Solving heterogeneous-agent models by projection and perturbation

The paper proposes a numerical solution method for general equilibrium models with a continuum of heterogeneous agents, which combines elements of projection and of perturbation methods. The basic idea is to solve first for the stationary solutionof the model, without aggregate shocks but with fully specified idiosyncratic shocks. Afterwards one computes a first-order perturbation of the solution in the aggregate shocks. This approach allows to include a high-dimensional representation of the cross-sectional distribution in the state vector. The method is applied to a model of household saving with uninsurable income risk and liquidity constraints. The model includes not only productivity shocks, but also shocks to redistributive taxation, which cause substantial short-run variation in the cross-sectional distribution of wealth. If those shocks are operative, it is shown that a solution method based on very few statistics of the distribution is not suitable, while the proposed method can solve the model with high accuracy, at least for the case of small aggregate shocks. Techniques are discussed to reduce the dimension of the state space such that higher order perturbations are feasible.Matlab programs to solve the model can be downloaded.

Consumer choice in competitive location models: Formulations and heuristics

A new direction of research in Competitive Location theory incorporatestheories of Consumer Choice Behavior in its models. Following thisdirection, this paper studies the importance of consumer behavior withrespect to distance or transportation costs in the optimality oflocations obtained by traditional Competitive Location models. To dothis, it considers different ways of defining a key parameter in thebasic Maximum Capture model (MAXCAP). This parameter will reflectvarious ways of taking into account distance based on several ConsumerChoice Behavior theories. The optimal locations and the deviation indemand captured when the optimal locations of the other models are usedinstead of the true ones, are computed for each model. A metaheuristicbased on GRASP and Tabu search procedure is presented to solve all themodels. Computational experience and an application to 55-node networkare also presented.

Money and prices in models of bounded rationality in high inflation economies

This paper studies the short run correlation of inflation and money growth. We study whether a model of learning can do better than a model of rational expectations, we focus our study on countries of high inflation. We take the money process as an exogenous variable, estimated from the data through a switching regime process. We findthat the rational expectations model and the model of learning both offer very good explanations for the joint behavior of money and prices.

Educational opportunity and the college premium

Since World War II, the United States government has made improved accessto higher education a priority. This e¤ort has substantially increasedthe number of people who complete college. We show that by reducing theeffective interest rate on borrowing for education, such policies canactually increase the gap in wages between those with a college educationand those without. The mechanism that drives our results is the signaling role of education first explored by Spence (1973). We argue that financialconstraints on education reduce the value of education as a signal. Wesolve for the reduced form relationship between the interest rate and thewage premium in the steady state of a dynamic asymmetric information model.In addition, we discuss evidence of decreases in borrowing costs for educationfinancing in the U.S.

On the quantitative importance of wage bargaining models

Four general equilibrium search models are compared quantitatively. Thebaseline framework is a calibrated macroeconomic model of the US economydesigned for a welfare analysis of unemployment insurance policy. Theother models make three simple and natural specification changes,regarding tax incidence, monopsony power in wage determination, and therelevant threat point. These specification changes have a major impacton the equilibrium and on the welfare implications of unemploymentinsurance, partly because search externalities magnify the effects ofwage changes. The optimal level of unemployment insurance dependsstrongly on whether raising benefits has a larger impact on searcheffort or on hiring expenditure.

Multiple filtering devices for the estimation of cyclical DSGE models

We propose a method to estimate time invariant cyclical DSGE models using the informationprovided by a variety of filters. We treat data filtered with alternative procedures as contaminated proxies of the relevant model-based quantities and estimate structural and non-structuralparameters jointly using a signal extraction approach. We employ simulated data to illustratethe properties of the procedure and compare our conclusions with those obtained when just onefilter is used. We revisit the role of money in the transmission of monetary business cycles.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Incorporating waiting time in competitive location models: Formulations and heuristics

In this paper we propose a metaheuristic to solve a new version of the Maximum CaptureProblem. In the original MCP, market capture is obtained by lower traveling distances or lowertraveling time, in this new version not only the traveling time but also the waiting time willaffect the market share. This problem is hard to solve using standard optimization techniques.Metaheuristics are shown to offer accurate results within acceptable computing times.

Subsampling inference in threshold autoregressive models

This paper discusses inference in self exciting threshold autoregressive (SETAR)models. Of main interest is inference for the threshold parameter. It iswell-known that the asymptotics of the corresponding estimator depend uponwhether the SETAR model is continuous or not. In the continuous case, thelimiting distribution is normal and standard inference is possible. Inthe discontinuous case, the limiting distribution is non-normal and cannotbe estimated consistently. We show valid inference can be drawn by theuse of the subsampling method. Moreover, the method can even be extendedto situations where the (dis)continuity of the model is unknown. In thiscase, also the inference for the regression parameters of the modelbecomes difficult and subsampling can be used advantageously there aswell. In addition, we consider an hypothesis test for the continuity ofthe SETAR model. A simulation study examines small sample performance.

Estimating learning models from experimental data

We study the statistical properties of three estimation methods for a model of learning that is often fitted to experimental data: quadratic deviation measures without unobserved heterogeneity, and maximum likelihood withand without unobserved heterogeneity. After discussing identification issues, we show that the estimators are consistent and provide their asymptotic distribution. Using Monte Carlo simulations, we show that ignoring unobserved heterogeneity can lead to seriously biased estimations in samples which have the typical length of actual experiments. Better small sample properties areobtained if unobserved heterogeneity is introduced. That is, rather than estimating the parameters for each individual, the individual parameters are considered random variables, and the distribution of those random variables is estimated.