# «On the Nominal Interest Rate Yield Response to Net Government Borrowing in the U.S.: GLM Estimates, 1972-2012 Richard J. Cebula* Jacksonville ...»

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Cebula, International Journal of Applied Economics, 12(1), March 2015, 1-14

On the Nominal Interest Rate Yield Response to Net Government Borrowing in

the U.S.: GLM Estimates, 1972-2012

Richard J. Cebula*

Jacksonville University

Abstract: This study provides current empirical evidence on the impact of net U.S. government

borrowing (budget deficits) on the nominal interest rate yield on ten-year Treasury notes. The model

includes an ex ante real short-term real interest rate yield, an ex ante real long-term interest rate yield, the monetary base as a percent of GDP, expected future inflation, the percentage growth rate of real GDP, net financial capital inflows, and other variables. This study uses annual data for the period 1972-2012. GLM (Generalized Linear Model) estimates imply, among other things, that the federal budget deficit, expressed as a percent of GDP, exercised a positive and statistically significant impact on the nominal interest rate yield on ten-year Treasury notes over the study period.

Keywords: nominal ten-year Treasury note yield, budget deficits, GLM estimates JEL Classification: E43, E52, E62, H62

1. Introduction The interest rate impact of central government budget deficits has been studied extensively. Studies of this topic have assumed a wide variety of models, techniques, and study periods (Afonso and Sousa, 2012; Aisen and Hauner, 2013; Al-Saji, 1992; 1993; Barth, Iden and Russek, 1984, 1985, 1986; Cebula, 1997B; 2005; Cebula and Cuellar, 2010; Choi and Holmes, 2014; Cukierman and Meltzer, 1989; Darrat, 1989; Evans, 1987; Feldstein and Eckstein, 1970; Findlay, 1990; Gale and Orszag, 2003; Hoelscher, 1983; 1986; Holloway, 1988; Johnson, 1992; Koch and Cebula, 1994;

Laubach, 2009; Ostrosky, 1990; Tanzi, 1985; Zahid, 1988). Many of these studies find that budget deficits raise longer-term rates of interest while not significantly affecting short-term, i.e., under one year from issuance to date of maturity, rates of interest. Since capital formation is presumably much more affected by longer-term than by short-term interest rates, the inference has often been made that government budget deficits may lead to "crowding out" (Carlson and Spencer, 1975; Cebula, 1985).

This interest rate/deficit literature has focused typically upon the yields on U.S. Treasury bills, U.S, Treasury notes, and U.S. Treasury bonds, as well as yields on Moody’s Aaa-rated and Baa-rated corporate bonds. The yield on tax-free bonds has also been examined, arguably in part because of its potential impact on income tax evasion (Cebula, 1997A; 2004). In recent years, however, the impact of government budget deficits on interest rate yields has received rather limited attention in the scholarly literature. Accordingly, this study provides current evidence as to the effect of the federal budget deficit on the yield on intermediate-term debt issues of the U.S. Treasury, namely, the Cebula, International Journal of Applied Economics, 12(1), March 2015, 1-14

**nominal interest rate yield on ten-year Treasury notes.**

In particular, this study investigates the post-Bretton Woods period from 1972 through 2012, in the pursuit of providing contemporary insights into whether federal budget deficits have in fact elevated nominal intermediate-term interest rate yields in the U.S. We begin with 1972 because in August of 1971 the U.S. abandoned the Bretton Woods agreement, i.e., abandoned the convertibility of the U.S.

dollar for gold, thereby bringing the Bretton Woods system to a de facto end (Cebula, 1997B).

Ending the study period with the year 2012 makes this study relatively current and hence pertinent.

Moreover, ending the study with the year 2012 can be regarded as relevant and important if for no other reason than because it was during the latter part of this period, namely, beginning in late November of 2008, that the Federal Reserve shifted from its traditional open market operations and initiated its “quantitative easing” policies. Indeed, the first of these quantitative easing policies, QE(1), involved significant and unprecedented Federal Reserve purchases of mortgage-backed securities, which by June, 2010 had totaled $2.1 trillion. In November of 2010, another stage of quantitative easing, QE(2), began and resulted in $600 billion of such purchases. Finally, beginning in September of 2012, stage QE(3) began, initially involving $40 billion per month of such purchases and escalating to $85 billion per month thereof as of December, 2012. Thus, the study period includes four full years during which the U.S. economy experienced both quantitative easing and huge (relative to the size of GDP) federal budget deficits.

