Estimating Causal Effects When the Treatment Affects All Subjects Simultaneously: An Application

Chiara Binelli

doi:10.3390/bdcc5020022

Abstract

Several important questions cannot be answered with the standard toolkit of causal inference since all subjects are treated for a given period and thus there is no control group. One example of this type of questions is the impact of carbon dioxide emissions on global warming. In this paper, we address this question using a machine learning method, which allows estimating causal impacts in settings when a randomized experiment is not feasible. We discuss the conditions under which this method can identify a causal impact, and we find that carbon dioxide emissions are responsible for an increase in average global temperature of about 0.3 degrees Celsius between 1961 and 2011. We offer two main contributions. First, we provide one additional application of Machine Learning to answer causal questions of policy relevance. Second, by applying a methodology that relies on few directly testable assumptions and is easy to replicate, we provide robust evidence of the man-made nature of global warming, which could reduce incentives to turn to biased sources of information that fuels climate change skepticism.

Highlights

An emerging literature has discussed the contributions of Machine Learning (ML) to address relevant policy questions [1,2,3,4,5]
The Bayesian Structural Time Series (BSTS) method generalizes the differences in differences (DID) estimator to a timeseries setting by modeling the counterfactual of a time series observed before and after a treatment
There are several research questions that cannot be answered using the standard social sciences’ quantitative toolkit of causal inference, since the treatment affects all subjects simultaneously. One example of this type of question is the causal impact of anthropogenic emissions on global warming

Summary

Introduction

In order to measure the causal impact of the increase in CO2 emissions on global temperature, we use the increase in CO2 emissions in 1960 as the treatment that could have affected the temperature time series, and, define the years between 1850 and 1959 as the pre-treatment period, and the years between 1960 and 2011 as the post-treatment period. We use the model to predict the counterfactual, that is, the time series of temperature anomalies in the post-treatment period if radiative forcing due to CO2 emissions had remained stable at the 1959 level. For every year between 1960 and 2011, the difference between the actual time series of temperature anomalies and the counterfactual series provides a causal estimate of the impact of CO2 emissions on global temperature. The vector αt is built by concatenating the individual state components, and Tt and Rt are blocks of diagonal matrixes

Prior Distributions and Elicitation

Inference

Estimation

Identification and Validity

Main Results

Discussion