Fiscal Policy and Interest Rates: The Role of Sovereign Default Risk

Previous articleNext article FreeFiscal Policy and Interest Rates: The Role of Sovereign Default RiskThomas LaubachThomas LaubachGoethe University Frankfurt Search for more articles by this author PDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionMuch ink has been spilled on the topic of the relationship between fiscal policy, especially between government debt, deficits, and government spending, and interest rates. A large body of empirical studies documents that an increase in government deficits or debt either has statistically insignificant effects on interest rates or raises them by a statistically significant but economically modest amount. As so often, most of this evidence is based on postwar U.S. data.As recent events in the euro area, however, have made abundantly clear, there are situations in which interest rates react very sensitively to fiscal policy changes. The purpose of this paper is to study the recent empirical evidence. The main theme that emerges is that there are times and circumstances in which the effects of fiscal policy on interest rates can be very large indeed. These are presumably times when sovereign default risk becomes an issue. When no risk of sovereign default is perceived, the effects of government debt or deficits on interest rates seem to be significant but modest. The paper develops models for either of these two situations and then asks what circumstances, including fiscal ones, trigger concerns about default risk in financial markets.The paper brings together ideas and techniques from several different strands of literature. The first part of the paper focuses on evidence from the United States prior to the onset of the financial crisis. It uses a structural vector autoregression (VAR) to measure the effects of fiscal policies on interest rates and other variables and combines this with an affine term structure model to decompose the effects into those coming from expectations of future interest rates and those coming from risk premia. This part focuses on the United States because it uses techniques that are appropriate only in the absence of default risk and therefore apply only to the few remaining issuers of Aaa-rated debt.A key issue regarding fiscal policies by member countries of the European Monetary Union (EMU) is the extent to which those policies affect the areawide level of interest rates and to what extent they affect yield spreads among EMU government bonds (defined vis-à-vis German government bonds). On the basis of data prior to 2008, the literature arrived at somewhat conflicting results. Whereas Faini (2006) finds in panel regressions for EMU members for the 1979–2002 sample that there are large spillover effects from individual member countries’ fiscal policies to the areawide level of interest rates, Manganelli and Wolswijk (2009), studying the 1999–2008 sample, conclude that government credit risk as measured by bond ratings is still being priced.In hindsight, it is difficult to avoid the impression that default risk was underpriced prior to 2008. For example, the average spread of 10-year Greek government bonds over German ones was 25 basis points (bps); for Italian bonds it was about the same magnitude and for Portuguese bonds 15 bps. Regardless of how one views the period of compressed EMU government bond spreads that lasted until early 2008, it is important to ask whether we can identify a threshold or estimate the nonlinear process by which the interest rate effects of fiscal policy become amplified. In Section III, I develop a link between the time-varying sensitivity of EMU government bond spreads to fiscal conditions and proxies for time-varying risk aversion. Section IV offers conclusions.II. Fiscal Policy and Interest Rates in the United StatesThis section provides evidence on the interest rate effects of fiscal policy in a situation in which it is plausible to assume that default risk was perceived by investors to be negligible. Specifically, we focus on the United States over the period since the 1980s. There is of course already an enormous empirical literature on the interest rate effects of fiscal policy in the United States (Gale and Orszag [2002] provide an excellent survey).Most of this literature is based on reduced-form regressions of interest rates on fiscal variables and possibly additional regressors. In this section I instead present estimates of an arbitrage-free term structure model in which (most of) the factors are observable macroeconomic variables, including fiscal variables. The law of motion of these factors is modeled as a VAR. Bonds at various maturities are priced under the restriction that their market prices of risk are linear functions of the factors. There are several advantages of this framework:• There is strong evidence against the expectations hypothesis of the term structure. Therefore, it is of interest to decompose yields into risk-neutral (expectations) components and risk premia and to ask how fiscal policy affects interest rates, whether mostly through changes in expected future short-term interest rates or through changes in risk prices.