Kalirajan 1990, Kumbhakar et. al 1991] 26. This specification has sound micro-economic foundations, and
treats both inputs and outputs as endogenous variables. The profit maximization method is obtained by
adding allocation equations for each endogenous input j to the stochastic frontier defined in equation [48].
For inputs such as fertilizer and pesticides that are obtained in competitive markets with exogenous prices,
the allocation equations are just the first order conditions of profit maximization:
w. = p. MPj exp( v. ) [49]
where j indexes inputs, wj is the exogenous input price, p is the output price, and MPj is the marginal
product of input j. The random variable vj is a two-sided error term that measures allocative inefficiency,
or the degree to which the farmer fails to satisfy the first order condition. This error term can be
interpreted as noise in the price signal that may be a result of imperfect information or measurement error,
or as errors in optimization. It is also assumed that input and output prices are exogenously given, and that
the technical efficiency is known to the farmer. The technical efficiency term enters the first order
condition through the marginal product (MPj) term.
This method can be used only if reliable price data are available and is limited to inputs that are
traded in a competitive market (with exogenous prices). In this paper, we estimate the frontier with
fertilizer as an endogenous input. The lack of suitable price data prevents us from estimating a complete
set of first order conditions. First order condition of this type cannot be formulated for inputs such as land,
animals and even labor, which are not traded in competitive markets at exogenously determined prices.
As a result, we assume the exogeneity of these inputs.
26 Several other studies have used a cost minimization framework where input levels are treated as endogenously
determined for given prices and technologies [Schmidt and Lovell 1979, Greene 1980, Kumbhakar 1997]. While the
behavioral assumption of cost minimization has a clear economic interpretation, the assumption of an exogenous
output level is clearly inappropriate except in the case of certain regulated environments. In addition, since price data
show very little variation (compared to input levels) in most household-level surveys, cost functions are difficult to
estimate. Finally, technical complications arise in the definition of allocative efficiency as a one-sided error in the cost
function and a two-sided term in the share equations [Bauer 1990]
30