Rediscovering old economic models

The point of all this is that models don’t have to model everything, and even “wrong” models can be helpful if used in the right way. And narrative has its uses too.

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By Frances Coppola

Krugman says we do not need new economic models, we just need to make better use of the ones we already have. Indeed, even very old models that we long since consigned to dusty archives can help remind us of things we have forgotten about. Financial crises, for example…..

In his response to my speech at Manchester University in February – which became the post that whipped up the “state of macro” debate to which Krugman responded – Andrew Lilico gave four examples of economic models that in his view form the foundation of modern economics and (he claims) have not been shown to be inadequate or wrong. Lilico’s four models are these:

Capital Asset Pricing Model
Modigliani-Miller Theorem
Efficient Market Hypothesis
Black-Scholes Option Pricing Model

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Hmm.Only the EMH would I think be regarded as a macroeconomic model – and even then, is it really more fundamental than Shiller’s irrational exuberance? When I was doing my MBA, we covered the other three in corporate finance, not macroeconomics. And all four have been seriously criticised.

But finance is the heart of a modern monetary economy and financial economics should be part of macroeconomics. I might disagree with Lilico’s choice of models – for example I would regard the quantity theory of money as more fundamental than Black-Scholes – but I don’t disagree with his point. The problem is that models of the financial economy DON’T form the heart of macroeconomics.

So, since Krugman pointed me towards Diamond & Dybvig’s model of banks, liquidity and deposit insurance, I got it out and re-read it.

For those of us used to endogenous money theory, there is an immediate and very obvious problem with Diamond & Dybvig’s model. It is a loanable funds model with no central bank – which is odd, considering that by 1983 when it was written the world had been off the gold standard for more than ten years and every Western country had a central bank. But this is how banking is modelled all too often: banks as passive intermediaries channelling household savings to corporate borrowers. If only that were true. For the last decade or so the flow has been in the other direction – corporate savings channelled by banks to households in the form of mortgages against ever-rising property prices.

But the problem with loanable funds models is bigger than simple reversal of the savings flow. Loanable funds models are unable to explain how exuberance in credit creation results in the buildup of unsustainable leverage. Hyung Song Shin used a loanable funds model in his Mundell-Fleming lecture on the role of regulatory arbitrage in the credit boom leading to the financial crisis, which unfortunately managed to give the impression that the money lent to American and European banks by American households came from Mars. When I translated Shin’s model into an endogenous money framework (though admittedly in a manner that was enormous fun and not at all rigorous) it became a dangerously unstable two-way leveraging spiral of credit creation and rising collateral prices, which is much closer to what we know actually happened. Loanable funds models do not adequately portray the role of credit creators in the modern monetary economy – banks, and things that aren’t called banks but behave like them.

So Diamond & Dybvig’s model needs to be used with some care. It can’t simply be “taken off the shelf” and deployed in a crisis, as Krugman suggests. Apart from anything else, providing unfunded deposit insurance ex ante to everything that looks or behaves like a credit creator, regulated or not, creates moral hazard on an almost galactic scale. We already worry about implicit taxpayer subsidies to too-big-to-fail banks: but explicit taxpayer guarantees to too-big-to-fail asset managers, wealth funds, conduits, SPVs? Really, Paul?

Diamond & Dybvig’s model is a multiple-equilibrium model, but it does not adequately model how leverage is created. It might be amusing to translate it into endogenous money terms, adding a central bank and establishing both the precedence of lending and the creation of deposits. This would of course make it a lot more complex, since endogenous money creation is by definition non-linear. It might make it a lot more fun, too. But does that mean it would necessarily be less rigorous, as Krugman seems to suggest? Surely not. “Fun” does not exclude rigour.  So, here is a challenge to a student econometrician who fancies a holiday project. Have some fun translating Diamond & Dybvig’s model into endogenous money terms. But do it rigorously.

A bank run can be defined as sudden unravelling of bank leverage. And just as leverage creates money, so deleveraging destroys money. This is implied in Diamond & Dybvig’s description of deposit insurance even though their model does not show it.

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It works like this. A bank faced with sudden unexpected demand for cash withdrawals by depositors or investors is forced to sell assets to obtain the cash. This depresses the price of the remaining assets, destroying value on the asset side of the balance sheet and making it impossible for the bank to realise enough cash to satisfy depositor demand.

