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Foreign official holdings of US treasuries, stock effect and the economy: a DSGE approach

  • John Nana Francois EMAIL logo
Published/Copyright: September 20, 2018

Abstract

This paper examines the effects of shocks to foreign official holdings of long-term U.S. Treasuries (FOHL) on macroeconomic aggregates using a dynamic general equilibrium model. The model treats short- and long-term bonds as imperfect substitutes through endogenous portfolio adjustment frictions. This provides a channel for changes in relative supply of assests to influence asset prices. Three key findings emerge: (1) positive shocks to FOHL impact the long-term interest rate and the term spread negatively through a stock effect channel – defined as persistent changes in interest rates as a result of movement along the Treasury demand curve. This result is consistent with findings in the empirical literature. (2) Through a feedback mechanism from an endogenous term structure in the model, the decline in the long-term interest rate induces an expansion in economic activity which leads to an increase in consumption, output and inflation. Both the stock effect and the feedback mechanism are generated by the portfolio frictions. (3) Higher degrees of persistence of FOHL shocks or imperfect asset substitution generate a prolonged negative stock effect following shocks to FOHL. This causes a longer delay of the term spread to return to its steady state after it falls; hence, inducing an extended and stronger stimulative feedback effect from the endogenous term structure into the modeled economy.  These findings help explain macroeconomic events such as the so-called ``Greenspan conundrum'' of the mid 2000s.

JEL Classification: E43; E52; E58; F21; G12

Acknowledgements

I want to thank the two anonymous referees and the editor for comments that have significantly improved the paper. I am grateful to Matteo Falagiarda for making his codes available for replication and for his technical assistance. I also want to thank Shu Wu, Alexander Richter, Lee Smith, Ted Juhl, John Keating, Brent Bundick, Chen Sun and Soumya Bhadury for useful comments and conversations. The paper has also benefited from presentations at the 2015 Southern Economic Meeting at New Orleans and the 26th Annual Meeting of the Midwest Econometrics Group at the University of Illinois at Urbana-Champaign. All errors are hereby mine.

Appendix A

The steady-state and implied parameters

Steady state values of the economic variables in the model are defined such that for any time period t, Xt=Xt+1=X. Hence, at steady state, the variable Xt is time invariant, so the time subscripts are dropped. Below are the equations defining steady state values of the economic variables that have closed form solutions.

FOC consumption:

(32)λ=(CθC)γ(1βθ)

FOC short term bond:

(33)R=πβ

FOC long term bond

(34)RL=πRβ

FOC labor

(35)χ=λwNφ

Velocity of money definition:

(36)m=Cvel.

FOC labor:

(37)ϑ=λ(11R)mη

Firm pricing:

(38)Ψ=ε1ε

Constant technology:

(39)A=YN

Marginal cost:

(40)w=AΨ

Government budget constraint:

(41)T=bπ+bLRLπ+G+mπmbRbRL

Appendix B

Full log-linearized model

The dynamic economic problem presented in the paper takes on a system of nonlinear difference equations. Since there are no closed form solutions, I employ a first order Taylor expansion to approximate the nonlinear model around the neighborhood of its steady state and solve it numerically. Particularly, for a smooth arbitrary function h(xt), the function is approximated linearly as:

h(xt)=h(x)+h(x)(xtx)

Below is the full log linearized model:

FOC consumption:

(42)(βθγ(Cc~t+1θCc~t)γ(Cc~tθCc~t1))(CθC)γ1=λλ~t

FOC real money balances:

(43)m~t=1η(ππβλ~tβπβEt(λ~t+1π~t+1))

FOC labor:

(44)w~t=φn~tλ~t

FOC short-term bond:

(45)Etβπ(λ~t+1π~t+1)=λ~tRR~tRκLϕLRL(b~thb~L,th)

FOC long-term bond:

(46)EtβπR(λ~t+1π~t+1R~t+1)=λ~tRLR~L,tRLϕLRL(b~thb~L,th)

Household budget constraint:

(47)bhRb~thbhRR~t+bLhRLb~L,thbLhRLR~L,t+mm~t=bhπb~t1hbhππ~t+bLhπRb~L,t1hbLhπRR~tbLhπRπ~t+mπm~t1mππ~t+Yy~tCc~t

Production technology:

