2. Model

To estimate the mobility responses to climate change, we set up an overlapping generations model of the world economy that endogenizes the dyadic and skill structures of migration. We model migration decisions as an outcome of a micro-founded, random utility maximization (RUM) model that jointly accounts for the main migration mechanisms through which climate change affects long-term migration. The RUM structure allows us to model the long-term mobility responses to climate change at various spatial scales, taking into account the interplay between alternative forms of migration: specifically local (i.e., very short distance), rural to urban (i.e., short distance), and international (i.e., long distance). Endogenous migration decisions are embedded in a general equilibrium framework with endogenous income distribution. Therefore, the effects of climate change on human mobility, global income inequality, and extreme poverty are jointly determined. Our framework assumes exogenous socio-demographic trends in line with the United Nations median scenario, and does not account for capital and trade. We discuss these assumptions in section 2.4. The model relies purely on a production technology and a migration technology.

More specifically, our model depicts a large set of countries and regions. Countries are denoted byj = 1, …, J, and comprise two regions (a region is equivalent to a production sector in our context) having heterogeneous productivity levels, with r ∈ {a, n} denoting agriculture (a) and non-agriculture (n). The double index jr is used to identify a country-region location. Each region consists of two areas of time-varying size, with the subscript b ∈ {f, d} denoting the flooded area (f) and the non-flooded/dry area (d). Floods are permanent and caused by rising sea levels; they materialize at the beginning of the period. There is no economic activity and no one can live in the flooded area. Hence, we distinguish between individuals who grew up in a region that becomes flooded and were forced to move in adulthood, and those who grew up in a non-flooded region and could choose between staying or leaving. This allows us to distinguish between forced displacements (driven by the sea level rise) and voluntary migration (driven by economic incentives).

Individuals live for two periods (childhood and adulthood). One period represents the active life of one generation (30 years); for simplicity, we ignore the retirement period. Adults are the only decision makers. For each location jr and each period, we distinguish between two types of adults, with s ∈ {h, l} denoting college-educated workers (h) and the less educated (l). This allows us to account for the high degree of heterogeneity in migratory behavior between people of different places of origin and levels of education. We use $N_{b, s, t}^{jr}$ to denote the number of new adults of type s born in the area b of location jr at time t − 1 (i.e., becoming adult at timet). The total native population in location jr is defined as $N_{s, t}^{jr} = N_{d, s, t}^{jr} + N_{f, s, t}^{jr}$. Adults maximize their utility by deciding where to live. That is, whether to stay in the region where they grew up (if the area where they were born does not become flooded), to move locally within the same region (if the area where they were born becomes flooded), to emigrate to the other region within the same country, or to emigrate abroad. This choice depends on the livability of the area of origin, on economic disparities across regions and countries, and on the cost of moving. It determines the number of residents in each (non-flooded) location, denoted by $L_{s, t}^{jr}$.

In this section, we describe our production and migration technologies (sections 2.1 and 2.2), and derive the profit and utility maximization conditions. We then define the world-economy intertemporal equilibrium in section 2.3. We discuss our simplifying assumptions in section 2.4.

2.1 Production technology

The production technology determines the wage rates in each location. Production is feasible only in the non-flooded area of each location jr. Output is proportional to labor in efficiency units, and for simplicity, we assume that firms in both sectors produce the same good. Each location is characterized by a constant elasticity of substitution production function with two types of workers [as in Burzyński et al. (Reference Burzyński, Deuster and Docquier2020); Gollin et al. (Reference Gollin, Lagakos and Waugh2014); Vollrath (Reference Vollrath2009)]. The output level in location jr at time t is given by:

(1)$$Y_t^{\,jr} = A_t^{\,jr} \left({\displaystyle{{\eta_t^{\,jr} } \over {1 + \eta_t^{\,jr} }}L{_{h, t}^{\,jr} }^{{{\sigma^r-1} \over {\sigma^r}}} + \displaystyle{1 \over {1 + \eta_t^{\,jr} }}L{_{l, t}^{\,jr} }^{{{\sigma^r-1} \over {\sigma^r}}}} \right)^{{{\sigma ^r} \over {\sigma ^r-1}}}\;\quad \forall t, \;r, \;$$

where $A_t^{jr}$ denotes the productivity scale factor in location jr at time t (referred to as TFP henceforth), $\eta _t^{jr}$ is a sector-specific variable governing the relative productivity of college-educated workers at time t (i.e., a skill bias in productivity), and σ ^r is the sector-specific elasticity of substitution between the two types of workers. Remember the number of adult workers of type s employed in location jr at time t is denoted by $L_{s, t}^{jr}$.