Thus, this study seeks to provide at least preliminary insights into the following question: “What has been the impact of budget deficits on intermediate-term nominal interest rates in the U.S. over the last 41 years?” Section 2 of this study provides the basic framework for the empirical analysis, an open-economy loanable funds model reflecting dimensions of the works of Barth, Iden and Russek (1984; 1985; 1986), Hoelscher (1986), Koch and Cebula (1994), Cebula (2005), Cebula and Cuellar (2010), and others. Section 3 defines the specific variables in the empirical model and describes the data used. Section 4 provides the empirical results of GLM (Generalized Linear Model) estimations using annual data for the study period1972-2012. Conclusions are found in Section 5.

2. The Model In developing the underlying framework for the empirical analysis, we first consider the following

**inter-temporal government budget constraint:**

**where:**

NDt+1 = the national debt in period t+1;

NDt = the national debt in period t;

Gt = government purchases in period t;

Ft = government non-interest transfer payments in period t;

ARt = average effective interest rate on the national debt in period t; and Tt = government tax and other revenues in period t.

Cebula, International Journal of Applied Economics, 12(1), March 2015, 1-14 The total government budget deficit in period t (TDt), which is the deficit measured considered in

**this study, is simply the difference between NDt+1 and NDt:**

Based extensively on Barth, Iden, and Russek (1984; 1985; 1986), and Hoelscher (1986), as well as Koch and Cebula (1994), Cebula (1997; 2005), and Cebula and Cuellar (2010), this study seeks to identify determinants of the nominal interest rate yield on ten-year U.S. Treasury notes, including the impact of the federal budget deficit on same. To do so, a loanable funds model is adopted in which the nominal intermediate-term (in this study, ten-year) interest rate yield is, assuming all other

**bond markets are in equilibrium, determined by an equilibrium of the following form:**

D + MY = TDY - NCIY (3)

**where:**

D = private domestic demand for ten-year U.S. Treasury notes;

MY = the monetary base, expressed as a percent of real GDP, adopted as a measure of the available potential domestic money supply;

TDY = net government borrowing, measured by the federal budget deficit (as above), expressed as a percent of real GDP; and NCIY = net financial capital inflows, expressed as a percent of real GDP.

**In this framework, it is hypothesized that:**

**where:**

RTEN = the interest rate yield on ten-year U.S. Treasury notes;

Y = the percentage growth rate of real GDP;

EARSTBR =the ex ante real interest rate yield on high quality (and hence close-substitute) shortterm bonds;

EARLTBR = the ex ante real interest rate yield on high quality (and hence close-substitute) longterm bonds; and PE = the currently expected percentage future inflation rate, i.e., for the upcoming period.

Following the conventional wisdom, it is expected that the demand for ten-year Treasury notes is an increasing function of the yield on those notes, RTEN (Barth, Iden, and Russek, 1984; 1985; 1986;

Hoelscher, 1986; Koch and Cebula, 1994; Cebula and Cuellar, 2010). Next, it is hypothesized that the greater the percent growth rate of real GDP (Y), the higher the private sector real transactions demand for money and the higher the private sector issuance of bonds and consequently the lower the demand for ten-year Treasury notes, ceteris paribus (Hoelscher, 1986; Cebula, 2005). It is further Cebula, International Journal of Applied Economics, 12(1), March 2015, 1-14 hypothesized that, paralleling Barth, Iden, and Russek (1984; 1985), Cebula (1997B; 2005), Hoelscher (1986), and Koch and Cebula (1994), the real domestic demand for ten-year Treasury notes is a decreasing function of the ex ante real short-term interest rate yield, which in this case is the ex ante real interest rate yield on three-month Treasury bills. In other words, as EARSTBR increases, ceteris paribus, bond demanders/buyers at the margin substitute shorter-term issues for longer-term issues in their portfolios. Similarly, it is hypothesized that, in principle paralleling Barth, Iden, and Russek (1984; 1985), Cebula (1997B; 2005), and Hoelscher (1986), the demand for tenyear Treasury notes is a decreasing function of one or more alternative high quality long-term interest rate yields, in this case represented by the ex ante real interest rate yield on Moody’s Aaa-rated corporate bonds (EARLTBR), ceteris paribus. Finally, according to the “conventional wisdom,” the private sector demand for intermediate-term bonds, such as ten-year Treasury notes, is a decreasing function of expected inflation (PE), ceteris paribus (Barth, Iden, and Russek, 1984; 1985; 1986;

Hoelscher, 1983; 1986; Ostrosky, 1990; Koch and Cebula (1994); Gissey (1999); Cebula, 2005;

Cebula and Cuellar, 2010).

