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.
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,
FOC consumption:
FOC short term bond:
FOC long term bond
FOC labor
Velocity of money definition:
FOC labor:
Firm pricing:
Constant technology:
Marginal cost:
Government budget constraint:
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:
Below is the full log linearized model:
FOC consumption:
FOC real money balances:
FOC labor:
FOC short-term bond:
FOC long-term bond:
Household budget constraint:
Production technology:
Supply of long-term bonds available to households:
Government budget constraint
Monetary policy rule:
Tax rule:
Firm pricing:
Marginal cost:
AR(1) process for FOHL:
AR(1) process for long-term bond supply:
AR(1) process for government spending:
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.
Moment comparison.
| Std. Dev. of variable | Data | Baseline Model | Model with | Model with |
|---|---|---|---|---|
| (ϕL = 0.01) | (ϕL = 0.005) | (ϕL = 0.015) | ||
| Macro-variables | ||||
| Output | 0.45 | 0.36 | 0.31 | 0.42 |
| Consumption | 0.67 | 0.27 | 0.23 | 0.34 |
| Inflation | 0.15 | 0.16 | 0.12 | 0.27 |
| Financial variables | ||||
| Short-term interest rate | 0.29 | 0.32 | 0.25 | 0.41 |
| Long-term interest rate | 0.12 | 0.14 | 0.19 | 0.18 |
| Term-Spread | 0.29 | 0.18 | 0.10 | 0.27 |
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:
with the duration of long-term bond given as
With this formulation of long-term bonds, the baseline model is updated as follows.
Modified household budget constraint:
Modified government budget constraint:
Modified tax rule:
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:
Long-term bonds:
The linearized version of the modified model for simulation are as follows:
Short-term bonds:
Long-term bonds:
The price of a long-term bonds:
The price of a short-term bonds:
Tax Policy:
Government Budget constraint:
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- An empirical study on the New Keynesian wage Phillips curve: Japan and the US
- Risk averse banks and excess reserve fluctuations
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Articles in the same Issue
- Contributions
- An empirical study on the New Keynesian wage Phillips curve: Japan and the US
- Risk averse banks and excess reserve fluctuations
- Advances
- Signaling in monetary policy near the zero lower bound
- Contributions
- Robust learning in the foreign exchange market
- Foreign official holdings of US treasuries, stock effect and the economy: a DSGE approach
- Discretion rather than rules? Outdated optimal commitment plans versus discretionary policymaking
- Agency costs and the monetary transmission mechanism
- Advances
- Optimal monetary policy in a model of vertical production and trade with reference currency
- The financial accelerator and marketable debt: the prolongation channel
- The welfare cost of inflation with banking time
- Prospect Theory and sentiment-driven fluctuations
- Contributions
- Household borrowing constraints and monetary policy in emerging economies
- The macroeconomic impact of shocks to bank capital buffers in the Euro Area
- The effects of monetary policy on input inventories
- The welfare effects of infrastructure investment in a heterogeneous agents economy
- Advances
- Collateral and development
- Contributions
- Financial deepening in a two-sector endogenous growth model with productivity heterogeneity
- Is unemployment on steroids in advanced economies?
- Monitoring and coordination for essentiality of money
- Dynamics of female labor force participation and welfare with multiple social reference groups
- Advances
- Technology and the two margins of labor adjustment: a New Keynesian perspective
- Contributions
- Changing demand for general skills, technological uncertainty, and economic growth
- Job competition, human capital, and the lock-in effect: can unemployment insurance efficiently allocate human capital
- Fiscal policy and the output costs of sovereign default
- Animal spirits in an open economy: an interaction-based approach to the business cycle
- Ramsey income taxation in a small open economy with trade in capital goods