Modelos dinâmicos e simulação estocástica

This paper presents new methodology for making Bayesian inference about dy~ o!s for exponential famiIy observations. The approach is simulation-based _~t> use of ~vlarkov chain Monte Carlo techniques. A yletropolis-Hastings i:U~UnLlllll 1::; combined with the Gibbs sampler in repeated use of an adjusted version of normal dynamic linear models. Different alternative schemes are derived and compared. The approach is fully Bayesian in obtaining posterior samples for state parameters and unknown hyperparameters. Illustrations to real data sets with sparse counts and missing values are presented. Extensions to accommodate for general distributions for observations and disturbances. intervention. non-linear models and rnultivariate time series are outlined.

Bertrand, Cournot and monopolistically competitive equilibria

Using an example, we study the analogs, for the differentiated product case, of the Cournot and Bertrand equilibria. These equilibria can be shown to exist and be uni que if we impose a sim pie and natural restriction on the elasticities of the demand functions for the differentiated products. Our characterizations of these equilibria make it possible to compare them and to determine how they are affected by the size of the market and the number of firms. We are also able to prove the existence of Cournot free-entry equilibria in which the number of firms is determined endogenously. In addition, we are able to prove that, in a large market, the Cournot free-entry equilibria approximate the Dixit-Stiglitz monopolistically competitive equilibria. The free-entry equilibrium concept we study is an analog of the one studied by Novshek for the case of firms selling products that are perfect substitutes. Our results are extensions of Novshek's. While we were unable to establish a general existence result for Bertrand free-entry equilibria, we were able to prove that, when these equilibria exist, they are unique and that in large markets they also approximate the Dixit-Stiglitz equilibria.

Demand-pull stagflation

This paper explores the possibility of stagflation emanating exc1usively from monetaJy sbocks, without concurrent supply shocks or shifts in potential output. This arises in connection with a tight money paradox. in the context of a fiscal theory of the price leveI. The paper exhibits perfect foresight equilibria with output and inflation fluctuating in opposite direetions as a consequence of small monetary shocks, and also following changes in monetaJy policy regime that launch the economy into hyperinflation or that produce dramatic stabilization of already high inflation. For that purpose, an analytically convenient dynamic general equilibrium macro model is deve10ped wbere nominal rigidities are represented by a cross between staggered two-period contracts and state dependent price adjustment in the presence of menu costs.

Simulation-based smoothing and filtering in factor stochastic volatility models : two econometric applications

In this article we use factor models to describe a certain class of covariance structure for financiaI time series models. More specifical1y, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. We build on previous work by allowing the factor loadings, in the factor mo deI structure, to have a time-varying structure and to capture changes in asset weights over time motivated by applications with multi pIe time series of daily exchange rates. We explore and discuss potential extensions to the models exposed here in the prediction area. This discussion leads to open issues on real time implementation and natural model comparisons.

Simulation -based smoothing and filtering in factor stochastic volatility models : two econometric applications (July-2001)

The past decade has wítenessed a series of (well accepted and defined) financial crises periods in the world economy. Most of these events aI,"e country specific and eventually spreaded out across neighbor countries, with the concept of vicinity extrapolating the geographic maps and entering the contagion maps. Unfortunately, what contagion represents and how to measure it are still unanswered questions. In this article we measure the transmission of shocks by cross-market correlation\ coefficients following Forbes and Rigobon's (2000) notion of shift-contagion,. Our main contribution relies upon the use of traditional factor model techniques combined with stochastic volatility mo deIs to study the dependence among Latin American stock price indexes and the North American indexo More specifically, we concentrate on situations where the factor variances are modeled by a multivariate stochastic volatility structure. From a theoretical perspective, we improve currently available methodology by allowing the factor loadings, in the factor model structure, to have a time-varying structure and to capture changes in the series' weights over time. By doing this, we believe that changes and interventions experienced by those five countries are well accommodated by our models which learns and adapts reasonably fast to those economic and idiosyncratic shocks. We empirically show that the time varying covariance structure can be modeled by one or two common factors and that some sort of contagion is present in most of the series' covariances during periods of economical instability, or crisis. Open issues on real time implementation and natural model comparisons are thoroughly discussed.

