James Tobin | Macro Paper Warehouse

A General Equilibrium Approach to Monetary Theory

This 1969 paper by James Tobin, published in the inaugural issue of the Journal of Money, Credit and Banking, sets out and illustrates what he describes as a widely shared, not novel, general-equilibrium framework for monetary analysis, built around the capital accounts of economic sectors. The approach specifies, for the economy as a whole and for each sector, a menu of assets and debts, the rates of return these assets carry, and demand functions – assumed homogeneous in wealth and required to satisfy an adding-up constraint, so that a given sector’s asset demands sum exactly to its net worth and are collectively unaffected by any single rate of return – that jointly determine, together with exogenously given asset supplies, the market-clearing structure of interest rates and asset prices; because the resulting system’s market-clearing equations are not independent, an n-asset economy can determine at most n-1 rates of return, so the framework is fundamentally about relative, not absolute, rates of return. Tobin develops this apparatus through a sequence of increasingly detailed illustrative models: a two-asset “money-capital” economy in which the standard Keynesian LM curve emerges as one special case of the asset-market equilibrium condition; a three-asset “money-securities-capital” economy that separates monetary policy proper (open-market operations altering the composition of government debt) from the purely fiscal financing of budget deficits with money; and a two-sector economy with a banking system, in which deposits and bank loans are added to the menu of assets and the money stock itself becomes an endogenous outcome of the joint portfolio behavior of banks and the public. Comparing how alternative policy variables affect the market valuation of capital relative to its reproduction cost – the model’s central channel connecting financial conditions to real investment and aggregate demand – Tobin arrives at the paper’s central diagnostic finding: what gives money a distinctive macroeconomic role is not any inherent property, such as serving as a medium of exchange or paying no interest, but simply that money’s own rate of return is institutionally or legally fixed while other assets’ rates are left to be determined by the market, so that the entire burden of portfolio adjustment to a change in asset supplies falls on those other, flexible rates.

Liquidity Preference as Behavior Towards Risk

This 1958 Review of Economic Studies paper by James Tobin asks what behavioral assumptions about individual “decision-making units” can justify the Keynesian liquidity preference schedule – an inverse relationship between the aggregate demand for non-interest-bearing cash and the rate of interest – given that, as Tobin puts it at the outset, “the apparent irrationality of holding cash is the same… whether the interest rate is 6%, 3% or 1/2 of 1%” (Introduction, p. 65). Tobin first formalizes the orthodox Keynesian “speculative motive” explanation (Section 2): if an individual investor holds a fixed, certain expectation of the future interest rate that is independent of the current rate, his portfolio choice between cash and a hypothetical perpetuity (“consols”) is an all-or-nothing step function around a critical current rate, and a smooth, downward-sloping aggregate demand-for-cash curve emerges only because different investors hold different critical rates (Sections 2.1-2.4, pp. 66-69); he shows this theory is vulnerable to Leontief’s and Fellner’s objections that in a genuinely stationary equilibrium such divergent expectations should eventually be arbitraged away (Section 2.6, pp. 70-71). Tobin then develops an alternative, and in his view logically more satisfactory, foundation in Section 3: if investors are uncertain (rather than falsely certain) about future capital gains or losses on interest-bearing assets, and evaluate portfolios by the expected return and risk (standard deviation of return) those portfolios offer, then a risk-averse investor’s optimal choice generally involves holding a mix of cash and the risky asset – diversification – rather than an all-or-nothing corner solution, and this holds however small the size of the expected capital loss the investor fears (Sections 3.1-3.4, pp. 71-81). Tobin proves this rigorously by showing that any risk-averse investor’s indifference curves between expected return and risk must be concave upward under either of two alternative rationalizations (restricting subjective probability beliefs to a two-parameter family, or assuming a quadratic utility-of-return function), so that, in his words, “all risk-averters are diversifiers; plungers do not exist” (Section 3.3, p. 76); he further extends the analysis to multiple risky assets, showing that the proportionate composition of an investor’s risky holdings is independent of how much of the total portfolio is allocated to cash versus risky assets (a separation result, Section 3.6, pp. 83-85), and works out the effects on cash demand of changes in the interest rate, in investors’ subjective risk estimates, and in taxation of interest and capital gains (Sections 3.4-3.5, pp. 78-82). Tobin concludes that the risk-aversion theory better matches the empirical fact that individual investors typically hold both cash and interest-bearing assets simultaneously, rather than only one or the other as the Keynesian model implies, though he notes it does not fully answer Leontief’s objection and remains ambiguous about the direction of the interest-rate/cash-demand relationship at high interest rates (Section 4, pp. 85-86).

The Interest-Elasticity of Transactions Demand For Cash

This paper works out, with a simple mathematical model, whether the ordinary transactions demand for cash – the money people hold just to bridge the gap between when they receive income and when they spend it – responds to the rate of interest, challenging the then-standard view that transactions balances are essentially interest-inelastic and only asset-motive money demand responds to rates. Tobin models an individual who receives income Y at the start of a period and spends it at a constant rate until it is exhausted, and who can hold part of that balance in interest-bearing bonds rather than cash, subject to a transaction cost with a fixed component plus a component proportional to the amount transferred each time cash and bonds are exchanged. Solving in three steps – the optimal timing and size of a given number n of cash-bond transactions, the profit-maximizing number of transactions n* for a given interest rate r, and how n* (and hence average cash and bond holdings) moves as r changes – the paper shows that whether cash demand responds to the interest rate at all depends on which of four regimes the interest rate, the volume of transactions, and the transaction-cost parameters place the individual in: below a threshold interest rate, no bond transaction is worthwhile and cash demand is completely insensitive to r, while above that threshold the share of the transactions balance held in bonds rises continuously with r. That threshold, and the degree of sensitivity above it, is not the same for everyone: because the fixed component of the transaction cost does not scale with income, the interest-elastic range of r widens as the volume of transactions Y grows, so small transactors may never find it worthwhile to economize on cash while large transactors become increasingly rate-sensitive, and the ratio of cash held to Y falls as Y rises within that elastic range. An appendix both proves the results formally and situates the model against Baumol’s (1952) inventory-theoretic transactions-demand paper, noting that Tobin’s paper proves rather than assumes that optimal cash withdrawals are equal in size and equally spaced, treats the number of transactions as an integer rather than a continuous variable, and – unlike Baumol – allows for the case in which no bond transaction is worth making at all.