Fire Sales and Debt Maturity

**Abstract:** How does debt maturity structure affect fire sales? By introducing debt maturity in a Fisherian deflation model, I demonstrate how it could trigger financial crises. Using a stock-flow analysis, I show that long-term debt could alleviate the risk of current binding collateral constraint, but an excessive reliance on long-term debt could generate future binding collateral constraints over long horizons. It is empirically confirmed by a study based on 121 developing countries over the period 1970-2012. I highlight that debt maturity structure is a good early-warning indicator of financial crises, which provides information that adds up to the level of external debt.

This paper aims to fill this gap by answering the following three questions: first, how do debt level and maturity structure predict financial crises? Figure 1 below analyze the relationship between these notions and the frequency of financial crises. At first glance, it suggests that both external debt stock and over the gross national income and debt maturity structure play a role in the likelihood of future financial crisis. Although there is no obvious relationship with the annual mean of debt maturity structure, the heterogeneous cases, particularly in the 1980s, raise policy concerns. Second, because the financial amplification mechanism *à la* Fisher (1933) is key to understand financial crises, how does debt maturity structure affect fire sales? Third, what is the optimal policy according to this stock-flow relationship?


This financial amplification mechanism appears when collateral constraint tightens. This collateral is based on the market value of assets that determines the borrowing ability of economic agents. When they are not able to repay their debt and/or they want to increase their consumption above this borrowing limit, they could sell their assets. Buf if many borrowers do the same, it may result in a well-known feedback loop between binding collateral constraints and a drop of asset prices and agent's wealth, as described by Bianchi and Mendoza (2018), among others. These labeled *Fisherian deflation* models use occasionally binding financial constraints with pecuniary externality, which means that decentralized agents do not internalize the effect of their decisions on asset markets. Therefore, there is a wedge between private and social marginal utilities of both asset and debt. As a conventional result, policy intervention via taxes and subsidies could fill the gap. Nevertheless, these recent theoretical foundations of Fisher (1933) *remain quite silent on debt maturity structure*.

By contrast, I highlight that a debt maturity structure essentially based on short-term debt is a good early-warning indicator of financial crises for the developing world over the period 1970-2012. This indicator has a higher predictive power than debt levels and complements the information obtained with proxies of global financial forces around the world. This empirical insight is then rationalized into a *Fisherian deflation* model in which domestic borrowers choose a mix of short and long-term debts. This debt maturity structure complexifies and potentially multiplies the risk of asset fire sales due to the binding collateral constraint. I find that the mix of these debts chosen by the agent follows a suboptimal path, which triggers fire sales. In addition, this path is not necessarily oriented towards short-term debt, because an excessive reliance on long-term debt generates future binding collateral constraints. It differs from the social planner's optimal path of debt, and more broadly from the social planner allocation including the capital assets.

The social planner can replicate its equilibrium via a set of taxes and subsidies, where all prices and term premium are still market-determined. Following Korinek and Davila (2018), the social planner implements taxes on debts and subsidies on capital but with two key differences. First, the taxes on debt are both macroprudential (i.e. *ex-ante*) and *ex-post* policies. Second, and perhaps more importantly, these taxes on debts are contingent to the debt maturity structure. When the stock of current short-term debt is relatively high compared to the collateral constraint, it yields a positive term premium for the long-term debt, which in turn reduces the need to impose high taxes on debts.

**Mechanism:** With only a *one-period* debt, the standard result holds. The decentralized agent is prone to overborrowing. He also under-invests in capital assets that makes the collateral constraint more vulnerable to asset fire sales. Given the debt maturity structure, the previous properties are still valid and the rational borrower chooses his path of debt, while the lender distinguishes these short from long-term bonds. Indeed, the concerns about liquidity and solvency risks are not the same. The lender here charges a term premium, since an excessive short-term debt causes liquidity troubles and exacerbates the risk of default with lower debt amortization process. This paper complements the findings of Jeanne and Korinek (2016) and Bianchi and Mendoza (2018), but differs in the intensity and the channel through which it generates fire sales.

Because of the pecuniary externality and their *unanticipated* shock on capital price, the level and the structure of debt of the decentralized agent could bind one or two collateral constraints. On the one hand, if there is too much short-term debt, the current collateral constraint becomes tight. As a consequence, asset fire sales occur and an *unanticipated* term premium appears, thus further reducing debt capacity. On the other hand, the choice of too much long-term debt alleviates the risk of current binding collateral constraint, but generates future binding collateral constraints over long horizons. When the borrower goes to the worst configuration with the two binding collateral constraints, it pays a term premium and suffers from multiple binding collateral constraints over time.


  1. Bianchi, J. and Mendoza, Enrique, G. (2018). Optimal Time-Consistent Macroprudential Policy. *Journal of Political Economy*, forthcoming.

  2. Fisher, I. (1933). The Debt-Deflation Theory of Great Depressions. *Econometrica: Journal of the Econometric Society*, 337–357.

  3. Jeanne, O. and Korinek, A. (2016). Macroprudential Regulation versus Mopping Up After the Crash.

  4. Korinek, A. and Dávila, E. (2018). Pecuniary Externalities in Economies with Financial Frictions. *Review of Economic Studies*, 85(1):352–395.