Abstract
The primary objective of this paper is to highlight the distinct roles of altruism and of self-interest in the political determination of a public education policy. I assess the relative importance of three factors in the determination of the equilibrium level of this policy: altruism, the impact of public funding of education on social security benefits, and its impact on factor prices. I then focus on the impact of implementing a social security system on the equilibrium levels of education funding and on welfare. I find that although in the benchmark economy, the presence of social security might generate support for public funding of education, its overall effect on the well-being of individuals is negative for any level of social security taxation.
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Notes
Boldrin and Montes (2002) analyzed the joint determination of public funding of education and social security to implement an intergenerational transfer system that finances education when market incompleteness restricts private funding of education. However, they did not look at any of the policies as the result of a political process. Rangel (2003) studied the implementation of public education and social security as the result of an intergenerational game.
I drop the time subscript to simplify the notation. A prime superscript will denote a variable from next period.
A variable with a hat indicates that the variable is expressed in per capita terms.
That is, if agents believe that the political system described by the sequence ϒ will be sustained, then the political outcome for the present period will be the level τ, such that τ=ϒ(X). Their decision functions will therefore be the same as the ones obtained when agents take the whole sequence of policy decisions as given (see Section 3.1).
The politico-economic equilibrium might not be unique. To find other possible equilibria, I initialized the numerical computations at different steady states corresponding to different public education tax rates. The economy converged to the same steady-state starting values independently of the initial guess.
Note that we are not recalibrating the other parameters of the model economy as we change the value of the altruism discount factor.
Once the bequest motive is active, we have a multiplicity of equilibria. I compute the politico-economic equilibria assuming that all agents are identical within each generation. In the absence of idiosyncratic shocks, this is a stable situation, and there is only one such equilibrium in a closed economy. Although there might be more than one partial equilibrium, I never encounter such cases in the experiments.
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Acknowledgements
I gratefully acknowledge support from the Human Capital Mobility, E.C., fellowship and the Innocenzo Gasparini Institute of Economic Research. I am also grateful to Thomas Cooley, Jeffrey Campbell, Sergio Rebelo, Per Krusell, Victor Rios-Rull, Guido Tabellini, Arun Malik, and two anonymous referees for helpful comments.
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Technical Appendix
Technical Appendix
In this appendix, I describe the procedure used to compute the political-economic equilibria for the model economy.
I apply an approach similar to the one used in Krusell et al. (1997) to solve for the politico-economic equilibrium of the economy. I solve for the recursive equilibria for a given political outcome function, and then I solve the political problem. An equilibrium is attained when the political choice corresponds to the one resulting from the given political outcome function; otherwise, the political outcome function is updated, and the procedure continues.
The procedure can be described as follows (see Krusell et al. 1997 for a more detailed description):
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1.
Make a guess on the tax rate on income τ 0 and compute the corresponding steady state (A 0, S 0).
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2.
Approximate the utility functions of the different-generation agents around this steady state with a quadratic function and solve for the value functions of these agents. Start from the old agents' problem and work backward to the first-generation agents'. As I solve the agents' problems, I get decision rules as functions of individual and aggregate state variables as well as the tax rate.
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3.
Substituting these decision rules in the agent's problem, I get the value function in function of individual and aggregate state variables as well as the tax rate.
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4.
Maximizing the value function corresponding to the pivotal voter with respect to the political parameter, I obtain a political decision in function of aggregate state variables and individual state variables of the pivotal voter. I can then aggregate this function and obtain a political outcome function that is only a function of aggregate state variables. I iterate on this approximation until I converge to a function ϒ 0(A 0, S 0|τ 0).
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5.
Compare the tax rate implied by this political outcome function τ=ϒ 0(A 0, S 0|τ 0) with the initial guess, τ 0. If the tax rates are different, I update the initial guess and go back to step 1. Otherwise, a political and economic equilibrium has been found.
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Soares, J. A dynamic general equilibrium analysis of the political economy of public education. J Popul Econ 19, 367–389 (2006). https://doi.org/10.1007/s00148-005-0034-y
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DOI: https://doi.org/10.1007/s00148-005-0034-y