New EM-type algorithms for the Heckman selection model

Abstract The Heckman selection model is widely used to analyse data for which the outcome is partially observable, and the missing part is not random. The 2-step method, maximum likelihood estimation (MLE), and EM algorithms have been developed to analyse this model; however, they have certain limitations. Three new algorithms (ECM, ECM(NR), and ECME) will be proposed with the advantages of the EM algorithm: easy implementation and numerical stability. Considering bias and mean squared error (MSE), simulations with different correlation values suggest that MLE performs similarly to the proposed algorithms; however, MLE as well as the proposed algorithms yield better estimations than the 2-step method. A simulation study in which standard error is also considered demonstrates that the new algorithms are more robust than MLE, and yield slightly better estimations than the 2-step and the robust 2-stage methods. Real data analyses are also provided to discuss the performance of MLE, 2-step, and the proposed algorithms. A real data analysis concerning the robustness issue further illustrates that, under certain conditions, the proposed algorithms are more efficient and stable.

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