Climate Change and Migration: A Dynamic Model

1. Introduction

With the ratification of the Paris Agreement in October 2015, the glimmer of a global solution to climate change has appeared. Even so, many millions or people are likely to be displaced as a result of the climate change we are almost certain to experience in the coming years. Impacts such as sea-level rise and increased exposure to extreme weather events have been associated with climate change (IPCC 2014, p. 16); such events are ‘projected to increase displacement of people’ (IPCC 2014, p. 73). Indeed, a recent World Bank report argues that migration is likely to become an increasingly important adaptation method for responding to climate change (Hallegatte et al. 2016, p. 161).

Individuals who originally reside in at-risk areas, such as low-lying areas, are particularly likely to migrate (McLeman and Smit 2006). For example, a 2011 study finds that over one-fifth of households affected by tidal-surge floods, and roughly one-sixth of households affected by riverbank erosion, migrated to safer areas (Black et al. 2011, p. 448). A recent World Bank report says ‘a significant deterioration of climatic conditions would lead to an increase of about one-tenth to one-fifth of current migration levels’ and ‘in the future, as the effects of climate change intensify, environmentally induced migration is expected to increase’ (Hallegatte et al. 2016, p. 161).¹ Bangladesh is particularly vulnerable (Hallegatte et al. 2016, p. 8, Figure O.6b). There moving to cities has become a common coping strategy in the face of flooding (Black et al. 2011, p. 448). Throughout the world, pressures to migrate seem likely to persist (Black et al. 2011).

Such migration has important consequences. For example, the Fifth Assessment Report of the United Nations Intergovernmental Panel on Climate Change argues that migration out of low-lying areas will likely cause ‘loss of sense of place and cultural identity’ (IPCC 2014, p. 98). Such psychological costs are in addition to the financial burdens migrants must bear to relocate. But the fact that people would incur such costs underscores the substantial loss in utility associated with increased exposure to climate-related damages.

A substantial literature has recently developed that analyzes the potential for climate change to induce migration (Millock 2015). In this article I turn the approach typically taken in extant literature on its head, by asking if in-migration might induce polluting countries to lower their emissions. In particular, if such countries incur costs associated with the in-migration, as 2015 events in Europe so painfully demonstrated, might the desire to reduce in-migration costs create a sort of pseudo carbon tax? One might think of the mechanisms leading to such an outcome as the result of lobbying by anti-immigration forces, where these groups influence the government of the polluting country to reduce its emissions so as to reduce climate change and, thereby, immigration tendencies. With such an interpretation, the channel I explore is a variant of political economy. This approach is, I believe, largely unexplored in the extant literature.² Alternatively, one can imagine that anti-immigrant groups are associated with skepticism about climate policy, as with Donald Trump in the USA or the UK Independence party in Great Britain. Confronted with the potential increasing influence for such groups, there is an incentive for the current establishment to take preemptive actions, including actions that blunt pressures for climate change (and thereby obviate migratory pressures).³

In this article I study the implications for in-migration to encourage reductions in greenhouse gas emissions. I develop a dynamic model involving the interaction between two countries, an upstream country (whom I refer to as ‘country 1’) that generates a flow of emissions and a downstream country (whom I refer to as ‘country 2’) that is the source of migration. The emissions are associated with a good produced only in Country 1 that is consumed in both countries.⁴ People living in Country 2 are assumed to bear larger damages than people living in Country 1, which creates a motivation for some citizens in Country 2 to migrate to Country 1. I consider four dynamic optimization problems. In the first two problems, migration is not possible, while in the second two, it is feasible. Within each of these two classes, I analyze two problems: the private optimization problem for a decision-maker in Country 1 who only cares about the present discounted flow of net benefits (utility less climate-related damages) to its citizens, and the social optimization problem for a mythical social planner who cares about the present discounted value of net benefits for all citizens (i.e., combined utility less all climate-related damages). I show that the potential for migration lowers the long-run carbon stock, as well as production rates. The degree to which output levels, and hence emission flows, are reduced depends on key parameters: differences in the initial distribution of population between the two countries, the slopes of demand and marginal production cost, the rate of decay in the carbon stock, and the marginal cost to Country 1 of in-migration.⁵

Two examples illustrate the general idea. The first example involves India, currently the third-largest CO₂ emitter in the world, and neighboring countries such as Bangladesh, Indonesia, and Pakistan. In the negotiations leading up to the 2015 Paris Agreement, India expressed concerns about curtailing its emissions, citing a desire to encourage economic growth. This inchoate growth is likely to be tied to increased use of coal, which would lead to substantial carbon emissions. Accordingly, any phenomenon that encourages India to lower its greenhouse gas emissions may generate important reductions in climate-related damages. Increased climate-related effects in nearby countries, such as Bangladesh, Indonesia, and Pakistan, seem likely to trigger migration at some point, perhaps into India.⁶ This combination of events suggests a potential offsetting incentive upon Indian decision-makers.