The labor market is competitive. Wage rates are determined by the marginal productivity of labor:

(2)$$\left\{{\matrix{ {w_{h, t}^{\,jr} = A{_t^{\,jr} }^{{1 \over {\sigma^r-1}}}{\left({\displaystyle{{\eta_t^{\,jr} } \over {1 + \eta_t^{\,jr} }}L{_{h, t}^{\,jr} }^{{{\sigma^r-1} \over {\sigma^r}}} + \displaystyle{1 \over {1 + \eta_t^{\,jr} }}L{_{l, t}^{\,jr} }^{{{\sigma^r-1} \over {\sigma^r}}}} \right)}^{{1 \over {\sigma^r-1}}}\displaystyle{{\eta_t^{\,jr} } \over {1 + \eta_t^{\,jr} }}L{_{h, t}^{\,jr} }^{{{-1} \over {\sigma^r}}}} \cr {w_{l, t}^{\,jr} = A{_t^{\,jr} }^{{1 \over {\sigma^r-1}}}{\left({\displaystyle{{\eta_t^{\,jr} } \over {1 + \eta_t^{\,jr} }}L{_{h, t}^{\,jr} }^{{{\sigma^r-1} \over {\sigma^r}}} + \displaystyle{1 \over {1 + \eta_t^{\,jr} }}L{_{l, t}^{\,jr} }^{{{\sigma^r-1} \over {\sigma^r}}}} \right)}^{{1 \over {\sigma^r-1}}}\displaystyle{1 \over {1 + \eta_t^{\,jr} }}L{_{l, t}^{\,jr} }^{{{-1} \over {\sigma^r}}}} \cr } } \right.\quad \forall t, \;r.. $$

It follows that the wage ratio between high-skilled and low-skilled workers in location jr at time t is given by:

(3)$$\varpi _t^{\,jr} \equiv \displaystyle{{w_{h, t}^{\,jr} } \over {w_{l, t}^{\,jr} }} = \eta _t^{\,jr} ( {z_t^{\,jr} } ) ^{{{-1} \over {\sigma ^r}}}\;\;\;\;\forall t, \;r, \;$$

where $z_t^{jr} \equiv L_{h, t}^{jr} {\rm /}L_{l, t}^{jr}$ is the skill ratio in employment in location jr at time t.

In our setting, climate change affects production and income differentials through two channels. First, variations in temperature influence TFP in agricultural and in the non-agricultural sector. Second, climate change affects mobility decisions, which in turn impact on the skill ratio in the labor force. To account for these effects, damage functions and technological externalities are factored in. For TFP, we assume that the aggregate TFP level in each sector depends on the temperature level and the average level of workers' education. We thus have:

(4)$$A_t^{\,jr} = \gamma ^t\bar{A}^{\,jr}G( {T_t^{\,jr} } ) F( {z_t^{\,jr} } ) \;\;\;\;\forall t, \;r, \;$$

where γ ^t is a time trend in productivity that is common to all countries (γ > 1), $\bar{A}^{jr}$ is the exogenous component of TFP in location jr (reflecting specific local factors such as the proportion of arable land, soil fertility, land ruggedness, etc.), $G( {T_t^{jr} })$ links TFP to temperature $( {T_t^{jr} })$, while $F( {z_t^{jr} })$ is a simple Lucas-type aggregate externality [see Lucas (Reference Lucas1988)] capturing the fact that college-educated workers facilitate innovation and/or the adoption of advanced technologies. We assume $F( {z_t^{jr} } ) = ( {z_t^{jr} } ) ^{\epsilon _r}$ is a concave function of the skill ratio in employment, where ε _r ∈ (0, 1) is the sector-specific elasticity of TFP to the skill ratio in region/sector r of all countries. With regard to the effect of temperature, existing literature suggests that TFP levels in agriculture and non-agriculture can be represented by sector-specific, inverted-U-shaped functions of $( {T_t^{jr} })$, as discussed in section 3 [Desmet et al. (Reference Desmet, Nagy and Rossi-Hansberg2018); Shayegh (Reference Shayegh2017)].

With regard to the skill bias, we assume directed technical change that affects different types of workers non-uniformly. As technology improves, the relative productivity of college-educated workers increases, particularly in the non-agricultural sector [Acemoglu (Reference Acemoglu2002); Restuccia and Vandenbroucke (Reference Restuccia and Vandenbroucke2013)]. The observed relative demand shift favors college-educated over non-college-educated labor. We thus have:

(5)$$\eta _t^{\,jr} = \bar{\eta }^{\,jr}( {z_t^{\,jr} } ) ^{\kappa _r}\;\;\;\;\forall t, \;r, \;$$

where $\bar{\eta }_{jr}$ is an exogenous term and κ _r ∈ (0, 1) is the sector-specific elasticity of the skill bias to the skill ratio in sector/region r of all countries.

