LAUSR

1Department of Earth System Science, Stanford University, Stanford, CA, USA. 2Center on Food Security and the Environment, Stanford University, Stanford, CA, USA. 3National Bureau of Economic Research, Cambridge, MA, USA. 4Instituto de Economia, Pontificia Univerdad Catolica de Chile, Santiago, Chile. 5Vancouver School of Economics, University of British Columbia, Vancouver, British Columbia, Canada. 6Department of Economics, University of Essex, Colchester, UK. 7Goldman School of Public Policy, University of California, Berkeley, CA, USA. ✉e-mail: [email protected] We thank Gammans1 for his careful replication of our work and engagement on this topic. Gammans is sceptical of our claim2 that future climate change might increase suicide risk, arguing that our data suggest that temperature increases merely hasten suicides that would have occurred soon after, and that our estimates represent the impact of ‘weather’ rather than ‘climate’. We address these concerns in order. There are two ways to study whether increased temperatures hasten deaths that would otherwise have occurred. The first is to estimate distributed lag models and examine whether a rise in temperature increases the likelihood of death by suicide in the contemporaneous period but reduces it in later periods. If the reduction of future suicides is equal to the magnitude of the initial spike, this would suggest that high temperatures simply hasten suicides that would have otherwise soon occurred and that the total number of suicides is unchanged (‘temporal displacement’). The second approach is to aggregate data temporally (for example, using annual rather than monthly data), with estimates from more aggregated data likely to net out any temporal displacement. Our original analysis2 used both of these approaches. We used monthly National Vital Statistics data from 1968 to 2004 (‘NHCS’ in our original analysis) to estimate distributed lag models with a single month lag, and used an independent annualized Underlying Cause of Death Dataset covering 1999–2013 (‘CDC’) to estimate impacts in more aggregated data (see Fig. 2 in Burke et al.2). Both approaches gave quantitatively similar estimates of the effect of temperature on suicide risk in the United States. Our original results in the United States suggested that some temporal displacement occurred, because roughly 40% of suicides that would have occurred in the next month occurred one month earlier due temperature. However, the remaining 60% of suicides associated with high monthly temperature were ‘additional’, either because a person who would have died by another cause, died instead by suicide or because they would have died by suicide in the far future (more than one month). Importantly, only these additional suicides were counted in our original projections of climate change. Gammans argues that including multiple additional lags in the 1968–2004 data causes the estimated combined effect of temperature to get smaller and to no longer be statistically significant (we replicate this result with six lags in Fig. 1a). In fact, Gammans’ results would suggest that warming temperatures save lives in Mexico because temporal displacement is greater than 100% by his approach. However, more recent detailed work3 on temperature and suicide in the United States by another research team shows that including additional lags does not diminish the cumulative effect of temperature when more recent data are used. Those authors attribute this result to earlier US temperature data being highly interpolated and thus measured with substantial error. This result is consistent with our original findings from the more recent CDC data (1999–2013). We also find support for this notion in our NHCS data that Gammans analysed. When we replicate Gammans’ analysis but restrict the sample to 1980–2004, the period during which the number of stations contributing to the PRISM dataset increased by roughly 50% (Fig. 2), the cumulative seven-month effect of temperature on suicide risk is positive, statistically significant and nearly identical to the effect in the contemporaneous month (Fig. 1b). The influence of sample years is made clear by re-estimating this six-lag model, starting with our full 1968–2004 sample and successively dropping earlier years (that is, 1969–2004, 1970–2004 and so on): estimates starting in the late 1970s using Gammans’ model converge to our original estimate and are statistically significant (Fig. 1c). We find the same pattern when we undertake an identical exercise in Mexico (Supplementary Fig. 1), although (as in our original paper) estimates in Mexico are much noisier overall and we cannot rule out either negative effects or very large positive effects once additional lags are included. In annually aggregated US data, Gammans shows that, in the full 1968–2004 sample, temperature is negatively but not statistically significantly correlated with suicide risk. However, similar to his monthly result, this is driven entirely by pre-1980 data. To show this, we again successively drop earlier years with less reliable data from the sample and find that once the sample is restricted to 1980–2004, estimated effects are positive, statistically significant and larger than our originally published estimate (Fig. 1d). We note that for these estimates, we estimate the model with year fixed effects rather than state-year fixed effects; when aggregating to the annual level, including state-year fixed effects eliminates ~63% of the remaining variation in our temperature variable relative to the model with year fixed effects, increasing concern (as in an earlier agricultural context4) that the remaining variation might be as much noise as signal. Indeed, when state-year fixed effects are included in the annually aggregated model, confidence intervals (CIs) are wider and estimates are no longer statistically distinguishable from zero. Reply to: Temporal displacement, adaptation and the effect of climate on suicide rates