(48)y~t=n~t

Supply of long-term bonds available to households:

(49)bLHb~L,tH=bLb~L,tbLFb~L,tF

Government budget constraint

(50)bR(b~tR~t)+bLRL(b~L,tR~L,t)+mm~t=bπ(b~t1π~t)+bLπ(b~L,t1π~tR~t)+mπ(m~t1π~t)+Gg~tTt~t

Monetary policy rule:

(51)R~=ρRR~t1+(1ρR)ρππ~t+(1ρR)ρYy~t+εtr

Tax rule:

(52)T~tT=ζ1bπ(b~t1π~)+ζ1bLRπ~(b~L,t1π~tR~t)

Firm pricing:

(53)π~t=Etβπ~t+1+ε1ψΨ~t

Marginal cost:

(54)Ψ~t=w~t

AR(1) process for FOHL:

(55)b~L,tF=ρFb~t1F+εtF

AR(1) process for long-term bond supply:

(56)b~L,t=ρbLb~L,t1+εtl

AR(1) process for government spending:

(57)g~t=ϕGg~t1+εtg

Appendix C

Fit of the model

In order to assess the goodness of fit of the model, I compare the theoretical moments implied by model with the second moments computed from data. As shown in Table 6, for the macroeconomic variables, the model generally under-predicts the standard deviation of output and consumption but does a good job in matching the the standard deviation of inflation. Moreover, although the model slightly over-predicts the standard deviation of short- and long-term interest rates, it does a decent job in capturing the the fact that short-term interest rates are generally more volatile than longer-term rates. Finally, as can be seen from the table, as the the degree of imperfect asset substitution decreases, the model tends to under-predict the standard deviation of the term spread. This suggests that imperfect asset substitution within the bond market can explain some of the unaccounted volatility in the term spread.

Table 6:

Moment comparison.

Std. Dev. of variableDataBaseline ModelModel withModel with
(ϕL = 0.01)(ϕL = 0.005)(ϕL = 0.015)
Macro-variables
 Output0.450.360.310.42
 Consumption0.670.270.230.34
 Inflation0.150.160.120.27
Financial variables
 Short-term interest rate0.290.320.250.41
 Long-term interest rate0.120.140.190.18
 Term-Spread0.290.180.100.27
  1. The table compares empirical moments from data and theoretical moments implied by the model. The data is treated similar to the variable in the model and it is filtered using the Hodrick-Prescott filter with a smoothing parameter of λ = 1600. All values are in percentages. Theoretical moments from sensitivity ananlyses on the FOHL persistence parameter (ρF) shows similar results.

Appendix D

Robustness, long-term bonds as consoles á la Woodford (2001)

To capture the full maturity of long-term bonds in the model, I follow the formulation in Woodford (2001) and consider long-term bonds with coupon equal to δs paid at time t + 1 + s, for s ≥ 0. In this way, the price of a long-term bond in the model is given by:

(58)QL,t=1RLδ,

with the duration of long-term bond given as RL,tRL,tδ. δ is therefore set to match the average duration of the 10-year Treasury Bill in the baseline simulation.

With this formulation of long-term bonds, the baseline model is updated as follows.

Modified household budget constraint:

(59)QtBtPt+QL,tBL,tHPt(1+ρt)+MtPt+TtBt1Pt+(1+δQL,t)Bt1HPt+WtPtNtCt+DtPt

Modified government budget constraint:

(60)QtBtPt+QL,tBL,tPt+MtPt+Tt=Bt1Pt+(1+δQL,t)BL,tPt+Gt+Mt1Pt

Modified tax rule:

(61)Tt=T(QL,t1BL,t1Pt1)ρτ

where  ρτ ∈ (0,1), Qt = 1/Rt with Rt being the short-term interest rate. QL,t is the current price of long-term bonds. The updated FOCs are:

Short-term bonds:

(62)βEtλt+1λtπt+1=Qt+QL,tϕLκL(κLBtBL,t1)Yt

Long-term bonds:

(63)βEtλt+1λtπt+1(1+δQL,t+1)=QL,t+QL,tϕL2κL(κLBtBL,t1)2YtQL,tϕLκL(BtBL,tH)(κLBtBL,t1)Yt

The linearized version of the modified model for simulation are as follows:

Short-term bonds:

