Supplement to "The Sorted Effects Method: Discovering Heterogeneous Effects Beyond their Averages"
This zip file contains the replication files for the manuscript. It also contains an online appendix. The supplementary material contains 7 appendices with additional results and some omitted proofs. Appendix C introduces some notation. Appendix D includes a brief review of differential geometry. Appendix E gathers the proofs of the key mathematical results in Appendix A. Appendix F provides sufficient conditions for the u-Donsker properties in Section 4. Appendix G extends the theoretical analysis to include discrete covariates. Appendices H and I report the results of 3 numerical simulations and an empirical application to the effect of race on mortgage denials, respectively.
Supplement to "Identifying Effects of Multivalued Treatments"
Appendix A gives an identification result for the zero-index case, which was not dealt with in the text. It also provides a characterization of Heckman and Pinto's unordered monotonicity property as a subcase of our more general framework. Appendix B collects proofs of some of the results in the main text. Finally, Appendix C fills in the details of the entry game introduced in Section 2, and Appendix D compares our results with those of Heckman, Urzua, and Vytlacil (2008) in more detail. Appendix E discusses a more general form of threshold conditions than the "rectangular"
threshold conditions in Assumption 2.1.
Supplement to "Long memory via networking"
This Supplement Material includes various extension of the paper’s main results, namely (i) deviations from power laws in the cn coefficients (ii) the presence of multiple sources of noise in the network (iii) the possibility of non integrable limiting power spectra and (iv) heterogeneity in the agents’ responses. It also includes the description of a simple and stylized variant of the Loss-Plosser model as well as a “toy” application based on the “input-output accounts” database compiled by the Bureau of Economic Analysis.