Rational expectations and the service of public debt: a recursive approach

This paper uses dynamic programming to study the time consistency of optimal macroeconomic policy in economies with recurring public deficits. To this end, a general equilibrium recursive model introduced in Chang (1998) is extended to include govemment bonds and production. The original mode! presents a Sidrauski economy with money and transfers only, implying that the need for govemment fmancing through the inflation tax is minimal. The extended model introduces govemment expenditures and a deficit-financing scheme, analyzing the SargentWallace (1981) problem: recurring deficits may lead the govemment to default on part of its public debt through inflation. The methodology allows for the computation of the set of alI sustainable stabilization plans even when the govemment cannot pre-commit to an optimal inflation path. This is done through value function iterations, which can be done on a computeI. The parameters of the extended model are calibrated with Brazilian data, using as case study three Brazilian stabilization attempts: the Cruzado (1986), Collor (1990) and the Real (1994) plans. The calibration of the parameters of the extended model is straightforward, but its numerical solution proves unfeasible due to a dimensionality problem in the algorithm arising from limitations of available computer technology. However, a numerical solution using the original algorithm and some calibrated parameters is obtained. Results indicate that in the absence of govemment bonds or production only the Real Plan is sustainable in the long run. The numerical solution of the extended algorithm is left for future research.

What causes violent crime?

This study uses a new data set of crime ratesfor a large sample of countriesfor the period 1970- 1994, based on information from the United Nations World Crime Surveys, to ana/yze the determinants ofnational homicide and robbery rates. A simple model of the incentives to commit crimes is proposed, which explicit/y considers possible causes of the persistence of crime over time (criminal inertia). Several econometric mode/s are estimated, attempting to capture the . determinonts of crime rates across countries and over time. The empirical mode/s are first run for cross-sections and then applie'd to panel data. The former focus on erplanatory variables that do not change markedly over time, while the panel data techniques consider both the eflect of the business cyc1e (i.e., GDP growth rate) on the crime rate and criminal inertia (accountedfor by the inclusion of the /agged crime rate as an explanatory variable). The panel data techniques a/so consider country-specific eflects, the joint endogeneity of some of the erplanatory variables, and lhe existence of some types of measurement e"ors aJjlicting the crime data. The results showthat increases in income inequality raise crime rates, dete"ence eflects are significant, crime tends to be counter-cyclical, and criminal inertia is significant even after controlling for other potential determinants of homicide and robbery rates.

On the cost of sympathy : a alternative model of insurance markets

The paper provides an alternative model for insurance market with three types of agents: households, providers of a service and insurance companies. Households have uncertainty about future leveIs of income. Providers, if hired by a household, perform a diagnoses and privately learn a signal. For each signal there is a procedure that maximizes the likelihood of the household obtaining the good state of nature. The paper assumes that providers care about their income and also about the likelihood households will obtain the good state of nature (sympathy assumption). This assumption is satisfied if, for example, they care about their reputation or if there are possible litigation costs in case they do not use the appropriate procedure. Finally, insurance companies offer contracts to both providers and households. The paper provides sufficient conditions for the existence of equilibrium and shows that the sympathy assumption 1eads to a 10ss of welfare for the households due to the need to incentive providers to choose the least expensive treatment.

On endogenous cost of altruism

The paper extends the cost of altruism model, analyzed in Lisboa (1999). There are three types of agents: households, providers of a service and insurance companies. Households have uncertainty about future leveIs of income. Providers, if hired by a household, have to choose a non-observable leveI of effort, perform a diagnoses and privately learn a signal. For each signal there is a procedure that maximizes the likelihood of the household obtaining the good state of nature. Finally, insurance companies offer contracts to both providers and households. The paper provides suflicient conditions for the existence of equilibrium and shows the optimal contract induces providers to care about their income and also about the likelihood households will obtain the good state of nature, which in Lisboa (1999) was stated as altruism assumption. Equilibrium is inefficient in comparison with the standard moral hazard outcome whenever high leveIs of effort is chosen precisely due to the need to incentive providers to choose the least expensive treatment for some signals. We show, however that an equilibrium is always constrained optimal.

Moral hazard and nonlinear pricing in a general equilibrium model

The paper analyzes a two period general equilibrium model with individual risk and moral hazard. Each household faces two individual states of nature in the second period. These states solely differ in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period households choose a non-observable action. Higher leveis of action give higher probability of the good state of nature to occur, but lower leveIs of utility. Households have access to an insurance market that allows transfer of income across states of oature. I consider two models of financiaI markets, the price-taking behavior model and the nonlínear pricing modelo In the price-taking behavior model suppliers of insurance have a belief about each household's actíon and take asset prices as given. A variation of standard arguments shows the existence of a rational expectations equilibrium. For a generic set of economies every equilibrium is constraíned sub-optímal: there are commodity prices and a reallocation of financiaI assets satisfying the first period budget constraint such that, at each household's optimal choice given those prices and asset reallocation, markets clear and every household's welfare improves. In the nonlinear pricing model suppliers of insurance behave strategically offering nonlinear pricing contracts to the households. I provide sufficient conditions for the existence of equilibrium and investigate the optimality properties of the modeI. If there is a single commodity then every equilibrium is constrained optimaI. Ir there is more than one commodity, then for a generic set of economies every equilibrium is constrained sub-optimaI.