• We can study how yields at all maturities (not only at one maturity as in reduced-form regressions) respond to fiscal policies while simultaneously imposing the assumption of no arbitrage, which seems plausible in as deep and liquid a market as that for U.S. Treasury securities.• By using a VAR as a law of motion, the results can also be related to the literature of identified fiscal policy shocks starting with Blanchard and Perotti (2002). Thus we can compute impulse responses to tax and spending shocks of yields for the full range of maturities.Dai and Philippon (2006) have estimated an affine term structure model along the lines just described. A central point of the papers by Gale and Orszag (2002) and Laubach (2009) is that the response of interest rates (especially of long maturities) to fiscal policy depends on expectations about the future course of fiscal policy. In the term structure model(s) these expectations are generated by the estimated VAR. However, the VAR-based expectations that the econometrician estimates in hindsight may be quite different from the expectations of investors at the time when the government bonds were priced.1 I therefore use Congressional Budget Office (CBO) projections for fiscal variables as additional observable variables in estimation, as in Canzoneri, Cumby, and Diba (2002) and Laubach (2009), using the method developed in Kim and Orphanides (2005). Because the CBO projections refer to the federal government, like Favero and Giavazzi (2007) and unlike Blanchard and Perotti (2002), I focus on measures of fiscal policy for the federal sector only.2Favero and Giavazzi (2007) and Perotti (2007) find evidence for a change in responses of macro variables to fiscal policy between samples ending before and starting after about 1980. This change has been interpreted as evidence for a change in the reaction of fiscal policy with regard to stabilization of the debt/GDP ratio. Moreover, the CBO projections are available only from 1976. The analysis therefore starts in 1980. I consider estimates based on samples ending before the onset of the crisis but excluding the crisis period. Despite the extreme deterioration in the U.S. fiscal outlook, long-term yields have remained low presumably because of safe-haven demand for Treasury securities. To estimate the effect of the increase in government debt on interest rates, it would therefore be important to quantify the extent to which (presumably temporary) safe-haven demand has held down yields, something I do not attempt here.A. An Affine Term Structure Model with Fiscal FactorsThe model used to estimate the dynamic effects of fiscal policy shocks consists of a reduced-form description of the relationships between major macroeconomic and fiscal variables and a specification of the stochastic discount factor that ensures that pricing of bonds at various maturities is arbitrage free. Two key assumptions underlying this pricing framework are that the bonds do not pay coupons and that they are free of default risk.Specifically, let denote the state vector comprising the detrended short rate (where the meaning of “detrended” will be explained shortly), a demeaned fiscal policy measure , detrended inflation , a measure qt of real activity relative to potential, and trend inflation . The first four of these variables are assumed to follow a VAR(2), whereas trend inflation is assumed to follow an exogenous random walk: where Trend inflation is a latent factor, which, however, will be tightly constrained in the estimation by a survey-based measure of long-horizon inflation expectations. The remaining four factors are observable macro variables.In specifying the stochastic discount factor that prices bonds at different maturities, I am following the large literature of affine term structure models (e.g., Duffee 2002). Let denote the Radon-Nikodym derivative that converts the data-generating to the risk-neutral probability measure, such that where denotes expectation under the risk-neutral measure and λt are the prices associated with the macroeconomic risks. These risks are given by the (as yet to be identified) fundamental innovations ϵt , which are assumed to be independent and identically distributed (i.i.d.) standard normal. The reduced-form innovations ut have covariance matrix Ω = ΣΣ′ .A key assumption is the specification of the prices of risk λt as a general linear function of the states: This specification plays an important role in enabling the model to explain the observed failures of the expectations hypothesis (Dai and Singleton 2002) and to forecast yields (Duffee 2002). I follow Dai and Philippon (2006) in assuming that the stochastic discount factor depends only on current innovations ϵt but that the prices of risk can depend on both current and lagged states. Therefore, λt is a 5 × 1 vector and λ1 a 5 × 10 matrix. Certain other assumptions are being imposed to conserve on the otherwise very large number of parameters to be estimated.3 It should be noted that the flexibility provided by the general specification (2) comes at the cost that it is unclear how to generate this specification from preferences of a representative investor.Besides the VAR specification (1) for the states, the stochastic discount factor, and the prices of risk (2), the model is completed by a specification for the one-period nominal risk-free interest rate where I assume that loads only on current states xt .4 The model then implies that the yield on a nominal zero-coupon bond with n periods to maturity is a linear function where the coefficients an and an are determined recursively.B. The Use of Survey Expectations and Fiscal Projections in EstimationThe parameters of the term structure model developed above, that is, the VAR parameters ϕ1 and ϕ2 and the unique elements of the covariance matrix Ω, the parameters δ0 and δ1 of the short-rate equation, and the parameters λ0 and λ1 of the risk price specification, are estimated by maximum likelihood. Because the term structure model implies the exact linear relationships (4) between the states and the yields, with k states and only one latent factor it is necessary to add measurement error to at least k − 1 yields to avoid stochastic singularity. The n-period yield is therefore assumed to equal By contrast, the macroeconomic variables are assumed to be observed without error. Observed inflation is simply the sum of trend inflation and detrended inflation, , where the mean of trend inflation equals that of observed inflation, whereas the observed short rate rt equals the sum of the mean real short-term interest rate, trend inflation, and the detrended short-term real rate: . Finally, the observed fiscal measure is equal to its mean and the deviation from that mean: . The time series of the first four elements of xt are shown in figure 1.Fig. 1. Data in the state spaceView Large ImageDownload PowerPointThe key function of the VAR is to generate expectations of the future states and, through (3), expectations of the future one-period yield. Yet expectations generated by a VAR estimated ex post on a given data sample can be poor guides to expectations held by investors at a given point in time. For example, if we were to estimate a VAR using actual inflation instead of decomposing it into trend inflation and detrended inflation, the VAR would generate long-horizon inflation expectations, and thereby long-horizon expectations of short-term nominal interest rates, that are not nearly volatile enough over our sample (Kozicki and Tinsley 2001). Similarly, long-horizon expectations of fiscal variables would not show nearly enough volatility compared to long-horizon projections such as the ones prepared regularly by the CBO. To address this shortcoming, I therefore include survey measures of long-horizon inflation expectations and CBO projections as information variables in the estimation and impose that the VAR-implied expectations at the respective horizons are equal to these survey measures and projections plus some i.i.d. measurement errors. This assumption implies linear relationships of the form where denotes survey-based long-horizon inflation expectations and the p-year-ahead CBO projection of the fiscal variable ft (details of the data are discussed in the appendix available on the author’s Web page, http://www.wiwi.uni-frankfurt.de/professoren/macro/people/isom.pdf). The coefficients ζπ and ζf,p are functions of the VAR parameters.With these assumptions, the state space model consists of the transition equation given by the VAR(1) and a measurement equation in which the vector of observables is given by where N denotes the longest maturity included in estimation.C. Identifying Fiscal Policy ShocksThe major challenge in assessing the effects of fiscal policy on interest rates is the endogeneity of fiscal policy measures such as spending, revenues, or the deficit to other economic variables and shocks. In Laubach (2009) I tried to overcome this problem in the context of reduced-form regressions by focusing on the effects of long-horizon (5-year-ahead) projections of deficits, debt, spending, and revenues on proxies for expectations at the same horizon of long-term interest rates. The implicit assumption in this strategy is that changes in fiscal policy measures, especially the deficit/GDP ratio, projected at long horizons reflect exclusively exogenous changes to fiscal policy.Given that the transition equation of the state vector is a VAR, I am instead following the methodology developed in Blanchard and Perotti (2002) and extended in Perotti (2004) for identifying exogenous shocks to government spending and taxes. In short, the key assumption underlying their strategy is that within the quarter, the fiscal authorities are not able to respond in a discretionary manner to economic news. Hence, the only contemporaneous responses are those implied by the “automatic fiscal stabilizers,” that is, the elasticities of spending and taxes with respect to the macro variables (output, prices, interest rates) included in the VAR. The relations between the VAR’s reduced-form residuals u for log real taxes τ and log real spending g and their structural shocks ε can then be written as The elasticities η can be calibrated from institutional information on tax codes and benefits rules, allowing us to identify the structural shocks.Since taxes and spending are not included separately in the VAR but only through the surplus ft = τt − g , I follow Dai and Philippon (2006) and calculate the structural “surplus shocks” by using ηf,q = ητ,q − ηg,q and so forth. To provide some additional information on properties of the VAR, below I also report impulse response functions to a “monetary policy shock” that is identified in the usual recursive manner by assuming that the funds rate responds contemporaneously to all variables in the VAR but that fiscal policy, inflation, and real activity do not respond within the quarter to rt . More details on the calibration of the elasticities η are provided in the appendix available on the author’s Web page.D. Results1. EstimationDespite the imposition of restrictions especially on the risk price parameters λ, the model is fairly highly parameterized, with a total of 78 parameters to be estimated.5 As in other studies in this literature, I therefore rely on finding good starting values for the VAR parameters ϕ1 , ϕ2 , and Ω and δ1 and only then estimate the price of risk and other parameters.6A natural way of assessing the model’s properties is the in-sample fit of the yields. Figure 2 shows for three maturities the historical and fitted yields. These are visually very close, reflecting the fact that the estimated standard deviations of measurement error range from 14 to 16 bps for any of the maturities included. The dotted line in each of the first three panels presents yields that are obtained from setting λ1 to zero, in which case the expectations hypothesis holds. The difference between the fitted yields and those dotted lines is shown in the lower-right panel of figure 2. These are the historical series of the term premia on nominal bonds. In the immediate aftermath of the “great inflation,” these stood at nearly 8% for 5-year Treasury bonds but then declined rapidly over the course of the 1980s and early 1990s and rose again during the late 1990s before falling to slightly negative levels during the “conundrum” period of 2004–5.Fig. 2. Actual and fitted yields and term premiaView Large ImageDownload PowerPointThe small size of the measurement error standard deviations is remarkable in light of the common finding that pure macro-factor term structure models tend to produce standard deviations on the order of 50 bps (e.g., Mönch 2008). Although strictly speaking the model does include one latent factor, it is important to point out that this factor is tightly linked to an observable series, the long-horizon survey expectations of inflation. As shown in figure 3, the latent factor (the solid line) follows the survey expectations (the dotted line) relatively closely because the match between the model-implied (the dotted-dashed line) and the survey-based long-horizon inflation expectation is forced to be close by calibrating the measurement error on the survey expectations to 20 bps.7Fig. 3. Trend inflation and long-horizon survey expectationsView Large ImageDownload PowerPointThe role of the CBO projections in estimating the model is illustrated in figure 4. The solid line shows the actual surplus/GDP ratio, where the x symbols indicate 5-year-ahead projections of the CBO in the quarter when the CBO released the projection (usually in January and July or August). For the sample 1980:1–2007:4, a total of 51 projections are available. In the estimation I use the 3-year- and 5-year-ahead projections of the surplus/GDP ratio. Because I am using the so-called baseline projections, which, as the CBO emphasizes, are not meant to be best forecasts but are by statute based on the continuation of current policies, I deliberately set the standard error on the measurement error to a large 100 bps because investors may have disagreed with the baseline projections. Nonetheless, including the CBO projections helps to impart substantially more variability to the model-implied surplus/GDP projections (the dashed line in fig. 4 for the 5-year horizon).Fig. 4. Surplus/GDP, VAR, and CBO 5-year-ahead projections: model with CBO projections.View Large ImageDownload PowerPoint2. The Interest Rate Effects of Fiscal ShocksFigures 5 and 6 present the main results of this section, that is, the impulse responses of the states and of yields at various maturities to a surplus shock and, for comparison with the large literature on measuring monetary policy, also to a funds rate shock.8Fig. 5. IRFs of state variablesView Large ImageDownload PowerPointFig. 6. IRFs of yields with and without term premiaView Large ImageDownload PowerPointAs shown in the upper-right panel of figure 5, an exogenous fiscal tightening of 1% of GDP is followed by a persistent deficit for the following 12 quarters. According to the VAR, the exogenous fiscal contraction leads to immediate, sharp in real activity and inflation, and these in the into negative through the In response to the in real activity and inflation, the short rate, shown in the by about 1 point for several before to its solid lines in the panels of figure 6 show the responses of yields at four different maturities to the surplus whereas the dotted-dashed lines provide some information on the of a monetary shock through the yield The dotted lines in each provide the impulse responses under the assumption that the prices of risk are zero, with the difference between the solid and dotted lines the of risk premia to the As the maturity the response of the yields is the 5-year the tightening leads to a in the yield that for about 4 and over the following 12 5 and 6 are it is that the by which exogenous fiscal tightening leads to a in yields is a sharp contraction in real activity and inflation. The effects of exogenous fiscal policy measures on real activity are of course a of recent The of detrended log real GDP to the real activity measure used (the is about the response in the lower-right panel of figure 5 implies a that is very large but at the same time short In line with the in Favero and Giavazzi what seems to be is any from the implied debt to interest rates. The impulse response of the surplus/GDP implies that the effect of an exogenous fiscal tightening is an increase in yet this effect is not by the VAR As of a debt is not since the of the law of motion of the state vector is necessary for the model’s to Fiscal Policy and Interest Rate in and in yield spreads between EMU government bonds since early have been Figure shows some of the data used in this These are yields of the government bond to 10-year maturity their German EMU 10-year government bond spreads vis-à-vis Large ImageDownload it would in be to have the same framework yields whether sovereign default risk is or key factor the in the are several the arbitrage-free term structure model developed in the section would be difficult to apply to euro yield while of the framework to the case of bonds with default risk and Singleton they would be to estimate on the relatively short sample that is to a change in 2008. such models are data zero-coupon yields on government bonds for maturities for all the countries an to three EMU member and In this section I therefore a more in the of the literature on EMU government bond spreads discussed in the on spreads of government bond yields between other EMU member countries and instead of to model the levels of the individual interest rate series (as in Faini has the that we do not to a on the of euro interest rates but can focus on The between EMU and Fiscal the level of a deficit/GDP or debt/GDP ratio, or affect the interest rate spread that it has to pay on a debt of a given maturity over a German In the time series, the seems to be the of In the of debt/GDP stood at its deficit/GDP at and the spread of its 10-year bond over the 10-year at bps. the of debt/GDP was its deficit/GDP and the 10-year spread bps. can be made about euro the fiscal of several euro countries over the period until late 2008, the spreads that they to pay since late are about the relationship between countries’ fiscal at a given in time and the spreads that they have to a panel of 10 euro member countries I address this through a of 16 regressions at between and of these regressions uses as a the current debt/GDP ratio, and the projection of deficit/GDP as projected by the where is yield spread at the level of debt/GDP at and the projection of the surplus/GDP the number of to be fitted at each is the fit of these regressions is the 16 only three produce an of whereas produce an between and Figure the fit of four of these regressions by the fitted on the against the actual spreads on the all points were on the the would be 1.Fig. Actual fitted spreads from regressions on fiscal variables. = = = = = = = = = and = Large ImageDownload can the poor of the fiscal variables for spreads in the time series be with the very good fit of these variables in the The main as shown in figure is significant time in the magnitude of the The estimates on the surplus/GDP and the debt/GDP are shown as in the and with the For the first regressions to the on the surplus/GDP between and a increase in the spread point in the surplus/GDP of the are or The estimates for the debt/GDP are between and with out of different from at the