# On indexed bonds and aggregate demand elasticity.

IntroductionInflation indexed government bonds, which were first issued by the Commonwealth of Massachusetts during the Revolutionary War, (1) have become rather popular and widely used in the industrialized world. Indeed, the United States joined 14 other countries (2) in 1997 when it began offering this particular type of asset. The US Federal government currently sells two types of inflation indexed instruments: Treasury Inflation Protection Securities, or TIPS, and Series I savings bonds.

The benefits and implications of indexed bonds are well-known and some of these have become incorporated into modern macroeconomics textbooks. For example, Mankiw states that these bonds will result in "less inflation risk, more financial innovation, better government incentives, more informed monetary policy, and easier lives for students and teachers of macroeconomics." (3) Gordon, on the other hand, emphasizes only that a bond indexed to inflation "protects savers from unexpected movements in the inflation rate." (4) Additionally, and earlier in the literature, both Jevons (5) and Marshall (6) believed that bond indexation would decrease the variability of the business cycle. Fisher (7), and later Friedman (8), thought that indexed bonds would contribute to increased price stability. Finally, Keynes (9) proposed that a government could reduce its borrowing costs with the use of these assets.

We believe that indexed bonds present yet another and to our knowledge unidentified implication for macroeconomics. In general, our hypothesis is that the existence of these assets will impact the price level elasticity of aggregate demand. (10) More specifically, our theory is that inflation indexed bonds, as a component of wealth and via the Pigou effect, cause aggregate demand to become more inelastic with respect to the general price level. The purpose of this paper, therefore, is to explore the relationship between indexed bonds and aggregate demand elasticity.

The paper proceeds as follows. The next section presents a model of aggregate demand which includes indexed bonds as a part of real wealth and derives an expression for aggregate demand elasticity from which we can assess our basic contention. This section also discusses briefly some implications of our findings. The final section concludes by providing a brief summary of the paper.

The Model

The model of aggregate demand developed here is an otherwise standard IS-LM framework augmented by the inclusion of both indexed and non-indexed bonds as components of total real wealth. The product market consists of real saving (s) that depends on real income (y) and real value of financial assets (A/p). Nominal financial assets (A) equal the sum of narrow money balances (M) and bonds, with the bond component being disaggregated into bonds indexed to changes in the general price level, [B.sup.I](p), and those bonds that are not indexed ([B.sup.N]). Aggregate real investment (i) is determined by the market rate of interest (r). The product market equilibrium condition can now be specified as:

s(y, A /p) = i(r) (1)

In the money market, the nominal money supply (M) is, assumed, determined by the central bank, and aggregate money demand ([M.sup.d]) is expressed as a function of real income (y) and the interest rate (r). Equilibrium in the money market is shown as:

M = pl(y, r) (2)

Total differentiation of simultaneous Eqs. 1 and 2, setting dA=dM=0, and rearranging the resulting expression in dy/dP space results in the following slope expression for the economy's aggregate demand function:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (3a)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (3b)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are the proportions of total assets held as money balances, non-indexed, and indexed bonds, respectively. The price-level elasticity of indexed bonds, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] measures the degree of indexation and assumes a positive value equal to either one, complete indexation to the price level, or less than one, partial indexation. Equation 3 shows that the total effect of a change in the price level is comprised of two component parts. The first ratio within brackets on the right-hand-side is the Keynes effect, or the change in the equilibrium aggregate quantity demanded that results from a price-level induced change in the real money supply, ceteris paribus. Similarly, the second term is the Pigou effect, or the change in the equilibrium aggregate quantity demanded which results from a price-level induced change in real saving, ceteris paribus. The Pigou effect is weighted by both the proportion of total financial assets held in the various forms and the price-level elasticity of bond indexation. Equation 3 is easily expressed in elasticity form as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

An examination of Eq. 4 (11) reveals the impact of indexed bonds on aggregate demand elasticity. Two basic conclusions emerge. First, the Pigou effect is smaller and the elasticity of aggregate demand is lower the larger the portion of assets held as indexed bonds [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Second, and similarly, both the Pigou effect and aggregate demand elasticity are reduced the greater is the price level elasticity of indexed bonds. In the extreme, the Pigou effect would disappear completely and aggregate demand elasticity is reduced by the greatest amount when bonds are indexed completely to the price level, i.e., when this particular elasticity is equal to one, and the proportion of assets held as indexed bonds is equal to 100%.

Jevons and Marshall supported bond indexation because they believed it would reduce the amplitude of the business cycle or decrease the variability of real gross domestic product. Fisher and Friedman thought that indexed bonds would reduce the fluctuations of the price level. Both of these assertions may be assessed within the context of the simple aggregate demand/aggregate supply model of macroeconomics textbooks and our conclusions above. The results depend crucially on the source of the changes in real GDP and the price level. In particular, when aggregate supply shocks occur, the change in real GDP is smaller and the change in the price level is larger when inflation indexed bonds exist and the elasticity of aggregate demand with respect to the general price level is consequently lower. In short, our results support the view of Jevons and Marshall regarding the advantage of indexed bonds and contradict the opinion of Fisher and Friedman when aggregate supply is variable. On the other hand, our results support neither Jevons and Marshall nor Fisher and Friedman when aggregate demand shocks occur since in this environment, both the changes of real GDP and the price level are larger when inflation indexed bonds exist and aggregate demand is more price level inelastic.

