Deficits, explicit debt, implicit debt, and interest rates: some empirical evidence.

• Author: Wang, Zijun

1. Introduction

   The effect of government borrowing on interest rates has been a controversial issue for about three decades. The federal deficits of the 1980s and the early 1990s caused speculation as to whether higher interest rates would follow. The current deficits have renewed interest in the link to higher interest rates. Since the influential work of Barro (1974), much of the discussion has focused on whether the Ricardian equivalence hypothesis holds. Bernheim (1987), Barth et al. (1991), Seater (1993), Elmendorf and Mankiw (1999), and Engen and Hubbard (2005) provide excellent reviews of the literature on the topic. Recent contributions include Cebula (1997); Gale and Orszag (2003); Laubach (2003); and Ardagna, Caselli, and Lane (2004) among others. Although empirical evidence obtained in earlier studies is mixed, as argued by Gale and Orszag (2003), major macroeconometric models imply an economically significant connection between changes in deficits and long-term interest rates. Empirical evidence assembled by recent studies seems to lean toward the existence of the relationship, but there is still no consensus about the magnitude of the effect.

   A missing piece in the debate is a formal investigation of the effect of the implicit debt, as embodied in unfunded obligations of Social Security and Medicare. Theoretically, it could be argued that because the Ricardian equivalence proposition assumes that households are rational and make decisions for long horizons, then like the often-discussed public debt (explicit debt), the implicit debt (computed based on 75-year, 100-year, or infinite horizons) might also have a role to play in the determination of interest rates. The point we raise here is not new. In his 1996 paper "Reflections on Ricardian Equivalence," Barro writes "... (T)he basic invariance proposition for intergenerational transfers ... (is) that the government's transfers implied by budget deficits or pay-as-you-go social security would be fully undone if family members were connected through voluntary transfers based on altruism" (p. 2). More recently, Gokhale and Smetters (2005) also note that (Social Security's) pay-as-you-go financing may "crowd out" private saving and hence increase interest rates (p. 12). (1) Therefore, it is problematic to test the Ricardian equivalence hypothesis without considering the effect of the implicit debt. Empirically, the explicit debt, although large in absolute amount (about $4300 billion by the end of 2004), is only a part of the federal government's total obligations. According to the Office of the Chief Actuary of the Social Security Administration, the Social Security program alone carries unfunded obligations ranging from about $3700 to $11,200 billion in present values at the beginning of 2004 under various assumptions. These numbers are even larger if the trust fund balances are subtracted. In particular, projected Old Age, Survivors, and Disability Insurance payroll tax income will begin to fall short of outlays in 2017, which means that Social Security will require transfers from general revenues in the next decade (Social Security Trustees 2005).

   While previous studies have investigated the effect of Social Security wealth on saving and consumption (e.g., Feldstein 1974, 1996; Smetters 1999), and some have also emphasized the importance of the implicit debt in the discussion of the relationship between government borrowing and interest rates (e.g., Gale and Orszag 2003, p. 463), little has been done to quantify the effect of the implicit debt on interest rates, with the exception of Wang (2005). The purpose of this paper is to characterize the dynamic effects of government borrowing on longo term interest rates using vector autoregression (VAR) models. This paper contributes to the discussion in two ways. First, we consider both explicit and implicit debt. Such a comprehensive total debt measure provides a more accurate indication of the burden imposed on future generations by government borrowing behavior than does a measure of annual deficits or a measure of the explicit debt alone. (2)

   Second, we also wish to contribute to the literature with respect to the econometric method employed in the analysis. It is well known that estimating the effects of government borrowing on interest rates is complicated by the need to isolate the effects of fiscal policy from other influences, for example, the impacts of monetary policy actions of the Fed. Empirically, the identification in the context of reduced form VAR models is often achieved by assuming a Wold-causal order for the elements of the multivariate process so as to organize the triangular factorization of the innovations covariance matrix (Cholesky factorization). The major problem of the Cholesky factorization is that it critically depends on the ordering of variables in the VAR. Different orderings may lead to quite different results depending on the degrees of correlation between different innovations. Empirical researchers thus often rely on economic theory or other prior knowledge to determine the variable ordering. As is evident in the debate on the relationship between deficits, debt, and interest rates, predictions of economic theory are often ambiguous.

   In this study, we adopt a structural VAR approach, which is of the Sims-Bernanke type (Bernanke 1986; Sims 1986). To achieve identification, we introduce a data-driven method to search for the causal structure in the innovations. The suggested method of directed graphs is the graph-theoretic analysis of causality. As demonstrated later in the paper, the study and application of the directed graph method is in line with the growing interest among econometricians and applied researchers in automated model discovery. (3)

   An approach similar to this study is used by Wang (2005), who studied the impact of the implicit debt on short-term interest rates using a generalized VAR approach. The basic finding of Wang (2005) is that the implicit debt appears to have some moderate influence on real interest rates only at long horizons. The current paper focuses on the effect on long-term rates because, as argued by Engen and Hubbard (2005), if federal government borrowing crowds out private capital formation, then one would expect to find a larger impact on long-term interest rates than on short-term interest rates. Both the generalized impulse responses used by Wang (2005) and the directed acyclic graphs-based impulse responses adopted in the current paper are invariant to the ordering of variables in the VAR model. However, one calculates generalized impulse responses by conditioning on the future shocks, which embody the empirical correlation between shocks. By doing this, the generalized method tries to "separate" the impact of a particular shock from others by integrating out the effects of other shocks to the system. In this sense, the generalized method probably does not have or build on a clear-cut "structural" assumption about shocks, while the directed graph method explicitly sorts out contemporaneous causal relationships among the variables (more about this in the next section).

   The overall evidence from our study suggests that deficits, explicit debt, and implicit debt all have some effects on the 10-year government bond interest rate, although with different dynamics. Based on our preferred model specification, we estimate that a 1 percentage point increase in the primary deficits, and explicit and implicit debt (all normalized by gross domestic product [GDP]) may lead to a maximum of a 56-, 10-, and 2-basis-point rise in the long-term interest rate, respectively. Nevertheless, these effects appear to be temporary and tend to die out within a 10-year horizon.

   The rest of the paper is organized as follows. Section 2 briefly introduces the directed graph method and discusses its use in the VAR identification. Section 3 presents the data. Section 4 examines the contemporaneous causal relationships between the set of variables under study and presents the dynamic effects of federal deficits, explicit debt, and implicit debt on long-term interest rates. Section 5 summarizes the major results and concludes.

2. Directed Graphs and Structural VAR Identification

   Directed graphs have been studied for decades. The recent developments are motivated by the research of Pearl (2000), Spirtes, Glymour, and Scheines (2000), and their coauthors. Swanson and Granger's (1997) work adapted the method to uncovering the causal order within a VAR model. Demiralp and Hoover (2003) and Hoover (2005) provide an accessible introduction to the method for causal analysis. In this section, we briefly describe how to conduct the directed graphs analysis using the variance-covariance matrix of the VAR innovations (residuals).

   The basic idea behind directed graphs is to represent causal relationships among a set of variables using an arrow diagram. Mathematically, directed graphs are designs for representing conditional independence as implied by the recursive product decomposition:

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)

   where pr is the probability of variables [v.sub.1], [v.sub.2] ..., [v.sub.n]. The symbol [[OMEGA].sub.i] refers to the realization of some subset of the variables that precede (come before in a causal sense) [v.sub.i] in order (i = 1, 2, ..., n), and [PI] is the product (multiplication) operator.

   As an important contribution to the literature, Pearl (1986, 1995) proposed "d-separation" as a...