An operational, nonlinear input–output system

Abstract

We develop a scale-dependent nonlinear input–output model which is a practical alternative to the conventional linear counterpart. The model contemplates the possibility of different assumptions on returns to scale and is calibrated in a simple manner that closely resembles the usual technical coefficient calibration procedure. Multiplier calculations under this nonlinear version offer appropriate interval estimates that provide information on the effectiveness and variability of demand-driven induced changes in equilibrium magnitudes. In addition, and unlike linear multipliers, the nonlinear model allows us to distinguish between physical and cost effects, the reason being that the traditional dichotomy between the price and quantity equations of linear models no longer holds. We perform an empirical implementation of the nonlinear model using recent interindustry data for Brazil, China and United States. When evaluating the robustness of the derived marginal output multipliers and the induced cost effects under the nonlinear approach, the results indicate that marginal indicators in physical terms can be perfectly used to infer average impacts; this is not the case, however, for the derived cost effects where average measures are seen to be more adequate. At the computational level, the analysis proves the operational applicability of the nonlinear system while at the methodological level shows that scale effects are relevant in determining sectoral multipliers.