**Substituting equation (4) into equation (3) and solving for RTEN yields:**

The first of these expected signs is positive to reflect the conventional wisdom that when the government attempts to finance a budget deficit, it forces interest rate yields upwards as it competes with the private sector to attract funds from the financial markets, ceteris paribus. The expected sign on the money supply variable (MY) is negative because the greater the available money supply relative to GDP, the greater the offset to debt issues, i.e., greater funds availability presumably helps to offset interest rate effects of budget deficits, ceteris paribus. It is noteworthy that the empirical results are effectively identical if the M2 measure of the money supply as a percentage of GDP is adopted in place of MY; nevertheless, the MY variable is adopted because it more directly reflects quantitative easy policies. The expected sign on the net capital inflows variable is negative because the greater the ratio of net capital inflows to GDP, the greater the extent to which these funds absorb domestic debt (Koch and Cebula, 1994; Cebula and Belton, 1993; Cebula and Cuellar, 2010). The introduction of this variable into the model acknowledges the nature of the global economy and global financial markets. Finally, the expected signs on fEARSTBR, fEARLTBR, fY, and fPE follow logically from equation (4) above. Expressing the nominal interest rate yield on ten-year Treasury notes as a function of ex ante real ling-term and short-term interest rates is based on the models by Barth, Iden, and Russek (1984), Hoelscher (1986), and Cebula (2005) and is intended to avoid multicollinearity and simultaneity problems.

3. Specification of the Variables Given the presence of the expected inflation rate and two ex ante real interest rates as explanatory Cebula, International Journal of Applied Economics, 12(1), March 2015, 1-14 variables in the model, the first step in the analysis is to develop a useful empirical measurement of expected inflation. Indeed, this first step is necessary to the measurement of the variables EARSTBR, EARLTBR, and PE. The measurement of this variable is described by equation (7) below; estimates based thereupon are provided in section 4 of this study.

Proceeding, one possible way to measure expected inflation is to adopt the well-known Livingston survey data. However, as observed by Swamy, Kolluri, and Singamsetti (1990, p. 1013), there may

**be serious problems with the Livingston series:**

Studies by some psychologists have shown that the heuristics people have available for forming expectations cannot be expected to automatically produce expectations that come anywhere close to satisfying the normative constraints on subjective probability judgments provided by the Bayesian theoryfailure to obey these constraints makes Livingstondata incompatible withstochastic law...

Accordingly, rather than using the Livingston series, the study adopts, for the estimates using annual data, a linear-weighted-average (LWA) specification involving actual current and past inflation (of the overall consumer price index, CPI) to construct the values for the expected (future) inflation rate in each period t, PEt+1t. In particular, to construct the values for the current year’s (year t’s) expected future (i.e., for next year, year t+1) inflation, the following approach is adopted (Al-Saji, 1992; 1993;

**Cebula, 1992; Koch and Cebula, 1994):**

**where:**

PAt = the actual percentage inflation rate in the current year (t);

PAt-1 = the actual inflation rate in the previous year (t-1); and PAt-2 = the actual inflation rate in year t-2.

Clearly, this construct weights current inflation more heavily that previous-period inflation in quantifying the inflationary expectation for the future period. Given this measurement of expected future inflation, variable EARSTBRt = the nominal interest rate yield on three-month Treasury bills in year t minus PEt+1t, while variable EARLTBRt = the nominal interest rate yield on Moody’s Aaarated long-term corporate bonds in year t minus PEt+1t. Interestingly, before proceeding, despite its technical limitations, it is observed that adoption of the Livingston series in place of the formulation in equation (7) yields quite similar results and the same basic overall conclusions as those obtained here.