Internal Migration and Public Policy

Michele G. Giuranno; Rongili Biswas

doi:10.1515/bejeap-2018-0203

Published by De Gruyter June 15, 2019

Internal Migration and Public Policy

Michele G. Giuranno and Rongili Biswas

From the journal The B.E. Journal of Economic Analysis & Policy

https://doi.org/10.1515/bejeap-2018-0203

Showing a limited preview of this publication:

Abstract

This paper studies the relation between internal migration and public spending on public goods. We describe centralized public policy when a central government is comprised of elected representatives from local electoral districts. Internal migration determines the median voter in the districts. The median voters decide the equilibrium policy through bargaining. We find the conditions under which voters’ mobility results in larger or smaller public spending. Furthermore, the distance between the actual size and the efficient size of government spending depends on the way internal migration changes the distribution of income within and between districts.

Keywords: public goods; bargaining; political economy

JEL Classification: D30; D78; H0; H41; H50

Appendix

Proof of Lemma 1. Denote by F the first order condition eq. (13),

(39)F=−γ1m+H′g−γ1mg+Hg+−γ2m+H′g−γ2mg+Hg=0.

We want to study dg∗dm≡−FmFg. It is straightforward to verify that the second order condition is negative, Fg<0, while the numerator is

(40)Fm=−γ1′mϕ1+γ1′mg∂ϕ1∂gϕ12+−γ2′mϕ2+γ2′mg∂ϕ2∂gϕ22.

After rearranging we get

(41)Fm=gH′g−Hgγ1′mϕ12+γ2′mϕ22.

Here, gH′g−Hg is negative because the marginal benefit is smaller than the average benefit, i.e. H′g<Hg/g.^[27] We conclude that Fm is positive when γ1′mϕ12+γ2′mϕ22 is negative. This proves the Lemma.

Proof of Proposition 4. In order to prove the proposition, we first show that the bargaining solution leads to the efficient solution when γ1=γ2=1. In this case, the bargaining first order condition eq. (13) becomes 2−1+H′g−g+Hg=0. This is satisfied when H′g=1, as in eq. (5). Second, consider the case y‾≥y1≥y2. The efficiency condition eq. (5) does not change when the distribution of the electorate changes between regions. On the contrary, condition eq. (19) shows that the provision of g increases as the median mean income ratios decline for both median voters. Third, consider the case y1≥y‾≥y2. The impact on g of moving away from the situation γ1=γ2=1 is explained by Proposition 2. Therefore g may either increase or decrease.

Proof of Lemma 2. Denote by V the first order condition eq. (32),

(42)V=∑j=1J−γjm+H′g−γjmg+Hg=0.

We want to study dg∗dm≡−VmVg. It is straightforward to verify that the second order condition is negative, Vg<0, while the numerator is

(43)Vm=∑j=1J−γj′mϕj+γj′mg∂ϕj∂gϕj2.

After rearranging we obtain

(44)Vm=gH′g−Hg∑j=1Jγj′mϕj2

where, we already know that gH′g−Hg is negative. We conclude that Vm is positive when ∑j=1Jγj′mϕj2 is negative.

Proof of Proposition 6. In order to prove the proposition, we need to show that the bargaining solution with J > 2 jurisdictions leads to the efficient solution when γj=1 for all j = 1, ..., J. In this case, the bargaining first order condition eq. (32) becomes J−1+H′g−g+Hg=0, which is satisfied when H′g=1, as in eq. (5).

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Published Online: 2019-06-15

Internal Migration and Public Policy

Abstract

Appendix

References

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