Risk premia in general equilibrium

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.     

CLAR(1) point forecasting under estimation uncertainty

Forecast error is not only caused by the randomness of the data-generating process but also by the uncertainty due to estimated model parameters. We investigate these different sources of forecast error for a popular type of count process, the Poisson first-order integer-valued autoregressive (INAR(1)) process. However, many of our analytical derivations also hold for the more general family of conditional linear AR(1) (CLAR(1)) processes. In addition, results from a simulation study are presented, to verify and complement our asymptotic approximations.     

Comparing solution methods for dynamic equilibrium economies

This paper compares solution methods for dynamic equilibrium economies. We compute and simulate the stochastic neoclassical growth model with leisure choice using first, second, and fifth order perturbations in levels and in logs, the finite elements method, Chebyshev polynomials, and value function iteration for several calibrations. We document the performance of the methods in terms of computing time, implementation complexity, and accuracy, and we present some conclusions based on the reported evidence.     

On a study of the exponential and Poisson characteristics of the Poisson process

Based on the exponential and Poisson characteristics of the Poisson process, in this work we present some characterizations of the Poisson process as a renewal process. More precisely, let γ_t be the residual life at time t of the renewal process A={A(t),t≥0 }, under suitable condition, we prove that if Var(γ_t)=E ² (γ_t),∀t≥0, then A is a Poisson process. Secondly, we show that if Var (A(t)) is proportional to E (A(t)), then A is a Poisson process also, and Var (A(t))=E (A(t)). Received: August 1999     

Optimal growth under model uncertainty

The optimal growth of a wealth process toward a goal is studied under ambiguous markets with first- and second-order moment uncertainties relating to stock returns. Optimal strategies and value functions are solved explicitly. A verification theorem is proved to show that the results solve the original stochastic control problem. Quantitative analyses of the investment strategies indicate that a rational individual with ambiguity aversion reduces market participation when return and volatility are uncorrelated, while there is an exception for synchronous return and volatility. The welfare of shorting a discounted reward is computed, which demonstrates that in an ambiguous pricing economy, investors can generate a positive premium via appropriate asset allocations.     

Locally D- and c-optimal designs for Poisson and negative binomial regression models

The research on optimal experimental designs for nonlinear regression models is of great interest because these models are used to characterize chemical, biological or agricultural phenomena. Much of them involve an exponential decay. In this paper, locally D- and c-optimal designs are derived analytically for Poisson and negative binomial regression models.     

Tapping the supercomputer under your desk: Solving dynamic equilibrium models with graphics processors

This paper shows how to build algorithms that use graphics processing units (GPUs) installed in most modern computers to solve dynamic equilibrium models in economics. In particular, we rely on the compute unified device architecture (CUDA) of NVIDIA GPUs. We illustrate the power of the approach by solving a simple real business cycle model with value function iteration. We document improvements in speed of around 200 times and suggest that even further gains are likely.     

Learning about fiscal policy and the effects of policy uncertainty

In this paper we ask how uncertainty about fiscal policy affects the impact of fiscal policy changes on the economy when the government tries to counteract a deep recession. The agents in our model are uncertain about the conduct of fiscal policy and act as econometricians by estimating fiscal policy rules that might change over time.We find that assuming that agents are not instantaneously aware of the new fiscal policy regime in place leads to substantially more volatility in the short run and persistent differences in average outcomes. We highlight issues that can arise when a policymaker wants to announce a policy change. From a methodological perspective, we introduce a novel way to model learning in the face of discrete policy changes.     

Unfolding intensity function of a Poisson process in models with approximately specified folding operator

Quasi-maximum likelihood histogram sieve estimators of the intensity function of an indirectly observed Poisson process are studied. The setup differs from the standard one in that the exact form of the folding operator may not be known. Instead, approximate knowledge on its discretized version is available. Conditions for strong L ²-consistency are given and admissible discretization rates are studied. In non-folding problems, the number of histogram bins may essentially increase at the usual maximal rate while folding reduces the allowed discretization rates. It is shown that, even in moderately ill-posed problems, the discretization effects may be critical for the strong L ²-convergence and that there is an essential need both for further regularization and for imposing stronger conditions on the estimated function. Not surprisingly, the most restrictive factor is the low approximation power of piecewise constant functions. A regularization method is proposed which suitably modifies the discrete approximation of the folding operator and ensures the strong consistency. Since no penalty term is being introduced, the EM algorithm can be used in its factorized, efficient form. Convergence rates are obtained in terms of the discrete problem. Received: July 1999     

Numerical solution of urban residential land-use models

Many recent papers have made drastic simplifications in urban residential land-use models, presumably for analytic tractability. In this one, numerical solutions to models embodying varying assumptions of substantive importance are obtained. These solutions are compared with estimated characteristics of 1950 residential population density functions. The comparisons suggest that a CES production function for housing with an elasticity of substitution of land for structures of 0.75 agrees more closely with observed 1950 characteristics than does the Cobb-Douglas function so commonly used for analytic simplicity. Assuming a constant marginal transport cost for commuters at all distances from the Central Business District (CBD), however, yields results agreeing somewhat better with 1950 characteristics used for comparison than does the more complicated model embodying congestion in commuter transport.     

Sequential decisions under uncertainty and the maximum theorem

For sequential decision problems in which the decision-maker observes a process of state variables and chooses an adapted process of action variables, the paper defines a topology on the space of measures of processes of state variables which ensures the applicability of Berge's maximum theorem to the decision-maker's optimal behavior. The topology controls for the information available to the decision-maker at each decision date. The paper also discusses the implications of the analysis for the dynamic-programming approach to sequential decision-making under uncertainty, and for equilibrium existence proof strategies in sequential-market models and games.     

