Abstract We explore the hypothesis that the substitutability/complementarity relationship between banking and shadow banking services is a major factor affecting the transmission mechanism of monetary policy. We take the parametric approach to demand analysis, which allows estimation and testing in a systems-of-equations context, and use the Minflex Laurent flexible functional form for the underlying aggregator function. We relax the homoskedasticity assumption and assume Markov regime switching to relax the assumption of fixed consumer preferences. We generate inference consistent with neoclassical microeconomic theory and provide evidence against simple-sum money supply measures. We also show that the emergence of shadow banking has increased the stability of money demand functions. This means that money supply measures based on a nonlinear aggregator function might be a better measure of the stance of monetary policy than the interest rate.