where TC is the total cost of a given bank s at time t , i y is the i th output, j w is the price of the j th
input and l z is the l th environmental variable. Based on the standard properties of the cost functions,
standard homogeneity and symmetry in all quadratic terms are imposed via parameter restrictions. In
order to impose linear homogeneity, total costs (TC) , the price of labor ( ) 1 w , price of physical capital
( ) 2 w , price of purchased funds ( ) 3 w are normalized. The symmetry condition requires