Climate change and international migration: Exploring the macroeconomic channel

The first term, depending on bG, is assumed to capture the desire to migrate, which reaches a maximum for Gi = 0 and approaches zero for large values of Gi. The second term, depending on ~G, is assumed to capture the dependence of the emigration rate on economic resources at the origin: it assumes a minimum for Gi = 0 and approaches the maximum of one for Gi � ~G. As we introduced at the beginnng of the Methods section, we test three alternative assump- tions about the relation between origin-country GDPc and emigration rates. The CR, constant rates, assumption is implemented in our model by keeping emigration rates constant at the value prescribed by Eq 8 using the country-level mean GDPc for the his- torical period (1990–2015). Under the T0 assumption countries undergo a transition along the migration hump with respect to their absolute real income levels. That is, we evaluate Eq 8 at the historical values of GDPc. Finally, under the TS assumption the migration transition occurs with respect to relative income levels. To this end, we shift the migration hump function towards higher GDPc values over time, along with rising global average GDPc. The shift depends on the growth rate r between the global mean GDPc for the historical period, �Ghist, and the period of interest �Gproj: r ¼ �Ghist �Gproj 1: ð9Þ The transformation Gi ! Gi � (1 + r), with r < 0, produces a shift of the migration hump towards the higher values of GDPc (Fig 2, dashed line) and the shifted migration-hump func- tion can be written as follows: FðGiÞ ¼ 1 1 þ Gi � ð1 þ rÞ bG � 1

1 þ e gðGi�ð1þrÞ ~GÞ : ð10Þ While the rate of change r is equal for all GDPc points, the actual shift depends on the specific GDPc value and is equal to Gi�r. This means that, on a linear scale, the function will appear as a combination of dilation and translation. If an individual country’s GDPc grows at the same rate as the global average GDPc, then the country’s emigration rate remains constant. We then produce global bilateral migration flows using a 5-years step and covering the 30-years period defined above. We calculate bilateral migration flows for each country of birth–country of origin–country of destination triad. We calculate this set of global bilateral flows for the baseline case as well as for the case of perturbed GDPc under global warming, for each impact method, GCM and SSP scenario. These computations are repeated under the three assumptions regarding emigration rates (CR,T0,TS). In principle, the baseline popula- tion distribution entering our calculations will be different for each climate model and sce- nario, reflecting the distribution of each 30-years period. For simplicity, we use the same baseline population distribution for all the simulations. Across climate models and SSP scenar- ios, the average period for reaching the 3˚C warming is [2046–2075]. We use the population in this period for all simulations. This means that we break the direct association between socio- economic development and GHG forcing implied in the SSP scenarios. This is not a problem

for our study because we are not aiming to produce transient, combined projections of climate, migration, population, and GDP; but rather, to isolate the effect of climate change on migra- tion through GDP while keeping other variables (including initial population) fixed. We construct our analysis by comparing, separately for each of the assumptions regarding emigration rates and each scenario, the migration flows under climate change impact to the baseline case, after averaging the migration flows on both dimensions of time and climate models. PLOS ONE Climate change and international migration: Exploring the macroeconomic channel PLOS ONE | https://doi.org/10.1371/journal.pone.0276764 November 16, 2022 9 / 25