Robust estimation of the carbon dioxide airborne fraction under measurement errors

The carbon dioxide (CO2) airborne fraction, the proportion of anthropogenic CO2 emissions that remain in the atmosphere, is a critical metric for research on the carbon cycle and climate change. One possible complication with its estimation is that the data may contain measurement errors given old or unreliable tools, particularly in early years. Hence, this paper obtains estimates that are robust to measurement errors. We are the first to present estimates and standard errors for the regression-based estimator that are robust to measurement errors. Our estimates for the airborne fraction are 44.8%(+/- 1.4%; 1σ) for the simple specification, and 47.3%(+/- 1.1%; 1σ) for an extended specification that adds additional explanatory variables to reduce the variance of the errors. To achieve this goal, we add to the literature in several ways: we generalise the Deming regression to handle multiple variables; we introduce a bootstrap approach to construct confidence intervals for Deming regression; and we propose to estimate the airborne fraction using instrumental variables, using as instruments the variation of additional data sets.