A note on deficit, implicit debt, and interest rates.

• Author: Wang, Zijun

1. Introduction

   In the past three decades, economists and policy makers have debated the following two questions: Does federal government borrowing cause changes in interest rates? If so, what is the timing of the impacts? Recently, people have also started to ask whether the debt implicit in the Social Security and Medicare programs plays a role in the discussions. Despite extensive research effort, the questions remain controversial. Feldstein (1982), Hoelscher (1986), Abell (1990), Miller and Russek (1991), Raynold (1994), Cebula (1993, 1997), and Vamvoukas (1997) provide evidence in favor of the existence of a positive relationship between government deficits and interest rates (often related to the Keynesian proposition). On the other hand, Barro (1987), Evans (1985, 1987, 1988), and Darrat (1990) argue that government borrowing does not crowd out private investment, hence, it does not lead to higher interest rates (the Ricardian equivalence outcome). Surveying both theoretical and empirical studies on the issue, Seater (1993) concludes that it can be almost certain that Ricardian equivalence "is not literally true; Nevertheless, equivalence appears to be a good approximation" (p. 184).

   In this paper, we plan to contribute to the discussions in two dimensions. First, we use a more comprehensive measure of federal government debt. The often-used public debt (official debt), although large in absolute amount (about $6400 billion in gross measure by the end of 2002), is only a part of the total obligations of the federal government. According to the Office of Chief Actuary of the Social Security Administration, the Social Security program alone carried unfunded obligations of approximately $3350 to $12,162 billion in present value at the beginning of 2002 under various assumptions. Recently, Liu, Rettenmaier, and Saving (2002) proposed that Social Security and Medicare entitlement commitments made by the federal government (implicit debt) should be added to its balance sheet as debts on par with the debt held by the public. They argue that such a comprehensive total debt measure conveys more accurate information on the burden imposed on future generations by government borrowing than does the official debt. (1) Because this implicit debt is still mounting and likely to persist in the future, it is important to quantitatively investigate its impact on financial markets. While many researchers have investigated the effect of Social Security wealth on saving and consumption (e.g., Feldstein 1974, 1996), it appears that no one has examined whether the unfunded Social Security obligations have a role to play in the determination of interest rates. By including the implicit debt in the analysis, we wish to provide some new evidence on the discussion of the debt and interest rates. (2)

   In this paper, we also hope to add to the literature with respect to the econometric method employed in the empirical analysis. Traditionally, univariate regressions have been widely used in the empirical studies. However, recognizing that most macro variables are probably determined simultaneously in the economy, researchers have increasingly relied on VAR models. Miller and Russek (1991, 1996) and Vamvoukas (1997) are a few researchers that use VAR models to investigate the dynamic relationships between interest rates and deficits and/or debt. Forecast error variance decomposition is an important tool, based on the VAR models, to summarize the dynamic interactions among economic series.

   There is an unresolved issue in VAR analysis. To provide parameter estimates from reduced form VAR structural interpretations, researchers often use either the recursive Cholesky factorization pioneered by Sims (1980), or a nonrecursive strategy suggested by Bernanke (1986), Blanchard and Watson (1986), and Sims (1986). Both methods rely on economic theory or other prior knowledge to determine the ordering of variables in VAR models and to provide information about the linkages between innovations. Different orderings may lead to quite different decomposition results, depending on the degree of correlations between shocks. A particular ordering implies that we impose in priori economic structure on the multivariate processes (when the structure itself is often the subject of study). Unfortunately, as is evident in the debate on interest rates and deficit and/or debt, predictions of economic theory are often ambiguous.

   Instead of relying on a particular form of matrix factorization, the generalized decompositions, as developed by Koop, Pesaran, and Potter (1996) and Pesaran and Shin (1998), measure the effect of a particular shock by integrating out the effects of other shocks to the system. Hence, these generalized decompositions are invariant to the ordering of variables in a VAR. For the question of whether there is a causal relationship between deficits and interest rates, Miller and Russek (1996) find that the answer is dependent on the sensitivity of the variance decompositions to the various structural specifications. Therefore, the use of the generalized variance decompositions in this paper may offer some help in solving the problem of ambiguity.

   The rest of the paper is organized as follows: Section 2 explains the VAR modeling and the forecast error variance decompositions; Section 3 briefly discusses the data; Section 4 examines the impact of deficits and implicit debt on short-term interest rates represented by three-month and one-year Treasury bill rates; and Section 5 summarizes the major results and concludes.

2. VAR and Forecast Error Variance Decompositions

   Let [Y.sub.t] denote an (m x 1) vector of stationary processes under investigation. The dynamic relationship among these processes can be modeled as a VAR of order k,

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

   where [Y.sub.t] = ([Y.sub.1t], [Y.sub.2t], ..., [Y.sub.mt])', [[PHI].sub.i] and B are (m x m) and (m x n) coefficient matrices, t is an (m x 1) vector of innovations following a multivariate normal distribution with variance [??]. Furthermore, [[epsilon].sub.t] can be correlated only contemporaneously. Model 1 has an infinite moving average representation,

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

   The error in forecasting [Y.sub.t] s periods into the future, conditional on information available at t - 1 is

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

   with a variance of

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

   The conventional orthogonalized variance decompositions are defined as

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (5)

   where [[theta].sub.ij,s] measures the contribution of the jth orthogonalized innovation to the total forecast error variance of variable [y.sub.it] at horizon s, P is the recursive-form Cholesky factor of [??], and [e.sub.i] is the selection vector that has all elements equal to 0 except for the ith element being 1. The variance decompositions based on Equation 5 critically depend on the ordering of [Y.sub.t], because P does.

   Koop, Pesaran, and Potter (1996) and Pesaran and Shin (1998) developed an alternative to the above method. Their basic idea is to consider the proportion of the s-period forecast error in Equation 3, which is explained by conditioning on the nonorthogonalized shocks, [[epsilon].sub.jt], [[epsilon].sub.j,t+1], ..., [[epsilon].sub.j,t+s], while explicitly allowing for the contemporaneous correlations between these shocks (recall that all future shocks are assumed to be 0 in computing orthogonalized decompositions). The conditional forecast error variance is

   [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)

   Comparing Equation 6 with Equation 4, it can be seen that by conditioning on future shocks to the jth variable, the forecast error variance declines. Similar to Equation 5, normalizing the ith diagonal element in Equation...