A second example involves the USA, currently the second-largest CO₂ emitter in the world, and Mexico, a major source of migration into the USA. Similar to the first example, the country from which migration occurs is likely to experience important climate-related damages, particularly to agriculture. Indeed, there is some evidence that such influences have a historical antecedent: both Munshi (2003) and Barrios Puente et al. (2015) find that decreases in precipitation in Mexico, a likely outcome of climate change, increase migration from Mexico to the USA. As in the first example, to the extent that US decision-makers perceive Mexican immigrants impose costs upon their constituents, they have an incentive to undertake actions that would reduce migratory tendencies. One response could be to take actions that render immigration more costly or difficult (e.g., building a wall along the border). An alternative approach, which I highlight in this article, is to reduce CO₂ emissions, for example, by reducing outputs that are linked to emissions.⁷

The rest of the article is organized as follows. Section 2 develops the dynamic model. In Section 3, I describe the general solutions in the absence of migration for both the private optimization problem facing the upstream country and the social optimization problem. In Section 4, I work through the private and social optimization problems when migration is feasible. In Section 5, I analyze a specific form of the problems when migration is feasible, where demand, marginal cost, and climate-related damages are linear functions; using this ‘linear-quadratic’ framework facilitates the development of closed-form solutions. I then compare the optimal paths of production and carbon stocks with and without migration. Concluding remarks are offered in Section 6.

2. Modeling Preliminaries

The decision-maker in Country 1 cares only about the well-being of its native population.¹¹ This well-being depends on the utility associated with the initial population, less damages borne by the initial population, plus any profits resulting from the production of the consumption good. Because the initial citizenry of Country 1 bears some disutility from carbon-related damages, the government of Country 1 has an incentive to take some action to reduce the flow of carbon emissions, which I assume they do through their choice of the time path of production. In addition, the residents of Country 1 bear crowding externalities when the population in 1 rises because of in-migration. I capture this effect through the function $E(α)$⁠, which I assume is increasing. For expositional simplicity, I assume $E=ηα$⁠. These crowding externalities could reflect greater demand on infrastructure or social services, or they could reflect a general preference to be in a more familiar society.¹² In any event, this externality induces a disutility associated with in-migration, which likely leads to political pressure on the government in Country 1 to take actions that impede in-migration. In particular, it creates a motive for the government in Country 1 to take greater actions to reduce the flow of carbon emissions.¹³

3. Analysis When Migration Is Not Feasible

I now describe the general optimization problem in the absence of migration, both from the private perspective of the government in Country 1 and from the combined (social) perspective. These results can be thought of as a benchmark against which the corresponding problems that arise when migration is possible are assessed.

3.1 Privately optimal path

3.2 Socially optimal path

4. Analysis When Migration Is Feasible

Consider next the situation where migration can occur. While the potential gains associated with relocation are available to all citizens originally living in Country 2, I assume migrants’ net gain from moving is heterogeneously distributed. In addition, the original inhabitants in Country 1 suffer a loss from increased crowding.

4.1 Privately optimal path

Also as above, the solution is governed by transversality conditions—here, there is one for each shadow value. These conditions require either that the corresponding state variable (Z for μ and α for λ) converges to a steady state value or that the long-run shadow value is nil. Because of the first term in Equation (14), the transversality condition for in-migration requires that $λ˙=0$⁠, so that either $α≤α0$ or $λ=−η/r$⁠. Because the first possibility is empirically implausible, I focus on the second possibility going forward.

As climate damages mount in Country 2, some citizens migrate to Country 1, so as to reduce the damages they perceive they are exposed to. This migration generates crowding costs in Country 1, which leads the upstream decision-maker to consider an extra cost; this induces a crude form of an implicit tax on production. Accordingly, the government in Country 1 may be motivated to amplify their use of a pollution control instrument, so as to blunt the migratory effect. They may also be motivated to take actions that directly impede migration, for example, border controls. To the extent that such efforts are less costly than adjusting output one expects Country 1 would be less inclined to lower production, so the effect I have described would be diminished.

4.2 Socially optimal path

This problem is more complex than the three other problems analyzed above, as the solution here depends on more equations (five, as opposed to three: Equations (1), (4), and (16)–(18)). Despite this extra complexity, it is possible to draw certain comparisons, as discussed in Subsection 5.5 below.

5. Linear–Quadratic Example

As it is difficult to obtain further insights in the general framework described above, I now turn my attention to a specific example in which analytic results are more readily obtained. In this simplified variant of the model, the key ingredients are linear–quadratic functions. Linear–quadratic models are considered to be a good approximation for more general problems and are characterized by equations of motion being linear in state and control variables and objective functionals being quadratic in state and control variables.

With these functional forms, it is relatively straightforward to derive the characterizations for optimal production, the associated path of carbon stocks and the shadow value of atmospheric carbon in each of the regimes. In the following subsections, I discuss these equilibrium values; derivations are relegated to the Appendix.

5.1 Privately optimal solution—no migration

5.2 Socially optimal solution—no migration

5.3 Privately optimal solution—migration

As per capita marginal damages are larger in Country 2 than Country 1 (i.e., $(β−1)δZ>0$⁠) and the probability density associated with opportunity costs of relocation is positive (i.e., $ϕ>0$⁠), the last parenthetical term on the right-hand side of Equation (27) will generally exceed μ in magnitude. On the other hand, the marginal effect of an increase in production is the same as in the privately optimal program without migration. It follows that the decision-maker for Country 1 is inclined to select a smaller rate of production in the presence of in-migration.

