Harold L. Cole
Infrequent Portfolio Re-balancing and the Volatility of the Market-Price of Risk (by YiLi Chien, Harold Cole, Hanno Lustig)


Wouter J. den Haan
How well-behaved are higher-order perturbation solutions?
Abstract / Link
They are not well-behaved. The main problem is that one cannot control the radius of convergence when using perturbation techniques. Just outside the radius of convergence, higher-order approximations can easily behave extremely badly, and even within the radius of convergence one can expect higher- but .nite-order perturbation solutions to display problematic oscillations. In contrast, with projection methods one can control the radius of convergence. Pruning, the solution proposed to deal with explosive behavior of higher-order perturbation solutions, is shown to be highly distortionary. A simple alternative based on short samples and rejection sampling is proposed and shown to be much less distortive.


Engelbert J. Dockner
Strategic Product Market Competition and Asset Returns (mit Mosburger) (in Überarbeitung)
In diesem Papier wird unterstellt, dass zwei Duopolisten auf dem Produktmarkt interagieren und beide Anbieter stochastischer Industrienachfrage ausgesetzt sind. Ziel der beiden Konkurrenten ist es über einen unendlichen Planungshorizont optimale Investitionsstrategien zu wählen, die in der Folge Anlass zu schwankenden Investitions- und Eigenkapitalrenditen geben. Da in diesem Setting eine analytische Ableitung des Investitionsgleichgewichts nicht mehr möglich ist, verwenden wir computational methods um die Wertfunktionen der beiden Anbieter und dadurch auch die Aktienrenditen abzuleiten. Der Schwerpunkt der Arbeit liegt in der Ableitung des Zusammenhangs zwischen Wettbewerbsintensität auf den Produktmärkten und Höhe der Aktienrenditen. Es ist uns mit dem Papier möglich, eine theoretische Fundierung für die empirischen Befunde von Hou and Robinson, Journal of Finance, 2006, zu geben.


Bernard J. Dumas
Incomplete-Market Equilibria Solved Recursively onan Event Tree / mit A. Lyasoff
Abstract / Link:
We develop a method that allows one to compute incomplete-market equilibria routinely for Markovian equilibria (when they exist). The main difficulty to be overcome arises from the set of state variables. There are, of course, exogenous state variables driving the economy but, in an imcomplete market, there are also endogenous state variables, which indtroduce path dependence. We write on an event tree the system of all first-order conditions of all times and states and solve recursively for state prices, which are dual variables. We illustrate this "dual" method and show its many practical advantages by means of several examples.


Zhigang Feng
Numerical Simulation of non optimal dynamic economies
Abstract / Link:
We develop a method that allows one to compute incomplete-market equilibria routinely for Markovian equilibria (when they exist). The main difficulty to be overcome arises from the set of state variables. There are, of course, exogenous state variables driving the economy but, in an imcomplete market, there are also endogenous state variables, which indtroduce path dependence. We write on an event tree the system of all first-order conditions of all times and states and solve recursively for state prices, which are dual variables. We illustrate this "dual" method and show its many practical advantages by means of several examples.


Andreas Fuster (co-author to Paul Willen)
Insuring Consumption Using Income-Linked Assets


Kenneth Judd
Multistage decision problems are numerically challenging. Typically the work to solve such problems is an exponential function both with respect to the number of stages and the number of decision parameters. The problems have been researched extensively and a wide variety of methods to solve them have been proposed. Inevitably all methods are limited in the size of problem they can solve. The purpose of our work is to develop a new more ecient algorithm and one that is suitable to run on parallel architectures and in so doing extend signicantly the size of problems that are tractable. We present a numerical dynamic programming algorithm that has three components: optimization, approximation and integration. A key feature of the approximation methods we use is to preserve mathematical features such as convexity and dierentiability, which enables us to use powerful optimization methods. To illustrate the eciency of the new method we present extensive results on optimal growth models and on dynamic portfolio problems obtained from implementation of the algorithm designed to run on the Condor Master-Worker system.


Dirk Krüger
Computing Stochastic Dynamic Economic Models with a Large Number of State Variables: A Description and Application of a Smolyak-Collocation
Abstract / Link:
We describe a sparse grid collocation algorithm to compute recursive solutions of dynamic economies with a sizable number of state variables. We show how powerful this method may be in applications by computing the nonlinear recursive solution of an international real business cycle model with a substantial number of countries, complete insurance markets and frictions that impede frictionless international capital flows. In this economy the aggregate state vector includes the distribution of world capital across different countries as well as the exogenous country-specific technology shocks. We use the algorithm to efficiently solve models with 2, 4, and 6 countries (i.e., up to 12 continuous state variables).


