New Evidence on the Interest Rate Effects of Budget Deficits and Debt

New Evidence on the Interest Rate E(cid:11)ects of Budget De(cid:12)cits and Debt Thomas Laubach(cid:3) Board of Governors of the Federal Reserve System May 2003 Abstract Estimating the e(cid:11)ects of governmentdebt and de(cid:12)cits on Treasuryyields is complicatedbytheneedtoisolatethee(cid:11)ectsof(cid:12)scalpolicyfromotherinfluences. Toabstract from the e(cid:11)ects of the business cycle, and associatedmonetary policy actions, on debt, de(cid:12)cits, and interest rates, this paper studies the relationship between long-horizon expected government debt and de(cid:12)cits, measured by CBO and OMB projections, and expected future long-terminterestrates. The estimatede(cid:11)ects ofgovernmentdebt and de(cid:12)cits on interest rates are statistically and economically signi(cid:12)cant: a one percentage point increase in the projected de(cid:12)cit-to-GDP ratio is estimated to raise long-term interest rates by roughly 25 basis points. Under plausible assumptions these estimates are shown to be consistent with predictions of the neoclassical growth model. JEL classi(cid:12)cation: E6, H6. Keywords: Government debt, government de(cid:12)cits, interest rate regressions, CBO projections, OMB projections. (cid:3)tlaubach@frb.gov. I gratefully acknowledge helpful comments from numerous colleagues at the Federal Reserve Board, in particular Darrel Cohen, Douglas Elmendorf, Glenn Follette, David Reifschneider, John Roberts,andDavidWilcox,aswellasfromKenMatheny. SarahAlvesprovidedexcellentresearchassistance. All remaining errors are mine. The views expressed herein are those of the author and do not necessarily reflect those of theBoard of Governors of theFederal Reserve System or its sta(cid:11).

1 Introduction Muchcontroversysurroundsthequantitativee(cid:11)ectsofgovernmentdebtandde(cid:12)citsonlongterm real interest rates. Economic theory provides di(cid:11)erent answers depending on issues suchaswhetherde(cid:12)citsreflectchanges ingovernmentexpendituresorshiftsinthetimingof taxes, and on the planning horizon of households who hold government debt and pay taxes. Onemight hopethat empirical evidence could bebroughtto bear on this question, buthere the results are just as ambiguous. One major obstacle in obtaining empirical estimates is the need to isolate the e(cid:11)ects of (cid:12)scal policy from the many other factors a(cid:11)ecting interest rates. The most obvious of these factors is the state of the business cycle. If automatic (cid:12)scal stabilizers raise de(cid:12)cits during recessions, while at the same time long-term interest rates fall due to monetary easing, de(cid:12)cits and interest rates may be negatively correlated even if the partial e(cid:11)ect of de(cid:12)cits on interest rates { controlling for all other influences { is positive. Thispaperproposestoaddressthisidenti(cid:12)cationproblembyfocusingontherelationship between long-horizon forecasts of both interest rates and (cid:12)scal variables. De(cid:12)cits and interest rates expected to prevail several years in the future are presumably little a(cid:11)ected by the current state of the business cycle, thus greatly reducing the reverse-causality e(cid:11)ects inducedbycountercyclicalmonetarypolicyandautomatic(cid:12)scalstabilizers. Ofcourse,there aremanyconceivable factors thatjointly determine(cid:12)scal variables andinterest rates, andit is unlikely that a reduced-form regression would ever completely overcome this endogeneity problem, but focusing on long-horizon forecasts is an important step in the right direction. Moreover, de(cid:12)cits projected several years into the future may be informative about the longer-run (cid:12)scal position, and may therefore approximate investors’ expectations about the eventual level of government debtrelative to GDP. Such measures of expectations thus hold out the prospectof uncovering any causal relationship from (cid:12)scal variables to interest rates. Expectations of future(cid:12)scalpolicyare proxied inthis paperbyprojections publishedby the Congressional Budget O(cid:14)ce (CBO) and the O(cid:14)ce of Management and Budget (OMB) for the federal government’s uni(cid:12)ed budget de(cid:12)cit, the stock of federal government debt held by the public, and other (cid:12)scal variables, all expressed as percentages of the respective agency’s own projection of GNP or GDP. The forecast horizon is (cid:12)ve years in the future, whichisthelongesthorizonforwhichareasonablylongtimeseriesofprojectionsisavailable. Consistent with the use of 5-year-ahead projections of (cid:12)scal variables by the CBO and the 1

