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Working Paper
The market resources method for solving dynamic optimization problems
We introduce the market resources method (MRM) for solving dynamic optimization problems. MRM extends Carroll?s (2006) endogenous grid point method (EGM) for problems with more than one control variable using policy function iteration. The MRM algorithm is simple to implement and provides advantages in terms of speed and accuracy over Howard?s policy improvement algorithm. Codes are available.
Working Paper
A Generalized Time Iteration Method for Solving Dynamic Optimization Problems with Occasionally Binding Constraints
We study a generalized version of Coleman (1990)’s time iteration method (GTI) for solving dynamic optimization problems. Our benchmark framework is an irreversible investment model with labor-leisure choice. The GTI algorithm is simple to implement and provides advantages in terms of speed relative to Howard (1960)’s improvement algorithm. A second application on a heterogeneous-agents incomplete-markets model further explores the performance of GTI.
Working Paper
Perturbation methods for Markov-switching DSGE models
Markov-switching DSGE (MSDSGE) modeling has become a growing body of literature on economic and policy issues related to structural shifts. This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of MSDSGE models. Our new method, called "the partition perturbation method," partitions the Markov-switching parameter space to keep a maximum number of time-varying parameters from perturbation. For this method to work in practice, we show how to reduce the potentially intractable problem of solving MSDSGE models to the manageable problem ...
Working Paper
Rational Bubbles in Non-Linear Business Cycle Models: Closed and Open Economies
This paper studies rational bubbles in non-linear dynamic general equilibrium models of the macroeconomy. The term ‘rational bubble’ refers to multiple equilibria due to the absence of a transversality condition (TVC) for capital. The lack of TVC can be due to an OLG population structure. If a TVC is imposed, the macro models considered here have a unique solution. Bubbles reflect self-fulfilling fluctuations in agents’ expectations about future investment. In contrast to explosive rational bubbles in linearized models (Blanchard (1979)), the rational bubbles in non-linear models here ...
Working Paper
Perturbation methods for Markov-switching DSGE models
This paper develops a general perturbation methodology for constructing high-order approximations to the solutions of Markov-switching DSGE models. We introduce an important and practical idea of partitioning the Markov-switching parameter space so that a steady state is well defined. With this definition, we show that the problem of finding an approximation of any order can be reduced to solving a system of quadratic equations. We propose using the theory of Grobner bases in searching all the solutions to the quadratic system. This approach allows us to obtain all the approximations and ...
Working Paper
Avoiding Nash Inflation : Bayesian and Robust Responses to Model Uncertainty
We examine learning, model misspecification, and robust policy responses to misspecification in a quasi-real-time environment. The laboratory for the analysis is the Sargent (1999) explanation for the origins of inflation in the 1970s and the subsequent disinflation. Three robust policy rules are derived that differ according to the extent that misspecification is taken as a parametric phenomenon. These responses to drifting estimated parameters and apparent misspecification are compared to the certainty-equivalent case studied by Sargent. We find gains from utilizing robust approaches to ...
Working Paper
Equilibrium Multiplicity in Aiyagari and Krusell-Smith
Repeatedly solving the Aiyagari (1994) model with random parameters, we construct hundreds of examples with multiple stationary equilibria. We never find multiplicity with risk aversion less than ≈ 1.49, depreciation less than ≈ 0.19, or income persistence less than ≈ 0.47, and multiplicity requires a disaster state for income. In cases with multiplicity, the lowest rental rate occurs near depreciation times the capital share. It is possible for the economy, without a change in fundamentals, to transition rationally from a higher-rate equilibrium to one with a lower rental rate, lower ...
Working Paper
Regulating Financial Networks Under Uncertainty
I study the problem of regulating a network of interdependent financial institutions that is prone to contagion when there is uncertainty regarding its precise structure. I show that such uncertainty reduces the scope for welfare-improving interventions. While improving network transparency potentially reduces this uncertainty, it does not always lead to welfare improvements. Under certain conditions, regulation that reduces the risk-taking incentives of a small set of institutions can improve welfare. The size and composition of such a set crucially depend on the interplay between (i) the ...
Working Paper
Firm Networks and Asset Returns
This paper argues that changes in the propagation of idiosyncratic shocks along firm networks are important to understanding variations in asset returns. When calibrated to match key features of supplier-customer networks in the United States, an equilibrium model in which investors have recursive preferences and firms are interlinked via enduring relationships generates long-run consumption risks. Additionally, the model matches cross-sectional patterns of portfolio returns sorted by network centrality, a feature unaccounted for by standard asset pricing models.