Climate change and international migration: Exploring the macroeconomic channel

results from the cross-sectional regression model [13], resulting in a log-linear damage func- tion on the GDPc level, as in Eq 10 in ref. [13]: lnðGw i ðtÞÞ lnðGiðtÞÞ ¼ aT DTiðtÞ ð2Þ where αT is a negative constant factor. Gi(τ) is the baseline GDPc level in country i at time τ, as prescribed by the SSP scenario. Gw i ðtÞ is the same but under the climate change impact. The temperature is redefined as the mean of the annual temperature over a 5-years period: TiðtÞ ¼ 1 5 P4 l¼0 Tiðt lÞ. The total warming in country i at time τ is defined relative to the tem- perature of the period of reference (i.e. 2011–2015): ΔTi(τ) = Ti(τ) − Ti (2015). This notation highlights the assumption that the warming happening during a 5-years period affects the GDPc at the end of that same period, and that the impacted GDPc trajectory starts diverging from the baseline after the period of reference. This means that, while considering a period of 3˚C level of global warming above pre-industrial conditions, the impact on the GDPc is calcu- lated relative to a recent period, which has already seen * 1˚C of warming. Therefore our impact study focuses on the effect of additional 2˚C global warming. By solving Eq 2 for Gw i ðtÞ we can calculate the projected GDPc under global warming, for a country i at time τ as in Eq 3: Gw i ðtÞ ¼ GiðtÞ � eaT DTiðtÞ: ð3Þ It is worth noting that in case of no further warming, Eq 3 reduces to the GDPc trajectory pre- scribed by the SSP scenario, otherwise the warming will affect the GDPc once and for all at any time τ in the future.

The second approach for estimating the impact of climate change on the economic produc- tivity of the country follows the results from a panel regression model [13]. From equation S3 in the supplementary materials of ref. [13], the warming effect term in the GDPc growth rate can be written as diðtÞ ¼ a1DTiðtÞ þ a2DTiðt 1Þþ ðb1DTiðtÞ þ b2DTiðt 1ÞÞ� Tið0Þ þ X t 1 j¼1 DTiðjÞ ! ð4Þ where α1, α2, β1, β2 are constant factors. The annual changes in temperature are defined as ΔTi(t) = Ti(t) − Ti(t − 1), where the Ti(t) represents the annual temperature in country i at time t. The temperature of reference Ti(0) is the observed temperature in the year 2015 and ΔTi(0) is assumed to be zero. Following the approach for defining the multiplicative damage function in equation S5 of the supplementary materials in ref [13], the GDPc projection under the global warming impact is prescribed by: Gw i ðtÞ ¼ GiðtÞ � e Pt l¼1 diðlÞ: ð5Þ That is, in this short-term approach, the history of temperature changes matters, and therefore differences in the rate of warming between climate models or scenarios can affect the results. 2.2.4 Migration model. We use a global model of international migration that is cali- brated on historical bilateral flow data [25], and has been shown to represent current patterns of bilateral migration well, despite relying on just a small number of predictor variables [26]. Note that refugee movements are not accounted for in the model, as these are assumed to have different causes and dynamics than regular migration [34]. PLOS ONE

Climate change and international migration: Exploring the macroeconomic channel PLOS ONE | https://doi.org/10.1371/journal.pone.0276764 November 16, 2022 7 / 25