I say banks, but it is actually easier to see the “fire sale” effect when there is a run on a money fund, such as the run on Reserve Primary after the fall of Lehman. Reserve Primary was unable to guarantee return of par value to its investors because the value of its assets crashed. A bank facing a similar crash of asset value is also unable to return par value to its depositors. But instead of “breaking the buck” as Reserve Primary did (i.e. returning less than par to its investors), in the absence of central bank liquidity support and/or deposit insurance, the bank must close its doors (in Diamond & Dybvig this is “suspension of convertibility”). If the bank’s balance sheet is very illiquid – for example, if it consists mainly of specialist loans for which there is no market – then doors will be closed earlier. Either way, the effect is the same. Deposit balances that cannot be withdrawn because the bank has closed its doors are effectively worthless.

Deposit insurance replaces the money destroyed in a run by drawing on future tax revenues (if unfunded) or drawing on money created by other banks ex post or ex ante. Central bank liquidity support does the same by drawing on future seigniorage. Without this, the economic effects of bank runs can be economically devastating. However, as Diamond & Dybvig point out, the essence of insurance is that it should not be called upon. The existence of credible deposit insurance and/or credible lender-of-last-resort support should be sufficient to prevent runs. In 2007, the run on Northern Rock occurred because deposit insurance was inadequate and it was not clear that lender-of-last-resort support would be forthcoming. In 2008, the most damaging runs occurred in the shadow banking network where there was no insurance or lender-of-last-support.

The fact that Diamond & Dybvig’s model is framed in loanable funds terms means that it does not fully show the destructive economic effects of bank runs. After all, in their model, the money still exists, it has simply been converted into a different form (cash) which is equally useful. And nowhere do they state that their single bank can call in illiquid loans to pay depositors. If it can’t, then investment is not suspended: the bank fails, but the borrowers still have their funds. Their assumption that production stops when money is removed from the bank is therefore questionable in terms of their own model, though it would be correct in a model that accurately modelled the destruction of money and the collapse of asset prices.

But this does not make the model useless. From the point of view of the depositors trying to remove their funds, whether those funds were created by the bank in the course of lending or came from Mars is irrelevant. What matters is whether depositors believe that they can convert their deposits to cash. And that, as Diamond & Dybvig note, depends on the depositors’ view of the creditworthiness of the bank. If depositors believe that the value of the bank’s assets is less than its liabilities, they will rush to withdraw their money: no-one will want to leave their money in the bank and risk not getting it back at all.

Deposit insurance in effect replaces the bank’s own deposit guarantee, which in Diamond & Dybvig’s “bad” equilibrium is not credible, with a guarantee from a more reliable source. In the past that has been the sovereign, though the public mood since Lehman has pushed regulators towards requiring the banking system as a whole to guarantee the deposits of each of its members and fund that guarantee at least in part ex ante. Those promoting full reserve banking might like to recall that bank funded guarantee schemes amount to full reserve banking for insured depositors. And those who think that deposit insurance schemes are about protecting depositors might like to think again. The original purpose of deposit insurance was to prevent banks failing.

Diamond & Dybvig explain that central bank liquidity support can have the same effect as deposit insurance, but with an important caveat: if depositors do not believe the bank is solvent then injections of central bank liquidity cannot stop the run. This is not just a theoretical effect. In 2007, injections of liquidity by the Bank of England failed to stop the run on Northern Rock. It took unlimited guarantees from HMG, including for wholesale deposits (which are more likely to run than retail deposits and can be far more destructive). This is the reason for Bagehot’s dictum about lending to SOLVENT banks, although for a very large bank mitigating the destructive economic effects may justify lending even if it is believed to be insolvent. And in a systemic crisis it can be hard to decide which bank is alive and which is dead anyway: throwing money at everything is usually the best approach until the panic calms down, as I have explained before.

The point of all this is that models don’t have to model everything, and even “wrong” models can be helpful if used in the right way. And narrative has its uses too. Diamond & Dybvig’s paper has some interesting insights into the behaviour of banks and their customers. I particularly like this:

If the technology is risky, the lender of last resort can no longer be as credible as deposit insurance. If the lender of last resort were always required to bail out banks with liquidity problems, there would be perverse incentives for banks to take on risk, even if bailouts occurred only when many banks fail together. For instance, if a bailout is anticipated, all banks have an incentive to take on interest rate risk by mismatching maturities of assets and liabilities, because banks will all be bailed out together.

Perverse incentives and moral hazard. This presumably is one of Krugman’s “self-fulfilling prophecies”. What a pity we forgot about it….

Then there is this:

Internationally, Eurodollar deposits tend to be uninsured and are therefore subject to runs, and this is true in the United States as well for deposits above the insured limit.

Uninsured deposits have a tendency to run. You don’t say. In the rush to limit taxpayer liability in a crisis and ensure that senior creditors – including large depositors – share in the losses, has everyone forgotten this?

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