Climate change and international migration: Exploring the macroeconomic channel

2.3 Model estimation We estimate the migration model defined in Eq 6a and 6b in three different steps. First we esti- mate the parameters that shape the emigration rate through the term F(Gi) on the right-hand side of Eq 6a. To this end we follow the method used in ref [26]. That is, where possible, we exclude return and refugee migration flows from the reported bilateral flows. We then aggre- gate the flows for each country of origin and divide the total outflow by the number of total population living in the country, to obtain emigration rates. Ultimately, we fit, through a non- linear least square (NLS) method, the emigration rate to the right-hand side of Eq 8: 1 Pi X l ~ M;i!l � ae � 1 1 þ Gi bG � 1 1 þ e gðGi ~GÞ ð11Þ where ae is a scaling factor. In the second step we fit international bilateral migration flows, that is the count of international population movements, against economic (e.g. GDP per cap- ita) and demographic (e.g. relative diaspora stocks) factors. We split the country specific scal- ing factors aj and bi into the product of a global factor a and b and country-specific factors ~aj and ~bi, respectively: ai ¼ a � ~aj and bi ¼ b � ~bi. While the migration data reports only aggre- gated origin to destination flows, our model would distinguish between the three different channels (transit, return and emigration from country of birth) contributing to the total bilat- eral flow. Reproducing the approach in ref. [26] we fit the reported [25] bilateral migration flows Mi,j to the sum of emigration from country of birth and return migration flows defined

in our model in Eq 6a and 6b: Mobs i!j � Mi;i!j þ Mj;i!j: ð12Þ Due to computational costs, we do not include the transit flows. These flows have been shown to have a very small share in the total emigration compared to return and emigration from country of birth flows [38]. While presenting its limitations this method is still an improve- ment in the granularity of the modeled flows compared to previous methods. The parameters entering in F(Gi) are set to the values estimated in the first step, while the country-specific scal- ing factors ~aj and ~bi are not included here. We use a (NLS) method of estimation which allows us to implement the additive form of the model. Commonly, previous studies log-transform the model in order to interpret the coefficients as elasticities. The additive form of our model does not allow us to follow this procedure. Nonetheless it produces results in line with previous works, with the diaspora representing a strong pulling factor and the destination GDPc being positively correlated to the migration flow. In the last step, using an OLS method, we estimate the country-specific scaling factors on the mean bilateral migration flows, while keeping the remaining parameters set at the values estimated in the previous steps. Gravity models are often estimated through a Pseudo-Poisson maximum likelihood (PPML) estimator, reducing the risk of obtaining biased estimates, or by a log-log transforma- tion which allows to interpret the coefficients as elasticities using OLS methods. Our model

specification refrains us from using any of these methods. The log-log transformation would reduce the data by dropping the zero migration flows as well as those flows that have a zero diaspora value. This could itself lead to strongly biased estimates. The additive form of our model, where we fit the bilateral migration flow as the sum of return and emigration from country of birth flow, makes the log-log transformation obsolete. The same considerations hold for using the PPML method. Finally, alternative specifications of the model where dyadic variables as common border, official language and colonial ties as well as the geographical PLOS ONE Climate change and international migration: Exploring the macroeconomic channel PLOS ONE | https://doi.org/10.1371/journal.pone.0276764 November 16, 2022 10 / 25