2.2 Migration technology

To model migration decisions, our RUM model assumes that the utility of moving to a given location is the sum of deterministic and random components. The deterministic part has a logarithmic functional form and depends on the local wage rate at destination and the costs of moving. The random part captures heterogeneity in preferences or in moving costs. Hence, the utility of an adult of type s, born in the area b of a location of origin jr, moving to the (non-flooded) area of a location j′r′ is given by:

(6)$$U_{b, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} = \ln w_{s, t}^{{\,j}^{\prime}{r}^{\prime}} + \ln \left( {1-x_{b, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} } \right) + \xi _{b, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} \quad \forall s, \;t, \;jr, \;{\,j}^{\prime}{r}^{\prime}$$

where $\ln w_{s, t}^{{j}^{\prime}{r}^{\prime}} \in {\rm {\opf R}}$ is the deterministic level of utility that can be reached in the location j′r′ at period t and $x_{b, s, t}^{jr, {j}^{\prime}{r}^{\prime}} \le 1$ captures the effort required to migrate from location jr to location j′r′. Migration costs are exogenous; they vary across location pairs and education levels. The individual-specific random taste shock for moving from location jr to j′r′ is denoted by $\xi _{b, s, t}^{jr, {j}^{\prime}{r}^{\prime}} \in {\rm {\opf R}}$ and follows an i.i.d. type I extreme value distribution with a common scale parameter μ > 0. This scale parameter governs the responsiveness of migration decisions to changes in $w_{s, t}^{{j}^{\prime}{r}^{\prime}}$ and to $x_{b, s, t}^{jr, {j}^{\prime}{r}^{\prime}}$. Although $\xi _{b, s, t}^{jr, {j}^{\prime}{r}^{\prime}}$ is individual specific, we omit individual subscripts for notational convenience.

It should be remembered that the number of new native adults of type s at time t is denoted by $N_{s, t}^{jr}$. Depending on the elevation structure of the location and on the sea level rise, part of the location of birth may be flooded at the beginning of the period. If so, a proportion $\Theta _t^{jr}$ of the native-born population is forced to leave. We label the number of forcibly displaced people as $N_{f, s, t}^{jr} = \Theta _t^{jr} N_{s, t}^{jr}$, and the rest of the native population as $N_{d, s, t}^{jr} = ( {1-\Theta_t^{jr} } ) N_{s, t}^{jr}$. Only the latter can decide whether to stay in the area of birth. Hence, those who grew up in the non-flooded area of location jr have the choice between emigrating to another region jr′ within the same country (at a cost $x_{d, s, t}^{jr, j{r}^{\prime}}$), emigrating to a foreign country (at a cost $x_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}}$), or staying. In the last case, they incur no cost associated with moving. This means that $x_{d, s, t}^{jr, jr} = 0$.

By contrast, individuals who grew up in the flooded area have the option to relocate within the same region (from a flooded to a non-flooded area). They incur a welfare loss that corresponds to a fraction $x_{f, s, t}^{jr, jr} > 0$ of their lifetime utility (which is equivalent to an income loss of $x_{f, s, t}^{jr, jr}$ percent in our context). They can also emigrate to another region or to another country at the same cost as those who grew up in the non-flooded area (i.e., $x_{f, s, t}^{jr, {j}^{\prime}{r}^{\prime}} = x_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}}$).

We first focus on people who grew up in the non-flooded area (d) of their location of birth. Given their taste characteristics (captured by ξ), each individual chooses the location that maximizes her utility, defined in equation (6). Under the type I extreme value distribution of ξ with a scale parameter μ, McFadden (Reference McFadden and Zarembka1974) shows that the probability of choosing region j′r′ for individuals originating from region jr is governed by a logit expression. Therefore, the emigration rate is given by

(7)$$\displaystyle{{M_{d, s, t}^{\,jr, j^{\prime}r^{\prime}} } \over {N_{d, s, t}^{\,jr} }} = \displaystyle{{\exp \left( {\ln {\left( {w_{s, t}^{\,j^{\prime}r^{\prime}} \left( 1-x_{d, s, t}^{\,jr, j^{\prime}r^{\prime}} \right) } \right) }^{1/\mu }} \right) } \over {\sum\limits_{kp} {\exp } \left( {\ln {\left( {w_{s, t}^{kp} \left( 1-x_{d, s, t}^{\,jr, kp} \right)} \right) }^{1/\mu }} \right)}} = \displaystyle{{{\left( w_{s, t}^{\,j^{\prime}r^{\prime}} \right)}^{1/\mu }{\left( 1-x_{d, s, t}^{\,jr, j^{\prime}r^{\prime}} \right) }^{1/\mu }} \over {\sum\limits_{kp} {{\left( w_{s, t}^{kp} \right) }^{1/\mu }} {\left( 1-x_{d, s, t}^{\,jr, kp} \right) }^{1/\mu }}}.$$

