Open Collections

Catalano, Joshua

University of British Columbia

Chapter 2, co-authored with Vadim Marmer and Paul Schrimpf, introduces the partition model, a novel extension of a multi-dimensional threshold model. In particular, this partition model permits more geometrically sophisticated subsets than previously existing threshold models. We formulate an extension of an existing tree regularization algorithm to estimate this model because the standard algorithm cannot guarantee consistent estimation of our model, even if the partition can be represented as a binary tree. While the preponderance of the regression tree literature focuses on non-parametric estimation, we establish the conditions under which our variation of the estimator can be interpreted parametrically. Notably, we assume partitioning variables are independent from one another. We prove that the partition estimator we propose is hyper-consistent. In Chapter 3, also co-authored with Vadim Marmer and Paul Schrimpf, we relax the independence assumption and allow for correlated partitioning variables. Under such correlation, the regression tree algorithm in Chapter 2 may not partition correctly. Consequently, we introduce a local version of the regression tree algorithm. It is local in the sense that observations closer to a proposed split are given more weight when estimating coefficients and evaluating fit. This modification allows us to recover a hyper-consistent estimation of the partition model even in the presence of heavy correlation. We demonstrate the properties of both the local and non-local estimators via simulations. In Chapter 4, we present a novel difference-in-differences framework, wherein groups of cross-sectional units are delineated by an unknown partition of some observable variables’ support. Units belonging to different groups may face heterogeneous treatment probabilities, and their untreated outcomes will follow distinct, group-level trends. As a result, the unconditional parallel trends assumption will generally not hold. To uncover this unknown partition, we model trends in the outcome variable as a partition model and estimate it using pre-treatment data. Subsequently, difference-in-differences estimation and inference can be carried out for each group separately, allowing for the expression of untargeted, inter-group treatment effect heterogeneity. We demonstrate this method via simulation and apply it to estimate the effect of recreational cannabis legalization in Washington State on agricultural employment using county- level data.

Text

2024-08-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/88872

Economics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/