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

? Selection model with tobit selection equation.                   =

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? User must define the data matrix with the following line:        =

?                                                                  =

?        NAMELIST         ; X = ... $                              =

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? User's dependent variable is Y.  Change the following line       =

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?        CREATE           ; Y = the dependent variable $           =

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? User must define the data matrix for the tobit model with        =

?                                                                  =

?        NAMELIST         ; V = ... $                              =

?                                                                  =

? Tobit  dependent variable is Z.  Change the following line       =

?                                                                  =

?        CREATE           ; Z = the dependent variable $           =

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? Lower and Upper must now be set to define the lower and upper

? limits of the selection region for y2.  Either or both may be

? infinite. For minus or plus infinity, use 10000 or -10000.

? These may be different from those used in the Tobit model. For

? example, if the limit values used in estimation were 0 and 1 and

? you want to select those at the upper limit value of 1 you would

? set Lower=1 and Upper=10000 in the command below.  Do note, in

? all cases, BOTH values must be provided below, even if one of

? them is plus infinity or minus infinity.



(*)    CALC    ; Lower = ...  ; Upper = ... $ 

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

? None of the commands below require any modification.

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



? Pick up tobit estimates, å and rho. Transform. Then get

? appropriate asymptotic covariance matrix for transformed estimates.



       TOBIT   ; LHS   = z  ;  RHS = V  ;  PAR $

       CALC    ; kz    = col(v) ; eta = 1/s ; etasq = -eta^2$

       MATRIX  ; beta  = part(b,1,kz)

               ; k11   = eta   * iden(kz)

               ; k12   = etasq * beta

               ; k21   = init(1,kz,0)

               ; k22   = etasq

               ; K     = k11,k12 / k21,k22

               ; SG    = K | VARB | K'

               ; gamma = eta * beta $



?  Isolate the selected sample.



       REJECT  ; y <= lower   +   y >= upper $ 



? Variables needed to compute estimates and asymptotic covariance matrix.



       CREATE  ; zgamma = dot(z,gamma) $ 

               ; zu     = eta * upper  - zgamma

               ; fu     = n01(zu)  

               ; pu     = phi(zu)

               ; zl     = eta * lower  - zgamma

               ; fl     = n01(zl)  

               ; pl     = phi(zl)

               ; pul    = pu - pl

               ; lambda = (fl-fu) / pul

               ; delta  = (zl*fl - zu*fu) / pul  -  lambda ^ 2

               ; dldeta = (upper*fu*(zu -lambda) 

                           - lower*fl*(zl-lambda)) / pul $



? Compute slopes in selectivity corrected regression

? Pick up a) c1=slope on lambda

?         b) sigma(1) = OLS disturbance standard deviation

?         c) b1=full set of slopes including c1

? Compute consistent estimates of sigma-squared and rho-squared



       REGRESS ; lhs    = y

               ; rhs    = X,lambda $ 

       MATRIX  ; b1     = b $ 

       CALC    ; c1     = b(kreg) 

               ; csq    = c1 ^ 2

               ; sigma1 = sqr(s ^ 2  -  csq * xbr(delta))

               ; rho12  = c1 / sigma1  $ 



? Compute components of variance matrix.  THETA = åý(1 - rhoýë)



       CREATE  ; theta = sigma1 - c1 ^ 2 * delta ; delta=abs(delta) $ 



? Matrix components.  We must deal with an extra column because of å.

? 

       NAMES   ; xt   = x1,lambda $

       MATRIX  ; psi1 = xdot(xt,xt,theta)

               ; f1   = xdot(xt,xt,delta)  

               ; f2   = xdot(xt,one,dldeta)

               ; f    = f1,f2

               ; xxi  = xpxi(xt)

               ; C    = xdot(xt,xt,theta) & csq * f | SG | f'

               ; C    = xxi | C | xxi

               ; stat(b1,f)  $