Estimation of dynamic latent variable models using simulated non-parametric moments

Authors

  • Michael Creel,

    1. Department of Economics and Economic History, Universitat Autònoma de Barcelona, Edifici B-Campus de Bellaterra, 08193 Bellaterra (Barcelona), Catalonia-Spain. E-mail: michael.creel@uab.es
    2. Barcelona Graduate School of Economics, Ramon Trias Fargas, 25-27, 08005 Barcelona, Catalonia-Spain.
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  • Dennis Kristensen

    1. Department of Economics, University College London, Gower Street, London WC1E 6BT, UK. E-mail: d.kristensen@ucl.ac.uk
    2. CEMMAP, Institute for Fiscal Studies, 7 Ridgmount Street, London WC1E 7AE, UK.
    3. CREATES, Department of Economics and Business, Aarhus University, Fuglesangs Alle 4, 8210 Aarhus V, Denmark.
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Abstract

Summary  We propose a novel estimation method for dynamic latent variable (DLV) models that combines simulations and non-parametric kernel smoothing techniques to obtain a generalised method of moments (GMM) estimator based on a set of conditional moments. As such it extends the simulated method of moments (SMM) of Duffie and Singleton (1993) to allow for the use of conditional moments, instead of unconditional ones. It can also be seen as a generalisation of the SMM for static models as proposed in McFadden (1989). It is shown that, as the number of simulations diverges and the bandwidth used in the kernel smoothing shrinks, the estimator is consistent and a higher order expansion reveals the stochastic difference between the infeasible GMM estimator based on exact computation of the conditional moment conditions and the simulated version. In particular, the expansion demonstrates how simulations impact the bias and variance of the proposed estimator. Extensive Monte Carlo results show how the estimator may be applied to a range of DLV models, and that it performs well in comparison to several other estimators that have been proposed in the literature.

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