The Aggregate Demand for Treasury Debt Arvind Krishnamurthy, - PowerPoint PPT Presentation

The Aggregate Demand for Treasury Debt Arvind Krishnamurthy, Northwestern University and NBER Annette Vissing-Jorgensen, Northwestern University, NBER and CEPR November 2011 Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Yield spread between Moody’s Aaa bond yield and long term Treasury yield versus Publicly held US Treasury Debt/US GDP . 1919-2009. 2 1975 1970 2008 1971 2001 1932 1976 1972 1982 1.5 1974 2000 Aaa−Treasury spread 2002 1930 1981 1927 1931 1928 1968 1933 1929 1998 1980 1925 1926 1983 1 1924 1969 2009 1984 1934 1977 1999 1973 1987 1921 1922 1935 2007 1978 1986 1923 1920 1989 1941 1993 1992 1967 1919 1979 1995 1938 1939 1991 1997 2004 2005 1988 1990 1940 2006 1960 1936 1994 .5 1961 1996 2003 1937 1985 1966 1954 1957 1949 1948 1942 1959 1952 1965 1962 1958 1951 1950 1947 1946 1964 1956 1945 1963 1953 1943 1944 1955 0 0 .2 .4 .6 .8 1 1.2 Debt/gdp Standard monetary theory: Money is (1) medium of exchange, (2) very liquid, (3) very safe (in nominal terms). Our paper: Treasury bonds offer (2) and (3). The figure is akin to a money-demand function, but for government debt. Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Time series version of the same relation: 2 1.5 1 .5 0 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Year Aaa−Treasury spread Debt/gdp Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Findings Investors value U.S. Treasury bonds (beyond CCAPM value) 1 ◮ Changes in Treasury supply have large effects on a variety of yield spreads. Low yield on Treasuries is due to their extreme safety and liquidity 2 ◮ Safety: Find two assets with similar liquidity but different safety. Show that Treasury supply moves spread. ◮ Liquidity: Find two assets with similar safety but different liquidity. Show that Treasury supply moves spread. Quantity evidence further shows that Treasuries have similarities to 3 money (safety, liquidity) ◮ When supply of Treasuries falls, reducing overall supply of liquid and safe assets, supply of bank-issued money (M2-M1, time and savings deposits) rises. Average convenience yield on Treasuries is large: 72 bps. 4 Implications: (1) Treasury seignorage, (2) riskless rate, (3) foreign Treasury holders, (4) QE1 and QE2, and (5) optimal Treasury structure Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Related prior literature Money demand literature 1 Ricardian equivalence literature: Barro (1974) 2 ◮ We show that government debt is non-Ricardian. Main novelty relative to literature is looking at spreads rather than level of Treasury interest rates. Non-default component of spreads (corporate-Treas, swap-Treas): 3 ◮ Literature estimates default component of spread. Large residual is referred to as non-default component. Collin-Dufresne, Goldstein, and Martin (2001), Longstaff, Mithal, and Neis (2005), Duffie and Singleton(1997), Grinblatt (2001), Liu, Longstaff, and Mandell (2004), Feldhutterand Lando (2005) ◮ We offer a direct test of Treasury convenience value: It should be affected by the supply of the convenient asset (Treasuries). ◮ Prior evidence on correlation between Treasury supply and spreads: Cortes (2003): Interest rate swap spreads, 1994-2003. Longstaff (2004): Refcorp bond yield minus Treasury yield, 1991-2001. Friedman and Kuttner (1998): CP-bill, 1975-1996. ◮ We use a much longer sample (1919-2008), control for default risk, isolate liquidity and safety effects, provide quantity evidence on relation to money. Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Related subsequent literature on supply effects in bond markets Is there a demand for particular Treasury maturities? Greenwood and Vayanos (2010): Yes, relative supply of long vs. short Treasuries drives the slope of the yield curve. Can corporations step in too fill in the maturity structure? Greenwood, Hanson and Stein (2010): Partially, corporate maturity structure responds negatively to Treasury maturity structure, but not one-for- one. Very recent literature on the impact of quantitative easing (buying long bonds, issuing short-term claims). Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

