Supplement to "Unwilling to Train?—Firm Responses to the Colombian Apprenticeship Regulation"
Caicedo, Santiago, Miguel Espinosa and Arthur Seibold
This supplement contains the online appendices of “Unwilling to Train? Firm Responses to the Colombian Apprenticeship Regulation” by Caicedo, Espinosa and Seibold (2021). Appendix A shows additional tables and figures. Appendix B provides additional information on training courses and apprentices. Appendix C presents reduced-form results using an alternative sector classification. Appendix D contains model proofs and extensions. Finally, Appendix E provides details of the quantitative exercises.
Supplement to "Optimal Discounting"
Noor, Jawwad, and Norio Takeoka
This supplementary appendix for Noor and Takeoka  provides (i) a characterization for the General Discounted Utility (GDU) model both on the deterministic streams and on the streams of lotteries, (ii) a weaker definition of present equivalents in the off-diagonal approach, (iii) omitted proofs for results in Noor and Takeoka , and (iv) a new axiomatization result about a variant of homogeneous CE representation, called the smooth homogeneous CE model.
Supplement to "Macro-Finance Decoupling: Robust Evaluations of Macro Asset Pricing Models"
Cheng, Xu, Winston Wei Dou, and Zhipeng Liao
This supplemental appendix provides the following supporting materials. Sections SA – SC provide the proofs of Lemmas A1 – A7 in the appendix to the main text Cheng, Dou, and Liao (2021). Section SA provides the proofs of several lemmas on the asymptotic convergence of the random components in the test statistic T and the conditional critical value cα( ˆd). Section SB verifies the bounded Lipschitz properties of the test statistic and the conditional critical value, which are used to show their weak convergence in large samples. Section SC includes some auxiliary lemmas. Section SD provides additional theoretical results on the power of the proposed conditional test. Section SE provides comparison with some power envelopes through simulations. Section SF collects details and additional results of the empirical application.
Supplement to "Global Banks and Systemic Debt Crises"
Morelli, Juan M., Pablo Ottonello, and Diego J. Perez
In this Appendix, we develop and solve an extension of the baseline model in which we allow for trading of securities in secondary markets. This version of the model features the same source of variation as in the empirical analysis. We show that a parameterization of the model that targets cross-sectional empirical estimates from the data delivers quantitative results similar to those in the baseline model.