Abstract
In this paper, we extend the home-attachment model to a setting with multiple (more than two) jurisdictions and consider non-cooperative policy making for provision of different types of metropolitan public goods in the presence of a common labor market. Migration and working place choices are independent. We show that the optimal redistributive policy implemented by a central authority always yields equalization of private consumption levels across jurisdictions. This result holds whether or not policy makers are able to anticipate migration responses to their policy choices. In the decentralized leadership games, jurisdictions make choices that fully internalize externalities.
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Notes
Mansoorian and Myers (1993) and Wellisch (1994) demonstrate that decentralized policy is efficient in the presence of home attachment if regional governments make transfers to each other and provide public goods whose consumption benefits are enjoyed by residents only. Caplan et al. (2000) show that regional authorities make efficient contributions to a federal pure public good in the presence of home attachment if the central government redistributes interregional income after it observes the regional governments’ contributions (regional and central governments play a “decentralized leadership game”). The linearity in the aggregation technology produces the necessary incentive equivalence, which yields their efficiency result. This fact is made clear by subsequent work (see, e.g., Silva and Yamaguchi 2010; Caplan and Silva 2011), in which the assumption that the federal public good is pure is relaxed. These papers demonstrate that, all else equal, the subgame-perfect equilibrium for the decentralized leadership game is not socially optimal. Aoyama and Silva (2013) also builds a model after Wellisch (1994) in which regional governments possess Rawlsian payoff functions and demonstrate that the decentralized non-cooperative equilibrium is efficient in the presence of home attachment and interregional spillovers.
This assumption guarantees that, in any equilibrium, all jurisdictions are populated.
In what follows, we use superscripts to denote functions.
Following the literature on home attachment, we ignore intra-jurisdictional commuting costs throughout. (Since average travel time from home to work in Canada is 25.4 min and this figure includes interjurisdictional travel time, it seems that the average intra-jurisdictional commuting cost in Canada is not very high. Nonetheless, neglecting it certainly implies a limitation of the analysis.) We consider the effects promoted by interjurisdictional commuting costs in Sect. 2.4. In future work, we plan to consider intra-jurisdictional commuting costs as well. To properly model intra-jurisdictional commuting costs, one would have to build a “spatial model” (see, e.g., Brueckner and Kim 2003; Brueckner and Helsley 2011; Agrawal and Hoyt 2014) where the distance between residence and working places would be taken into account. The model would also need to account for the location of one’s house and differing property and income tax payments. In equilibrium, assuming standard housing size and quality and no amenity differences across locations, all individuals would have to be indifferent between commuting costs and property and income tax payments (which would be an increasing function of the housing value) within any region and across regions (see, for example, Brueckner and Helsley 2011; Agrawal and Hoyt 2014).
Examples include \(\Phi \left( {q_1 ,q_2 } \right) =q_1^\theta q_2^{1-\theta } \) and \(\Phi \left( {q_1 ,q_2 } \right) =\theta q_1 +\left( {1-\theta } \right) q_2 \), \(0<\theta <1\).
This assumption guarantees that \(x_j >0\), \(\forall j\), in the social optima and equilibria examined in this paper.
If the utility function for the representative individual in jurisdiction j is \(u\left( {x_j ,G_j } \right) , j=1,2,\) instead, there are no public goods that yield consumption spillovers. In such a case, the model would be similar to the one examined by Mansoorian and Myers (1993). Decentralized policy yields efficient provision of jurisdictional public goods provided the jurisdictions make transfers to each other.
We use the symbol “\(^\wedge \)” on the functions in this section in order to distinguish them from their counterparts in the previous section.
Alternatively, one can use \(\hat{{\tau }}^{1}\left( {G_1 ,G_2 ,q_1 ,q_2 } \right) \!=\!{\left[ {\left( {M_2 \pi ^{2}\left( w \right) \!-\!G_2 \!-\!q_2 } \right) \!-\!\left( {M_1 \pi ^{1}\left( w \right) -G_1 -q_1 } \right) } \right] }/2\) to express the metropolitan government’s best response function in the second stage. Plugging this function into conditions (3a) and utilizing the fact that \(n_1 =n_2 =N/2\) yields Eq. (4a).
Norway, for example, allows commuters from other European Economic Area countries to deduct commuting costs in their income taxes. See https://www.skatteetaten.no/en/International-pages/If-you-work-in-Norway-you-need-to/Norwegian-employer/Norwegian-employer/Brochures/Information-for-foreign-employees-Deductions-for-commuters/?chapter=6650.
This assumption is for expositional convenience. Assuming that some workers who reside in jurisdiction 2 work full time in region 1, while others work full time in jurisdiction 2 does not modify the qualitative results of this section.
Clearly, if the metropolitan government is unable to implement income transfers, incentive equivalence fails and the jurisdictions do not have incentives to internalize externalities. As a result, jurisdiction 2 may not find it desirable to adopt the reimbursement program.
By symmetry, \(N_{h,1} =N_{1,h} \), \(h=2,\ldots ,J\).
As discussed in the text, every individual also considers the benefits of establishing residence in any of the \(J-2\) regions where he or she does not enjoy an attachment benefit. Hence, there is a larger number (indeed, a continuum) of potential conditions that may characterize the migration equilibrium. However, as we will show below, the full set of conditions that describe every individual’s residential choice between a region where he or she enjoys an attachment benefit and a region where he or she does not derive an attachment benefit can be ignored. In equilibrium, the utility from residing in any region in which an individual does not enjoy attachment benefit is strictly lower than the utility that this individual obtains from residing in the preferred choice between the two regions in which he or she obtains attachment benefits.
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Acknowledgments
The authors thank the reviewer and editor for comments and suggestions that improved the paper. Vander Lucas also thanks CNPq (Brazil) and FAP-DF (Brasilia) for financial support.
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Silva, E.C.D., Lucas, V.M. Common labor market, attachment and spillovers in a large metropolis. Int Tax Public Finance 23, 693–715 (2016). https://doi.org/10.1007/s10797-016-9401-8
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DOI: https://doi.org/10.1007/s10797-016-9401-8