Hence, emigration rates are endogenous, destination- and skill-specific, and fall between 0 and 1. The choices of emigrating internally or internationally are interdependent. Staying rates $( M_{d, s, t}^{jr, jr} {\rm /}N_{d, s, t}^{jr} )$ are expressed by a similar logit expression. It follows that the emigrant-to-stayer ratio $( m_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}} )$ is governed by:

(8)$$m_{d, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} \equiv \displaystyle{{M_{d, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} } \over {M_{d, s, t}^{\,jr, jr} }} = \left({\displaystyle{{w_{s, t}^{{\,j}^{\prime}{r}^{\prime}} } \over {w_{s, t}^{\,jr} }}} \right)^{1{\rm /}\mu }\left( {1-x_{d, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} } \right) ^{1{\rm /}\mu }, \;$$

such that $m_{d, s, t}^{jr, jr} = 1$.

Equation (8) is a gravity-like migration equation, which states that the ratio of emigrants from location jr to location j′r′ to stayers in region jr (i.e., individuals born in jr who remain injr) is an increasing function of the wage rate in the destination location j′r′ and a decreasing function of the utility in jr. The proportion of migrants from jr to j′r′ also decreases with the bilateral migration cost $x_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}}$. Labor is not perfectly mobile across sectors/regions; internal migration costs capture all private costs that migrants must incur to move between regions.Footnote ⁴ Similarly, international migration costs capture private costs as well as the legal/visa costs imposed by destination countries. They are also assumed to be exogenous. Heterogeneity in migration tastes implies that emigrants select all destinations for which $x_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}} < 1$ (if $x_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}} = 1$, the corridor is empty).

Individuals raised in the flooded area of location jr (denoted by the superscript f) are forced to move. If they relocate to the non-flooded area of their region of birthjr, they face a local relocation cost equivalent to $x_{f, s, t}^{jr, jr} > 0$. If they move to another country or region, they will incur the same moving costs as individuals born in the non-flooded area (i.e., $x_{f, s, t}^{jr, {j}^{\prime}{r}^{\prime}} = x_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}} \;\forall jr\ne {j}^{\prime}{r}^{\prime}$). The local relocation cost influences decisions to emigrate to another region or country. The emigrant-to-stayer ratio $( m_{r^\ast r, s, t}^f )$ for forcibly displaced people is governed by:

(9)$$m_{\,f, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} \equiv \displaystyle{{M_{\,f, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} } \over {M_{\,f, s, t}^{\,jr, jr} }} = \left({\displaystyle{{w_{s, t}^{{\,j}^{\prime}{r}^{\prime}} } \over {w_{s, t}^{\,jr} }}} \right)^{1{\rm /}\mu }\left({\displaystyle{{1-x_{d, s, t}^{\,jr, {\,j}^{\prime}{r}^{\prime}} } \over {1-x_{\,f, s, t}^{\,jr, jr} }}} \right)^{1{\rm /}\mu }, \;$$

such that $m_{f, s, t}^{jr, jr} = 1$. In addition, since $x_{f, s, t}^{jr, jr} > 0$, $m_{f, s, t}^{jr, {j}^{\prime}{r}^{\prime}} > m_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}}$, forcibly displaced people are more likely to migrate than those who grew up in non-flooded regions.

For simplicity, we assume that international migrants settle in the urban region of their destination country. This choice is guided by the fact that the data used to calibrate the migration technology do not document the region of destination for international migrants. This means that $m_{b, s, t}^{jr, {j}^{\prime}a} = 0$ or, equivalently, $x_{b, s, t}^{jr, {j}^{\prime}a} = 1\;\forall j\ne {j}^{\prime}$. We can define the ratio of international emigrants to stayers as:

(10)$$m_{b, s, t}^{\,jr, F} \equiv \mathop \sum \limits_{{\,j}^{\prime}\ne j} m_{b, s, t}^{\,jr, {\,j}^{\prime}n} , \;$$

Once emigrant-to-stayer ratios are determined, we can characterize the equilibrium structure of the resident labor force in (the non-flooded area of) all regions and by education level. We thus have:

