Abstract
This paper develops a parameter-expanded Monte Carlo EM (PX-MCEM) algorithm to perform maximum likelihood estimation in a multivariate sample selection model. In contrast to the current methods of estimation, the proposed algorithm does not directly depend on the observed-data likelihood, the evaluation of which requires intractable multivariate integrations over normal densities. Moreover, the algorithm is simple to implement and involves only quantities that are easy to simulate or have closed form expressions.
Highlights
Sample selection models, pioneered in [1]-[3], are indispensable to researchers who use observational data for statistical inference
The objective of this paper is to develop a simple maximum likelihood (ML) estimation algorithm for a commonly used multivariate sample selection model
The standard EM algorithm using (7) and (8) is difficult to implement for the multivariate sample selection model (MSSM) as the expectation step (E-step) and maximization step (M-step) are intractable
Summary
Sample selection models, pioneered in [1]-[3], are indispensable to researchers who use observational data for statistical inference. (2014) Estimation of Multivariate Sample Selection Models via a Parameter-Expanded Monte Carlo EM Algorithm. [9] discusses the ML estimation of these models and proposes to use the popular Geweke, Hajivassiliou, and Keane (GHK) algorithm to approximate these integrals in a simulated ML framework. While this strategy works reasonably well, the GHK algorithm can be difficult to implement. Another popular approach is to use two-step estimation (see [10] for a survey). The objective of this paper is to develop a simple ML estimation algorithm for a commonly used multivariate sample selection model.
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