Dual allocative efficiency parameters

Estimation of either price or quantity allocative efficiency parameters provides an empirical method for taking into account the presence of allocative inefficiency. We show that the researcher can either (a) estimate a system of input demand functions of the form, $x=h(y,k\circ w),$ obtain estimated values of the price allocative efficiency parameters (the k′s), and then derive the quantity allocative efficiency parameters with a simple calculation or (b) estimate a system of shadow price functions of the form, $w=g(y,\delta \circ x),$ obtain estimated values of the quantity allocative efficiency parameters (the δ′s), and then derive the price allocative efficiency parameters with a simple calculation. These input‐specific efficiency measures are then related to the standard measures of efficiency that have appeared in the literature.