Lecturer: Peng Ding (丁鹏), UC Berkeley

Title: Causal inference: a non-magical perspective

Abstract: Causal inference is a trendy topic in statistics and machine learning in recent years. Although it has a long history, it is often dismissed by mathematical statisticians possibly due to its controversial foundations and untestable assumptions. This short course will take a non-magical perspective in causal inference and examine the fundamental assumptions critically. It will cover the following topics:

1. Design-based inference for causal inference and its connections with the model-based analogue in randomized experiments;

2. Sensitivity analysis with respect to unmeasured confounding in observational studies;

3. The interplay of causal inference and machine learning.

Lecturer: Ruodu Wang (王若度), University of Waterloo

Title: Optimal transport: some recent results and applications in economics

Abstract: Optimal transport is a core problem in economics and mathematics. At least one Nobel prize laureate (Kantorovich) and two Fields medalists (Villani, Figalli) primarily worked on optimal transport theory, and many others contributed to the research area substantially. Optimal transport also has wide applications in statistics, data science, image processing, programming, and finance.

In this short course we introduce basic concepts in optimal transport theory and discuss some recent applications in economics. We will focus on the setting of transport on the real line where results have the simplest forms. We will proceed to consider two specific models. First, we study a matching problem between workers and jobs in a labour market where discrepancy between worker skills and job tasks leads to output losses. In this setting, both positive and negative sorting assignments appear at the market equilibrium, which can be applied to data on wages, task content, and automation by occupation. Second, we propose a general framework which we call the simultaneous optimal transport. This framework is motivated by the need to transport resources of different types simultaneously, i.e., in single trips, from specified origins to destinations. In terms of matching, one needs to couple two groups, e.g., buyers and sellers, by meeting supplies and demands of different goods at the same time.

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