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Solving dynamic programming problems using stochastic grids and nearest-neighbor interpolation
Stockholm University, Faculty of Social Sciences, Department of Economics.
Stockholm University, Faculty of Social Sciences, Department of Economics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We propose two modications to the method of endogenous grid points that greatly decreases the computational time for life cycle models with many exogenous state variables. First, we use simulated stochastic grids on the exogenous state variables. Second, when we interpolate to nd the continuation value of the model, we split the interpolation step into two: We use nearest-neighbor interpolation over the exogenous state variables, and multilinear interpolation over the endogenous state variables. We evaluate the numerical accuracy and computational eciency of the algorithm by solving a standard consumption/savings life-cycle model with an arbitrary number of exogenous state variables. The model with eight exogenous state variables is solved in around eight minutes on a standard desktop computer. We then demonstrate the usefulness of the algorithm by solving a model which includes a more realistic income process estimated by Guvenen et al. (2015).

National Category
Economics
Research subject
Economics
Identifiers
URN: urn:nbn:se:su:diva-155078OAI: oai:DiVA.org:su-155078DiVA, id: diva2:1196758
Available from: 2018-04-11 Created: 2018-04-11 Last updated: 2018-04-11Bibliographically approved
In thesis
1. Public Policy, Household Finance and the Macroeconomy
Open this publication in new window or tab >>Public Policy, Household Finance and the Macroeconomy
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The thesis contains four separate essays, spanning questions of the interaction between public policy, household finance and the macroeconomy. How does public policy affect macroeconomic outcomes, and the choices and welfare of households, and what are households’ optimal financial responses to changes in macroeconomic environments? Furthermore, the thesis includes a development of a method, which is helpful to answer questions like the ones stated above. 

The first essay, Optimal Public Policy in a Multi-Sector Economy with Asymmetric Shocks, shows how fiscal policy can complement monetary policy. It is shown that fiscal policy can be used to improve macroeconomic outcomes and make the economy more efficient. Since fiscal policy, in general, includes more instruments than monetary policy, it is possible to neutralize several frictions in the economy simultaneously. This is shown in a general equilibrium model with dynastic households, where firms face monopolistic competition, sticky prices, productivity shocks and cost-push shocks. 

The second essay, On the Design of Mortgage Default Legislation, asks how different types of mortgage contracts interact with different types of mortgage default policies regarding the probability of a default on home-owner’s mortgage. The different types of mortgage contracts analyzed are fixed rate annuity mortgages, adjustable rate amortized mortgages and adjustable rate non-amortized mortgages. The mortgage default policies span from non-recourse (where the mortgage lender takes all the default risk) to full recourse (where the borrower takes all the default risk). It is shown that a “borrower friendly” non-recourse policy is, as the one implemented in many parts of the United States, not necessarily borrower friendly due to its effect on the risk premium. This is investigated in a model with finitely lived households and an endogenous risk premium. 

The third essay, On The Empirical Relevance of Cointegration Between Stock Market Returns and Labor Income on Optimal Portfolio Choice, investigates how finitely lived households optimally choose a portfolio consisting of risk-free bonds and risky equity, and how this choice is affected by the long-run correlation between risky (cumulative) equity returns and stochastic labor income. More specifically, I investigate if the empirical cointegration (long-run correlation) between the two variables is strong enough to affect the optimal portfolio choice.  It is shown that it is not. Cointegration exists between the two variables, but the speed-of-adjustment back to the cointegration equilibrium is to slow to have a significant effect on the households’ optimal portfolios. 

The fourth essay, Solving Dynamic Programming Problems Using Stochastic Grids and Nearest-Neighbor Interpolation, describes a new computational method, which is used in the second and third essays. The method is developed to solve models with finitely lived households who face a complex economic environment. Post-state decision rules for the households are used together with simulated stochastic grids over the exogenous variables. By simulating the grids it is possible to reduce the number of grid points that the model is solved for, thereby making it significantly faster to solve models with many exogenous state variables. It is shown that it is possible to solve non-linear life-cycle models including at least eight state variables relatively quickly on a standard desktop computer.

Place, publisher, year, edition, pages
Stockholm: Department of Economics, Stockholm University, 2018
Series
Dissertations in Economics, ISSN 1404-3491 ; 2018:3
Keywords
Public policy, household finance, macroeconomics, numerical models, housing finance
National Category
Economics
Research subject
Economics
Identifiers
urn:nbn:se:su:diva-155083 (URN)978-91-7797-250-1 (ISBN)978-91-7797-251-8 (ISBN)
Public defence
2018-05-29, De Geersalen, Geovetenskapens hus, Svante Arrhenius väg 14, Stockholm, 13:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Manuscript. Paper 4: Manuscript.

Available from: 2018-05-04 Created: 2018-04-11 Last updated: 2018-04-20Bibliographically approved

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