Andrew Lyasoff
Incomplete-Market Equilibria Solved Recursively on an Event Tree / mit B. Dumas
Abstract / Link:
as described with Bernard Dumas


Jochen Mankart
Personal Bankruptcy Law, Debt Portfolios and Entrepreneurship
Every year 400,000 entrepreneurs fail and 60,000 file for bankruptcy. Thus the personal bankruptcy law has important implications for entrepreneurship. The option to declare bankruptcy encourages entrepreneurship through providing insurance since entrepreneurs may default on unsecured credit in bad times. However, perfectly competitive financial intermediaries take the possibility of default into account and they charge higher interest rates which reflect these default probabilities. Thus personal bankruptcy provides insurance at the cost of worsening credit conditions. Since the benefits depend on agents degree of risk-aversion but the costs depend on intertemporal preferences, we use Epstein-Zin preferences to investigate the robustness of our results. We develop a quantitative general equilibrium model of occupational choice that examines the effects of the US personal bankruptcy law on entrepreneurship. The model explicitly incorporates the US legislative framework and replicates empirical features of the US economy regarding entrepreneurship, wealth distribution and bankruptcy filings by entrepreneurs. Entrepreneurs in the model can obtain secured and unsecured credit. Secured credit must be repayed and therefore provides no insurance but is cheap. Our quantitative evaluations show: First, the current US bankruptcy law is too harsh. It does not provide enough insurance. According to our simulations, increasing the wealth exemption level to the optimal one would increase entrepreneurship, the median firm size, welfare and social mobility without increasing inequality. Second, and this is an important methodological contribution, the modeling of the credit market matters. Any analysis of unsecured credit and bankruptcy has to include secured credit as well. If agents had only access to unsecured credit (as is the case in most of the previous literature), the optimal bankruptcy law would be harsher.


Thomas Mertens
Excessively Volatile Stock Markets: Equilibrium Computation and Policy Analysis
This paper incorporates excess volatility in stock prices into a standard general equilibrium model and finds large welfare gains from stabilizing policies. Stock prices in this model aggregate information about fundamentals which is dispersed in the economy but also reflect excess volatility stemming from correlated distortions in beliefs. To solve the model, this paper develops a novel solution method for nonlinear models with dispersed information which can be applied to a large class of dynamic general equilibrium models. The innovation lies in a nonlinear change of variables which, when combined with perturbation methods, yields the nonlinear price function consistent with equilibrium expectation operators. The main positive result shows that dispersion of information allows arbitrarily small distortions in beliefs to generate large amounts of excess volatility and renders arbitrage infeasible. The government cannot observe whether a given stock price movement originates from information or noise. As a normative result, price stabilizing policies lead to a higher level of consumption: a fall in the risk premium lowers the marginal product of capital and raises the capital stock and production. History-dependent policies may improve the information content of prices and result in even higher welfare gains.


Paul Pichler
Sparse-grid Galerkin methods for solving medium-scale dynamic economic models
This paper proposes a numerical strategy, sparse-grid Galerkin methods, to obtain globally accurate solutions of medium-scale dynamic equilibrium models. By using monomial rules instead of product rules to compute the projection conditions, our approach largely avoids the curse of dimensionality associated with standard projection methods. We apply sparse-grid Galerkin methods to solve several versions of an international real business cycle model with complete insurance markets and frictions in international capital °ows, demonstrating that these methods are straightforward to implement, fast, and highly accurate. Importantly, we show that our numerical strategy is feasible for models with a sizeable number of state variables and, therefore, provides an interesting alternative to sparse-grid collocation methods based on the Smolyak algorithm.


Michael Reiter
Nonlinear Approximate Aggregation in Heterogeneous Agent Models


Thomas F. Rutherford
Stochastic control model applied to research and development expenditures for climate policy


Manuel Santos
Long Term Asset Price Volatility and Macroeconomic Fluctuations
We analyze a stochastic growth model with lags in the operation of new technologies. Stock values are impacted by news on technological innovations and some other external shocks affecting the economy. Episodes of technology adoption may generate long fluctuations in the aggregate value of stocks. We assess the quantitative importance of various macroeconomic variables in accounting for the observed volatility in stock values while preserving the volatilities of real macroeconomic aggregates. Our analysis gives a prominent role to price markups and leverage, and places much less importance on adjustment costs, taxes, and labor and financial frictions.


Benjamin Skrainka
Enhance your productivity and software quality with techniques from Silicon Valley


Adam L. Speight
Fast Multigrid Solvers for Calibration and Estimation of Dynamic Structural Models
A new methodology for calibrating parameters when working with intractable, dynamic structural models is developed. A straight-forward extension also allows for formal estimation and hypothesis testing in a Generalized Method of Moment framework. The method is based on multigrid techniques used in many state of the art solvers from engineering applications. These techniques are adapted to solve Bellman and Euler-type equations and to handle subtleties arising from the interaction of statistical and numerical errors. The method works on a joint mode of analysis incorporating both statistical and numerical errors in the spirit of "forward-backward" error analysis of Kubler and Schmedders (2005). Numerical results from example problems - and experience from thirty years of multigrid literature - support the papers main finding: a fully-identified model that is smooth in parameters can be calibrated and solved with only about three to five times the work required to solve the model and compute associated "moments" for a single set of parameters. As with other multigrid methods, the solvers can be efficiently and naturally implemented on parallel processors. This work also shows that the size of numerical error can be less important than the qualitative type of error when parameters are fitted to a numerically solved model subject to discretization error. An example is presented in which a popular, consistent discretization of a portfolio problem with endogenous retirement produces an ill-posed, unstable calibration problem. This example and subsequent analysis show greater care must be taken when discretizing a model for a calibration or estimation problem: To avoid corrupting sensitivity analysis, identification, and inference, it is important to perform a joint error analysis that includes both discretization and statistical errors.


Tim Stitt
Supercomputing in Switzerland