We explore the long-run demand for M1 based on a dataset comprising 38 countries and relatively long sample periods, extending in some cases to over a century. Overall, we find very strong evidence of a long-run relationship between the ratio of M1 to GDP and a short-term interest rate, in spite of a few failures. The standard log-log specification provides a very good characterization of the data, with the exception of periods featuring very low interest rate values. This is because such a specification implies that, as the short rate tends to zero, real money balances become arbitrarily large, which is rejected by the data. A simple extension imposing limits on the amount that households can borrow results in a truncated log-log specification, which is in line with what we observe in the data. We estimate the interest rate elasticity to be between 0.3 and 0.6, which encompasses the well-known squared-root specification of Baumol and Tobin.
Online appendix: [Staff Report 588](https://doi.org/10.21034/sr.588 "Online Appendix")
Data file: [LongRunMoneyDemandFinalDatabase.xls](https://researchdatabase.minneapolisfed.org/downloads/kk91fk69h "Data file")
An earlier version of this Staff Report circulated as [Working Paper 737](https://doi.org/10.21034/wp.737 "Working Paper 737").
Published in _Journal of Monetary Economics_ (vol. 117, January 2021, pp. 43-63), https://doi.org/10.1016/j.jmoneco.2020.07.003.