(64)βπ(λ~t+1)=Q(λ~t+Q~t)+ϕLQLκL(b~tb~L,t)

Long-term bonds:

(65)Q~L,t=(λ~t+1λ~tπ~t+1)+δβπQ~L,t+ϕL(b~tb~L,t)

The price of a long-term bonds:

(66)Q~L,t=RLRLδR~L,t

The price of a short-term bonds:

(67)Q~t=R~t

Tax Policy:

(68)T~t=ρτ(b~L,t1+Q~L,t1)

Government Budget constraint:

(69)Q(b~t+Q~t)+QLbLb(b~L,t+Q~L,t)+mbm~t+TbT~t=b~t1π+bLbπ(1+δQL)b~L,t1π~tπbLbππ~t+δQLbLbπ(Q~L,tπ~t)+Gbg~t+mbπ(m~t1π~t)

References

Altig, D., L. J. Christiano, M. Eichenbaum, and J. Linde. 2011. “Firm-Specific Capital, Nominal Rigidities and the Business Cycle.” Review of Economic Dynamics 14: 225–247.10.1016/j.red.2010.01.001Search in Google Scholar

Andrés, J., J. D. Loṕez-Salido, and E. Nelson. 2004. “Tobin’s Imperfect Asset Substitution in Optimizing General Equilibrium.” Journal of Money, Credit, and Banking 36: 655–690.10.20955/wp.2004.003Search in Google Scholar

Beltran, D. O., M. Kretchmer, J. Marquez, and C. P. Thomas. 2013. “Foreign Holdings of US Treasuries and US Treasury Yields.” Journal of International Money and Finance 32: 1120–1143.10.1016/j.jimonfin.2012.09.005Search in Google Scholar

Bernanke, B., V. Reinhart, and B. Sack. 2004. “Monetary Policy Alternatives at the Zero Bound: An Empirical Assessment.” Brookings Papers on Economic Activity 2004: 1–100.10.1353/eca.2005.0002Search in Google Scholar

Bernanke, B. S. 2005. The Global Saving Glut and the US Current Account Deficit, Remarks by Governor Ben s. Bernanke at the Homer Jones Lecture, St. Louis, Missouri, April 14.Search in Google Scholar

Bertaut, C., L. P. DeMarco, S. Kamin, and R. Tryon. 2012. “Abs Inflows to the United States and the Global Financial Crisis.” Journal of International Economics 88: 219–234.10.1016/j.jinteco.2012.04.001Search in Google Scholar

Bertaut, C. C., and R. W. Tyron. 2007. Monthly Estimates of U.S. Cross-Boarder Securities Positions, International Finance Discussion Papers 910, Board of Governors of the Federal Reserve System.10.17016/IFDP.2007.910Search in Google Scholar

Borio, C. E., G. Galati, and A. Heath. 2008. FX Reserve Management: Trends and Challenges, BIS Papers 40, Bank for International Settlements.Search in Google Scholar

Chari, V. V., P. J. Kehoe, and E. R. McGrattan. 2000. “Sticky Price Models of the Business Cycle: Can the Contract Multiplier Solve the Persistence Problem?” Econometrica 68: 1151–1179.10.1111/1468-0262.00154Search in Google Scholar

Chen, H., V. Cúrdia, and A. Ferrero. 2012. “The Macroeconomic Effects of Large-Scale Asset Purchase Programmes.” The Economic Journal 564: F289–F315.10.1111/j.1468-0297.2012.02549.xSearch in Google Scholar

D’Amico, S., and T. B. King. 2013. “Flow and Stock Effects of Large-Scale Treasury Purchases: Evidence on the Importance of Local Supply.” Journal of Financial Economics 108: 425–448.10.1016/j.jfineco.2012.11.007Search in Google Scholar

Davig, T., and E. M. Leeper. 2007. “Fluctuating macro policies and the fiscal theory.” In NBER Macroeconomics Annual 2006, edited by Daron Acemoglu, Kenneth Rogoff, and Michael Woodford, Vol. 21, 247–316. Cambridge, Massachusetts: MIT Press.10.1086/ma.21.25554956Search in Google Scholar

Falagiarda, M. 2014. “Evaluating Quantitative Easing: a Dsge Approach.” International Journal of Monetary Economics and Finance 7: 302–327.10.1504/IJMEF.2014.067724Search in Google Scholar

Falagiarda, M., and M. Marzo. 2012. A DSGE model with Endogenous Term Structure, Working Papers wp830, Dipartimento Scienze Economiche, Universita’ di Bologna.10.2139/ssrn.2078094Search in Google Scholar

Favilukis, J., D. Kohn, S. C. Ludvigson, and S. Van Nieuwerburgh. 2012. “International Capital Flows and House Prices: Theory and Evidence.” In Housing and the Financial Crisis, edited by Edward L. Glaeser, and Todd Sinai, 235–299. Chicago: University of Chicago Press.10.3386/w17751Search in Google Scholar

Favilukis, J., S. C. Ludvigson, and S. Van Nieuwerburgh. 2014. Foreign Ownership of US Safe Assets: Good Or Bad? Tech. rep., National Bureau of Economic Research.10.3386/w19917Search in Google Scholar

Fuhrer, J. C. 2000. “Habit Formation in Consumption and its Implications for Monetary-Policy Models.” American Economic Review 90: 367– 390.10.1257/aer.90.3.367Search in Google Scholar

Gertler, M., and P. Karadi. 2011. “A Model of Unconventional Monetary Policy.” Journal of Monetary Economics 58: 17–34.10.1016/j.jmoneco.2010.10.004Search in Google Scholar

Greenwood, R., S. G. Hanson, J. S. Rudolph, and L. H. Summers. 2015. “The Optimal Maturity of Government Debt,” In The $13 Trillion Question: Managing the US Government’s Debt, edited by David Wessel, Vol. 1, 1–41. Washington, D.C: Brookings Institution Press.10.5771/9780815727071-1Search in Google Scholar

Harrison, R. 2011. “Asset Purchase Policies and Portfolio Balance Effects: a DSGE Analysis.” In Interest Rates, Prices and Liquidity: Lessons from the Financial Crisis, edited by Jagjit S. Chadha, and Sean Holly, 117–143. Cambridge: Cambridge University Press.10.1017/CBO9781139044233.005Search in Google Scholar

Harrison, R. 2012. Asset Purchase Policy at the Effective Lower Bound for Interest Rates, Bank of England working papers 444, Bank of England.10.2139/ssrn.1992980Search in Google Scholar

Ireland, P. N. 2004. “Technology Shocks in the New Keynesian Model.” The Review of Economics and Statistics 86: 923–936.10.1162/0034653043125158Search in Google Scholar

Jones, C., and M. Kulish. 2013. “Long-Term Interest Rates, Risk Premia and Unconventional Monetary Policy.” Journal of Economic Dynamics and Control 37: 2547–2561.10.1016/j.jedc.2013.07.004Search in Google Scholar

Joyce, M., D. Miles, A. Scott, and D. Vayanos. 2012. “Quantitative Easing and Unconventional Monetary Policy–an Introduction.” The Economic Journal 122: F271–F288.10.1111/j.1468-0297.2012.02551.xSearch in Google Scholar

Kaminska, I., and G. Zinna. 2014. Official Demand for US Debt: Implications for US Real Interest Rates, 14-66, International Monetary Fund.10.5089/9781475590081.001Search in Google Scholar

Kim, J. 2000. “Constructing and Estimating a Realistic Optimizing Model of Monetary Policy.” Journal of Monetary Economics 45: 329–359.10.1016/S0304-3932(99)00054-9Search in Google Scholar

Kohn, D. 2015. Addicted to Debt: Foreign Purchases of US Treasuries and the Term-Premium. Tech. rep., Universidad Torcuato Di Tella.10.2139/ssrn.2630695Search in Google Scholar

Krishnamurthy, A., and A. Vissing-Jorgensen. 2012. “The Aggregate Demand for Treasury Debt.” Journal of Political Economy 120: 233–267.10.1086/666526Search in Google Scholar

Leeper, E. 1991. “Equilibria Under’Active’and’Passive’Monetary and Fiscal Policies.” Journal of Monetary Economics 27: 129–147.10.1016/0304-3932(91)90007-BSearch in Google Scholar

Leeper, E. M., N. Traum, and T. B. Walker. 2017. “Clearing up the Fiscal Multiplier Morass.” American Economic Review 107: 2409–2454.10.1257/aer.20111196Search in Google Scholar

