Method of simulated moments
Encyclopedia
In econometrics
, the method of simulated moments (MSM) (also called simulated method of moments) is a structural estimation
technique introduced by Daniel McFadden
. It extends the generalized method of moments
to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve high-dimensional integral
s. MSM's earliest and principal applications have been to research in industrial organization
, after its development by Ariel Pakes and others, though applications in consumption
are emerging.
where
is the moment condition.
where
is the simulated moment condition and 
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
, the method of simulated moments (MSM) (also called simulated method of moments) is a structural estimation
Structural estimation
Structural estimation is a technnique for estimating deep "structural" parameters of theoretical economic models. In this sense, "structural estimation" is contrasted with "reduced-form estimation," which generally provides evidence about partial equilibrium relationships in a regression...
technique introduced by Daniel McFadden
Daniel McFadden
Daniel Little McFadden is an econometrician who shared the 2000 Nobel Memorial Prize in Economic Sciences with James Heckman ; McFadden's share of the prize was "for his development of theory and methods for analyzing discrete choice". He was the E. Morris Cox Professor of Economics at the...
. It extends the generalized method of moments
Generalized method of moments
In econometrics, generalized method of moments is a generic method for estimating parameters in statistical models. Usually it is applied in the context of semiparametric models, where the parameter of interest is finite-dimensional, whereas the full shape of the distribution function of the data...
to cases where theoretical moment functions cannot be evaluated directly, such as when moment functions involve high-dimensional integral
Integral
Integration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...
s. MSM's earliest and principal applications have been to research in industrial organization
Industrial organization
Industrial organization is the field of economics that builds on the theory of the firm in examining the structure of, and boundaries between, firms and markets....
, after its development by Ariel Pakes and others, though applications in consumption
Consumption (economics)
Consumption is a common concept in economics, and gives rise to derived concepts such as consumer debt. Generally, consumption is defined in part by comparison to production. But the precise definition can vary because different schools of economists define production quite differently...
are emerging.
GMM v.s. SMM
,
where
is the moment condition.
,
where
is the simulated moment condition and