handoutsmm06 - Estimation of Deep Parameters by Simulated...

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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 fmomen t s . Ini t ,wechoo sethepa rame tersinthemode l 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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handoutsmm06 - Estimation of Deep Parameters by Simulated...

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