Solving Finite Mixture Models in Parallel

Many economic models are completed by finding a parameter vector that optimizes a function f, a task that only be accomplished by iterating from a starting vector. Use of a generic iterative optimizer to carry out this task can waste enormous amounts of computation when applied to a class of problems defined here as finite mixture models. The finite mixture class is large and important in economics and eliminating wasted computations requires only limited changes to standard code. Further, the approach described here greatly increases gains from parallel execution and opens possibilities for re-writing objective functions to make further efficiency gains.

[1]  Christopher A. Swann,et al.  Maximum Likelihood Estimation Using Parallel Computing: An Introduction to MPI , 2002 .

[2]  K Schittkowski NLPQLP : A New Fortran Implementation of a Sequential Quadratic Programming Algorithm for Parallel Computing , 2001 .

[3]  J. Heckman,et al.  A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data , 1984 .

[4]  José-Víctor Ríos-Rull,et al.  Computation of equilibria in heterogeneous agent models , 1997 .

[5]  Andrew T. Ching,et al.  Bayesian Estimation of Dynamic Discrete Choice Models , 2009 .

[6]  N. Shephard,et al.  Computationally intensive econometrics using a distributed matrix-programming language , 2002, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[7]  S. Goldfeld,et al.  Maximization by Quadratic Hill-Climbing , 1966 .

[8]  Ian M. Mitchell,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[9]  Victor Aguirregabiria,et al.  Swapping the Nested Fixed-Point Algorithm: a Class of Estimators for Discrete Markov Decision Models , 2002 .

[10]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[11]  V. J. Hotz,et al.  Conditional Choice Probabilities and the Estimation of Dynamic Models , 1993 .

[12]  Christopher A. Swann,et al.  Software for parallel computing: the LAM implementation of MPI , 2001 .

[13]  John Rust Structural estimation of markov decision processes , 1986 .

[14]  John Rust Numerical dynamic programming in economics , 1996 .

[15]  A. E. Fincham,et al.  Parallel Computation , 1999, Algorithms and Theory of Computation Handbook.

[16]  Zvi Eckstein,et al.  ESTIMATING A MARKET EQUILIBRIUM SEARCH MODEL FROM PANEL DATA ON INDIVIDUALS , 1990 .

[17]  Peter Arcidiacono,et al.  Finite Mixture Distributions, Sequential Likelihood and the EM Algorithm , 2003 .

[18]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

[19]  K. Judd Numerical methods in economics , 1998 .

[20]  Gerard Debreu,et al.  A Social Equilibrium Existence Theorem* , 1952, Proceedings of the National Academy of Sciences.