{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PanelDataNotes-12

PanelDataNotes-12 - Econometric Analysis of Panel Data...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business
Background image of page 1

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

View Full Document Right Arrow Icon
Econometric Analysis of Panel Data 12. Random Parameters Linear Models
Background image of page 2
Agenda ‘True’ Random Parameter Variation Discrete – Latent Class Continuous Classical Bayesian
Background image of page 3

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

View Full Document Right Arrow Icon
Parameter Heterogeneity i,t it it i,t (1) Regression model      y ε (2) Conditional probability model      f(y | x , ) (3) Heterogeneity - how are parameters distributed across      individuals?     (a)  Discrete - the populatio = + i,t i i x β β n contains a mixture of J           types of individuals.     (b)  Continuous. Parameters are part of the stochastic           structure of the population.
Background image of page 4
Discrete Parameter Variation ,j The Latent Class Model (1) Population is a (finite) mixture of J types of individuals.      j =  1,...,J.  J 'classes' differentiated by ( , )     (a) Analyst does not know class memberships. ('latent ε σ j β J 1 J j=1 J i,t it i,t ,j .')     (b) 'Mixing probabilities' (from the point of view of the          analyst) are  ,..., ,  with  1 (2) Conditional density is       P(y | class j) f(y | x , , ) ε π π Σ π = = = σ j β
Background image of page 5

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

View Full Document Right Arrow Icon
Estimating an LC Model i i i,t it i,t ,j i T i1 i2 i,T ,j it i,t ,j t 1 i Conditional density for each observation is  P(y | class j) f(y | x , , ) Joint conditional density for T  observations is f(y , y ,..., y | , ) f(y | x , , ) (T  may be 1. Th ε ε ε = = = σ σ = σ j i j j β X , β β i T J i1 i2 i,T j it i,t ,j j 1 t 1 is is not only a 'panel data' model.) Maximize this for each class if the classes are known.  They aren't. Unconditional density for individual i is f(y , y ,..., y | ) f(y | x , , ) ε = = = π σ i j X β ( 29 ( 29 i i ,1 ,J T N J j it i,t ,j i 1 j 1 t 1 LogLikelihood LogL(( , ),...,( , ))      log f(y | x , , ) ε ε ε = = = σ σ = π σ 1 J j β β β
Background image of page 6
Unmixing a Mixed Sample Sample  ; 1 – 1000$ Calc        ; Ran(123457)$ Create ; lc1=rnn(1,1) ;lc2=rnn(5,1)$ Create ; class=rnu(0,1)$ Create ; if(class<.3)ylc=lc1 ; (else)ylc=lc2$ Kernel ; rhs=ylc $ Regress; lhs=ylc;rhs=one;lcm;pts=2;pds=1$ YLC .045 .090 .135 .180 .224 .000 -2 0 2 4 6 8 10 -4 Kernel density estim ate for YLC Density
Background image of page 7

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

View Full Document Right Arrow Icon
Mixture of Normals 2 it j it j it j j j j T 2 it j T i1 iT t 1 j j T N J it j T j t 1 i 1 j 1 j j y y 1 1 1 f(y | class j) exp =   2 2 y 1 1 f(y ,..., y | class j) exp 2 2 y 1 1 logL log exp 2 2 = = = = - μ - μ = = - φ ÷ ÷ ÷ ÷ σ σ σ σ π - μ ÷ = = - Σ ÷ ÷ ÷ σ σ π - μ ÷ = π - Σ ÷ σ σ π 2 ÷ ÷
Background image of page 8
Mixture of Normals +---------------------------------------------+ | Latent Class / Panel LinearRg Model | | Dependent variable YLC | | Number of observations 1000 | | Log likelihood function -1960.443 | | Info. Criterion: AIC =
Background image of page 9

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

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}