Econometrics-I-23

# ˆ ˆ v v are reused for all co β σ φ σ t n r it

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= rth draw from standard normal for individual i. ˆ ˆ (v ,...,v ) are reused for all co = = = β σ ≈ Φ - + σ T n R it it ir i r t L y v R β x mputations of function or derivatives.

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Part 23: Simulation Based Estimation Application: Innovation ™    15/25
Part 23: Simulation Based Estimation Application: Innovation ™    16/25

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Part 23: Simulation Based Estimation (1.17072 / (1 + 1.17072) = 0.578) ™    17/25
Part 23: Simulation Based Estimation Quadrature vs. Simulation p Computationally, comparably difficult p Numerically, essentially the same answer. MSL is consistent in R p Advantages of simulation n Can integrate over any distribution, not just normal n Can integrate over multiple random variables. Quadrature is largely unable to do this. n Models based on simulation are being extended in many directions. n Simulation based estimator allows estimation of conditional means  essentially the same as Bayesian posterior means ™    18/25

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Part 23: Simulation Based Estimation A Random Parameters Model ™    19/25 Φ β + β β + β + β β β β σ σ   ÷  ÷ β β σ σ   1i 2i 3 4 5 6 1i 1 11 12 2i 2 12 22 Prob(Innovation)= ( FDI Imports                logSales Employment +   Productivity) ~ N , and four fixed (nonrandom) parameters.
Part 23: Simulation Based Estimation Estimates of a Random Parameters Model ---------------------------------------------------------------------- Probit Regression Start Values for IP Dependent variable IP Log likelihood function -4134.84707 Estimation based on N = 6350, K = 6 Information Criteria: Normalization=1/N Normalized Unnormalized AIC 1.30420 8281.69414 --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Constant| -2.34719*** .21381 -10.978 .0000 FDIUM| 3.39290*** .39359 8.620 .0000 .04581 IMUM| .90941*** .14333 6.345 .0000 .25275 LOGSALES| .24292*** .01937 12.538 .0000 10.5401 SP| 1.16687*** .14072 8.292 .0000 .07428 PROD| -4.71078*** .55278 -8.522 .0000 .08962 --------+------------------------------------------------------------- ™    20/25

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Part 23: Simulation Based Estimation RPM ™    21/25
Part 23: Simulation Based Estimation ™    22/25

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Part 23: Simulation Based Estimation Parameter Heterogeneity ™    23/25
Part 23: Simulation Based Estimation ™    24/25

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Part 23: Simulation Based Estimation Movie Model     25/25
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• Fall '10
• H.Bierens
• Econometrics, Likelihood function, Simulation Based Estimation

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