##### Department of Mathematics,

University of California San Diego

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### Department Colloquium

## Chan Park

#### Department of Statistics, Wharton School of Business, University of Pennsylvania

## Single Proxy (Synthetic) Control

##### Abstract:

A negative control outcome (NCO) is an outcome that is associated with unobserved confounders of the effect of a treatment on an outcome in view, and is a priori known not to be causally impacted by the treatment. In the first half of the talk, we discuss the single proxy control (SPC) framework, a formal NCO method to detect and correct for residual confounding bias. We establish nonparametric identification of the average causal effect for the treated (ATT) by treating the NCO as an error-prone proxy of the treatment-free potential outcome, a key assumption of the SPC framework. We characterize the efficient influence function for the ATT under a semiparametric model in which nuisance functions are a priori unrestricted. Moreover, we develop a consistent, asymptotically linear, and locally semiparametric efficient estimator of the ATT using modern machine learning theory. Shifting to the second half of the talk, we introduce the single proxy synthetic control (SPSC) framework, an extension of the SPC framework designed for a synthetic control setting, where a single unit is treated and pre- and post-treatment time series data are available on the treated unit and a heterogeneous pool of untreated control units. Similar to SPC, the SPSC framework views the outcomes of untreated control units as proxies of the treatment-free potential outcome of the treated unit, a perspective we formally leverage to construct a valid synthetic control. Under this framework, we establish alternative identification and estimation methodology for synthetic controls and, in turn, for the ATT. Additionally, we adapt a conformal inference approach to perform inference on the treatment effect, obviating the need for a large number of post-treatment data. We illustrate the SPC and SPSC approaches with real-world applications from the Zika virus outbreak in Brazil and the 1907 financial crisis.

### February 5, 2024

### 4:00 PM

APM 6402

Research Areas

Statistics****************************