**Extensive Margins and the Demand for Money at Low Interest Rates**

**Casey B. Mulligan and Xavier Sala-i-Martin**

**JOURNAL OF POLITICAL ECONOMY (2000)**

**Abstract: **

In this paper we argue that the relevant decision for the majority of U.S. households is not the fraction of assets to be held in interest bearing form, but whether to hold any of such assets at all (we call this "the decision to adopt" the financial technology). We show that the key variable governing the adoption decision is the product of the interest rate times the total amount of assets. The implication is that, instead of studying money demand using time series and looking at historical interest rate variations, we can look at a cross-section of households and analyze variations in the amount of assets held. We use this methodology and the 1989 Survey of Consumer Finances to estimate the interest elasticity of money demand at interest rates close to zero.

We find that (a) the elasticity of money demand is very small when the interest rate is small, (b) the probability that a household holds any amount of interest bearing assets is positively related to the level of financial assets, and (c) the cost of adopting financial technologies is negatively related to the level of education and participation in a pension program. The finding that the elasticity is very small for interest rates below 5 percent suggests that the welfare costs of inflation are small. At interest rates of 5 percent, roughly one half of the elasticity can be attributed to the Baumol-Tobin or intensive margin and half to the new adopters or extensive margin. The intensive margin is less important at lower interest rates and more important at higher interest rates.

Finally, we argue that ignoring extensive margins may lead to an empirically important overestimation of the cost of inflation at low interest rates.

Keyword: Money demand, Optimal Inflation Tax, Adoption of Financial technologies, Welfare Cost of Inflation, Monetary Policy.

JEL Classification: E40, E41, E44, E52.