulation (MCMC) to obtain the MCC tree using BEAST v. 1.5.3. Results: From 58 anti-HCV positive samples, 22 were positive to the NS5B fragment and successfully sequenced. Genotype 1b was the most prevalent in this population (50%), followed by 1a (27.2%), 2b (13.6%) and 3a (9.0%). Conclusions: This study is the first report of HCV genotypes from Rondonia State and subtype 1b was found to be the most prevalent. This subtype is mostly found among people who have a previous history of blood transfusion but more detailed studies with a larger number of patients are necessary to understand the HCV dynamics in the population of Rondonia State, Brazil.

Characterization of Hepatitis B virus (HBV) genotypes in patients from Rondonia, Brazil

Background: Hepatitis B virus (HBV) can be classified into nine genotypes (A-I) defined by sequence divergence of more than 8% based on the complete genome. This study aims to identify the genotypic distribution of HBV in 40 HBsAg-positive patients from Rondonia, Brazil. A fragment of 1306 bp partially comprising surface and polymerase overlapping genes was amplified by PCR. Amplified DNA was purified and sequenced. Amplified DNA was purified and sequenced on an ABI PRISM (R) 377 Automatic Sequencer (Applied Biosystems, Foster City, CA, USA). The obtained sequences were aligned with reference sequences obtained from the GenBank using Clustal X software and then edited with Se-Al software. Phylogenetic analyses were conducted by the Markov Chain Monte Carlo (MCMC) approach using BEAST v.1.5.3. Results: The subgenotypes distribution was A1 (37.1%), D3 (22.8%), F2a (20.0%), D4 (17.1%) and D2 (2.8%). Conclusions: These results for the first HBV genotypic characterization in Rondonia state are consistent with other studies in Brazil, showing the presence of several HBV genotypes that reflects the mixed origin of the population, involving descendants from Native Americans, Europeans, and Africans.

Detection of Hepatitis B virus subgenotype A1 in a Quilombo community from Maranhao, Brazil

Background: The Brazilian population is mainly descendant from European colonizers, Africans and Native Americans. Some Afro-descendants lived in small isolated communities since the slavery period. The epidemiological status of HBV infection in Quilombos communities from northeast of Brazil remains unknown. The aim of this study was to characterize the HBV genotypes circulating inside a Quilombo isolated community from Maranhao State, Brazil. Methods: Seventy-two samples from Frechal Quilombo community at Maranhao were collected. All serum samples were screened by enzyme-linked immunosorbent assays for the presence of hepatitis B surface antigen ( HBsAg). HBsAg positive samples were submitted to DNA extraction and a fragment of 1306 bp partially comprising HBsAg and polymerase coding regions (S/POL) was amplified by nested PCR and its nucleotide sequence was determined. Viral isolates were genotyped by phylogenetic analysis using reference sequences from each genotype obtained from GenBank (n = 320). Sequences were aligned using Muscle software and edited in the SE-AL software. Bayesian phylogenetic analyses were conducted using Markov Chain Monte Carlo (MCMC) method to obtain the MCC tree using BEAST v.1.5.3. Results: Of the 72 individuals, 9 (12.5%) were HBsAg-positive and 4 of them were successfully sequenced for the 1306 bp fragment. All these samples were genotype A1 and grouped together with other sequences reported from Brazil. Conclusions: The present study represents the first report on the HBV genotypes characterization of this community in the Maranhao state in Brazil where a high HBsAg frequency was found. In this study, we reported a high frequency of HBV infection and the exclusive presence of subgenotype A1 in an Afro-descendent community in the Maranhao State, Brazil.