In addition, the coefficients of the translog are constrained to be symmetric so that the cost
function is well behaved in its second derivatives (Christensen et al., 1973). Hence, the condition
a ij ¼ a ji ði; j ¼ L; E; FÞ is imposed together with the analogous conditions for the other coeffi-
cients. In order to improve the precision of the parameter estimates, in the estimation process we
use Eq. (2) jointly with the following factor cost share equations, as implied by Shephard’s lemma
(Shephard, 1970):