(11)$$L_{s, t}^{\,jr} = \mathop \sum \limits_{b, {\,j}^{\prime}, {r}^{\prime}} \displaystyle{{m_{b, s, t}^{{\,j}^{\prime}{r}^{\prime}, jr} N_{b, s, t}^{{\,j}^{\prime}{r}^{\prime}} } \over {1 + m_{b, s, t}^{{\,j}^{\prime}{r}^{\prime}, {\,j}^{\prime}r} + m_{b, s, t}^{{\,j}^{\prime}{r}^{\prime}, jr} }}.$$

2.3 Dynamics and intertemporal equilibrium

The dynamics of the native population are governed by fertility and education decisions. In contrast to Burzyński et al. (Reference Burzyński, Deuster and Docquier2020) and Burzyński et al. (Reference Burzyński, Deuster, Docquier and de Melo2019), we assume that these decisions are exogenous. We use $n_{s, t}^{jr}$ to denote the number of children of parent of type s living in (the non-flooded area of) location jr at time t. We denote by $p_{s, t}^{jr}$ the proportion of children acquiring a college education. It follows that the dynamic structure of the model is totally recursive. Accordingly, we have:

(12)$$\left\{{\matrix{ {N_{h, t + 1}^{\,jr} = \sum\limits_{s, b} {L_{s, t}^{\,jr} } n_{s, t}^{\,jr} p_{s, t}^{\,jr} } \hfill \cr {N_{l, t + 1}^{\,jr} = \sum\limits_{s, b} {L_{s, t}^{\,jr} } n_{s, t}^{\,jr} ( 1-p_{s, t}^{\,jr} ) } \hfill \cr } } \right.$$

An inter-temporal equilibrium for the world economy can be defined as follows:

Definition 1 For a set {μ, γ, σ _r, ε _r, κ _r} of common parameters, a set of location-specific exogenous characteristics $\{ {\bar{A}_t^{jr} , \;\bar{\eta }_t^{jr} , \;\Theta_t^{jr} , \;n_{s, t}^{jr} , \;p_{s, t}^{jr} , \;x_{b, s, t}^{jr, {j}^{\prime}{r}^{\prime}} } \}$, and a set $\{ {N_{s, 0}^{jt} } \}$ of predetermined variables, an intertemporal competitive equilibrium is a set of endogenous variables $\left\{ {w_{s, t}^{jr} , \;A_{r, t}, \;\eta_t^{jr} , \;m_{d, s, t}^{jr, {j}^{\prime}{r}^{\prime}} , \;m_{f, s, t}^{jr, {j}^{\prime}{r}^{\prime}} , \;L_{s, t}^{jr} , \;N_{s, t + 1}^{jr} } \right\}$, that simultaneously satisfies profit maximization conditions and technological constraints (2), (4) and (5), utility maximization conditions (8) and (9) in all countries and regions of the world, and such that the equilibrium structure and dynamics of population satisfy equations (11) and (12).

3. Parameterization

Our model is calibrated for 179 countries accounting for more than 99% of the world population. Our parameterization strategy involves three steps. First, we calibrate common and location-specific parameters in order to (perfectly) match socio-demographic and economic moments for the year 2010 (referred to as the year 0 below) or for the period 1980–2010. The set of socio-demographic moments includes internal and international migration flows. Second, we define a socio-demographic trajectory for the twenty-first century that is in line with official projections of population, urbanization, and human capital. Third, we describe our climate damage functions under three climate scenarios.

Matching the current state of the world: We collect data on the socio-demographic and economic characteristics of 179 countries in 1980 and 2010. We use data on Gross Domestic Product (GDP) from the United States Department of Agriculture (USDA) and the proportion of agricultural production in value added from the Food and Agriculture Organization of the UN (FAOSTAT). This determines $Y_0^{jr}$. For the structure of the resident labor force by education level and by sector $( L_{s, 0}^{jr} )$, we use the estimates described in Burzyński et al. (Reference Burzyński, Deuster and Docquier2020). Data on wages by education level $( w_{s, 0}^{jr})$ are obtained from Biavaschi et al. (Reference Biavaschi, Burzyński, Elsner and Machado2020) for the non-agricultural sector and from the Gallup World Polls for the agricultural sector. We extract the dyadic numbers of international migrants by education level for 2010 from the Database on Immigrants in OECD and non-OECD countries. Within each country, we split the number of emigrants by region of origin and education level, assuming that the structure of migration aspirations (obtained from the Gallup World Polls) is identical to the structure of actual emigration stocks. This gives $M_{s, 0}^{jr, {j}^{\prime}{r}^{\prime}}$.

