Structural inference from reduced forms with many instruments

• Main Authors: PHILLIPS, Peter C. B., GAO, Wayne Yuan
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2017
• Subjects: Endogeneity; Exact distributions; Partial identification; Partially restricted reduced form; Structural inference; Unidentified structure; Weak reduced form; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2081; https://ink.library.smu.edu.sg/context/soe_research/article/3081/viewcontent/1_s20_S0304407617300659_main.pdf
• Institution: Singapore Management University

This paper develops exact finite sample and asymptotic distributions for structural equation tests based on partially restricted reduced form estimates. Particular attention is given to models with large numbers of instruments, wherein the use of partially restricted reduced form estimates is shown to be especially advantageous in statistical testing even in cases of uniformly weak instruments. Comparisons are made with methods based on unrestricted reduced forms, and numerical computations showing finite sample performance of the tests are reported. Some new results are obtained on inequalities between noncentral chi-squared distributions with different degrees of freedom that assist in analytic power comparisons.