We propose a sieve maximum likelihood (ML) estimation procedure for a broad class of semiparametric multivariate distribution models. A joint distribution in this class is characterized by a parametric copula function evaluated at nonparametric marginal distributions. This class of models has gained popularity in diverse fields due to a) its flexibility in separately modeling the dependence structure and the marginal behaviors of a multivariate random variable, and b) its circumvention of the "curse of dimensionality" associated with purely nonparametric multivariate distributions. We show that the plug-in sieve ML estimates of all smooth functionals, including the finite dimensional copula parameters and the unknown marginal distributions, are semiparametrically efficient; and that their asymptotic variances can be estimated consistently. Moreover, prior restrictions on the marginal distributions can be easily incorporated into the sieve ML procedure to achieve further efficiency gains. Two such cases are studied in the paper: (i) the marginal distributions are equal but otherwise unspecified, and (ii) some but not all marginal distributions are parametric. Monte Carlo studies indicate that the sieve ML estimates perform well in finite samples, especially so when prior information on the marginal distributions is incorporated.

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We develop an envelope condition method (ECM) for dynamic programming problems-a tractable alternative to expensive conventional value function iteration. ECM has two novel features: First, to reduce the cost, ECM replaces expensive backward iteration on Bellman equation with relatively cheap forward iteration on an envelope condition. Second, to increase the accuracy of solutions, ECM solves for derivatives of a value function jointly with a value function itself. We complement ECM with other computational techniques that are suitable for high-dimensional problems, such as simulationbased grids, monomial integration rules and derivative-free solvers. The resulting value-iterative ECM method can accurately solve models with at least up to 20 state variables and can successfully compete in accuracy and speed with state-of-the-art Euler equation methods. We also use ECM to solve a challenging default risk model with a kink in value and policy functions, and we …nd it to be fast, accurate and reliable.

We compare the performance of the perturbation-based (local) portfolio solution method of Sutherland (2010a, 2011) with a global solution method. We find that the local method performs very well when the model is designed to capture stylized macroeconomic facts and countries/agents are symmetric, i.e. when the latter have similar size, face similar risks and trade assets with similar risk properties. It performs less satisfactory when the agents engaged in financial trade are asymmetric. The global solution method performs substantially better when the model is parameterized to match the observed equity premium, a key stylized finance fact.