Supplement to "Deep Neural Networks for Estimation and Inference"
This supplement to “Deep Neural Networks for Estimation and Inference” contains resultsfrom a simulation study of the finite sample properties of deep neural networks and their use in semiparametric causal inference. The code (in Python/Tensorflow) used for the simulation exercise is available.
Supplement to "Dynamic Belief Elicitation"
This supplement includes additional results omitted from the main paper. In Section S.1, we provide an algorithm that computes the payoffs for a simple instanceof strategy proof protocol in the general setting of Section 4. In Section S.2, we show how to construct elicitation protocols for information structures involving potentially infinitely many time periods using menus with random deadlines. Sections S.3–S.5 are relevant to situations in which expert knowledge is solicited or evaluated for thepurpose of helping decision makers. In Section S.3, we show that, subject to regularity conditions, the knowledge of high-order beliefs elicited by the protocols we studyis sufficient to solve essentially any dynamic decision problem. In Section S.4, we argue that knowledge of these high-order beliefs is much needed when the decision environment is dynamic: we ask what decision problems can be solved using the classical methods that elicit only first-order beliefs, and show they form a degenerate class. Finally, in Section S.5, we illustrate our results in the context of simple principal-agent problems.