| Economists often have to deal with integration problems due to the introduction of more flexible model specifications. These integration problems usually do not have analytical solutions nor can they be accurately evaluated by conventional numerical methods since the dimensions of these integration problems are typically high. It has, therefore, become increasingly important to develop efficient numerical methods for the evaluation of high-dimensional integrals. We propose a new generic algorithm to construct efficient importance samplers for the evaluation of such integrals. Although the method is aimed at the evaluation of the likelihood functions of dynamic latent variable models, it is generic and can also be applied to other econometric models with numerical integrals. The performance of our method is strikingly illustrated by two applications. The first application consists of the analysis of a first-order inverted-gamma dynamic stochastic volatility model for daily stock returns, whose likelihood for an actual sample of size 1447 is evaluated with high numerical accuracy by means of only 10 Monte Carlo replications. The second application consists of a dynamic latent variable generalization of a Walrasian nonlinear price-adjustment equation for second-hand house prices in the UK, as initially modeled by D. F. Hendry. Maximum likelihood estimation unequivocally supports a specification whereby prices perfectly adjust to excess demand which is modeled as a dynamic latent variable whose distribution depends upon observable characteristics of the housing market. |