Ljungqvist, L., and T. J. Sargent. 2004. Recursive Macroeconomic Theory, Vol. 1, 2nd ed. Cambridge: The MIT Press.Search in Google Scholar

Lucas, R. E. 1988. “Money Demand in the United States: A Quantitative Review.” Carnegie-Rochester Conference Series on Public Policy 29: 137– 167.10.1016/0167-2231(88)90009-7Search in Google Scholar

Mankiw, N. G., and L. H. Summers. 1986. “Money Demand and the Effects of Fiscal Policies.” Journal of Money, Credit and Banking 18: 415–429.10.2307/1992462Search in Google Scholar

Marzo, M., U. Söderström, and P. Zagaglia. 2008. The Term Structure of Interest Rates and the Monetary Transmission Mechanism. Manuscript, Sveriges Riksbank.Search in Google Scholar

Morrison, W. M., and M. Labonte. 2011. China's Holdings of U.S. Securities: Implications for the U.S. Economy. Washington, DC: Congressional Research Service.Search in Google Scholar

Papaioannou, E., R. Portes, and G. Siourounis. 2006. “Optimal Currency Shares in International Reserves: the Impact of the Euro and the Prospects for the Dollar.” Journal of the Japanese and International Economies, 20: 508–547.10.1016/j.jjie.2006.07.002Search in Google Scholar

Rotemberg, J. J. 1982. “Monopolistic Price Adjustment and Aggregate Output.” Review of Economic Studies 49: 517–531.10.2307/2297284Search in Google Scholar

Rudebusch, G., E. Swanson, and T. Wu. 2006. “The Bond Yield “Conundrum” from a Macro-Finance Perspective.” Monetary and Economic Studies 24: 83–109.10.2139/ssrn.1003033Search in Google Scholar

Schmitt-Grohé, S., and M. Uribe. 2004. “Optimal Fiscal and Monetary Policy Under Imperfect Competition.” Journal of Macroeconomics 26: 183–209.10.1016/j.jmacro.2003.11.002Search in Google Scholar

Sierra, J. 2014. “International Capital Flows and Bond Risk Premia.” The Quarterly Journal of Finance 4: 1450001.10.1142/S2010139214500013Search in Google Scholar

Sims, C. A., and T. Zha. 1999. “Error Bands for Impulse Responses.” Econometrica 67: 1113–1155.10.1111/1468-0262.00071Search in Google Scholar

Swanson, E. T. 2011. “Let’s Twist Again: a High-Frequency Event-Study Analysis of Operation Twist and its Implications for qe2.” Brookings Papers on Economic Activity 2011: 151–188.10.1353/eca.2011.0006Search in Google Scholar

Taylor, J. B. 1993. “Discretion Versus Policy Rules in Practice.” Carnegie-Rochester Conference Series on Public Policy 39: 195–214.10.1016/0167-2231(93)90009-LSearch in Google Scholar

Tobin, J. 1969. “A General Equilibrium Approach to Monetary Theory.” Journal of Money, Credit and Banking 1: 15–29.10.2307/1991374Search in Google Scholar

Tobin, J. 1982. “Money and Finance in the Macroeconomic Process.” Journal of Money, Credit and Banking 14: 171–204.10.2307/1991638Search in Google Scholar

Warnock, F. E., and V. C. Warnock. 2009. “International Capital Flows and US Interest Rates.” Journal of International Money and Finance 28: 903–919.10.1016/j.jimonfin.2009.03.002Search in Google Scholar

Wolcott, E. L. 2016. “Impact of Foreign Official Purchases of US Treasuries on the Yield Curve.Search in Google Scholar

Woodford, M. 2001. “Fiscal Requirements for Price Stability.” Journal of Money, Credit, & Banking 33: 669.10.3386/w8072Search in Google Scholar

Zagaglia, P. 2013. “Forecasting Long-Term Interest Rates with a General-Equilibrium Model of the Euro Area: What Role for Liquidity Services of Bonds?” Asia-Pacific Financial Markets 20: 383–430.10.1007/s10690-013-9172-5Search in Google Scholar

Zellner, A. 1962. “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias.” Journal of the American Statistical Association 57: 348–368.10.1080/01621459.1962.10480664Search in Google Scholar

Published Online: 2018-09-20

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