With regard to technological parameters are concerned, we calibrate the elasticity of substitution between college graduates and less educated workers (σ ^r), relying on existing studies. For the non-agricultural sector we follow Ottaviano and Peri (Reference Ottaviano and Peri2012), who suggest setting the elasticity close to 2, whereas for the agricultural sector, it is usually assumed that the substitution is perfect [e.g., Lucas (Reference Lucas2009); Vollrath (Reference Vollrath2009)]. Using equation (3), we then calibrate the skill-bias term, $\eta _t^{jr}$, so as to match the observed income ratio between skill groups. Using equation (1), we calibrate the TFP level, $A_0^{jr}$, in order to match the observed level of GDP. Regressing the logs of $\eta _0^{jr}$ and $A_0^{jr}$ on the log of the skill ratio, we identify the size of the technological externalities (ε ^randκ ^r). Last, $\bar{A}^{jr}$ and $\bar{\eta }^{jr}$ are identified as residuals from equations (4) and (5).

With regard to the migration technology, Bertoli and Fernández-Huertas Moraga (Reference Bertoli and Fernández-Huertas Moraga2013) find a value between 0.6 and 0.7 for the migration elasticity to income disparities, captured by 1/μ in our model. Hence, we use μ = 1.4. We obtain international and internal migration costs $( x_{s, 0}^{jr, {j}^{\prime}{r}^{\prime}} )$ as residuals from equation (8). As climate change is expressed in terms of deviations from the current state of the world, we do not account for any climate change-related flooded areas in the year 2010. For internal migration costs, we assume positive migration from rural to urban regions (i.e., $x_{s, 0}^{ja, jn} < 1$), but no migration from urban to rural region $( x_{s, 0}^{jn, ja} = 1)$. For local migration costs in flooded areas, we pessimistically assume $x_{f, s, t}^{jr, jr} = 0.5$ (i.e., relocating within the location where a person was born induces an income loss equal to 50% of the lifetime utility), in line with literature on conflict-related displacements [e.g., Fiala (Reference Fiala2015); Ibáñez and Moya (Reference Ibáñez and Moya2006); Kellenberg and Mobarak (Reference Kellenberg and Mobarak2011)]. Using a similar parameterization strategy, Burzyński et al. (Reference Burzyński, Deuster and Docquier2020) predict variations in the dyadic stocks of migrants between 1950 and 1980 and obtain a close fit to the observed values.

Socio-demographic environment: Unless otherwise stated, we assume constant migration costs over the twenty-first century (i.e., $x_{s, t}^{jr, {j}^{\prime}{r}^{\prime}} = x_{s, 0}^{jr, {j}^{\prime}{r}^{\prime}} \forall t$). For $n_{s, t}^{jr}$ and$p_{s, t}^{jr}$, we use the projections of Burzyński et al. (Reference Burzyński, Deuster and Docquier2020), who endogenize the trajectory of socio-demographic variables in a similar overlapping generations framework without climate change. They constrain their baseline trajectory to be compatible with medium-term official demographic projections, as reflected by the UN projections of the national adult population and the proportion of college graduates for 2040. This can be achieved by assuming a process of quadratic convergence in access to education. This implies that middle-income countries converge towards high-income countries, while low-income countries diverge or converge less rapidly. For subsequent years and in all climate variants, we assume a continuation of this quadratic convergence process. The resulting changes in the size and structure of the population partly determine the skill ratio and the level of the technology in all locations.

Climate scenarios: Our climate scenarios involve temperature changes and rising sea levels. Temperature and sea level projections are available from the CCKP portal [Taylor et al. (Reference Taylor, Stouffer and Meehl2012)], which distinguishes between several emissions scenarios labeled as representative concentration pathways (RCP) [Moss et al. (Reference Moss, Edmonds, Hibbard, Manning, Rose, van Vuuren, Carter, Emori, Kainuma, Kram, Meehl, Mitchell, Nakicenovic, Riahi, Smith, Stouffer, Thomson, Weyant and Wilbanks2010)]. They are organized in 20-year climatological windows. The median-emissions scenario is termed RCP-4.5, which predicts that emissions will peak around 2040 before declining. For each RCP, the CCKP provides data for 16 models obtained from different research institutes. When these 16 models are ranked in ascending order according to the secular temperature variation, the medium resolution model of the Institute Pierre Simon Laplace (the ipsl_cm5a_mr variant) takes the eighth (median) position in RCP-4.5. We select this “median of the medians” variant as our baseline scenario and consider three alternative scenarios:

• • No climate change (No CLC): No change in temperature and in sea levels. Most probably unattainable, this scenario serves as the no climate change reference.

• • Baseline (RCP-4.5): Median temperature scenario corresponding to the median emissions scenario (RCP-4.5). This baseline involves mean increases in temperature and sea levels of 1.8 °C and 0.47 m, respectively.

• • Higher temperature (Higher T): Starting from the baseline, we double the predicted changes in temperature in all regions, keeping the rise in the sea levels identical to that used in the baseline.

