Monetary Economics at 30: A Reexamination of the Relevance of Money in Cashless Limiting Monetary Economies

The cashless-limiting result in Woodford (1998) — that as money velocity diverges the allocation of a monetary economy converges to that of the corresponding economy without money — is the theoretical foundation for thirty years of monetary policy analysis conducted in models without money. This paper rebuilds that limit inside a model whose credit microstructure nests Woodford’s as a special case, and shows the result survives only when credit is perfectly competitive: once the loan rate is endogenous and intermediaries have market power, the opportunity cost of holding money continues to move real allocations and welfare even though real money balances go to zero. The mechanism is specific and it is the heart of the paper. Under Woodford’s inherited Lucas–Stokey credit structure, an extra dollar cannot expand what a consumer can buy, because zero-interest deferred payment is available without limit; so in the pure-credit limit the marginal value of money falls to zero, the Euler equation for money can no longer hold with equality, and the opportunity cost of money — which appears only in that equation — drops out of the equilibrium altogether, taking every monetarist transmission channel with it. When credit instead carries an endogenous interest rate, a dollar brought into the goods market still saves the borrowing cost it would otherwise take to buy, so the Euler equation continues to bind and monetary policy keeps working through the equilibrium loan rate. The paper is careful about what it is and is not claiming: Woodford’s approximation result “is not wrong—at least not in the narrow mathematical sense,” and it is recovered exactly in the paper’s own model when intermediaries have no market power or when all credit is of the zero-interest deferred-payment kind. The objection is that the assumption doing the work — frictionless credit and payments — is conceptually unrelated to how far an economy has travelled along the high-velocity limit, so the limit cannot be read as a statement about high-velocity economies in general. A separate strand of the argument dismantles Woodford’s “Monetarism versus Wicksellianism” framing, showing that a money-growth rule can deliver a finite price level in the cashless limit and that Woodford’s contrary conclusion depends on an ad hoc restriction keeping the money supply bounded away from zero.

Ricardo Lagos | Macro Paper Warehouse

Monetary Economics at 30: A Reexamination of the Relevance of Money in Cashless Limiting Monetary Economies