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Working Paper
A moment-matching method for approximating vector autoregressive processes by finite-state Markov chains
This paper proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and tends to outperform the existing methods for approximating multivariate processes over a wide range of the parameter space, especially for highly persistent vector autoregressions with roots near the unit circle.
Journal Article
Convergence to Rational Expectations in Learning Models: A Note of Caution
We show in a simple monetary model that the learning dynamics do not converge to the rational expectations monetary steady state. We then show it is necessary to restrict the learning rule to obtain convergence. We derive an upper bound on the gain parameter in the learning rule, based on economic fundamentals in the monetary model, such that gain parameters above the upper bound would imply that the learning dynamics would diverge from the rational expectations monetary steady state.
Journal Article
Stability and Equilibrium Selection in Learning Models: A Note of Caution
Relative to rational expectations models, learning models provide a theory of expectation formation where agents use observed data and a learning rule. Given the possibility of multiple equilibria under rational expectations, the learning literature often uses stability as a criterion to select an equilibrium. This article uses a monetary economy to illustrate that equilibrium selection based on stability is sensitive to specifications of the learning rule. The stability criterion selects qualitatively different equilibria even when the differences in learning specifications are small.
Working Paper
Reliably Computing Nonlinear Dynamic Stochastic Model Solutions: An Algorithm with Error Formulas
This paper provides a new technique for representing discrete time nonlinear dynamic stochastic time invariant maps. Using this new series representation, the paper augments the usual solution strategy with an additional set of constraints thereby enhancing algorithm reliability. The paper also provides general formulas for evaluating the accuracy of proposed solutions. The technique can readily accommodate models with occasionally binding constraints and regime switching. The algorithm uses Smolyak polynomial function approximation in a way which makes it possible to exploit a high degree of ...
Report
Constructing Pure-Exchange Economies with Many Equilibria
We develop a restart algorithm based on Scarf’s (1973) algorithm for computing approximate Brouwer fixed points. We use the algorithm to compute all of the equilibria of a general equilibrium pure-exchange model with four consumers, four goods, and 15 equilibria. The mathematical result that motivates the algorithm is a fixed-point index theorem that provides a sufficient condition for uniqueness of equilibrium and a necessary condition for multiplicity of equilibria. Examining the structure of the model with 15 equilibria provides us with a method for constructing higher dimensional models ...
Working Paper
Convergence to Rational Expectations in Learning Models: A Note of Caution
This paper illustrates a challenge in analyzing the learning algorithms resulting in second-order difference equations. We show in a simple monetary model that the learning dynamics do not converge to the rational expectations monetary steady state. We then show that to guarantee convergence, the gain parameter used in the learning rule has to be restricted based on economic fundamentals in the monetary model.
Working Paper
Default Clustering Risk Premium and its Cross-Market Asset Pricing Implications
This study examines the market-implied premiums for bearing default clustering risk by analyzing credit derivatives contracts on the CDX North American Investment Grade (CDX.NA.IG) portfolio between September 2005 and March 2021. Our approach involves constructing a time series of reference tranche rates exclusively derived by single-name CDS spreads. The default clustering risk premium (DCRP) is captured by comparing the original and reference tranche spreads, with the former exceeding the latter when investors require greater compensation for correlated defaults at the portfolio level. The ...
Working Paper
Convergence to Rational Expectations in Learning Models: A Note of Caution
This paper illustrates a challenge in analyzing the learning algorithms resulting in second-order difference equations. We show in a simple monetary model that the learning dynamics do not converge to the rational expectations monetary steady state. We then show that to guarantee convergence, the gain parameter used in the learning rule has to be restricted based on economic fundamentals in the monetary model.
Working Paper
Optimal Taxation with Endogenous Default under Incomplete Markets
How are the optimal tax and debt policies affected if the government has the option to default on its debt? We address this question from a normative perspective in an economy with noncontingent government debt, domestic default and labor taxes. On one hand, default prevents the government from incurring future tax distortions that would come along with the service of the debt. On the other hand, default risk gives rise to endogenous credit limits that hinder the government's ability to smooth taxes. We characterize the fiscal policy and show how the option to default alters the near-unit ...
Report
The Great Leverage 2.0? A Tale of Different Indicators of Corporate Leverage
Many policymakers have expressed concerns about the rise in nonfinancial corporate leverage and the risks this poses to financial stability, since (1) high leverage raises the odds of firms becoming a source of adverse shocks, and (2) high leverage amplifies the role of firms in propagating other adverse shocks. This policy brief examines alternative indicators of leverage, focusing especially on the somewhat disparate signals they send regarding the current state of indebtedness of nonfinancial corporate businesses. Even though the aggregate nonfinancial corporate debt-to-income ratio is at ...