Link

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. For this broad class of models, I derive an analytical linear state-space representation that accommodates kinked decision rules and the emergence of mass-points in the endogenous distribution. I show that the numerical characterisation of this representation reduces to an eigendecomposition problem, which also provides a criterion for establishing the uniqueness of the stable manifold of the model. In the spirit of Dynare, the implementation of my method relieves analysts of the cumbersome task of manually deriving this representation and instead requires only that they express their model’s equations in the provided template. My approach does not impose certainty equivalence and achieves accuracy levels comparable to global methods, even in highly nonlinear environments. These features make it particularly well-suited for studying the macroeconomic effects of aggregate uncertainty (e.g. the valuation impact of climate risk or business-cycle risk on household portfolios) and dynamic economies that are poorly approximated by time-invariant steady states (e.g. models with disaster risk or slow-moving structural change). My method relies exclusively on first-order Taylor approximations, and therefore unlike other perturbation methods that rely on second-order Taylor approximations to break certainty equivalence and capture nonlinearities, its numerical implementation does not suffer from the curse of dimensionality.

Link

Rising inequality across much of the developed world in recent decades has fuelled growing calls to tax those with the “broadest shoulders”. Critics, however, warn that “those with the broadest shoulders often have the niftiest feet”, highlighting the increasing ease with which capital can move across tax jurisdictions in a globalised economy. In such an environment, how can policymakers reconcile the distortionary effects of capital taxation with the fiscal demands of redistribution? To answer this, I develop a multi-country dynamic incomplete markets model in which governments engage in a non-cooperative capital tax competition game. The model features internationally mobile capital and within-country heterogeneity in both physical and human capital ownership. I show that domestic inequality amplifies the “race-to-the-bottom” dynamics commonly feared in the capital tax competition literature, but that incorporating households’ long-run savings responses mitigates this concern. A quantitative application to the four largest EU economies demonstrates that cross-country asymmetries—where some countries are net capital exporters and others importers—imply that neither a transition to capital market autarky nor full tax harmonisation yields a Pareto improvement.

Draft coming soon.

This paper studies the different mechanisms for regional risk sharing available to fiscal and monetary unions. I focus on the US, which is particularly interesting in this regard because it combines a high degree of regional economic integration with a sizeable federal tax-and-transfer system. Using methodological advances from Jain (2025), I solve a spatial HANK model that incorporates incomplete markets, wage rigidities, frictional trade between states, a realistic federal fiscal system and both demand- and supply-side sources of aggregate uncertainty. Drawing on quarterly regional data for the post-war period, I estimate the sources of US business cycle fluctuations and assess the extent of inter-state insurance. Counterfactual simulations quantify the importance of four key mechanisms shaping the nature of regional risk sharing: (i) the federal tax-and-transfer system, (ii) interstate trade costs, (iii) monetary policy, and (iv) the nature of underlying shocks.