• • Higher sea levels (Higher SL): Starting from the baseline, we double the predicted rise in the sea levels in all parts of the world, keeping temperature changes identical to those used in the baseline.

Projections of temperature and changes in sea levels by pixel of 1 km × 1 km can be obtained from Giorgetta et al. (Reference Giorgetta, Jungclaus, Reick, Legutke, Brovkin, Crueger, Esch, Fieg, Glushak, Gayler, Haak, Hollweg, Kinne, Kornblueh, Matei, Mauritsen, Thorsten, Mikolajewicz, Müller, Notz, Raddatz, Rast, Roeckner, Salzmann, Schmidt, Schnur, Segschneider, Six, Stockhause, Wegner, Widmann, Wieners, Claussen, Marotzke and Stevens2012). With regard to temperature, and for the baseline, Figure 1(a) illustrates the predicted variations in temperature between 2010 and 2100 by latitude and longitude. The largest variations are observed in the extreme north as well as some regions located close to the equator and in the east. Similarly, global changes to sea levels will not be uniform, but will exhibit substantial regional deviations [Oppenheimer et al. (Reference Oppenheimer, Glavovic, Hinkel, van de Wal, Magnan, Abd-Elgawad, Cai, Cifuentes-Jara, DeConto, Ghosh, Hay, Isla, Marzeion, Meyssignac and Sebesvari2019)]. Thermal expansion, ocean dynamics, and land ice loss contributions will generate regional departures from the global mean sea-level rise of about ±30%. Figure 1(b) shows that the rise in sea levels will be more pronounced in the extreme north, in the northern part of the Atlantic Ocean, and in the south-east of the Cape of Good Hope. This determines the surface of flooded areas. In order to account for such heterogeneities, we combine sea level projection data by pixel with high-resolution, geo-referenced information on topography [Tadono et al. (Reference Tadono, Ishida, Oda, Naito, Minakawa and Iwamoto2014)] and distance to coastlines [Stumpf (Reference Stumpf2012)].

Figure 1. RCP-4.5 scenario and its effects on TFP and forced displacement.

Notes: Own calculations based on climate data by Giorgetta et al. (Reference Giorgetta, Jungclaus, Reick, Legutke, Brovkin, Crueger, Esch, Fieg, Glushak, Gayler, Haak, Hollweg, Kinne, Kornblueh, Matei, Mauritsen, Thorsten, Mikolajewicz, Müller, Notz, Raddatz, Rast, Roeckner, Salzmann, Schmidt, Schnur, Segschneider, Six, Stockhause, Wegner, Widmann, Wieners, Claussen, Marotzke and Stevens2012). Subfigures (a) and (b) represent deviations from the baseline situation in 2010 at the pixel level. Subfigures (c)–(f) represent relative deviations from the NoCLC scenario in the year 2100 and at the region level.

Climate damage functions: To predict the long-term implications of climate change, we consider two mechanisms of transmission. First, we allow changes in the mean level of temperature to affect productivity, expected income, and incentives to migrate [as in Dallmann and Millock (Reference Dallmann and Millock2017); Desmet and Rossi-Hansberg (Reference Desmet and Rossi-Hansberg2015); Shayegh (Reference Shayegh2017)]. Second, we model forced displacements linked to rises in sea levels [as in Desmet et al. (Reference Desmet, Nagy and Rossi-Hansberg2018); Rigaud et al. (Reference Rigaud, de Sherbinin, Jones, Bergmann, Clement, Ober, Schewe, Adamo, McCusker, Heuser and Midgley2018)].Footnote ⁵

To model the effect of temperature, we follow Desmet and Rossi-Hansberg (Reference Desmet and Rossi-Hansberg2015), who estimate the relationship between temperature and TFP in agricultural and manufacturing sectors. This function corresponds to $G( {T_t^{jr} })$ in equation (4). The curve is inverted-U-shaped for both sectors but flatter in manufacturing. Desmet and Rossi-Hansberg (Reference Desmet and Rossi-Hansberg2015) find an optimal temperature of 21.1 °C for agriculture, and 17.4 °C for non-agriculture. The level of TFP increases with temperatures in regions with average temperatures below these optimal levels; it decreases with temperature in warmer regions.

It is important to note that our two-sector model does not distinguish between pixels and only establishes a difference between rural/agricultural and urban/non-agricultural regions within each country. Climate literature suggests that temperature levels observed at the centroid of each country may not accurately reflect the impact of climate change. This may be due to the fact that aggregate measurements poorly capture population concentration and individuals' average exposure to temperature change in large countries with regions of heterogeneous population densities. Hence, we use population-weighted changes in temperature from Dell et al. (Reference Dell, Jones and Olken2012). Figures 1(c) and 1(e) show the direct effect of temperature on agricultural and non-agricultural TFP levels for each country and for the year 2100. On average, in the RCP-4.5 scenario, agricultural productivity decreases by 20–25% in countries close to the equator and increases by the same amount at high latitudes. Similarly, non-agricultural productivity decreases by 10–15% in countries close to the equator, and increases slightly at high latitude levels.