OMB, the analysis focuses on expectations of future nominal interest rates derived from forward rates 5 to 14 years ahead embedded in the term structure of interest rates. Theresultsreportedbelowshowthatapercentagepointincreaseintheprojectedde(cid:12)citto-GDP ratio raises the 10-year bond rate expected to prevail (cid:12)ve years into the future by 20 to 40 basis points; a typical estimate is about 25 basis points. The estimates are very precise compared to most of the literature mentioned below. Similarly, a percentage point increasein theprojected debt-to-GDP ratio raises futureinterestrates byabout4to5basis points, and these estimates are statistically signi(cid:12)cant, too. Importantly, these estimates are shown to be robust along many dimensions. Moreover, under plausible assumptions about the persistence of changes in projected de(cid:12)cits, the estimated 25 basis point e(cid:11)ect on interestratesofapercentagepointincreaseintheprojectedde(cid:12)cit-to-GDP ratioisshownto be consistent with the 4-to-5 basis point e(cid:11)ect of an increase in the projected debt-to-GDP ratio. Thisstudyisbynomeansthe(cid:12)rsttousepublishedprojections offuturebudgetde(cid:12)cits. Wachtel and Young (1987) use CBO and OMB projections to analyze changes in long-term 1 interest rates on the day of the release of the respective projection. Unlike those shown here, their results therefore dependon correctly identifying the unanticipated component of therelease. They(cid:12)ndthata$1billionincreaseintheprojectedde(cid:12)cit(atthattimeroughly 0.025 percent of nominal GDP) raises interest rates by between 0.15 and 0.4 basis points, dependingonthematurityoftheinterestrateseriesandthesourceoftheprojections. Their estimates therefore imply an increase in interest rates on the order of 6 to 16 basis points in response to a percentage point increase in the de(cid:12)cit-to-GDP ratio. However, many of their estimates are statistically insigni(cid:12)cant. Cohen and Garnier (1991) and Elmendorf (1993) present results concerning the e(cid:11)ect of de(cid:12)citprojectionsonthechangeininterestratesbetweenreleasedates. Likethepresentone, these studies are based on the weaker assumption (in comparison to Wachtel and Young’s) that the de(cid:12)cit projections are good proxies of private agent’s expectations of future (cid:12)scal policyatthetimeof therelease. Theprojections usedinthesestudies,as well as inWachtel and Young, are relatively short { for the current and next (cid:12)scal year in Wachtel and Young and in Cohen and Garnier; for up to eight quarters ahead in Elmendorf. Forecasts at this horizon are presumably still a(cid:11)ected by the state of the business cycle. Cohen and 1Otherstudies using similar event analysis are Elmendorf (1996) and Kitchen (1996). 2

Garnier address this problem by using projections for the cyclically adjusted federal de(cid:12)cit, thus in principle eliminating the business cycle e(cid:11)ects. Using OMB projections, they (cid:12)nd statistically signi(cid:12)cante(cid:11)ects of apercentage pointincreasein theprojected de(cid:12)cit-to-GDP ratio on interest rates on the order of 40 to 55 basis points. Using DRI forecasts, Elmendorf (cid:12)nds a statistically signi(cid:12)cant increase in interest rates at maturities up to (cid:12)ve years of about50basispoints, butthee(cid:11)ects onlong-term interestrates aresmallerandstatistically insigni(cid:12)cant. Canzoneri,Cumby,andDiba(2002) use5-year-ahead and10-year-ahead CBO projections of cumulative budget de(cid:12)cits and study their e(cid:11)ects on the spread between 5year or 10-year, and 3-month Treasury yields. Their estimates are of similar magnitude as those reported in Cohen and Garnier and in Elmendorf, but are considerably more precise. The present study con(cid:12)rms the importance of using measures of long-horizon expecta- 2 tions of de(cid:12)cits and debt for identifying their e(cid:11)ects on interest rates. It departs from the previous studies in several respects. Unlike Canzoneri et al., this study uses the level of interest rates expected to prevail 5 years ahead instead of the slope of the term structure. As shown below, omitting the near-term component from the long-term interest rate measures further helps to identify the e(cid:11)ects of the (cid:12)scal variables. In comparison to previous studies, I also include additional variables suggested by economic theory in the regressions; doingsoagain helpstoidentifymorepreciselythee(cid:11)ects of (cid:12)scalvariables oninterest rates. Moreover, I present results concerning the e(cid:11)ects of both government de(cid:12)cits and government debt on interest rates. Feldstein (1986) argues that the interest rate e(cid:11)ects of de(cid:12)cits depend on how persistent these de(cid:12)cits are assumed to be. The relative magnitudes of the estimated e(cid:11)ects of de(cid:12)cits and the estimated e(cid:11)ects of debt reported below are consistent with the assumption that increases in projected de(cid:12)cits are persistent, but not permanent. Finally, the fourth section discusses the predictions of the neoclassical growth model { the simplest general equilibrium framework for this purpose { for the relationship between the stock of debt and interest rates. Under plausible assumptions, the empirical results are consistent with the predictions from this model. 2This point is convincingly illustrated in Elmendorf (1993). He examines the (cid:12)ndings of studies that proxy for expectations of (cid:12)scal variables by using forecasts from VARs (see Plosser 1982, 1987, and Evans 1987). Elmendorf shows that these VAR forecasts are poor compared to projections available at the time, andthat theconclusions ofthesestudiesareoverturnedoncebettermeasuresof expectationsareused. For a taxonomy of studies in this area according to their measurement of expectations see Gale and Orzsag (2002). 3