Because $λ<0$⁠, the denominator in this expression is larger than the denominator in Equation (23). Since the numerators in the two expressions are identical, it follows that the privately optimal steady state carbon stock is smaller in the presence of migration: $Z˜<Z^$⁠.

5.4 Socially optimal solution—migration

5.5 Comparison

The central question in this article is: to what extent does migration create incentives for the upstream country to lower its carbon emissions? That question has two dimensions, long- and short-run. The long-run comparison is based on steady state carbon stocks with and without migration, while the short-run analysis requires a comparison of emission paths.

5.5.1 Comparison of private optima

5.5.2 Comparison of social optima

Comparing time paths with and without migration is more difficult. But as the two paths start from the same initial condition, Z₀, the carbon stock path with migration must lie below the path without migration after some point in time.

6. Concluding Remarks

Climate change has been called the most difficult externality problem ever confronted by humankind. This characterization is underscored by the likely human costs associated with efforts to adapt to climate damages, particularly via migration. My goal in this article has been to evaluate what I believe to be an underappreciated offsetting effect from migration: that pressures upon countries that experience in-migration might encourage such countries to reduce their greenhouse gas emissions, thereby offering benefits on a global scale. Such pressures induce a sort of pseudo carbon tax, which motivates lower emissions. I show that the long-run carbon stock, and the entire time path of production, is smaller in the presence of migration, offering an offset to the costs incurred as a result of climate change.

One way to think of this problem is as a tension between two competing effects. Actions taken by Country 1 generate costs borne by Country 2, through the transboundary externality associated with the carbon stock. At the same time, actions taken by citizens in Country 2 impose costs on Country 1, through the costs citizens in Country 1 perceive arising from in-migration. In my model, as climate damages rise, there is greater pressure on the destination country to curtail its emissions. But if Country 1 thinks that some in-migration is beneficial, say because the migrants had particular skills or human capital that was deemed attractive by firms in Country 1, then one could imagine migration leading to increased, as opposed to decreased, emissions. In addition, it is conceivable that the government of Country 1 could explore a variation of cooperation, wherein they commit to reduce emissions if the government of Country 2 commits to stem the flow of migration. Such a regime has the flavor of linked policies, in the manner of Limão (2005).

In my model, the government of Country 1 undertakes actions unilaterally, by reducing its output levels—and thereby partially mitigating the flow of emissions. Country 1 does not utilize other instruments, such as border controls or limits on migrants. One could imagine extending the model to allow for this alternative policy, along the lines of Ethier (1986). In such an extension, the government of Country 1 could inhibit migration by expending resources; in this way, the costs associated with migration would be increased, lowering the rate of in-migration. If the cost function describing the level of expenditure required to mitigate a given level of in-migration as convex in the degree of ‘migration abatement’, as seems plausible, then there will be an interior level of expenditures that balances the marginal cost of migration abatement against the marginal cost of migration, as measured by the parameter η in my model. In this way, the incentive to reduce emissions is partially offset. In particular, the migration control efforts would seem to lower the magnitude of the negative shadow value of in-migration. At the same time, it is unclear that such efforts are socially desirable: while the reduction of costs associated with in-migration is a tangible social benefit, this gain comes at the cost of larger emissions, and accordingly larger carbon stocks. It seems unlikely that the damages associated with this adjusted time path of carbon stocks would exactly match the net costs of limiting migration (enforcement costs less benefits from reduced in-migration), and so the inclusion of this policy lever seems likely to influence the comparison of private and social optima. It is also possible that migration policies will have other effects, not considered in my model. For example, targeted immigration policies can influence the pattern of welfare payments (Storesletten 2000).

Working against the potential global gains that emerge in this scenario is the opportunity costs borne by migrants. While the monetary magnitude of these dislocation costs might not be particularly large, the non-pecuniary impact could be substantial. Accordingly, I do not argue that the global net benefits associated with migration are positive. Rather, I want to point out that migration can serve a purpose that it can induce emission reductions that would otherwise not be forthcoming. Whether such indirect benefits are large in comparison to the opportunity costs related to migration is of course an empirical question. Perhaps in raising this possibility, this article will encourage investigations of this empirical question.

Footnotes

Acknowledgements

The author thanks, without implicating, participants in the CESifo workshop on migration and climate change for lively discussion. He particularly is grateful to Matthias Kalkuhl and Jesús Fernández-Huertas Moraga. Two anonymous referees provided useful feedback that aided in the development of this article. The usual disclaimer applies.

References

Appendix

In this Appendix, I present the analytics underlying the discussion in Section 5. These analytics are presented in parallel fashion to the main text: first, I work through the problem when migration is not possible, taking the private and social optimization problems in turn. Then I work through the problem when migration is possible, again taking the private and social optimization problems in turns.

1 Privately Optimal Solution, No Migration

2 Socially Optimal Solution, No Migration

3 Privately Optimal Solution with Migration

4 Socially Optimal Solution with Migration