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# Adv Macroeconomics II ECON 526

Yale

GPA 3.89

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This 2 page Class Notes was uploaded by Alan Doyle on Thursday October 29, 2015. The Class Notes belongs to ECON 526 at Yale University taught by Staff in Fall. Since its upload, it has received 17 views. For similar materials see /class/231034/econ-526-yale-university in Economcs at Yale University.

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Date Created: 10/29/15

Readme document for iim George J Hall February 2006 This note accompanies the Matlab code ii m This code performs a monte carlo experiment estimating a single factor model using Tony Smith s JAE 1993 extended method of simulated moments procedure Consider the following structura model x1 px VHq state equation z x1 I x I e observ equation 1 y x2 yx 92 observ equation 2 where x is a latent factor and z and y are observable variables w e and 92 are iid normally distributed innovations V is distributed N 07 6 e is distributed N 07 6 92 is distributed N 07 5 To estimate the parameters of the structural model p the X s B y and the 6 s using indirect inference we need to specify an auxiliary model I use the following VAR2 2 l71 J4722171 7324 b4yzi1 bsyziz 71 y 76 b72171 7824 b9yz71 b10yz4 mt I perform a monte carlo exercise on the above model using the above VAR2 as the auxiliary model The number of monte carlo draws is nruns the length of each simulation is T The number of simulation used when estimating each run is NS IM Since the criterion may be nearly at along certain dimensions I draw initial parameter values from Normal distributions centered around the true values I am doing EMSM in that I want to match the coef cients b1 b2 1710 across the simulations and observed data I augmented these ten moments with the variances of the two VAR errors ee T 7 k and the covariance across the two VAR errors So I have a total of 13 moments In the table below I report the results for rnuns 2 0 0 NS IM l 00 and T l 0 00 In the rst column with numbers I report the true parameter values In the next two columns I report the mean and standard deviation of the initial parameter guess used in the estimation of the 200 monte carlo runs I then report the mean and standard deviation of the point estimates Since the standard deviations for all three shock processes are not identi ed I X 51 01 its true value prior to estimation true meanstart stdstart meanpoint stdpoint meanstand parameter value value value estimate estimate error p 085 08558 00934 08508 00247 00231 x1 10 09899 01260 09765 03050 03456 x 15 15062 01829 14958 00754 00842 B 20 20116 02550 19969 01953 01439 7 05 04990 00621 04996 00535 00404 51 01 52 02 01992 00250 01992 00096 00138 53 01 01000 00129 00997 00075 00131 In general the estimation procedure does a good job recovering the true parameter values The differ ence between the mean point estimates and the true values is small ie generally one percent or less with the exception of on Also note that the standard deviation of the estimated point estimates is in general less than the standard deviation of the starting values with the exception of x1 The standard deviations of the point estimates coincide with the mean of the asymptotic standard errors To see how the estimator does in small sample I redid the eXperiment with NSIM25 and T180 This yields true meanstart stdstart meanpoint stdpoint meanstand parameter value value value estimate estimate error p 085 08513 00992 08302 00653 00525 x1 10 10018 01082 10516 04649 02943 x 15 15240 01922 15157 01160 00745 B 20 20117 02500 19296 04907 02971 7 05 04975 00639 04967 01257 00846 51 01 52 02 01999 00213 01991 00254 00284 53 01 01007 00111 00983 00065 00218

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