Country-level sensitivity analysis

Let CAI denote the index for country i at time t. The world climate attention index is defined as follows:

where ω is a country-specific weight. We provide results based on three alternative weighting schemes: (i) by equally weighting all countries, (ii) by weighting each country proportionally to its share of global GDP, and (iii) by weighting each country proportionally to its share of Twitter volume. We then estimate the following regression:

where Δ refers to a percentage change over time. We regard β as a measure of exposure to a common, i.e., global, component, and u as a pure local component.