2 Speci(cid:12)cation and Data The empirical method used in this paper is to regress expected future interest rates on projections published by the CBO and the OMB for the de(cid:12)cit-to-GDP ratio and the debtto-GDP ratio (cid:12)ve years ahead, as well as other determinants of long-term interest rates suggested by economic theory. As regards the latter, the Ramsey model of optimal growth, combined with a representative household with CES utility, implies that the net real return on capital, i.e. the real interest rate, is determined by r = (cid:27)g+(cid:18) where g denotes the net growth rate of technology, output, and consumption, (cid:27) is the coe(cid:14)cient of relative risk aversion, and (cid:18) is the household’s rate of time preference. This relationship therefore suggests that both trend growth and risk aversion should play a role in determining yields on risk-free Treasury instruments: an increase in trend growth should raise interest rates, whereas an increase in risk aversion should lower Treasury yields because it raises the demand for safe assets. The regressions reported in the next section are therefore variants of rt = (cid:12)0+(cid:12)1ft+(cid:12)2gt+(cid:12)3et+(cid:15)t (1) wherert is therealTreasuryyield expected toprevailatsomehorizon, ft is a(cid:12)scalvariable, e.g. the projected de(cid:12)cit-to-GDP ratio, gt is a measure of potential GDP growth, and et is a measure of the equity premium discussed below. The following discussion of the data used in this study is deliberately kept short; more details can be found in the appendix. From the CBO, (cid:12)ve-year-ahead projections for both the uni(cid:12)ed budget de(cid:12)cit and GDP (GNP until 1991) are available at an annual frequency from1976to1984, andatasemiannualfrequencyfrom1985untilthemostrecentprojection in January 2003. For the early years, the CBO did not publish projections for federal debt held by the public; those projections are therefore computed by adding the CBO’s de(cid:12)cit projections for the current and next (cid:12)ve (cid:12)scal years to the stock of debt held by the public attheendoftheprevious(cid:12)scalyear. FromtheOMB,(cid:12)ve-year-ahead projectionsofde(cid:12)cits, debt held by the public, and GNP or GDP are available at an annual frequency from 1983 on. Ialsocollect projections forthenetinterestcomponentofoutlays, andfortotal outlays, 3 which I will use later on. 3The 5-year-ahead projections of debt held by the public are of course a(cid:11)ected by projected near-term 4

Figures1and2showtheactualde(cid:12)cit-to-GDPratiosanddebt-to-GDPratios,expressed as percent of GDP, together with CBO’s and OMB’s (cid:12)ve-year-ahead projections. The projections are shown for the ((cid:12)scal) year for which they were made. Clearly, both agencies madelarge forecast errors, butthis is irrelevant for our purpose. Theonly relevant question is whether these agencies’ projections accurately reflect market expectations at the time the projections were made. While it is impossible to assess that issue directly, arguably these agencies’ projections are using most of the information about future de(cid:12)cits and debt available at the time, although in di(cid:11)erent ways: Whereas the CBO’s projections are usually based on (cid:12)scal policies that have been enacted at the time the projection is made, theOMB’s projections includetheadministration’s policyproposals. Ifmarketparticipants believe that the administration’s policies are likely to pass as proposed, their expectations may be closer to the OMB’s projections; in other instances, they may be closer to the CBO’s. It is worth noting that over the sample for which both agencies’ 5-year-ahead projections can be evaluated ((cid:12)scal years 1988 to 2002), the biases of the CBO projections (1.2 percent for the de(cid:12)cit/GDP ratio, 5.1 percent for the debt/GDP ratio) are larger in absolutevaluethanthoseoftheOMBprojections(-0.7percentand-1percentrespectively), but the standard deviations of the CBO’s forecast errors (2.9 percent and 10.4 percent) are slightly smaller than those of the OMB (3.1 percent and 12 percent). There is no obvious reason why investors should prefer one agency’s projections over the other, and below I will present results using both sets of projections. For the regressions involving CBO projections, the interest rate data are sampled on the last trading day of the month of the CBO release. For the regressions involving OMB projections, I use the value of interest rates as recorded on the last trading day of February, exceptinthoseyearsinwhichanewadministrationtooko(cid:14)ce,whenIuseobservationsfrom the last trading day of March. Three di(cid:11)erent interest rate series are considered below: the yield expected to prevail (cid:12)ve years ahead on a 10-year Treasury note, the yield expected to prevail (cid:12)ve years ahead on a 5-year Treasury note, and the (conventional) 10-year constant 4 maturityTreasuryyield. The(cid:12)rsttwoaremeasuredassimpleaverages ofone-year forward cyclical de(cid:12)cits; however, the e(cid:11)ects of the de(cid:12)cit in any one given year on the stock of debt is generally small. 4Althoughthisstudyfocusesongovernmentyields,itshouldbenotedthattheresultsarelikelytocarry overtocorporateyields. Basedonregressionanalysis,I(cid:12)ndnoevidencethatyieldspreadsbetweencorporate bondsandTreasuries, adjusted forcyclicalvariation, aresystematically related toprojected de(cid:12)cit-to-GDP 5

rates 5 to 9 years and 5 to 14 years ahead, respectively, calculated from the zero-coupon 5 yield curve. Nominal interest rates are converted into real interest rates using a proxy for 10-year consumer price inflation expectations that is based on survey data for most of the sample; details are provided in the appendix. In some regressions the dependent variable is the real interest rate, whereas in others it is the nominal interest rate; in these latter regressions, inflation expectations are allowed to enter with a coe(cid:14)cient di(cid:11)erent from 1. Theseries of nominalinterest rates andexpected inflation, sampledinthemonths of annual CBO releases, are shown in (cid:12)gure 3. For trend growth, I use CBO’s 5-year-ahead projections of the growth rate of real GNP or GDP as a proxy for agents’ views about the trend growth rate of the economy at a given point in time. It is also the growth rate that is consistent with CBO’s de(cid:12)cit projections (cid:12)ve years ahead. The equity premium, used as a proxy for risk aversion, is calculated as the dividend component of national income, expressed as percent of the market value of corporateequityheld(directlyorindirectly)byhouseholds,minusthereal10-year Treasury yield, plus the trend growth rate. I usethe value of the equity premiumin the quarter prior to the release of the respective budget projections, assuming that this is the best available forecast of this variable (cid:12)ve years ahead. Because the equity premium is a function of the real 10-year Treasury yield, the issue of simultaneity of the dependent variable and this measure of the equity premium is addressed below. Both series are shown in (cid:12)gure 4. 3 Empirical Results Table 1 presents some baseline results, using the real 5-year-ahead 10-year Treasury yield as the dependent variable. It reports the estimated coe(cid:14)cients on the de(cid:12)cit-to-GDP and debt-to-GDP ratios, both expressed as percentages of GDP, trend growth, and the equity 2 premium; the intercept estimate is omitted from all tables. Also shown are the R , the standard error of the regression, the Durbin-Watson statistic, and the number of observaratios. 5It has often been noted that forward rates are biased predictors of future interest rates, presumably because they include term and/or risk premia. For the 5-year-ahead 10-year interest rate used here, for example, the bias throughout the 1990s is about 2 percent. Because forward rates are a(cid:11)ecting current interestratesandhencethecurrentcostofcapitalrelevantforbusinessandresidentialinvestment,however, thefact that forward rates may not be unbiased predictors of futureinterest rates is not a concern. 6

