Different specifications and implications of the supermultiplier model

We analyze, compare, and discuss two distinct econometric specifications of the supermultiplier model. Specifically, we contrast the empirical strategy that examines the relationship between output ($y_t$) and autonomous demand ($z_t$) with the specification that focuses on the relationship between induced demand ($x_t$) and $z_t$. Although both specifications are theoretically valid from a macroeconomic standpoint, we use econometric theory to show that they may lead to different conclusions regarding cointegration and causality. This paper challenges the findings of existing empirical research based on the $y_t$–$z_t$ specification, which should be interpreted with caution, particularly those suggesting unidirectional Granger causality from autonomous demand to output.