MSM.jl

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MSM.jl is a package designed to facilitate the estimation of economic models via the Method of Simulated Moments.

Why

An economic theory can be written as a system of equations that depends on primitive parameters. The aim of the econometrician is to recover the unknown parameters using empirical data. One popular approach is to maximize the likelihood funtion. Yet in many instances, the likelihood function is intractable. An alternative approach to estimate the unknown parameters is to minimize a (weighted) distance between the empirical moments and their theoretical counterparts.

When the function mapping the set of parameter values to the theoretical moments (the expected response function) is known, this method is called the Generalized Method of Moments. However, in many interesting cases the expected response function is unknown. This issue may be circumvented by simulating the expected response function, which is often an easy task. In this case, the method is called the Method of Simulated Moments.

Philosophy

MSM.jl is being developed with the following constraints in mind:

1. Parallelization within the expected response function is difficult to achieve. This is generally the case when working with the simulated method of moments, as the simulated time series are often serially correlated.
2. Thus, the minimizing algorithm should be able to run in parallel
3. The minimizing algorithm should search for a global minimum, as the objective function may have multiple local minima.
4. Do not reinvent the wheel. Excellent minimization packages already exist in the Julia ecosystem. This is why MSM.jl relies on BlackBoxOptim.jl and Optim.jl to perform the minimization.

Installation

pkg> add https://github.com/JulienPascal/MSM.jl.git

Usage

See the following notebooks:

• notebooks/LinearModel.ipynb for an introduction to the package
• notebooks/LinearModelCluster.ipynb to see how to use the package on a cluster

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Experiments

See the following notebooks for experiments with ApproxBayes.jl, Surrogates.jl, SurrogateModelOptim.jl and MSM-MCMC using AffineInvariantMCMC.jl (not yet supported within the package):

• notebooks/ABC.ipynb
• notebooks/Surrogates.ipynb
• notebooks/SurrogateModelOptim.ipynb
• notebooks/MSM-MCMC

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Notebooks

Linear Model

Surrogates

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Related Packages

• SMM.jl: a package to do SMM using MCMC algorithms in parallel