tions. The t statistics are based on standard errors using the Newey-West correction for heteroskedasticity and serial correlation; the lag truncation, based on automatic selection 6 criteria, is 3 for the CBO data, and 2 for the OMB data. The (cid:12)rst two columns show the results for the largest data set, the CBO projections including the mid-year updates from 1985 on. Thecoe(cid:14)cient on the de(cid:12)cit-to-GDP ratio is 0.29 and its t statistic is large. The coe(cid:14)cient on the debt-to-GDP ratio is also highly signi(cid:12)cant, andas arguedbelow,its sizeappearstobeconsistent withtheestimated coe(cid:14)cient on the de(cid:12)cit-to-GDP ratio. Trend growth and the equity premium enter with statistically signi(cid:12)cant and economically meaningful coe(cid:14)cients. The Durbin-Watson statistics indicate some degree of serial correlation in the residuals of both regressions. As shownin columns 3 and4, omitting themid-year updateseliminates thisproblemwithoutsigni(cid:12)cantlya(cid:11)ecting the other results; in the following I will only use the annual CBO data. Columns 5 and 6 show that similar results are obtained using OMB’s projections, except that the coe(cid:14)cients on the (cid:12)scal variables are no longer estimated as precisely as for the CBO projections. To provide some idea of the interest rate e(cid:11)ects predicted by these regressions, consider the CBO’s annual projections. Between January 2001 and January 2003, the CBO’s 5year-ahead projection of the surplus-to-GDP ratio declined from 3.8 percent to about 0.5 percent. The regression shown in column 3 implies that this swing raised the 5-year-ahead real interest rate by 92 basis points, everything else equal. Similarly, the projected 5-yearahead debt-to-GDP ratio increased from about 9.5 percent to 28.5 percent; the regression shownincolumn4impliesthat,allelseequal,thisswingraisedthe5-year-aheadrealinterest rate by 99 basis points. Tables 2 and 3 examine the robustness of these results along several dimensions. The dependent variable in these tables continues to be the 5-year-ahead 10-year Treasury yield. Despite the use of long-horizon projections, it is possible that the results may not only reflect the e(cid:11)ects of (cid:12)scal policy on interest rates, but may also confound those e(cid:11)ects with monetary policy. The early 1980s in particular are an episode in which both projected de(cid:12)cits and interest rates rose sharply, with the latter arguably driven at least in part by the Volcker disinflation. The (cid:12)rst two columns of table 2 therefore present the same regressions shown in table 1, using annual CBO projections only from 1985 on { that is, 6AcaveatininterpretingthetstatisticsisthataugmentedDickey-Fullertestsdonotrejectthehypothesis of a unit root at the 5 percent level for either the dependent variable or for the regressors. In view of the small numberof observations, however, thesetests have verylow power. 7

7 after the most intense phase of the disinflation had been completed. As shown in column 1, the coe(cid:14)cient on the de(cid:12)cit-to-GDP ratio is slightly larger, and its t statistic very high. The results shown in column 2 using the debt-to-GDP ratio are nearly identical to those for the full sample. A di(cid:11)erent approach to assessing the role of the early 1980s is to use nominal yields as the dependent variable, and to include expected inflation as an additional regressor. As shown in columns 3 to 6, the coe(cid:14)cient on expected inflation is always estimated to be larger than 1. This (cid:12)nding may reflect a demand by investors for increased risk premia on nominal assets to compensate for greater uncertainty about future inflation when the current level of inflation is elevated (see e.g. Okun (1971) and Ball and Cecchetti (1990)). In addition, Feldstein (1976) points out that, because taxes are levied on nominal returns, nominal interest rates have to increase more than one-for-one with expected inflation. Consequently, in these regressions the implied e(cid:11)ect of the rising de(cid:12)cits of the early 1980s on real interest rates is attenuated. This is because, relative to the earlier regressions in which nominal yields and expected inflation move one for one by assumption, a larger portion of thehighlevel ofnominalinterestrates duringthisperiodisnowattributed tohighexpected inflation. Consistent with this reasoning, the estimated coe(cid:14)cients on the (cid:12)scal variables are slightly smaller than those presented in table 1, but still highly signi(cid:12)cant. Returning to the example above, the results shown in columns 3 and 4 imply that the revisions to the CBO’s projections between January 2001 and January 2003 added about 75 basis points to 2 5-year-ahead long-term interest rates, all else equal. The improvement in the regression R is almost entirely due to the change in the dependent variable, as shown by the nearly unchanged regression standard errors. Because of the economic arguments mentioned before, however, thefollowing tables reportresultsforregressions withnominalyieldsas dependent variables. Two issues related to including trend growth and the equity premium in the regressions are addressed in table 3. The (cid:12)rst is how omitting one or both of these variables a(cid:11)ects the estimated coe(cid:14)cients on the (cid:12)scal variables. To be concise, results are shown only for annual CBO data. The (cid:12)rst two columns show results when both variables are omitted from the regression, and the next two columns show results when only the equity premium 7ResultsusingOMBprojectionsfrom1985onarelittlechangedfromthoseshownintable1,asonlythe (cid:12)rst two observations are omitted. 8

is omitted. Comparing those results to the ones shown in the middle two columns of table 2, we (cid:12)nd that the coe(cid:14)cients on both (cid:12)scal variables are quite similar whether one or both of the non-(cid:12)scal regressors are omitted. However, the coe(cid:14)cients on growth are essentially zero when the equity premium is omitted. For the theoretical reasons discussed in the 8 previous section, I will continue to include both variables in the regressions. A di(cid:11)erent concern is that the equity premium contains the real 10-year Treasury yield, and is therefore correlated with the residual. In the last two columns of table 3 I report results from regressions in which I use the lagged equity premium as instrument for the current equity premium. Compared to the results shown in the middle two columns of table 2, the only notable di(cid:11)erence is that the t statistics on the equity premium fall to 1.7. The results concerning the (cid:12)scal variables, however, are robust. Table 4 assesses the e(cid:11)ects of using either the current 10-year Treasury yield, or the 5-year Treasury yield expected to prevail (cid:12)ve years ahead, instead of the 10-year Treasury yield expected to prevail (cid:12)ve years ahead. For convenience, the last two columns repeat the results shown in the middle two columns of table 2. The results using the conventional 10-year Treasury yield show clearly that controlling for the cyclical variation embedded in the short end of the yield curve is important for identifying the e(cid:11)ects of (cid:12)scal variables 9 on interest rates. Once the (cid:12)rst (cid:12)ve years of the term structure are omitted, the point estimates using the 5-year-ahead 5-year yield are similar to those using the 5-year-ahead 10 10-year yield, but not as precise. Finally, table 5 considers the e(cid:11)ects of using two other combinations of (cid:12)scal variables. The (cid:12)rst column in table 5 addresses the concern of reverse causation from the interest rate to projected de(cid:12)cits through higher outlays on debt service. Here the regressor is the ratio of the primary de(cid:12)cit, de(cid:12)ned as the projected de(cid:12)cit less projected net interest outlays, to projected GDP. The coe(cid:14)cient on the primary de(cid:12)cit is larger than the coe(cid:14)cient on the de(cid:12)cit shown in table 2, and its t statistic about the same. The second column shows 8Qualitatively the same results obtain when using OMB projections, except that the coe(cid:14)cient on the debt-to-GDP ratio in the regression including growth remains signi(cid:12)cant at the 5% level, with a t statistic of 2.28. It should also be noted that the coe(cid:14)cient on trend growth remains signi(cid:12)cant in the regressions shown in tables 3 through 5 when thedependentvariable is thereal 5-year-ahead Treasury yield. 9Whenusingthereal10-yearyieldasdependentvariable,however,thecoe(cid:14)cientsonthe(cid:12)scalvariables remainsigni(cid:12)cantandofsimilarmagnitudeasthosereportedinthemiddletwocolumnsoftable1,although their t statistics are lower than those reported there. 10Again, thesame conclusions obtain using OMB projections. 9

the results from including the projections for the primary de(cid:12)cit and total outlays, both expressed as percentage of GDP, in the regressions. The question is whether the e(cid:11)ects of de(cid:12)cits on interest rates depend on whether the de(cid:12)cits are caused by spendingincreases or bychanges inthetimingoftaxes. AccordingtoRicardianequivalence, forexample, changes inprojectedde(cid:12)citswithoutchangesingovernmentpurchasesshouldleaveexpectedinterest rates unchanged. If so, the coe(cid:14)cient on the projected de(cid:12)cit-to-GDP ratio in a regression including projected government purchases should be zero. By contrast, the coe(cid:14)cient on the de(cid:12)cit-to-GDP ratio shown in the second column is even higher than before, whereas that on projected total outlays is negative, but statistically insigni(cid:12)cant. The sum of the coe(cid:14)cients on the two (cid:12)scal variables in column 2 is close to thecoe(cid:14)cient on the projected de(cid:12)cit-to-GDP ratio in column 1, and its t statistic is 2.67. The counterintuitive sign on total outlays may in part reflect the fact that total outlays include transfer payments as 11 well as government purchases. Is the result that the estimated coe(cid:14)cients on the de(cid:12)cit-to-GDP ratio are about seven times as large as the ones on the debt-to-GDP ratio economically plausible? If increases in de(cid:12)cits were serially uncorrelated, so that the e(cid:11)ect of a projected increase in the de(cid:12)cit on the stock of debt in subsequent years would be simply one for one, the coe(cid:14)cients on the de(cid:12)cit-to-GDP ratio and the debt-to-GDP ratio ought to be the same. But consider the opposite extreme, in which every increase in projected de(cid:12)cits is expected to bepermanent. The steady-state e(cid:11)ect on the debt-to-GDP ratio of a permanent one percentage point increase in the de(cid:12)cit-to-GDP ratio is (1+g)=g percent, where g is the net growth rate of nominal GDP. Over the sample 1976-2003, this growth rate averaged about 8 percent per year, implying that the coe(cid:14)cient on the de(cid:12)cit-to-GDP ratio ought to be 13.5 times as largeasthecoe(cid:14)cientonthedebt-to-GDP ratio. Thefactthattheestimated coe(cid:14)cients on thede(cid:12)cit-to-GDP ratio areaboutseven times as large as thoseon thedebt-to-GDP ratio is consistent with the view that investors perceive increases in projected de(cid:12)cit-to-GDP ratios as highly persistent (as they are in the historical data), but not strictly permanent. 11The results shown in table 5 are nearly una(cid:11)ected when using instead the real (cid:12)ve-year-ahead 10-year yield as dependentvariable. 10

4 Are the Results Consistent with Economic Theory? A skeptical view of the evidence presented in the previous section would hold that the identi(cid:12)cation problems involved in these kinds of regressions are too severe to be ever completelyovercome. Onemaythereforeaskwhethertheempiricalresultscanbereconciled with priors based on economic theory. One potential answer to this question, based on the neoclassical growth model, is sketched below; the argument is closely akin to the one 12 developed in Elmendorf and Mankiw (1999). Because in the neoclassical growth model the real interest rate is determined by the capital-output ratio, the discussion below focuses on the link between the stock of debt and the capital stock, and assesses the plausibility of the results for the debt-to-GDP ratio reported in the previous section. As Elmendorf and Mankiw (1999) point out, however, whether it is de(cid:12)cits or debt that matter for the determination of interest rates depends ultimately on which model of consumer behavior oneassumes. Theanalysisbelowthereforeillustratesonlyoneparticularargumentbywhich the empirical results can be related to economic theory. Suppose that an increase in government debt reduces the private capital stock by a fraction c; that is, if D denotes the stock of government debt, and K the private capital stock, @K=@D = −c. The parameter c denotes the degree of crowding out, with the remaining fraction 1−c being the increase in private savings or capital inflows from abroad in response to the increase in the interest rate. Assuming factors of production earn their marginal product, the share of capital in income, s, is equal to the marginal product of capital times the capital-output ratio k = K=Y. Moreover, the marginal product is equal to the sum of the depreciation rate d of the private capital stock and the real interest rate r. Hence we can solve for r as r = s=k−d. The e(cid:11)ect of a one percentage point increase in the debt-to-GDP ratio on r can now be computed by calculating the partial derivative @r=@D = @r=@k (cid:1)@k=@K (cid:1)(−c). Using s 1−s 1−s −(1−s) a Cobb-Douglas production function Y = K L , we (cid:12)nd that k = K L , and therefore @k=@K = (1−s)=Y. Putting the pieces together, an increase (cid:1)D = 0:01Y raises the interest rate by (1−s)cs=k 2 basis points. The (cid:12)nal step in obtaining numerical predictions of the interest rate e(cid:11)ects is to choose values for c;s, and k. As an example, consider s = 0:33, consistent with a capital share 12A similar argument is used in Council of Economic Advisers(2003). 11

in national income accounts data of about 1/3. For the parameter k, consider the BEA’s estimate of private (cid:12)xed assets at the end of 2001 ($22.2 trillion) divided by output in the nonfarm business sector in 2002 (approximately $8.4 trillion). This yields k = 2:5. The most di(cid:14)cult parameter to quantify is the degree of crowding out, c. Elmendorf and Mankiw (1999) survey a number of studies which show that, under assumptions for households’ intertemporal elasticity of substitution consistent with household data, the increase in private savings in response to the change in interest rates is close to zero. Moreover, recent studies in the vein of Feldstein and Horioka (1980) suggest that roughly two-thirds of saving in developed countries is retained for domestic investment in the long run,implyingthatcapital inflowsfromabroado(cid:11)setaboutone-thirdoftheincreaseindebt. Suppose, therefore, that c = 0:6. Then a one percentage point increase in the debt-to-GDP ratioraisestherealinterestrateby2.1basispoints. Thisisonlyhalfofthee(cid:11)ectreportedin the regressions using the real interest rate as dependent variable, but only slightly less than the estimates reported in Tables 2 and 3 using the nominal interest rate as the dependent variable. Itshouldbenoted, however, thattheestimate of 2.1 basispoints isconservative because it takes into consideration the endogenous response of output to the decline in the capital stock, butit omits the second-round e(cid:11)ect that the debt-to-GDP ratio is e(cid:11)ectively increasing by more than one percentage point. Moreover, as pointed out in the previous section, increases in projected de(cid:12)cits tend to be highly persistent, and hence a given increase in the 5-year-ahead projected debt-to-GDP ratio might be expected to be followed by larger increases in the debt-to-GDP ratio beyond (cid:12)ve years into the future. If so, a percentage point increase in the debt-to-GDP ratio projected (cid:12)ve years ahead should be associated with an increase in interest rates larger than the one implied by a percentage point increase in the steady state debt-to-GDP ratio predicted by the model. 5 Conclusions This study has shown that statistically signi(cid:12)cant and economically plausible estimates of the e(cid:11)ects of government de(cid:12)cits and debt on interest rates can be obtained by focusing on long-horizon forecasts offuturede(cid:12)citsordebt,andfutureinterestrates. Theprojections of de(cid:12)cits anddebtpublishedbytheCBO andtheOMBarearguablyamongthebestpublicly 12

available forecasts for these variables. The e(cid:11)ects of these projections manifest themselves at the longer end of the yield curve, as economic reasoning would predict. All else equal, the results of this study suggest that interest rates rise by about 25 basis points in response to a percentage point increase in the projected de(cid:12)cit-to-GDP ratio, and by about 4 basis points in response to a percentage point increase in the projected debt-to-GDP ratio. References [1] Ball, Laurence, and Stephen G. Cecchetti. \Inflation and Uncertainty at Long and Short Horizons." Brookings Papers on Economic Activity 1:1990, 215-245. [2] Canzoneri, Matthew B., Robert E. Cumby, and Behzad Diba. \Should the European Central Bank and the Federal Reserve be Concerned About Fiscal Policy?" In Rethinking Stabilization Policy, Federal Reserve Bank of Kansas City 2002. [3] Cohen, Darrel, and Olivier Garnier. \The Impact of Forecasts of Budget De(cid:12)cits on Interest Rates in the United States and other G-7 Countries." Federal Reserve Board, 1991. [4] Council of Economic Advisers. Economic Report of the President. Washington, D.C., February 2003. [5] Elmendorf,Douglas W.\ActualBudgetDe(cid:12)citExpectationsandInterestRates."Harvard Institute of Economic Research, May 1993. [6] Elmendorf,DouglasW.\TheE(cid:11)ectsofDe(cid:12)citReductionLawsonRealInterestRates." Federal Reserve Board, Finance and Economics Discussion Series 1996-44. [7] Elmendorf, Douglas W., and N. Gregory Mankiw. \Government Debt." Chapter 25 in John B. Taylor and Michael Woodford (eds.), Handbook of Macroeconomics, Vol. 1, Amsterdam: Elsevier Science 1999. [8] Evans, Paul. \Interest Rates and Expected Future Budget De(cid:12)cits in the United States." Journal of Political Economy 95 (1987), 34-58. [9] Feldstein, Martin S. \Inflation, Income Taxes, and the Rate of Interest: A Theoretical Analysis." American Economic Review 66 (1976), 809-820. 13

[10] Feldstein, Martin S. \Budget De(cid:12)cits, Tax Rules, and Real Interest Rates." NBER Working Paper No. 1970, July 1986. [11] Feldstein,MartinS.,andCharlesHorioka.\DomesticSavingsandInternationalCapital Flows." Economic Journal 90 (1980), 314-329. [12] Gale, William G., and Peter R. Orszag. \The Economic E(cid:11)ects of Long-Term Fiscal Discipline." Tax Policy Center, Urban Institute and Brookings Institution, December 2002. [13] Kitchen, John. \Domestic and International Financial Market Responses to Federal De(cid:12)cit Announcements." Journal of International Money and Finance 15 (1996), 239- 254. [14] Kozicki, Sharon, and Peter A. Tinsley. \Shifting Endpoints in the Term Structure of Interest Rates." Journal of Monetary Economics 47 (2001), 613-652. [15] Okun, Arthur. \The Mirage of Steady Inflation." Brookings Papers on Economic Activity 2:1971, 485-498. [16] Plosser, Charles I. \Government Financing Decisions and Asset Returns." Journal of Monetary Economics 9 (1982), 325-352. [17] Plosser, Charles I. \Fiscal Policy and the Term Structure." Journal of Monetary Economics 20 (1987), 343-367. [18] Wachtel, Paul, and John Young. \De(cid:12)cit Announcements and Interest Rates." American Economic Review 77 (1987), 1007-1012. A The Data The OMB data are taken from the annual releases of the administration’s budget published inFebruary, orslightly later inyears inwhichanewadministration tooko(cid:14)ce. Themonths of CBOreleases usedinthisstudy(releases omitted fromtheannualdatasetaremarkedby (cid:3) (cid:3) (cid:3) )are1/76, 12/76, 1/78, 1/79, 2/80, 7/81, 2/82, 2/83, 2/84, 2/85, 8/85 ,2/86, 8/86 , 1/87, (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) 8/87 , 2/88, 8/88 , 1/89, 8/89 , 1/90, 7/90 , 1/91, 8/91 , 1/92, 8/92 , 1/93, 9/93 , 1/94, (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) (cid:3) 8/94 , 1/95, 8/95 , 12/95 , 5/96, 1/97, 9/97 , 1/98, 8/98 , 1/99, 7/99 , 1/00, 7/00 , 1/01, 14

(cid:3) (cid:3) 8/01 , 1/02, 8/02 , 1/03. For the early years of the sample (1976-1982), constructing the seriesofbothprojectedde(cid:12)citsanddebtentailsachoicebecausetheCBOreporteddi(cid:11)erent projections of future de(cid:12)cits depending mainly on alternative assumptions regarding policy responses to the inflation-induced uptrend in tax receipts. To be consistent across the entire sample, I used the estimates based on the assumption of no policy change. The January 1991 projections are not the CBO baseline, but are based on the already legislated discretionary spending caps, which were the CBO’s baseline for the remainder of the 1990s. The December 1995 projections are included despite the fact that they were based on a budget resolution already vetoed by the President. By contrast, the August 1996 update is omitted because of incomplete projections, given that the annual projections had only been published in May. The series of inflation expectations, which is taken from the Federal Reserve Board’s FRB/US model, consists of three di(cid:11)erent pieces. Until 1981:Q1, the series is an estimated step function based on the changepoint model developed in Kozicki and Tinsley (2001). From 1981:Q2 until 1991:Q2, the series is based on the Hoey survey of decision makers, which was conducted by Drexel-Burnham-Lambert, and later by Barclays De Zoete Wedd. Participants in this survey were polled for their expectation of CPI inflation ten years ahead. Finally, since 1991:Q3 the series is based on the Survey of Professional Forecasters conducted by the Federal Reserve Bank of Philadelphia, in which participants are asked for their expectation of CPI inflation over the next ten years. Thus, while the series is not idealforourpurposes,itshouldprovideagoodmeasureofinflation expectations over either of the horizons of the nominal yield series described above. The series is extrapolated to monthly frequency, and is sampled in the months corresponding to the yield data. 15

