Supplementary Appendix to \Sequential Estimation of Structural Models with a Fixed Point Constraint"

This supplementary appendix contains the following details omitted from the main paper due to space constraints: (A) numerical implementation of the sequential algorithm based on the RPM, (B) the sequential GMM estimator, (C) the convergence properties of the NPL algorithm for models with unobserved heterogeneity, (D) relative efficiency of the NPL, q-NPL, and MLE, and (E) the equivalence of the NPL estimator using Λ(P, θ) and the NPL estimator using Ψ(P, θ). A Numerical Implementation of the Sequential Algorithm based on the RPM in Section 4.2 Implementing the sequential algorithm based on the RPM in Section 4.2 requires evaluating (I − Π ( ˜ θj−1, ˜ Pj−1)∇P ′Ψ( ˜ θj−1, ˜ Pj−1)Π ( ˜ θj−1, ˜ Pj−1)) −1 as well as computing an orthonormal basis Z ( ˜ θj−1, ˜ Pj−1) from the eigenvectors of ∇P ′Ψ( ˜ θj−1, ˜ Pj−1) for j = 1,..., k. This is potentially costly when the analytical expression of ∇P ′Ψ(θ, P) is not available. In this section, we discuss how to reduce the computational cost of implementing the RPM algorithm by updating (I − Π ( ˜ θj−1, ˜ Pj−1)∇P ′Ψ( ˜ θj−1, ˜ Pj−1)Π ( ˜ θj−1, ˜ Pj−1)) −1 and Z ( ˜ θj−1, ˜ Pj−1) without explicitly computing ∇P ′Ψ(θ, P) in each iteration. Denote ˜ Πj−1 = Π ( ˜ θj−1, ˜ Pj−1),

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