7.0 TOBIT Command                                                               
                                                                                
     The TOBIT command allows estimation of TOBIT (bounded left hand            
variable problems) with up to 97 variables on the right hand side. An           
excellent reference is:                                                         
                                                                                
    -  McDonald, John & Robert Moffitt, "The Uses of Tobit Analysis,",          
       Review of Economics and Statistics, Vol. LXII, # 2, May 1980, pp.        
       318 - 321.                                                               
                                                                                
Form of the TOBIT command:                                                      
                                                                                
     B34SEXEC TOBIT options parameters$                                         
         MODEL Yvar = Xvar1 Xvar2  $                                            
         B34SEEND$                                                              
                                                                                
The MODEL sentence is required.                                                 
                                                                                
TOBIT options:                                                                  
                                                                                
     NOINT   -  Set if no constant is desired.                                  
                                                                                
     LOWER   -  Sets the limit of Y as lower. This is the default.              
                                                                                
     UPPER   -  Sets the limit of Y as upper.  Default = LOWER.                 
                                                                                
     ISUMM   -  Gives a summary table for each observation.                     
                                                                                
     ROUTPUT -  Reduce output to save paper. Variable means, second             
                moments about means, first and second derivatives               
                not printed.                                                    
                                                                                
TOBIT parameters:                                                               
                                                                                
     NIT=n1        - Sets number of iterations. Default =25.                    
                                                                                
     LIMIT=value   - Sets limit value. Default = 0.0  . A maximum of 10         
                     digits can be supplied.                                    
                                                                                
     NEQU=n2       - Sets equation number. Default = 1.   Max = 99.             
                                                                                
     WEIGHT=Vname  - Sets the variable to use as a weight. If WEIGHT is         
                     not set, the weight used is 1.00 .                         
                                                                                
Sample use of TOBIT command:                                                    
                                                                                
B34SEXEC TOBIT LOWER LIMIT=1.50 NIT=50$                                         
      MODEL Y = X1 X2 X3 X4 $                                                   
  B34SEEND$                                                                     
                                                                                
Note:  The TOBIT command calculates the following values:                       
                                                                                
B(i)         = Estimated Coefficient.                                           
F(Z)         = Probability for given Z value.                                   
f(Z)         = Density of cumulative normal distribution for that Z.            
SIGMA        = standard error of regression.                                    
B(i)/SIGMA   = Normalized coefficient.                                          
PARTIAL1     = f(Z) * (B(i) / SIGMA )                                           
PARTIAL2     = B(i) * (1.0 - (Z*f(Z) / F(Z) ) - (f(Z) ** 2 / F(Z) **2))         
B(i)*F(Z)    = The total effect [ d(Ey) / d(X(i)) ]                             
E(y)         = XB * F(Z)  +  (SIGMA * f(Z) )                                    
Z            = XB / SIGMA                                                       
                                                                                
Note:  Z and XB are calculated for mean X(i) in the output. Often other         
X(i) values are of interest. If we assume a model of the form Y = 10 +          
1.2 * X1 + 2.2 * X2, where  SIGMA = .9, the below listed SAS program            
will calculate the desired values. The SAS program makes use of the fact        
that f(Z) = EXP( -(Z*Z)/2.0) / SQRT( 2 * pi).                                   
                                                                                
    TTi = B(i) * F(Z)                                                           
    PARTIAL1i = f(Z) * (B(i) / SIGMA)                                           
    PARTIAL2i = B(i) * (1.0 - (Z*f(Z) / F(Z)) -(f(Z)**2 / F(Z)**2))             
                                                                                
                                                                                
DATA TEST;                                                                      
    INPUT X1 X2;                                                                
    B1 = 10.0 ;                                                                 
    B2 = 1.2  ;                                                                 
    B3 = 2.2  ;                                                                 
    SIGMA = .9  ;                                                               
    XB = B1  + (B2 * X1)  + (B3 * X2) ;                                         
    Z=XB / SIGMA;                                                               
    FZ = PROBNORM(Z) ;                                                          
    DENSITY = EXP(-1.0 * (Z*Z)/2.0) * .3989423  ;                               
    TT1 = B1 * FZ ;                                                             
    TT2 = B2 * FZ ;                                                             
    TT3 = B3 * FZ ;                                                             
    PART11 = DENSITY * (B1 / SIGMA);                                            
    PART12 = DENSITY * (B2 / SIGMA);                                            
    PART13 = DENSITY * (B3 / SIGMA);                                            
    PART21 = B1 * (1.0 - (Z * DENSITY / FZ) - ((DENSITY *DENSITY) /             
                                     (FZ * FZ)))  ;                             
    PART22 = (B2 / B1) * PART21 ;                                               
    PART23 = (B3 / B1) * PART21 ;                                               
CARDS;                                                                          
     X1  X2 values here                                                         
;                                                                               
PROC PRINT DATA=TEST;                                                           
                                                                                
The above program can be modified to run under B34S as follows:                 
                                                                                
B34SEXEC DATA TEST FILEF=@@$                                                    
    INPUT X1 X2$                                                                
    BUILD B1 B2 B3 SIGMA XB FZ DENSITY TT1 TT2 TT3 PART11 PART12                
          PART13 PART21 PART22 PART23$                                          
    GEN B1 = 10.0 $                                                             
    GEN B2 = 1.2  $                                                             
    GEN B3 = 2.2  $                                                             
    GEN SIGMA = .9  $                                                           
    GEN XB = B1  + (B2 * X1)  + (B3 * X2) $                                     
    GEN Z=XB / SIGMA$                                                           
    GEN FZ = PROBNORM(Z) $                                                      
    GEN DENSITY = EXP(-1.0 * (Z*Z)/2.0)  /(DSQRT(TIMESPI(2.0))  $               
    GEN TT1 = B1 * FZ $                                                         
    GEN TT2 = B2 * FZ $                                                         
    GEN TT3 = B3 * FZ $                                                         
    GEN PART11 = DENSITY * (B1 / SIGMA)$                                        
    GEN PART12 = DENSITY * (B2 / SIGMA)$                                        
    GEN PART13 = DENSITY * (B3 / SIGMA)$                                        
    GEN PART21 = B1 * (1.0 - (Z * DENSITY / FZ) - ((DENSITY *DENSITY) /         
                                     (FZ * FZ)))  $                             
    GEN PART22 = (B2 / B1) * PART21 $                                           
    GEN PART23 = (B3 / B1) * PART21 $                                           
DATACARDS$                                                                      
     X1  X2 values here                                                         
B34SRETURN$                                                                     
B34SEEND$                                                                       
B34SEXEC LIST$ B34SEEND$