The safe asset frontier

Abstract

We identify the frontier between safe and unsafe assets and show how the growth rate of the economy and its fiscal capacity interact with differences of opinion amongst investors to determine the safe asset equilibrium. Multiple equilibria emerge in our set-up due to strategic complementarities across counterparties, and the safety of the bond depends on the extent to which investors' opinions diverge from the credit rating of the asset.

Keywords:

• Safe assets
• international liquidity
• discrete choice

JEL Classifications:

• E44
• D81
• F02
• F41
• G15

Acknowledgments

We are grateful to our discussant Martin Uribe and seminar participants at the Bank of Canada, the University of Auckland, BI Norwegian Business School and the Reserve Bank of New Zealand for helpful comments and suggestions. All remaining errors are our own. The views expressed in this paper are those of the authors and do not necessarily represent those of the Deutsche Bundesbank or the Eurosystem.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 The Bank of England (2012) estimates that, in the event of a reappraisal of US Treasuries, some $850 million of additional collateral would be required for every 50 basis point increase in haircuts on US-backed collateral in bilateral OTC derivatives markets.

2 Accordingly, the future expected value of GDP is $\begin{array}{rl}{\mathbb{E}}_t[X_{t+k}]& =(1-\alpha )(1+g){\mathbb{E}}_t[X_{t+k-1}]+\alpha g{\mathbb{E}}_t[X_{t+k-1}]\\ & ={\mathbb{E}}_t[X_{t+k-1}](1+g-\alpha )\\ & =((1-\alpha )(1+g){\mathbb{E}}_t[X_{t+k-2}]+\alpha g{\mathbb{E}}_t[X_{t+k-2}])(1+g-\alpha )\\ & =\cdots =X_t(1+g-\alpha {)}^k.\end{array}$

3 To ensure dynamic efficiency, we tacitly assume the presence of an additional island i = N + 1, in which the agent born at t = 0 is endowed with a bond and lives forever. In the event of default in period t, this agent does not consume the dividend in period t, but consumes it instead at period t + 1.

4 While reduced form, our modeling of information acquisition captures a key feature from the recent literature on Bayesian updating and search models for information diffusion and percolation, e.g. Duffie, Giroux, and Manson (2010) and Livan and Marsili (2013). Specifically, when two agents meet and exchange information, the posterior belief held by both agents is the sum of their individually held beliefs. If, however, one of the agents has an uninformed prior, then a chance meeting with that agent does not alter the views held by the other agent. In this context, γ may be regarded as the probability agent j acquires information from an informed agent, while $1-\gamma$ is the probability that j is matched with an uninformed agent.

5 Formally, according to the de Moivre-Laplace theorem we have that $\underset{k\to \mathrm{\infty }}{lim}(\genfrac{}{}{0ex}{}{k}{\ell }){\overline{\pi }}^{\ell }(1-\overline{\pi }{)}^{k-\ell }\to \frac{1}{2\pi k\overline{\pi }(1-\overline{\pi })}{\mathrm{e}}^{-(\ell -k\overline{\pi }{)}^2/2k\overline{\pi }(1-\overline{\pi }).}\to \delta (\ell -k\overline{\pi }),$ where $\delta (x)$ is the Dirac-delta function.

6 By the same argument, starting from a high γ state, where all agents choose to monitor, following an incremental decrease in γ, all agents will continue to monitor. The probability must decrease all the way to the tipping point for the high r solution to emerge. If, however, a large enough fraction of agents start to doubt whether future generation agents will monitor, the high r solution may be regained earlier.

Additional information

Funding

We would like to acknowledge the financial support of the Centre for International Finance and Regulation (CIFR) [grant number E201].