Estimation of Deep Parameters by
Simulated Method of Moments
A way to assign numerical values other than calibration is known as the
s
imu
la
tedme
thodo
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t
s
. Ini
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,wechoo
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such that the moments of simulated data are as close as possible to the moments
of the data. The following material is from Lee and Ingram (1991).
•
In particular, let
b
be an
k
×
1 vector of parameters of interest.
•
Let
{
x
t
}
T
t
=1
be a realization of an
m
×
1 vector valued stationary and
ergodic stochastic process generating the observed data (e.g. detrended
GDP).
•
Let
{
y
n
(
b
)
}
N
n
=1
be a realization of an
m
×
1 vector valued stationary
stochastic and ergodic process generating the simulated data (e.g. GDP
generated by the model).
•
Let
M
T
(
x
)bea
J
×
1 vector of data moments (e.g. standard deviation
of detrended GDP) and
M
N
(
y
(
b
)) be a
J
×
1 vector of model moments of
the simulated data.
•
Assume that
M
T
(
x
)
a.s.
→
µ
(
x
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 Spring '07
 CORBAE
 Estimation theory, weighting matrix, data moments, model moments

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