Econometrics-I-23

# Μ σ ir drawing u by random sampling eg requires

This preview shows pages 11–16. Sign up to view the full content.

μ σ ir Drawing u  by 'random sampling'   E.g.,      Requires many draws,  typically  hundreds or thousands

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Part 23: Simulation Based Estimation The Simulated Log Likelihood ™    11/25 ( 29 0 1 1 log log , ( ) ,..., i i1 iR where v  is the normally distributed effect.   Use the law of large numbers: let v v a random sample of R draws from  the standard normal po = = -∞ = + σ φ = T N it it i i i i t L g y v v dv x β ( 29 ( 29 0 0 1 1 1 , , ( ) pulation. 1 R = = = -∞ + σ → + σ φ T T R P it it iR it it i i i r t t g y v g y v v dv x x β β
Part 23: Simulation Based Estimation Quasi-Monte Carlo Integration Based on Halton Sequences ™    12/25 0 1 0 ( ) I i i i I i r i i p = r b p H p b p = - - = = = Coverage of the unit interval is the objective, not randomness of the set of draws. Halton sequences --- Markov chain a prime number,               For example, using  × × × 0 1 2 -1 -2 -3 37 base p = 5, the integer r = 37 has b  = 2, b  = 2, b  = 1.  Then H (5) = 2 5  + 2 5  + 1 5  = 0.448.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Part 23: Simulation Based Estimation Panel Data Estimation A Random Effects Probit Model ™    13/25 2 1 2 2 2 2 , 1,..., , 1,..., , ( 0), (observation mechanism) , ,..., ] ~ [ , ], ~ [0, ] ( , ) 1 1 [...] (1 ) , 1 1 it it it i it it i i iT i it it y u t T i N y y N u N Var = + ε + = = = ε ε σ ε σ = + σ = + σ x 1 0 x K L M O M K β Ι ρ ρ ρ ρ ρ ρ ρ ρ
Part 23: Simulation Based Estimation Log Likelihood ™    14/25 1 1 2 2 1 1 1 h h log ( , ) log [(2 1)( )] ( ) = 1+ Quadrature log ( , ) log [(2 1)( )] W quadrature weight, z = quadrature = = -∞ = = = β σ = Φ - + σ φ σ ρ σ β σ ≈ Φ - + σ = T n it it i i i i t T n H h it it h i h t L y v v dv L W y z β x β x 1 1 1 ir i1 iR node Simulated 1 ˆ log ( , ) log [(2 1)( )] ˆ v = rth draw from standard normal for individual i.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern