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 declines in real activity and inflation, and these declines in turn drive the budget balance into negative territory through the automatic stabilizers. In response to the declines in real activity and inflation, the short rate, shown in the upper-left panel, declines by about 1 percentage point for several quarters before gradually returning to its original level.The solid lines in the panels of figure 6 show the responses of yields at four different maturities to the surplus shock, whereas the dotted-dashed lines provide some information on the transmission of a monetary shock through the yield curve. The dotted lines in each case, labeled “risk-neutral IRFs,” provide the impulse responses under the assumption that the prices of risk are zero, with the difference between the solid and dotted lines showing the contribution of risk premia to the overall response. As the maturity increases, the response of the yields is muted. At the 5-year maturity, the tightening leads to a 40-bps decline in the yield that persists for about 4 quarters and gradually dissipated over the following 12 quarters.When figures 5 and 6 are combined, it is apparent that the mechanism by which exogenous fiscal tightening leads to a reduction in yields is inducing a sharp contraction in real activity and inflation. The effects of exogenous fiscal policy measures on real activity are of course a subject of much recent controversy. The regression coefficient of detrended log real GDP to the real activity measure used here (the Chicago Fed National Activity Index [CFNAI]) is about 1.25. Thus, the response in the lower-right panel of figure 5 implies a “fiscal multiplier” that is very large but at the same time short lived. In line with the arguments in Favero and Giavazzi (2007), what seems to be missing is any influence from the implied debt accumulation to interest rates. The impulse response of the surplus/GDP ratio implies that the long-run effect of an exogenous fiscal tightening is an increase in debt/GDP, yet this effect is not captured by the VAR analysis. As mentioned before, inclusion of a debt accumulation identity is not straightforward since the linearity of the law of motion of the state vector is necessary for the model’s ability to derive closed-form bond-pricing formulas.III. Fiscal Policy and Interest Rate Spreads in Europe Before and Since 2008Developments in yield spreads between EMU government bonds since early 2008 have been rather dramatic. Figure 7 shows some of the data used in this section. These are yields of the currently outstanding government bond closest to 10-year maturity minus their German counterpart.Fig. 7. EMU 10-year government bond spreads vis-à-vis GermanyView Large ImageDownload PowerPointAlthough it would in principle be desirable to have the same framework explaining yields whether sovereign default risk is negligible or not—a key factor behind the dramatic rise in the spreads—there are several reasons why the arbitrage-free term structure model developed in the previous section would be difficult to apply to euro area yield spreads. First, while extensions of the framework to the case of bonds with default risk exist (e.g. Duffie and Singleton 1999), they would be challenging to estimate on the relatively short post-EMU sample that is apparently subject to a regime change in 2008. Second, such models are data demanding, requiring zero-coupon yields on government bonds for sufficiently many maturities for all the countries considered (for an application to three EMU member countries, see, e.g., Monfort and Renne [2010]). In this section I therefore pursue a more limited exercise in the spirit of the existing literature on EMU government bond spreads discussed in the introduction.Focusing on spreads of government bond yields between other EMU member countries and Germany instead of trying to model the levels of the individual interest rate series (as in Faini 2006) has the advantage that we do not need to take a stand on the determinants of euro area interest rates but can focus directly on country-specific influences.A. The Relation between EMU Government Spreads and Fiscal PolicyDoes the level of a country’s deficit/GDP ratio or debt/GDP ratio, or both, affect the interest rate spread that it has to pay on a debt instrument of a given maturity over a comparable German yield? In the time series, the answer seems to be clearly “no.” Consider the example of Italy. In the middle of 2002, Italy’s debt/GDP ratio stood at 118%, its deficit/GDP ratio at 2.9%, and the spread of its 10-year bond over the 10-year bund at 22 bps. At the end of 2009, Italy’s debt/GDP ratio was 115%, its deficit/GDP ratio 2.9%, and the 10-year spread 60 bps. Qualitatively similar observations can be made about many euro area countries: although the fiscal position of several euro area countries improved over the period until late 2008, the spreads that they had to pay since late 2008 are dramatically higher.What about the cross-sectional relationship between countries’ fiscal position at a given moment in time and the spreads that they have to pay? Given a panel of 10 euro member countries (Greece, Portugal, Spain, Belgium, Netherlands, Austria, Finland, Ireland, Italy, France), I address this question through a sequence of 16 regressions at semiannual intervals between May 2002 and November 2009. Each of these regressions uses as regressors a constant, the country’s current debt/GDP ratio, and the (1–2-year-ahead projection of the) deficit/GDP ratio as projected by the OECD:9 where is country i’s yield spread at date t, the level of debt/GDP at date t, and the OECD’s projection of the surplus/GDP ratio.10Although the number of observations to be fitted at each date is small, the fit of these regressions is nonetheless surprisingly good. Of the 16 regressions, only three produce an adjusted R2 of less than 0.5, whereas 11 produce an adjusted R2 between 0.7 and 0.9. Figure 8 illustrates the fit of four of these regressions by plotting the fitted value on the horizontal against the actual spreads on the vertical axis. If all points were lying on the 45-degree line, the R2 would be 1.Fig. 8. Actual versus fitted spreads from regressions on fiscal variables. AT = Austria, BE = Belgium, ES = Spain, FI = Finland, FR = France, GR = Greece, IE = Ireland, IT = Italy, NL = Netherlands, and PT = Portugal.View Large ImageDownload PowerPointHow can the (presumably) poor explanatory power of the fiscal variables for spreads in the time series be reconciled with the very good fit of these variables in the cross section? The main explanation, as shown in figure 9, is significant time variation in the magnitude of the coefficients. The coefficient estimates on the surplus/GDP ratio and the debt/GDP ratio are shown as x’s in the upper and lower panels, respectively, with the vertical bars indicating 90% confidence intervals. For the first 13 regressions (May 2002 to May 2008), the regression coefficient on the surplus/GDP ratio falls between 0 and −3, indicating a 3-bp increase in the spread per percentage point decline in the surplus/GDP ratio; half of the t-statistics are 1.75 or higher. The coefficient estimates for the debt/GDP ratio are clustered between 0.1 and 0.3, with 11 out of 13 significantly different from zero at the 5% level.Fig. 9. Evol