A Critical Comment on Oosterhaven-Stelder Net Multipliers

Recently, Oosterhaven and Stelder (OS, 2002) have introduced the operational idea of a 'compensated net multiplier' (CNM) to take into account the double counting that occurs when output replaces final demand as an exogenous entry when the Leontief model is used to evaluate operationally the impact of large investments. Each output gross multiplier is compensated by multiplying it by the ratio of final demand to output. Oosterhaven (2004) have demonstrated that CNM fulfills an axiom of 'total output preservation,' namely that the sum of effects equals the total output. It is shown in the present paper that the original CNM is only a homogenous formula with no causal link between the cause (the exogenous output) and the effect (the total output), so that it cannot be a multiplier. The paper explores all the other possibilities for deriving CNM by considering an exogenous output: (1) in absolute value; (2) in variation; and finally (3) at final equilibrium. Possibilities (1) and (2) do not work while only the variation from zero is option (3) working, although imperfectly. The derivations yield two results: 1) the final demand ratio, and so CNM, cannot be stable even if the technical coefficient matrix is fixed, except for very small perturbations; 2) even if total output preservation derives from the definition of a multiplier, CNM cannot fulfill total output preservation when an exogenous output is taken as the initial shock. De Mesnard (2002) has proposed another solution, 'iterative net multiplier' (INM), derived by considering the successive rounds after an exogenous impact of output. INM is stable and makes a link between cause and the effect. In contrast to the assertions by OS (2002), INM fulfills output preservation when an exogenous output is taken as the initial shock. Neither CNM nor INM must be confused with the so-called 'output-to-output multipliers'