Consumer surplus analysis under uncertainty: A general equilibrium perspective

This paper derives an exact form of partial equilibrium efficiency measure under uncertainty which is consistent with expected utility maximization in a general equilibrium situation with ex-post spot markets for many goods and asset markets which are in general incomplete.We consider that the good under consideration tends to be negligibly small compared to the entire set of commodity characteristics which is assumed to be a continuum, and look into the limit property of preferences over state-contingent consumption of the good and state-contingent income transfer associated to it. We show that the limit preference exhibits risk neutrality, not only that it exhibits no income effect, meaning that the two conditions are tied together. We also show that the marginal rate of substitution between extra income transfers at different states of the world converges to the ratio between the Lagrange multipliers associated to those states. When the asset markets are complete such ratios are equalized between consumers, but it is not the case in general when the asset markets are incomplete. This means that using the aggregate expected consumer surplus as the welfare measure will be in general inconsistent with individuals’ expected utility maximization in the general equilibrium environment or with ex-ante Pareto efficiency.     

Econometric analysis of linearized singular dynamic stochastic general equilibrium models

In this paper I propose an alternative to calibration of linearized singular dynamic stochastic general equilibrium models. Given an a-theoretical econometric model as a representative of the data generating process, I will construct an information measure which compares the conditional distribution of the econometric model variables with the corresponding singular conditional distribution of the theoretical model variables. The singularity problem will be solved by using convolutions of both distributions with a non-singular distribution. This information measure will then be maximized to the deep parameters of the theoretical model, which links these parameters to the parameters of the econometric model and provides an alternative to calibration. This approach will be illustrated by an application to a linearized version of the stochastic growth model of King, Plosser and Rebelo.     

Indirect inference and calibration of dynamic stochastic general equilibrium models

We advocate in this paper the use of a sequential partial indirect inference (SPII) approach, in order to account for calibration practice where dynamic stochastic general equilibrium models (DGSE) are studied only through their ability to reproduce some well-chosen moments. We stress that, despite a lack of statistical formalization, the controversial calibration methodology addresses a genuine issue on the consequences of misspecification in highly nonlinear and dynamic structural macro-models. We argue that a well-driven SPII strategy might be seen as a rigorous calibrationnist approach, that captures both the advantages of this approach (accounting for structural “a-statistical” ideas) and of the inferential approach (precise appraisal of loss functions and conditions of validity). This methodology should be useful for the empirical assessment of structural models such as those stemming from the real business cycle theory or the asset pricing literature.     

A theory of stochastic choice under uncertainty

In this paper we propose a characterization of stochastic choice under risk and under uncertainty. We presume that decision makers’ actual choices are governed by randomly selected states of mind, and study the representation of decision makers’ perceptions of the stochastic process underlying the selection of their state of mind. The connections of this work to the literatures on random choice, choice behavior when preference are incomplete; choice of menus; and grades of indecisiveness are also discussed.     

Solid waste planning under uncertainty using evolutionary simulation-optimization

A key aspect of effective public planning design is to minimize the impact of negative outcomes that can arise from the violation of pre-established system constraint criteria. These planning situations can be especially complicated when several components within the studied system are either unknown or contain considerable stochastic uncertainty. In this paper, the concept of outcome minimization through the use of penalty functions is combined with grey programming (GP) into an evolutionary simulation-optimization (ESO) procedure in order to solve solid waste management problems containing significant sources of uncertainty. By employing outcome minimization concurrently with GP and ESO, it can be shown that plans that meet, or come close to meeting, required system criteria can be efficiently created. The efficacy of the procedure is demonstrated through its application to a solid waste planning case from the Municipality of Hamilton-Wentworth in the Province of Ontario, Canada. Since ESO techniques can be adapted to a wide variety of problem types in which some or all of the system components are stochastic, the practicality of this approach can be adapted to many operational and strategic planning situations containing significant sources of uncertainty.     

A general method for addressing forecasting uncertainty in inventory models

In practice, inventory decisions depend heavily on demand forecasts, but the literature typically assumes that demand distributions are known. This means that estimates are substituted directly for the unknown parameters, leading to insufficient safety stocks, stock-outs, low service, and high costs. We propose a framework for addressing this estimation uncertainty that is applicable to any inventory model, demand distribution, and parameter estimator. The estimation errors are modeled and a predictive lead time demand distribution obtained, which is then substituted into the inventory model. We illustrate this framework for several different demand models. When the estimates are based on ten observations, the relative savings are typically between 10% and 30% for mean-stationary demand. However, the savings are larger when the estimates are based on fewer observations, when backorders are costlier, or when the lead time is longer. In the presence of a trend, the savings are between 50% and 80% for several scenarios.     

Investment behavior under Knightian uncertainty – An evolutionary approach

The ‘as if ’ view of economic rationality defends the profit maximization hypothesis by pointing out that only those firms who act as if they maximize profits can survive in the long run. Recently, the problem of arriving at a logically consistent definition of rational behavior in games has shown that one must sometimes study explicitly the evolutionary processes that form the basis of this view. The purpose of this paper is to investigate the usefulness of genetic programming as a tool for generating hypotheses about rational behavior in situations where explicit maximization is not well defined. We use an investment decision problem with Knightian uncertainty as a borderline test case, and show that when the artificial agents receive the same information about the unknown probability distributions, they develop behavior rules as if they were expected utility maximizers with Bayesian learning rules.