A General Equilibrium Approach to Monetary Theory

Tobin states that his purpose, writing for the first issue of a journal devoted to monetary economics, is exposition and recapitulation of a general framework for monetary analysis that he shares “at least in spirit” with many monetary economists, not a new approach of his own (Section 1, p. 15). The approach centers on the capital accounts of economic units, sectors, and the economy as a whole: a model of the capital account specifies a menu of assets and debts appearing in portfolios and balance sheets, the factors determining the demand and supply of each, and the way asset prices and interest rates clear these interrelated markets, with monetary assets treated as only one part – not the whole – of that menu, and the banking system as one sector among several whose balance-sheet behavior must be specified (Section 1, p. 15).

Tobin’s accounting framework arrays assets or debts as rows and sectors of the economy (including the central government) as columns, with entries that can be positive, negative, or zero depending on whether a sector is a net holder or net debtor of a given asset; summing across a row gives the net exogenous supply of that asset to the economy as a whole, while summing down a column gives a sector’s net worth, and the sum of all columns’ net worth equals national wealth (Section 2, Table 1, pp. 16-17). Because private wealth equals national wealth minus government net worth, and because a government is typically a net debtor, private wealth in these models generally exceeds national wealth – an accounting relationship illustrated schematically in Tobin’s Figure 1, which links government obligations, monetary policy, and fiscal policy through asset markets to income and to the commodity and labor markets (Section 2, Figure 1, Table 1, p. 17).

Tobin assigns each asset a rate of return r_i and each sector a net demand function f_ij for that asset, a function of the whole vector of rates of return (and possibly other variables), with sectors constrained at any moment by their existing net worth (Section 3, p. 18). Because these demand functions are homogeneous in wealth, an “adding-up requirement” follows: the sum, across all assets, of a sector’s demand responses to a change in any given rate of return must be zero, while the sum of responses to a change in wealth must be one; applied economy-wide, this means the n market-clearing equations across n assets are not independent, so the system can determine at most n-1 rates of return, with the value of aggregate or sectoral wealth itself often depending on the very asset prices being determined (Section 3, pp. 18-19).

Model I considers an economy with only money and physical capital as assets, with wealth defined as the sum of the market value of capital and real money balances, two portfolio-balance equations linking each asset’s share of wealth to its own and the other’s rate of return and to the ratio of income to wealth, and two rate-of-return equations linking capital’s return to its price and money’s real return to the nominal interest rate on money net of expected inflation (Section 4, eqs. I.0-I.4, pp. 19-20). Under a short-run interpretation in which the capital stock, money supply, income, prices, and the marginal efficiency of capital are exogenous, Tobin shows the money-market equilibrium condition reduces to a single equation in the price of capital relative to reproduction cost, q, which traces out a relationship between income and the rate of return on capital equity that he identifies as “a species of the standard Keynesian LM curve,” differing from the textbook LM curve mainly in using the return on capital equity rather than Keynes’s long-term bond rate (Section 5, eq. I.5, Figure 2, pp. 21-22).

Under the long-run interpretation, capital is valued at its reproduction cost (q = 1), which Tobin treats as a condition of long-run equilibrium at which the short-run equilibrium point (E in his Figure 3) coincides with a steady-growth position (G) consistent with the economy’s natural rate of growth and saving ratio (Section 6, Figure 3, pp. 22-23). In this long-run equilibrium, given real income, real balances, and the capital stock, the model determines both the real rate of return on capital and wealth, but reconciling the fixed real supplies of capital and money with the public’s portfolio preferences over time requires that some variable be free to adjust – Tobin identifies price-level flexibility (which lets any nominal money supply convert into whatever real balance the public wants at prevailing real rates) and fiscal policy (adjusting the size and growth rate of government debt) as two possible such mechanisms (Section 6, p. 23).

In Model I, Tobin notes, there is no monetary policy in the usual sense because the money supply is identical to government debt: increasing money necessarily increases private wealth by the same amount, making an increase in nominal money a monetary consequence of fiscal policy rather than monetary policy per se (Section 7, p. 23). Model II remedies this by allowing government debt to take non-monetary form (government securities) as well as monetary form, so that open-market operations can alter the composition of a fixed total government debt; solving the resulting system, Tobin’s Table 2 shows that increases in the money supply financed by fiscal deficits, increases in securities financed by deficits, and open-market purchases of securities with money all raise q, but that open-market operations are the one policy that, unlike Model IA, can shift the LM curve of Figures 2 and 3 in the usual textbook monetary-policy sense (Section 7, Table 2, pp. 24-25).

Tobin poses directly the question of what feature of money produces the differential effects tabulated in Table 2, and answers that it is not that one asset is called “money” and another “securities,” not that money serves as a means of payment, and not that money is non-interest-bearing (since in his framework it may or may not be) – none of these properties enter the analysis except in the general sense of explaining why the assets are imperfect substitutes (Section 7, pp. 25-26). The essential characteristic is instead that money’s own interest rate is exogenously fixed by law or convention while the rate of return on securities is endogenous and market-determined, so that when the supply of any asset changes, if that asset’s own rate cannot adjust, the whole burden of the necessary adjustment falls on reductions in other rates or increases in the prices of other assets – the “secret” of money’s special role, which Tobin notes would equally be shared by any other asset with a similarly fixed interest rate (Section 7, p. 26).

Model III adds a banking sector and two new assets, deposits and private loans, alongside government securities and capital, with both a market-determined deposit rate and a legal reserve requirement (k) governing banks’ balance sheets; because bank deposits and borrowed reserves are now part of the picture, “M” no longer represents the conventionally defined money stock but rather central-bank (“high-powered”) money, with total money supply – currency plus deposits – becoming an endogenous quantity determined jointly by public and bank portfolio behavior (Section 8, eqs. III.0-III.11, pp. 26-28). Tobin notes that fractional-reserve banking means a given increase in high-powered money requires a larger reshuffling of portfolios and bigger changes in rates of return to be absorbed than under the 100-percent-money regimes of Models I and II, since the new supply must be absorbed partly into excess bank reserves and partly into deposits, in some combination determined by the interaction of public and bank asset demands (Section 8, p. 28).

Tobin notes that once banks are modeled as a distinct behavioral sector with their own portfolio choices, the “gross substitutes” property – that every asset’s demand rises with its own rate of return and falls with every other rate – can be satisfied by each sector individually (banks, public) considered separately, yet still be violated in the market as a whole; for example, an increase in the deposit rate or a fall in the securities rate might raise, rather than lower, the combined net demand for currency or government securities, because even as the public’s own direct asset demands shift as expected, banks’ demand for reserves can rise simply because they now hold more deposits requiring reserve backing (Section 8, p. 29).

Tobin describes all the models in the paper as illustrative only, meant to convey the general observations of the approach rather than to be definitive, and emphasizes that the basic framework is flexible enough to be extended with more sectors, more assets, additional categories of government and private debt, and a disaggregated, non-homogeneous treatment of physical capital across different types of goods (housing, plant, equipment, consumer durables) (Section 9, p. 29). He closes by cautioning that because financial policies and events chiefly affect aggregate demand through their impact on the valuation of physical assets relative to replacement cost (q) – a variable not directly observable – and because the underlying asset-demand functions depend on shifting expectations, risk estimates, and risk attitudes that the framework does not itself explain, the essential impact of monetary policy and other financial events will not be easy to measure using any single observable variable, whether a monetary aggregate or a market interest rate (Section 9, p. 29).