We study the convergence of recursive least-squares learning schemes in economic environments in which there is private information. The presence of private information leads to the presence of hidden state variables from the viewpoint of particular agents. By applying theorems of Ljung, we extend some of our earlier results to characterize conditions under which a system governed by least-squares learning will eventually converge to a rational expectations equilibrium. We apply insights from the learning results to formulate and compute the equilibrium of a version of Townsend's model.

We study optimal Pareto-improving factor taxation when agents are heterogeneous in their labor productivity and wealth and markets are complete. Pareto-improving policies require a gradual reform: labor taxes should be cut, and capital taxes should remain high for a long time before reaching the limit. This policy redistributes wealth in favor of workers, promotes growth, and causes early deficits and government debt in the long run. We address several technical issues, such as sufficiency of Lagrangian solutions in a Ramsey problem, their relation to welfare functions, and solution algorithms. We also provide a proof that long-run capital taxes are zero.

We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.

We use a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the 1980’s. In a standard monetary model we replace the assumption of full rational expectations by a formal definition of quasi-rational learning. The model under learning matches some crucial stylized facts observed during the recurrent hyperinflations experienced by several countries in the 1980’s remarkably well. We argue that, despite being a small departure from rational expectations, quasi-rational learning does not preclude falsifiability of the model, it does not violate reasonable rationality requirements, and it can be used for policy evaluation.

We study the convergence of recursive least-squares learning schemes in economic environments in which there is private information. The presence of private information leads to the presence of hidden state variables from the viewpoint of particular agents. By applying theorems of Ljung, we extend some of our earlier results to characterize conditions under which a system governed by least-squares learning will eventually converge to a rational expectations equilibrium. We apply insights from the learning results to formulate and compute the equilibrium of a version of Townsend's model.

Abstract Standard optimal Debt Management (DM) models prescribe a dominant role for long bonds and advocate against issuing short bonds. They require very large positions in order to complete markets and assume each period that governments repurchase all outstanding bonds and reissue (r/r) new ones. These features of DM are inconsistent with U.S. data. We introduce incomplete markets via small transaction costs which serves to make optimal DM more closely resemble the data : r/r are negligible, short bond issuance substantial and persistent and short and long bonds positively co-vary. Intuitively, long bonds help smooth taxes over states and short bonds over time. Solving incomplete market models with multiple assets is challenging so a further contribution of this article is introducing a novel computational method to find global solutions.

Investors' subjective capital gains expectations are a key element explaining stock price fluctuations. Survey measures of these expectations display excessive optimism (pessimism) at market peaks (troughs). We formally reject the hypothesis that this is compatible with rational expectations. We then incorporate subjective price beliefs with such properties into a standard asset-pricing model with rational agents (internal rationality). The model gives rise to boom-bust cycles that temporarily delink stock prices from fundamentals and quantitatively replicates many asset-pricing moments. In particular, it matches the observed strong positive correlation between the price dividend ratio and survey return expectations, which cannot be matched by rational expectations. (JEL D83, D84, G12, G14)

In an economy studied by Lucas and Stokey, tax rates inherit the serial correlation structure of government expenditures, belying Barro's earlier result that taxes should be a random walk for any stochastic process of government expenditures. To recover a version of Barro's random walk tax-smoothing outcome, we modify Lucas and Stokey's economy to permit only risk-free debt. Having only risk-free debt confronts the Ramsey planner with additional constraints on equilibrium allocations beyond one imposed by Lucas and Stokey's assumption of complete markets. The Ramsey outcome blends features of Barro's model with Lucas and Stokey's. In our model, the contemporaneous effects of exogenous government expenditures on the government deficit and taxes resemble those in Lucas and Stokey's model, but incomplete markets put a nearunit root component into government debt and taxes, an outcome like Barro's. However, we show that without ad hoc limits on the government's asset holdings, outcomes can diverge in important ways from Barro's. Our results use and extend recent advances in the consumption-smoothing literature.