Default and DSGE models

Charles Goodhart, Dimitri Tsomocos 26 November 2009

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Martin Shubik described money as an “institutionalised symbol of trust”, and Nobu Kiyotaki and John Moore coined a nice phrase, “Evil is the root of all money”. And they are correct in this. If everyone always repaid all their debts with certainty, then there would be no need for money, most financial instruments, nor intermediaries like banks. All that would be needed to complete a transaction would be a handshake and the acknowledgement that the buyer is indebted to the seller. Of course, the good that the seller would like to receive at some future date would not necessarily be what the buyer could offer, but that discrepancy could easily be resolved in complete financial markets.

This proposition already indicates one problem with the assumption that no one defaults, which is that it must imply, as a corollary, a complete set of financial markets. But, as is already well known, a complete set of financial markets not only does not exist but would allow for an Arrow/Debreu Walrasian general equilibrium in which all transactions could be established at time zero. That would prevent default arising as a result of future bad outcomes, since all such potential outcomes could be hedged in the complete financial markets.

Perhaps even more importantly, a no default assumption would require all agents to be completely and perfectly moral, in the sense that they never take advantage of an opportunity not to repay the debt that they owe. Thus, if you were to take a taxi, even though you would certainly never meet that taxi driver again, you would always pay him (oddly, it’s almost always a him). This latter assumption really stretches credulity too far. If the ordinary person could get out of repaying her due debt with impunity, then she would!

The shortcomings of standard DSGE models

Unfortunately, the standard dynamic stochastic general equilibrium (DSGE) macro models that are used everywhere actually incorporate this assumption of no default. It arises specifically as part of the transversality condition, but it also stems from the fact that there is no real trade and no bargaining in most DSGE models. This has two important implications. First, DSGE models are not properly micro-founded, in that their basic assumptions are totally at odds with human behaviour in this respect. Second, it means that there is no real role for money or banks in any DSGE model. There is no need for cash in advance if you can always be trusted to repay your debts in full, and liquidity plays no role whatsoever. And the idea of money in the utility function is just laughable. By the same token, there is no need for banks; nor do they generally exist in such DSGE models.

It follows that the standard DSGE model has been completely useless as a guide to the recent financial crisis, which has, of course, been characterised by default and sharply increasing risk premia driven by concerns about the rising probability of default. One way of trying to rescue such DSGE models has been to incorporate such enhanced risk premia, but this has usually been done as if such premia were entirely exogenous, whereas of course they arise from concern with default and, consequently, are determined in equilibrium. Including such risk premia in models without explaining their relationship with default represents a failure of basic analysis and theory. Put differently, liquidity and default are endogenous variables, and it is an oxymoron to conduct analysis when we are treating them as exogenous!

Incorporating default into the DSGE framework

In our view, the essential way forward from this unfortunate state of affairs is to include the potential for default in our macro models. This would also have the side-benefit of restoring a union between macro theory and finance, since the probability of default is a prime element within finance. While we in finance are not wedded to DSGE models (and tend to prefer the rational inattention theory to rational expectations), such DSGE models represent a useful discipline and framework and are also the workhorse of most macro modelling. So, our priority in our current research exercise is to see how far we can embed an analytical approach to default within an otherwise standard DSGE model. Doing so has the great advantage that it provides a rationale for the use of money. If you think that the buyer of your product may not meet his resultant debt, you will ask him to pay on the nail, i.e. it provides a rationale for the cash in advance requirement. Similarly, the main role for banks is to be able to assess probabilities of default better than you or I. So we need them in order to be able to reduce risk premia and lower the spread between bid and ask rates. Thus banks become an essential element of any model incorporating default.

Nevertheless, incorporating default into a DSGE model makes the analytical exercise significantly more complex. In particular, one can no longer use the representative agent model, because only a (small) proportion of agents default at any time. The inclusion of heterogeneous agents, banks, and default greatly increases the scale of parameterisation and the dimension of such models. Nevertheless, such an extended model would at least be micro-founded, whereas current DSGE models are not. Moreover, it would have the benefit of having a proper foundation for the inclusion of money and financial intermediaries within the system. Of course, during normal times when default is low and constant, one can ignore money and banks as an inessential veil; but that would not help under those circumstances when default probability becomes prominent.

We have constructed (with Carolina Osorio) a first shot at a DSGE model with default as a key feature. We can show how the working of the system changes, first just to take account of heterogeneous agents, and then to take account of the existence of potential default. Heterogeneous agents affect outcomes because of much more extensive distributional effects. In many simulations, some agents gain and others lose, and that makes it much more difficult to assess the welfare implications of various economic developments. When we incorporate the effect of default on our system, it has significant effects on how the economy responds to various stimuli, with some notable differences from the results of models, especially in the short and medium term, in which default is assumed away, e.g. by the transversality condition. Moreover, default enables the proper assessment of the importance of collateral and the emergence of leverage cycles. Finally, incomplete financial markets allow for an active role for policy.

Of course, such a model is quite complex and cannot be reduced to the three-equation-reduced form guise in which most DSGE models are now presented. Moreover, we do realise that the addition of a credit risk premium into the output equation enables the three-equation-reduced form to remain in disturbed times. However, such a stratagem completely undermines the assertion that such a model has proper theoretical micro-foundations. If one wants to understand what has been happening to our economies over the last few years, we do not think that there is any alternative to a modelling strategy in which both default and money are essential attributes of the working of the macro-economy. Such a new paradigm would offer an integrated framework to address both monetary and regulatory policy.

References

Goodhart, C. A.E., C. Osorio, and D.P. Tsomocos (2009), “Analysis of Monetary Policy and Financial Stability: A New Paradigm”, University of Oxford mimeo, October.

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Topics:  Frontiers of economic research

Tags:  default, DSGE, transversality condition

Emeritus Professor in the Financial Markets Group, London School of Economics

Professor of Financial Economics and Fellow, Said Business School and St. Edmund Hall, University of Oxford

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