?===================================================================

? Sample selection with ordered probit selection equation.         =

? Only the following must be set by the user prior to using this routine.

? RHS variables in the ordered probit selection model:

?

?    NAMES   ;  W  =  the rhs variables in the ordered probit   $

?

? Dependent variable in the ordered probit model.

?

?    CREATE  ;  Z  =  the LHS variable in the ordered probit  $

?

? RHS variables in the primary regression

?

?    NAMES   ;  X  =  the rhs variables in the regression model  $

?

? Dependent variable in the regression.

?

?    CREATE  ;  Y  =  the LHS variable in the regression  $

?

? Selection rule.  User must provide this value.

?

?    CALC    ;  j  =  the value on which sample selection is based  $

?===================================================================

?

? Estimate the ordered probit model and collect results   =



       ORDERED PROBIT  ; Lhs = Z  ;  RHS = W  ;  PAR $



? The number of values taken by the dependent variable in the ordered probit

? model is JP = J+1.



       CALC    ; Nolist ; JP = max(Z)   +   1  ;  JP1 = JP + 1



? Retrieve dimensions and estimates from ordered probit

? KP = number of variables in ordered probit, KP1=KP+1

? M  = number of threshold parameters estimated

? L  = total number of parameters estimated



                 ; KP = col(W) ; KP1 = KP+1 ; M = JP-2 ; L=KP+M $



? 1.  Retrieve slope vector



       MATRIX  ; nolist ; alpha=part(b,1,kp) 



? 2.  full threshold vector is -ì,0,æ(1),æ(2),...,æ(J-1),+ì

?     The name MU is used by the ordered probit program, so we use MUA.



                 ; u1=-10000 / 0 

                 ; u2=part(b,kp1,l)

                 ; u3= 10000

                 ; mua=u1/u2/u3



? 3.  Covariance matrix of this full parameter vector, 



               ; z11=part(varb,1,KP,1,KP)

               ; z21=init(2,KP,0) 

               ; z22=0,0/0,0

               ; z31=part(varb,KP1,L,1,KP) 

               ; z32=init(M,2,0) 

               ; z33=part(varb,KP1,L,KP1,L)

               ; z41=init(1,KP,0)   

               ; z42=0,0 

               ; z43=init(1,M,0)

               ; z44=0



? Now gather the parts into the partitioned matrix



               ; v=z11 /  z21,z22 /  z31,z32,z33 /  z41,z42,z43,z44  $



?=======================

? Sample selection     =

?=======================



       INCLUDE ;  new  ;  Z  =  j  $



?===========================================

? Construct some variables needed for the regression    =

?===========================================



       CALC    ;  j1  = j + 1  

               ;  j2  = j + 2 $

       CREATE  ;  aj1 = mua(j1)-dot(W,alpha) 

               ;  aj  = mua(j2)-dot(W,alpha)

               ;  dj1 = n01(aj1)

               ;  dj  = n01(aj)

               ;  fj1 = phi(aj1)  

               ;  fj  = phi(aj)

               ;  lambda = (dj1-dj)/(fj-fj1)

               ;  delta = (aj1*dj1 - aj*dj)/(fj-fj1) - lambda ^ 2 $



?========================================

? Selectivity corrected regression      =

?========================================



       NAMES   ;  XL = X,lambda $

       REGRESS ;  LHS  =  Y  ;  RHS  =  X, lambda  $

       CALC    ;  P  =  col(XL)  ;  c = b(P)

               ;  s2  =  sumsqdev/nreg - c^2 *xbr(delta)

               ;  rhosqd  =  c^2/s2  $

       CREATE  ;  pj1 = (j > 1) *  dj1/(fj-fj1) * (lambda-aj1)

               ;  pj  = (j > 0) * (j < (JP-1)) * (-dj/(fj-fj1) * (lambda-aj)) $

       MATRIX  ; Xp1 = XDOT(XL,one,pj1) 

               ; Xp = XDOT(XL,one,pj) 

               ; zero=init(P,1,0)

               ; R   = init(3,JP1,0) 

               ; R(1,j1)=1

               ; R(2,j2)=1

               ; XPP = Xp1,Xp,Zero 

               ; XG1 = XDOT(XL,W,delta)

               ; XG2 = XPP | R 

               ; XG = XG1,XG2  $



?    Obtain the covariance matrix:



       CREATE  ;  h   =  1 -rhosqd * delta $

       MATRIX  ;  XXI = xpxi(XL)

               ;  VC  =  XDOT(XL,XL,h) & rhosqd*XG | V | XG'

               ;  VC   =  s2 * XXI | VC | XXI  $



?    Display the results



       TYPE    ;  Uncorrected results $

       MATRIX  ;  Stat   (  b , Varb) ; Pause $

       TYPE    ;  Corrected results   $

       MATRIX  ;  Stat   (  b , VC )  ; Pause $