Conclusion

The hypothesis of this paper is that bond indexation results in a decrease in the price level elasticity of aggregate demand with the rationale supporting this proposition being straightforward and centering around the Keynes and Pigou effects. The results of our model support this hypothesis. Specifically, this paper shows that when bonds are not indexed to inflation, any increase in the price level reduces overall real wealth by proportionately decreasing both real money balances and the real value of bonds, increasing saving, and thereby decreasing the aggregate demand for goods and services. Alternatively, when bonds are partially or fully indexed to inflation, a similar increase in the price level mitigates the reduction in real wealth since, in this case, only real money balances are fully and proportionately impacted by the movement of the price level. Consequently, the resulting increase in aggregate savings and decrease in aggregate demand is unambiguously less in an environment where a portion of financial assets are held in the form of indexed bonds. Therefore, the introduction of price-indexed bonds will result in a less elastic aggregate demand schedule.

Published online: 2 September 2008

References

Apergis, N., & Elestherio, S. (2000). Measuring price elasticity of aggregate demand in Greece: 1961-1995. Public Finance Review, 28(5), 452467 (September).

Fisher, I. (1911). The purchasing power of money: its determination and relation to credit, interest and crises. New York: MacMillan.

Friedman, M. (1971). Purchasing power bonds. Newsweek, April 12, 1971, p. 86.

Gambs, C. M. (1974). A note on macroeconomic textbooks: the use of the aggregate demand curve. Journal of Economic Literature, 12(3), 896-898 (September).

Gordon, R. J. (2003). Macroeconomics (9th ed.). Boston, MA: Addison-Wesley.

Green, J. R., Hickman, B. G., Howrey, E. P., & Hymans, S. H. (1991). The IS-LM cores of three macroeconomic models. In L. R. Klein (Ed.), Comparative performance of US econometric models. Oxford: Oxford University Press.

Jevons, W. S. (1876). Money and the mechanism of exchange. New York: Appleton.

Keynes, J. M. (1927). Testimony Before the Committee on National Debt and Taxation (Colwyn Committee), Minutes of Evidence, London: (Vol. I, pp. 286-287).

Kyer, B. L., & Maggs, G. E. (1995). Monetary policy roles, supply shocks, and the price level elasticity of aggregate demand: a graphical approach. Journal of Economic Education, 26(4), 364-372 (Autumn).

Kyer, B. L., & Maggs, G. E. (1996). Supply side economics and the price level elasticity of aggregate demand. Public Finance Quarterly, 24(1), 88-98 (January).

Kyer, B. L., & Maggs, G. E. (1997). Price level elasticity of aggregate demand in the United States: quarterly estimates, 1955-1991. International Review of Economics and Business, 44(2), 407-417 (June).

Mankiw, N. G. (2003). Macroeconomics (5th ed.). New York: Worth.

Marshall, A. (1925). Remedies for fluctuations of general prices. In A. C. Pigou (Ed.),Memorials of Alfred Marshall. London: Macmillan.

Shiller, R. J. (2003). The invention of inflation-indexed bonds in early America. Cowles Foundation Discussion Paper No. 1442, October.

(1) For more detail, see Shiller (2003).

(2) These nations include Argentina, Australia, Brazil, Canada, Chile, Colombia, Finland, France, Iceland, Israel, Mexico, New Zealand, Sweden, and the United Kingdom.

(3) Mankiw (2003), page 426.

(4) Gordon (2003), page 290.

(5) See Jevons (1876).

(6) See Marshall (1925).

(7) See Fisher (191 I).

(8) See Friedman (1971).

(9) See Keynes (1927).

(10) The price level elasticity of aggregate demand is a relatively neglected concept in macroeconomics. From the theoretical perspective and its foundation in the quantity theory of money, the Classical school believed that aggregate demand was unit elastic with respect to the general price level. For more detail, see Gambs (1974). Alternatively, Keynes and his early disciples believed that aggregate demand had a variable elasticity and, in the special case of a liquidity trap, could be perfectly price level inelastic. In earlier papers, we have shown the relevance of aggregate demand elasticity for monetary policy rules and supply-side economics. See Kyer and Maggs (1995, 1996), respectively. Few empirical studies of aggregate demand elasticity are available. Perhaps the earliest are found in Green et al. (1991). We have estimated this elasticity for the United States (Kyer and Maggs 1997) and Apergis and Elestherio (2000) calculated aggregate demand elasticity for Greece.

(11) By substituting the a priori signed coefficients along with the signs of p, 3; M, and A, it can easily be shown that Eqs. 3 and 4 are unambiguously negative.

B. L. Kyer

Economics, Francis Marion University, Florence, SC, USA

e-mail: BKyer@FMarion.Edu

G. E. Maggs ([mail])

St. John Fisher College, Rochester, NY, USA

e-mail: gmaggs@sjfc.edu

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Author: | Kyer, Ben L.; Maggs, Gary E. |
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Publication: | Atlantic Economic Journal |

Geographic Code: | 1USA |

Date: | Mar 1, 2009 |

Words: | 1855 |

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