Testing Intertemporal Budget Constraints: Theory and Applications to U.S. Federal Budget and Current Account Deficits

By Trehan, Bharat; Walsh, Carl E. | Journal of Money, Credit & Banking, May 1991 | Go to article overview

Testing Intertemporal Budget Constraints: Theory and Applications to U.S. Federal Budget and Current Account Deficits


Trehan, Bharat, Walsh, Carl E., Journal of Money, Credit & Banking


Testing Intertemporal Budget Constraints: Theory and Applications to U.S. Federal Budget and Current Account Deficits

1. INTRODUCTION

RECENT RESEARCH HAS EMPHASIZED the role of intertemporal budget constraints in a variety of contexts. For example, Sargent and Wallace (1981) examined the implications of the government's budget constraint for the behavior of monetary and fiscal authorities, while Obstfeld (1986) examined the implications of intertemporal current account balance for the behavior of exchange rates. However, until just a few years ago, researchers were content to assume the existence of such constraints, with little effort being directed towards determining whether the data generating processes were consistent with intertemporal budget balance.

More recently, several different researchers have devised and implemented tests of the intertemporal budget constraint in a variety of different contexts. Hamilton and Flavin (1986), Hansen, Roberds, and Sargent (1987), (1) Trehan and Walsh (1988), Wilcox (1989), Hakkio and Rush (forthcoming), and Haug (forthcoming) develop and implement tests related to the government's budget constraint. Campbell and Shiller (1987) test present-value models of stock and bond prices that are formally equivalent to tests of intertemporal budget balance.

With the exceptions of Hamilton and Flavin (1986) and Wilcox (1989), all the cited papers develop their tests by exploiting the presence, under intertemporal budget balance, of a cointegrating relationship linking net-of-interest expenditures, revenues, interest payments, and the outstanding stock of debt. These tests generally require the auxiliary assumptions of a constant expected real rate of interest and difference stationarity of the revenue and expenditure processes. (2)

In this paper we extend this work in two directions. First, we relax the requirement that expenditures and revenues be difference stationary, while maintaining the assumption of a constant expected real rate of interest, and show that the cointegration test continues to be valid as long as quasi difference of the net-of-interest deficit is stationary. The formulation we employ has an added advantage in that it leads naturally to an error correction specification for the joint adjustment of the revenue and expenditure processes. Specifically, if the interest-inclusive deficit is stationary, intertemporal budget balance holds, and this measure of the deficit is the appropriate error correction term. Second, we examine what happens if the expected real rate of interest is not a constant. We show that the cointegration test is generally no longer valid, but the test developed in Trehan and Walsh (1988) is still applicable. Specifically, we show that, as long as the expected real rate of interest is positive, intertemporal budget balance holds if the inclusive-of-interest deficit is stationary. We then empirically examine two budget balance questions that have been of concern recently. Does the size of the federal government's deficits imply that the intertemporal budget balance constraint is being violated? Do the recent U.S. current account deficits imply that foreigners now hold "too large" an amount of U.S. assets?

While several recent studies have attempted to assess the consistency of the time path of federal government expenditures, revenues, and debt with the assumption of intertemporal budget balance, different researchers have arrived at different conclusions. For instance, Trehan and Walsh (1988) were unable to reject the hypothesis of intertemporal budget balance using U.S. data from 1890 to 1986; Haug (forthcoming) reached the same conclusion using quarterly U.S. data from 1960 to 1986. By contrast, Wilcox (1989), Hakkio and Rush (forthcoming), and Hansen, Roberds, and Sargent (1987) conclude that the postwar U.S. data are inconsistent with this hypothesis. One obvious problem in reconciling these results is the different sample periods employed by different researchers. …

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