1. The convenience yield on Treasuries Representative agent who maximizes, ∞ X β t u ( C t ) E t = 1 where C t is the agent’s consumption plus “convenience" benefits: C t = c t + ν ( θ A t , GDP t ; ξ t ) . Convenience assets (A=total, T=treasuries, P=private sector substitutes): θ A t = θ T t + k P θ P t . Assume homogeneity of degree 1 in income and holdings. Define: θ A „ « t GDP t ≡ ν ( θ A v GDP t ; ξ t t , GDP t ; ξ t ) . and assume and v ′ ( · ) > 0, v ′′ ( · ) < 0, and v ′ ( · ) → 0 for large holdings. Work out spreads between corporate bonds and Treasuries (short, long). Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Treasury (zero-coupon, any maturity): " # − P T P T + P T t t + 1 Q t v ′ ( θ A t Q t u ′ ( C t ) + β E t u ′ ( C t + 1 ) t / GDP t , ξ t ) u ′ ( C t ) = 0 Q t + 1 Q t is price level at date t. Buy zero coupon Treasury bond for a nominal price P T t . Real P T P T holdings θ A Q t v ′ ( θ A t rises by Q t , which gives convenience t t t / GDP t , ξ t ) u ′ ( C t ) . E t [ M t + 1 P T t + 1 ] t / GDP t ; ξ t ) ≈ e v ′ ( θ A P T t / GDP t ; ξ t ) E t [ M t + 1 P T t = t + 1 ] 1 − v ′ ( θ A where M t + 1 = β u ′ ( C t + 1 ) Q t u ′ ( C t ) Q t + 1 Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Corporate bond (zero-coupon, one-period): ] ≈ e − λ t L t + 1 − cov t [ M t + 1 , ˜ “ ” P C 1 − ˜ L t + 1 ] / E t [ M t + 1 ] E t [ M t + 1 ] t = E t [ M t + 1 L t + 1 where ˜ L t + 1 = 0 if no default, ˜ L t + 1 = L t + 1 if default, and L t + 1 is loss given default and default happens with probability λ t . Corporate bond (zero-coupon, any maturity): P C t = λ t E t [ M t + 1 ( 1 − L t + 1 ) | Default ] + ( 1 − λ t ) E t [ M t + 1 P C t + 1 | No Default ] Simplify using Duffie-Singleton (1997) formulation: Default over next period is uncorrelated with M (but changes in expectations about future default, i.e. downgrades, can be correlated with M). Payoff if default is fraction 1 − D t of market value if no default: E t [ M t + 1 ( 1 − L t + 1 )] = E t [ M t + 1 P C t + 1 ]( 1 − D t ) Then P C λ t E t [ M t + 1 ( 1 − L t + 1 )] + ( 1 − λ t ) E t [ M t + 1 P C = t + 1 ] t t + 1 ] ≈ e − λ t D t E t [ M t + 1 P C ( λ t ( 1 − D t ) + ( 1 − λ t )) E t [ M t + 1 P C = t + 1 ] . Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Prediction 1-3: Impact of Treasury supply on spreads, expected returns One-period spread: S t , 1 = i C t , 1 − i T t , 1 = − ln P C t + ln P T 1 t θ A „ « + λ t L t + 1 + cov t [ M t + 1 , ˜ t S t , 1 = v ′ GDP t ; ξ t L t + 1 ] / E t [ M t + 1 ] . θ A „ « S t , 1 = v ′ t ; ξ t + λ t D t GDP t τ -period spread: 2 t ,τ = − 1 t + 1 i C t ,τ − i T τ ln P C τ ln P T S t ,τ = t t + τ − 1 t + τ − 1 t + τ − 1 1 1 1 X τ E t [ v ′ ( θ A j / GDP j ; ξ L X X τ cov t ( m j + 1 , ˜ = j )] + τ E t [ λ j D j ] − R j + 1 ) j = t j = t j = t Expected excess returns: 3 E t [ M t + 1 ˜ R t + 1 ] = v ′ ( θ A t / GDP t ; ξ t ) 1 “ ” E t [˜ v ′ ( θ A t / GDP t ; ξ t ) − cov t ( M t + 1 , ˜ R t + 1 ] = R t + 1 ) . E t [ M t + 1 ] (Realized excess return involves updates to expectations about future v’s, future default, and future covariances – lots of noise.) Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Testing predictions 1, 2, 3 Test whether increases in θ T t cause the spreads to fall and predicts lower excess returns. Regression coefficients are net of private-sector response – this is the most interesting outcome ◮ But finding our hypothesized negative relation requires that θ A t = θ T t + k P θ P t increases in θ T t . ◮ Private sector reaction should not offset more than one-for-one. Extremely unlikely, and we can also check for this using quantities. Our regressions assume that θ T t does not respond to the spread ◮ If anything government probably expands Treasury supply if spreads rise, making it harder to find our hypothesized negative relation. Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011

Estimation of yield regressions Spread t = a + b 1 ln Debt t / GDP t + b 2 controls t + error t Log functional form: Only one parameter to estimate, but does not asymptote to zero. Different functional form later. Both left and right-hand side persistent. We run OLS, modeling error as AR(1) (based on Box-Jenkins analysis) Why not GLS? Convenience yield term is E t [ P v ′ ( θ A t )] , proxied by ln Debt t / GDP t . Measurement error magnified by GLS Controls for expected default: EDF , stock market volatility Control for time-varying risk premium ( cov t ): Slope of yield curve (state of business cycle) Krishnamurthy, Vissing-Jorgensen (Northwestern ) The Aggregate Demand for Treasury Debt November 2011