Econometric estimation of allocative and technical efficiency has frequently been carried out using a shadow cost function and its associated share or demand equations. Since the problem is formulated in terms of shadow prices, the effect of allocative inefficiency on input usage must be computed indirectly from input share or demand equations. As an alternative approach, we derive and estimate an input shadow distance system comprising the dual shadow input distance function and the price equations derived from the shadow cost minimization problem. Estimated shadow quantities provide direct estimates of the effect of allocative inefficiency on input usage. One can also easily calculate firm- and time-varying technical inefficiency by decomposing the residuals. We also compute returns to scale and the cost savings obtained by eliminating both types of inefficiency. Our approach is illustrated using a panel of U.S. railroads. Both the cost function and the distance function are valid representations of multioutput technologies. The arguments of the cost function are output quantities and input prices, while the arguments of the distance function are input and output quantities. The input distance function measures the extent to which the firm is input efficient in producing a given set of outputs, while the cost function assumes cost minimization by a firm which is input efficient. The shadow cost function is a generalization of the cost function and depends on output quantities and shadow (internal to the firm) input prices rather than actual (market) input prices. Thus, the shadow cost function assumes shadow cost minimization but not actual cost minimization. This function has frequently been employed in fixed-effects estimation of allocative efficiency (AE) and technical efficiency (TE). An observed input vector is technically efficient if it is on the isoquant of the observed output vector. An input vector is allocatively efficient if the radial contraction of the input vector to the isoquant is cost minimizing. Identification of parameters that measure AE can be achieved by the estimation of a shadow cost system comprising the actual cost equation and the share or input demand equations, which are expressed in terms of shadow prices and output quantities. Shadow cost systems have been estimated by Atkinson and Halvorsen (1984), Sickles, Good, and Johnson (1986), Eakin and Kniesner (1988), Kumbhakar (1992), and Atkinson and Cornwell (1994), among others. Given panel data, the deviation of shadow from actual input prices can be measured by price-specific inefficiency parameters that may vary across firms and over time. However, the estimation of the effect of