Table 1: Results for Real 5-Year-Ahead 10-Year Treasury Yield Source of Projections CBO, Semiann. CBO, Annual OMB Proj. De(cid:12)cit/GDP .29 { .28 { .40 { (10.83) (12.07) (4.45) Proj. Debt/GDP { .053 { .052 { .053 (5.52) (5.22) (3.32) Trend Growth 1.11 1.53 1.02 1.45 1.01 1.51 (4.10) (3.70) (3.39) (3.10) (2.69) (2.77) Eq. Premium -.41 -.45 -.41 -.48 -.40 -.36 (4.83) (3.69) (4.32) (3.88) (2.29) (2.05) R2 .61 .44 .65 .48 .58 .49 S.E. .64 .76 .70 .85 .64 .70 DW 1.14 .97 2.06 2.07 2.20 2.16 N 46 46 28 28 21 21 Notes: Newey-West t statistics in parentheses. 16

Table 2: Results for Shorter Sample and for Nominal Yields CBO, 1985-2003 CBO, Nom. Yield OMB, Nom. Yield Exp. Inflation { { 1.19 1.32 1.12 1.16 (5.63) (5.96) (10.88) (10.37) Proj. De(cid:12)cit/GDP .30 { .23 { .36 { (6.36) (4.17) (3.29) Proj. Debt/GDP { .053 { .036 { .046 (5.05) (2.46) (2.68) Trend Growth 1.11 1.58 .68 .72 .86 1.26 (3.43) (3.12) (1.53) (1.06) (2.28) (2.28) Eq. Premium -.37 -.41 -.40 -.45 -.41 -.37 (3.58) (2.98) (4.30) (3.33) (2.41) (2.19) R2 .68 .58 .92 .90 .91 .90 S.E. .56 .64 .69 .79 .64 .70 DW 1.86 2.16 2.05 2.04 2.38 2.33 N 19 19 28 28 21 21 Notes: Newey-West t statistics in parentheses. Table 3: The Role of Trend Growth and the Equity Premium CBO, 1976-2003 OLS IV Exp. Inflation 1.23 1.35 1.20 1.37 1.19 1.32 (9.62) (9.96) (4.44) (5.40) (5.73) (6.29) Proj. De(cid:12)cit/GDP .21 { .23 { .23 { (3.96) (2.60) (3.96) Proj. Debt/GDP { .030 { .029 { .036 (2.68) (1.54) (2.20) Trend Growth { { .10 -.05 .57 .76 (.18) (.07) (1.14) (.94) Eq. Premium { { { { -.33 -.47 (1.72) (1.70) R2 .89 .86 .89 .86 .92 .90 S.E. .80 .90 .81 .92 .71 .80 DW 1.57 1.55 1.59 1.54 1.92 2.02 Notes: Newey-West t statistics in parentheses. 17

Table 4: The Role of Forward Rates and Maturities CBO, 1976-2003 10-Year Yield 5-Y-Ah-5-Y Yield 5-Y-Ah-10-YYield Exp. Inflation 1.62 1.71 1.21 1.31 1.19 1.32 (7.13) (7.85) (5.94) (6.71) (5.63) (5.96) Proj. De(cid:12)cit/GDP .09 { .19 { .23 { (1.40) (2.38) (4.17) Proj. Debt/GDP { .007 { .033 { .036 (.45) (2.14) (2.46) Trend Growth .73 .59 .65 .76 .68 .72 (1.25) (.80) (1.40) (1.23) (1.53) (1.06) Eq. Premium -.72 -.72 -.50 -.54 -.40 -.45 (4.93) (4.13) (3.66) (3.31) (4.30) (3.33) R2 .93 .93 .90 .89 .92 .90 S.E. .76 .79 .79 .84 .69 .79 DW 1.47 1.53 1.50 1.62 2.05 2.04 Notes: Newey-West t statistics in parentheses. Table 5: Other Combinations of Fiscal Variables CBO, 1976-2003 Primary Pr. De(cid:12)cit De(cid:12)cit and Outlays Exp. Inflation 1.22 1.28 (6.63) (6.04) Proj. De(cid:12)cit/GDP .32 .41 (4.35) (4.75) Outlays/GDP { -.13 (.97) Trend Growth .58 .48 (1.46) (1.09) Eq. Premium -.41 -.41 (4.16) (3.79) R2 .93 .93 S.E. .68 .68 DW 2.00 2.13 Notes: Newey-West t statistics in parentheses. 18

Figure 1: Actual and Projected De(cid:12)cits as Percent of GDP 8 6 4 2 0 -2 -4 -6 1980 1985 1990 1995 2000 2005 100*ActualDeficit/GDP CBO5-Year-AheadDeficit/GDPProjection OMB5-Year-AheadDeficit/GDPProjection Figure 2: Actual and Projected Debt as Percent of GDP 70 60 50 40 30 20 10 0 1980 1985 1990 1995 2000 2005 100*ActualDebt/GDP CBO5-Year-AheadDebt/GDPProjection OMB5-Year-AheadDebt/GDPProjection 19

Figure 3: Interest Rates and Inflation Expectations 16 14 12 10 8 6 4 2 1980 1985 1990 1995 2000 10-Year TreasuryYield 5-Year-Ahead10-Year Yield 5-Year-Ahead5-Year Yield ExpectedInflation Figure 4: Projected GDP Growth and Equity Premium 8 7 6 5 4 3 2 1 0 1980 1985 1990 1995 2000 CBO5-Year-AheadRealGDPGrowth EquityPremium 20