FOX: FITTING THE GENERALIZED STOCK PRODUCTION MODEL 



APPENDIX 



Miscellaneous Equations for PRODFIT 



Elements of the X -matrix 



Lett/, = (a + 0/,) 

 Then 



9f/, ^ ,, - (2 - m)/(m - 1) 



g^ =l/(m - l)(a + )3/-,) 



a^ ' bq 



^^i , . - l/(m - 1) _ 



-g7^ = - (a + 0/;) X ln(a + (3/",)[l/(m - DP 



Derivatives for the Delta Method Variance Estimates 



y 



-' max 



"_£_max _ TT- r , 



a - i'^ maxim/ (m - l)]/a 



a 

 ay 



a^ 



•^ max'P 



9"^ ma 



^^^r^ = ^max X In (m/a)/(m - 1)2 



Z'. 



opt 

 ^/'opt 



9~- = (1/m - 1)//? 

 9/ opt 



a /"opt 



3^r- = -a/((3m2) 



t^opt 



at/opt 



a a f^opt/[a(m -1)] 



■^ - -t/opt [m In (a/m) + m -l]/[m(m - 1)2] 



37 



