Finite Horizons, Infinite Horizons, and the Real Interest Rate

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FINITE HORIZONS, INFINITE HORIZONS, AND THE REAL INTEREST RATE

Using an overlapping-generations model in which households may have either finite

or infinite horizons, I derive the implications of each horizon for the steady-state real

interest rate. I then formulate an econometric model of the steady-state real interest

rate and devise tests that can distinguish between finite and infinite horizons. These

tests are applied to annual and quarterly U.S. data, which span the period 1875-1988.

The results are inconsistent with finite horizons, and broadly consistent with infinite

horizons.

I. INTRODUCTION

In conventional macroeconomic analysis, government budget deficits raise perceived wealth and stimulate aggregate demand because households are modeled as having finite horizons. If households are instead modeled as having infinite horizons, budget deficits need not stimulate aggregate demand and hence need not affect output, employment, interest rates, and the price level. The reason is that households with infinite horizons do not view the government debt as net wealth; thus they may treat budget deficits (i.e., future taxes) and current taxes as equivalent. Ricardian equivalence is said to hold if households treat budget deficits as equivalent to current taxes.(1)

Three reasons are typically advanced for assuming households have finite horizons. First, the individuals who comprise current households have finite lifetimes. Second, some households face binding liquidity constraints either now or in the future.(2) Third, boundedly rational households may choose to behave myopically, acting as if their current decisions do not affect allocations occurring beyond some horizon.(3)

These three reasons, however, do not necessitate modeling households as having finite horizons. First, Barro [1974] has shown that finite lifetimes need not imply finite horizons. Second, Hayashi [1987] and Yotsuzuka [1987] have shown that lenders may impose liquidity constraints that vary one-for-one with the government debt. In such an environment, the government debt relaxes no liquidity constraints. Third, because bounded rationality assumes fixed costs of decision making, it may be able to explain why aggregate demand would respond to small, short-term budget deficits but cannot explain why aggregate demand would respond to large, or long-term, budget deficits.

Because logically consistent reasons can be adduced for modeling households as having either finite or infinite horizons, the issue of which is the better modeling strategy should ultimately be decided by empirical analysis. This paper offers such an analysis. It investigates the implications of finite and infinite horizons for the steady-state behavior of the real interest rate. The evidence reported here is inconsistent with finite horizons and broadly consistent with infinite horizons.

The rest of the paper is organized as follows. Using Barro's [1974] overlapping-generations model, I derive its implications for the steady-state real interest rate in section II. These implications differ according to whether households have inoperative bequest motives and finite horizons or operative bequest motives and infinite horizons. In section III, I formulate an econometric model that encompasses the implications of the theoretical model of section II for both of these cases. In sections IV, V, VI, and VII, I test these implications using U.S. data. In section VIII, I investigate whether the real interest rate evidences any short-term departures from Ricardian equivalence. Finally, in section IX, I draw some tentative conclusions.

II. AN OVERLAPPING-GENERATIONS MODEL OF THE STEADY STATE

In this section, I lay out Barro's overlapping-generations model, which is the simplest model in which one can derive the implications of finite and infinite horizons for the steady-state real interest rate. …