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I develop new perturbation techniques for solving discrete time rational expectations models in which the state of the economy is an infinite-dimensional distribution. I propose a general template for such models that encompasses, as special cases, the incomplete market models that have become the mainstay of quantitative work on fiscal and monetary policy analysis, as well as spatial and trade models in which agents' decisions depend on a continuum of prices. I derive an analytical linear state space representation for this broad class of models while accomodating features such as kinked decision rules and the development of mass-points in the endogenous state distribution. I reduce the numerical characterisation of this representation to an eigendecomposition problem that is fast and provides a criterion for establishing the uniqueness of the stable manifold for the model's dynamics. In the spirit of Dynare, the implementation of my method simply requires the analyst to provide a steady state solver for their model of interest and to express their model's equations in the template I provide. This First-Order Approximation (FA) method generalises, but also inherits two important limitations, of the widely used linearisation method for representative agent models. In particular, it suffers from certainty equivalence and loses accuracy in the presence of strong nonlinearities. To address these issues I propose a Nonlinear Approximation (NA) method that captures the effects of aggregate uncertainty and achieves an accuracy level comparable to global solution techniques—even in highly nonlinear environments. It is able to do so because at any point during the model simulation, NA uses an appropriately computed approximation to future decision rules of agents to exactly solve the nonlinear equilibrium restrictions at the current state of the model.
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Rising inequality across much of the developed world in recent decades has been accompanied by growing calls to tax those with the “broadest shoulders”. Critics, however, caution that “those with the broadest shoulders often have the niftiest feet”, pointing to the increasing ease with which capital moves across tax jurisdictions in a globalised economy. In such a world, how can policymakers balance the distortionary effects of capital taxation with the fiscal demands of redistribution? In this paper, I develop a multi-country dynamic incomplete markets model in which governments engage in a non-cooperative tax competition game in a setting with freely mobile capital and within-country heterogeneity in both physical and human capital ownership. I derive two key analytical results that characterise the reaction functions of governments. First, I show that the covariances between households’ social marginal welfare weights and the distributions of physical and human capital serve as sufficient statistics for how inequality in labour and capital incomes shapes redistributive motives. Second, I show that the elasticity of the domestic capital stock with respect to tax policy—which governs the distortionary cost of capital taxation—can be decomposed into two components: one stemming from strategic interactions induced by tax competition, and another from the savings response of households. The former dominates in the short run, while the latter becomes increasingly relevant over time and determines the long run elasticity. Combining these insights with numerical experiments, I show that inequality exacerbates race-to-the-bottom dynamics in the short run, while the non-zero and finite savings elasticity tempers this concern in the long run. A quantitative application to the four largest EU economies shows that asymmetries causing some countries to be capital exporters and others to be importers imply that neither moving from tax competition to capital market autarky nor to tax harmonisation constitutes a Pareto improvement.