Generalized Comparative Statics for Political Economy Models

Dotti, Valerio (2014): Generalized Comparative Statics for Political Economy Models.

Abstract

Abstract I investigate the equilibrium properties of a deterministic voting model in which the policy space is multidimensional and politicians have limited ability to commit to platforms. This analysis is useful to answer Political Economy questions in which the multidimensional nature of the policy is crucial to model voters’ trade-offs. The use of unidimensional models to study such problems is prevalent in the literature. This usually implies that one or more policy dimensions are assumed to be exogenous. This choice delivers sharp theoretical predictions, but implies an oversimplification of the problem, which often results in implausible or empirically inconsistent predictions.

I show that under suitable restrictions on the individuals’ capability of committing to policy platforms and on individual preferences a Median Voter Theorem holds even if the policy space is multidimensional. Moreover, I show that the comparative statics of the equilibrium policy outcome induced by a change in the voters’ distribution is monotone. I use this tool to extend the Meltzer-Richard model about size of the government. I show this model delivers empirically consistent predictions if a sufficiently rich policy space is assumed. Finally, I show that this framework can be used to study other Political Economy problems beyond simple voting problems.

• Item Type: MPRA Paper
• Language: English
• Keywords: median voter, multidimensionality, monotone comparative statics
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D78 - Positive Analysis of Policy Formulation and Implementation

References

Arrow, K.J., (1950). “A Difficulty in the Concept of Social Welfare”, Journal of Political Economy 58(4), 328–346.

Bergson, A. (1976). “Social Choice and Welfare Economics under Representative Government”, Journal of Public Economics, 6, 171-190.

Besley, T., Coate, S. (1997). “An Economic Model of Representative Democracy”, Quarterly Journal of Economics, 108(1), 85-114, 1997.

Birkhoff, H. (1967). Lattice Theory. Vol. 25 of Colloquium publications. American Mathematical Soc.

Black, D. (1948). “On the Rationale of Group Decisionmaking”, Journal of Political Economy, 56: 23-34.

Davis, O.A., DeGroot, M.H., Hinich, M.J. (1972). “Social Preferences Orderings and Majority Rule”, Econometrica, Vol. 40, No. 1: 147-157.

De Mello, L. and Tiongson, E.R. (2006), “Income Inequality and Redistributive Government Spending”, Public Finance Review, 34, 282-305.

Downs, A. (1957). An Economic Theory of Democracy. New York: Harper Collins.

Dotti, V. (2014). “The Political Economy of Publicly Provided Private Goods”, Working Paper.

Enelow, J.M., Hinich, M.J. (1989). “A general probabilistic spatial theory of elections”, Publ& Choice 61: 101-113.

Gibbard, A. (1973). “Manipulation of voting schemes: a general result”, Econometrica 41 (4): 587–601.

Grandmont, J.-M. (1978). “Intermediate preferences and the majority rule”, Econometrica, 46, 317–330.

Hotelling, H. (1929). “Stability in Competition”, The Economic Journal, Vol. 39, 41–57.

Levy, G. (2004). “A model of political parties”, Journal of Economic Theory, 115, 250-277.

Levy, G. (2005). “The Politics of Public Provision of Education”, The Quarterly Journal of Economics, Vol. 120, No. 4, pp. 1507-1534.

Lindbeck A., Weibull, J.W. (1987). “Balanced-budget redistribution as the outcome of political competition”, Public Choice, 52, Number 3, 273-297.

Meltzer, A.H., Richards, S.F. (1981). “A Rational Theory of the Size of Government”, The Journal of Political Economy, 89, Issue 5, 914-927.

Milgrom, P., Shannon, C. (1994). “Monotone Comparative Statics”, Econometrica, Vol. 62(1): 157-180.

Osborne, M.J., Slivinski, A. (1996). “A Model of Political Competition with Citizen-Candidates”, The Quarterly Journal of Economics, Vol. 111(1), 65-96.

Plott, C.R. (1967). “A notion of equilibrium and its possibility under majority rule”, American Economic Review, 57 (Sept.): 787-806.

Quah, J.K.-H. (2007). “The Comparative Statics of Constrained Optimization Problems”, Econometrica, Vol. 74, No. 2: 401-431.

Ray, D., Vohra, R. (1997). “Equilibrium Binding Agreements”, Journal of Economic Theory, 73, 30-78.

Roemer, J.E. (1999). “The Democratic Political Economy of Progressive Taxation”, Econometrica, 67, 1-19.

Satterthwaite, M.A. (1975). “Strategy-proofness and Arrow's Conditions: Existence and Correspondence Theorems for Voting Procedures and Social Welfare Functions”. Journal of Economic Theory, 10: 187–217.