On Integrating the Ricardian Equivalence Theorem and the IS-LM Framework

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ON INTEGRATING THE RICARDIAN EQUIVALENCE THEOREM AND THE IS-LM FRAMEWORK

I. INTRODUCTION

It is well established that government bond sales have no real macroeconomic consequences if the Ricardian Equivalence Theorem (RET) is true. Specifically, sales of government bonds have no independent effect on the rate of interest, and a switch from tax finance to bond finance (or vice versa) does not alter the level of aggregate demand. While the conditions under which the RET holds are quite stringent, (1) many economists believe it should be taken seriously, at least as a first-order approximation of reality, and discussion of the theory has, in recent years, crept into the leading undergraduate macroeconomic texts. (2) It is our impression that many teachers at the undergraduate level would like to incorporate the RET into their courses, but have refrained from doing so under the mistaken belief that the technical demands are too great. Quite the contrary, we show in this paper that the RET is easily integrated with the textbook IS-LM model that we teach our students. Moreover, and somewhat surpringsinly, it turns out that the IS-LM model already incorporates a healthy dose of the RET in that bond sales to finance an increase in government purchases of goods and services have no independent effect on the rate of interest. This result is shown to derive from an implicit restriction on the arguments of the money demand function.

II. THE STANDARD IS-LM MODEL

We begin with the following wholly-conventional IS-LM model: y = c([y.sup.d]) + i(r) + g (1)

M/P = M(y,r) (2) [y.sup.d] = y - t, (3) where lower case letters denote real variables and upper case letters nominal variables. The IS curve (Equation 1) requires no explanation. The LM curve (Equation 2) is also conventional; however, we show below that there is an important, but neglected, relationship between the standard money demand function and the validity of the RET. Equation 3 defines disposable income in the usual way as total income minus net taxes.

Two conditions must be satisfied if this model is to be consistent with the RET. First, the level of aggregate demand (hence output) must be independent of the method by which government expenditures are financed. A switch from tax finance to bond finance (holding g constant) should leave output unchanged, and an increase in g financed by bond sales should have the same effect on output as an increase in g financed by taxes. Essentially, this is because in the RET households view government bonds sales as being equivalent, in present value terms, to an increase in future taxes. Second, government bond sales to finance a deficit should have no independent effect on the interest rate. This counterintuitive result arises because households increase their current demand for bonds in order to afford the higher taxes they expect to be levied in the future to pay interest on bonds being sold today. The increased supply of government bods is, therefore, passively absorbed into private sector portfolios.

To show that the RET does not hold in the textbook IS-LM model, consider bond-financed and tax-financed increases in g of equal amounts (see Figure 1). The bond-financed rise in g shifts the IS curve horizontally by [(1/1-[derivative]c/[derivative]y)][DElta]g from [IS.sub.0] to [IS.sub.2], while the tax-financed rise in g shifts the IS horizontally by only [Delta]g to [IS.sub.1]. The first condition required by the RET is not satisfied since the effects on y are not the same. What about the second condition that the bond sales have no independent effect on the interest rate? Curiously, it is satisfied. When the increase in g is financed by bond sales, the rise in the interest rate from [r.sub.0] to [r.sub.2] is fully explained by the increase in transactions demand for money induced by the increase in output from [y.sub.0] to y.sub.2. (3) We return to this point below. …

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