This implies that climate change will affect income convergence over the twenty-first century. From equation (4), it appears that TFP levels are also affected by changes in the skill ratio $( z_t^{jr} )$, which result from our (exogenous) socio-demographic hypotheses and (endogenous) migration outcomes. For each climate scenario and sector, we can run a cross-country regression of the mean annual growth rate of TFP over the twenty-first century on its initial level (in logs). The results of these beta-convergence regressions are illustrated in Figure 2. The left-hand panel gives the results obtained for agriculture (each country is represented by a red bubble), while the right-hand panel shows the results for non-agriculture (each country is represented by a blue bubble).

Figure 2. Convergence vs. divergence in TFP under alternative climate scenarios.

Notes: Mean annual growth rates of TFP levels over the period 2010–2100 are represented on the vertical axes. The 2010 levels of TFP (in logs) are represented on the horizontal axes. The trends correspond to the quadratic relationship between the two variables. A negative slope indicates a convergence process; a positive slope indicates divergence.

In the No CLC scenario (top panel), we abstract from climate change. The beta-convergence regression results are governed by the assumed quadratic convergence process in human capital formation (i.e., in domestic investment in education). In line with the median socio-demographic scenario of the United Nations, our socio-demographic environment assumes that progress in education is greater in middle-income countries than in rich and in poor countries. The resulting effect on the skill ratio and TFP is reinforced by internal and international mobility responses—people moving from low-productivity to high-productivity regions and countries. Hence, this scenario implies quadratic convergence in TFP levels. Roughly speaking, in both sectors, TFP levels converge among countries and regions belonging to the top quartile of the initial TFP distribution. Countries and regions below the top quartile diverge.

The convergence implications of climate change are illustrated in the bottom panels in Figure 2. Under the RCP-4.5 scenario, the divergence forces are strengthened. Variations in temperature will induce dramatically different effects on productivity in countries above and below the 35th parallel. Over the twenty-first century, agricultural productivity decreases by 20–25% in countries close to the equator, and increases by 10–15% at high latitudes. Non-agricultural productivity decreases by 10–15% in countries close to the equator, and slightly increases at high latitudes. Over the twenty-first century, the annual growth rate of TFP is 2 percentage points higher in the wealthiest regions compared with the poorest ones. Hence, low-latitude countries in general, and their rural regions in particular, will be the most adversely affected by climate change. The magnitudes of these effects are greater when temperature variations are doubled (see Higher T), whereas higher sea level rise has almost no impact on TFP convergence (see Higher SL).

We now turn our attention to forced displacements, which are predicted by combining sea level projection data from Giorgetta et al. (Reference Giorgetta, Jungclaus, Reick, Legutke, Badedr, Bottinger, Brovkin, Crueger, Esch, Fieg, Glushak, Gayler, Haak, Hollweg, Ilyina, Kinne, Kornblueh, Matei, Mauritsen, Mikolajewicz, Müller, Notz, Pithan, Raddatz, Rast, Redler, Roeckner, Salzmann, Schmidt, Schnur, Segschneider, Six, Stockhause, Timmreck, Wegner, Widmann, Wieners, Claussen, Marotzke and Stevens2013) with high-resolution geo-data on population density [CIESIN-Columbia University (2018))] and data on the rural/urban divide from Balk et al. (Reference Balk, Deichmann, Yetman, Pozzi, Hay and Nelson2006). Our approach by pixel enables us to proxy the number of individuals at risk from coastal flooding on a 1 km × 1 km grid and by region. Coupling this information with data on the geographical extent of urban/rural areas [Balk et al. (Reference Balk, Deichmann, Yetman, Pozzi, Hay and Nelson2006)] allows us to compute the fraction of population affected by rises in sea levels $( \Theta _t^{jr})$ by country.

Figures 1(d) and 1(f) give the total number of displaced persons over the twenty-first century in rural and urban regions, respectively. Rising sea levels mostly affect countries where a large proportion of the population is located along the coasts of seas and oceans, or in the major river deltas. The proportion of displaced persons is large in South Asian and East Asian countries. Some Pacific islands situated a few centimeters above sea level (e.g., Tuvalu, Kiribati) are in a position of extreme vulnerability. Wealthy and poor countries will be equally adversely affected by rising sea levels.