The paper presents a theory of the demand for money that combines a special case of the shopping time exchange economy with the cash-in-advance framework. The model predicts that both higher inflation and financial innovation - that reduces the cost of credit - induce agents to substitute away from money towards exchange credit. This results in an interest elasticity of money that rises with the inflation rate rather than the constant elasticity found in standard shopping time specifications. A number of the key predictions of the banking time theory are tested using quarterly data for the US and Australia. We find cointegration empirical support for the model, with robustness checks and a comparison to a standard specification.