Implementing Econometric Estimators on Parallel Computers

Vassilis Argyrou Hajivassiliou
Columbia University
vassilis@ariadne.econ.columbia.edu

Abstract

Recently developed parametric simulation estimation methods for static and dynamic limited dependent variables econometric models have two general features. First, they are defined as the solution, obtained by searching iteratively over an unknown vector of parameters, of non-linear optimization problems of suitable criterion functions. Second, the functions to be optimized are approximated by monte-carlo simulators possessing certain properties. Both these features exhibit the potential of significant computational benefits of implementing these estimators on massively parallel architectures, because the necessary calculations can be organized in essentially an independent pattern. In this paper, I investigate the practical benefits of parallel computation of simulation estimators using the Connection Machine CM-5 at the national center for supercomputing applications with 1024 identical processors in a multiple-instruction/multiple-data (MIMD) configuration.

First, I investigate the benefits of such a parallel architecture on the problem of solving an econometric optimization classical estimator that does not involve simulation. In this case the calculations that are distributed in parallel across the processors involve the evaluation of contributions to the criterion (e.g., likelihood) function in the case of independently and identically distributed (i.i.d.) observations. Since typical applications in modern applied econometrics using cross-sectional and longitudinal data sets involves several thousands of i.i.d. observations, the potential benefits of parallel calculations of such estimators are very significant.

Second, I study the effects of a massively parallel architecture on accurately simulating the criterion function of simulation estimators at a given trial value of the parameter vector. Leading simulation estimation methods are investigated, as for example the smooth Recursive Conditioning Simulator of Geweke , Hajivassiliou, and Keane (GHK), the Parabolic Cylinder Function simulator (PCF) (McFadden (1989) and Hajivassiliou, McFadden, and Ruud (1996)), as well as the Crude Frequency Simulator (CFS) originally proposed in the early monte-carlo integration literature. The results suggest strongly that the more sophisticated methods, like GHK and PCF, lose some of their advantages relative to the more basic CFS when a parallel architecture is used.

Finally, the paper examines the solution of a full econometric simulation estimator where parallel calculations are used both for the simulation of each contribution to the criterion function, as well as in the overall iterative optimization of the simulated criterion function. The findings support preliminarily the claim that very significant benefits exist from the implementation of simulation estimators on massively parallel machines. This opens up for the first time the study of more realistic econometric models that currently are computationally intractable on single-processor computers.