## Inspecting the Mechanism: Dealing with Sudden Stops, the Euro Periphery, the Exorbitant Privilege-Possessing Floating-Rate Sovereigns of the Global North, and the Debt

I found myself procrastinating this morning by trying to work through why I found myself in so much disagreement with the able, intelligent, hard-working, and honest Antonio Fatas in his Dealing with a Sudden Stop:

A country with a current account deficit must have a matching capital inflow to finance the excess of spending above its income (this is an accounting identity). During the financial crisis many European countries faced a sudden stop.... This is something that any textbook discusses although normally in the context of emerging markets [by the way, it is not easy to use the IS-LM model to deal with sudden stops given that the IS-LM model is not the best model to analyze current account imbalances and situations where there is no price at which capital will fund a current account deficit]....

The standard way to analyze a sudden stop is to say:

• IM = mY * Y :: imports IM are a constant fraction mY of real GDP Y.
• GX = constant :: gross exports GX are a constant.
• IM - GX = PCI + IMF :: the current-account deficit is equal to imports IM minus gross exports GX, and is also equal to the private capital inflow PCI plus International Monetary Fund credits IMF.
• ΔY = ΔPCI/(mY) :: In a sudden stop, PCI falls by an amount ΔPCI, and in the absence of IMF support real GDP Y falls by ΔPCI/(mY)

But we know that every monetary economic model has an IS-LM representation--the quantity theory of money is the LM curve, and the rest of the model is the IS curve. What is the IS-LM interpretation of a sudden stop that generates the conclusion that in the absence of IMF support ΔY = ΔPCI/(mY) in a sudden stop?

Let's build up the IS curve:

• Y = C + I + G + (GX - IM) :: national income identity
• IM = mY * Y :: imports IM are a constant fraction mY of real GDP Y.
• GX = GXo - xε * ε :: gross exports GX are equal to a baseline amount of exports GXo minus a propensity to export xε time stye real value of the currency ε.
• C = Co + cy * Y :: consumption C equals baseline consumption Co plus the marginal propensity to consume cy times national income Y
• G = Go constant :: government spending G is a constant
• I = Io - Ir * rL :: investment spending I is equal to baseline investment spending Io minus the interest elasticity of investment Ir times the domestic long-term real interest rate rL
• ε = εo + εr * rL :: the real value of the currency equals speculators' beliefs about the fundamental value of the currency εo plus the responsiveness of the currency to domestic real interest rates εr times the domestic long-term real interest rate rL

This then gives us:

• Y = co+cyY + Io-Irr + Go + (GXo-xεε - mYY)

Substituting in the real exchange rate and collecting terms:

• Y = [(co+Io+Go+GXo) - (Ir+xεεr)rL - xεεo]/(1-cy+mY)

This is the Krugman argument about the effect on the economy of a loss of confidence in the debt: as long as the central bank controls rL, a loss of confidence in the debt shows itself in this equation as a fall in εo--a fall in the real value of the currency at which foreign exchange speculators are willing to hold the stock of debt for each possible value of rL. The country thus gains competitiveness, and exports boom. Thus a loss of confidence is expansionary.

So where does the "sudden stop" logic come from? It comes from the fact that in a "sudden stop" the central bank loses control of the real interest rate rL. In a sudden stop, the central bank can make the economy awash in liquidity--it can credibly commit to keep the short-term safe nominal interest rate is at zero until the end of time--swap out cash and pull in bonds with abandon--and this will have no effect on the economy's real equilibrium. Why not? Because in a sudden stop, on the relevant margin government-printed cash is as unsatisfactory an asset as government bonds: it is not that people want to dump government bonds for cash or for foreign securities, it is that people want to dump both government bonds and cash for foreign securities, and also that economic chaos is so great that foreigners are unwilling to increase the amount of their own currencies they trade for either currently-produced domestic goods and services or domestically-located property.

And that requires an extraordinary degree of dysfunction: not just a reduction in foreign exchange speculators' views of the long-term fundamental value of the currency, but a shutting-down of all margins on which changes in present and expected future monetary policy have any effect on the long-term real interest rate, and on which changes in the exchange rate drive changes in foreign purchases of anything domestic.

Thus when Antonio Fatas writes:

If any of these [peripheral] countries had been outside of the Euro area they would have struggled with other issues and the outcome might not have been too different...

I think he misses the point. There are countries and eras in which this sudden-stop mechanism is at work--where monetary policy loses its ability to affect domestic real interest rates and where economic chaos means that exchange-rate depreciation no longer leads to greater foreign purchases of either currently-produced goods or domestically-located assets--but those are countries with very large foreign currency-denominated debts and countries already near the edge of hyperinflation. They are not the industrialized economies of peripheral Europe in 2007.

And, similarly, when Olivier Blanchard and Daniel Leigh in theirRethinking Macroeconomic Policy write:

The second related cost [of high debt] is the risk of multiple equilibria. At high levels of debt, there may well be two equilibria, a "good equilibrium'' at which rates are low and debt is sustainable, and a "bad equilibrium'' in which rates are high, and, as a result, the interest burden is higher, and, in turn, the probability of default is higher. When debt is very high, it may not take much of a change of heart by investors to move from the good to the bad equilibrium.

I suspect that this is partly at work behind the Italian and the Spanish bond spreads. In this context, Martin Wolf asked a provocative question: why are the spreads so much higher for Spain than for the United Kingdom? Debt and deficits are actually slightly lower in Spain than in the United Kingdom. No doubt, the overall economic situation of Spain is worse than in the United Kingdom's, but does this explain fully the difference in spreads? Could the answer lie in the difference in monetary policy? In the case of the United Kingdom, investors expect the Bank of England to intervene if needed to maintain the good equilibrium, whereas they believe the European Central Bank does not have the mandate to do? These are central questions, which we need to study more.

I think they miss the big point.

In the IS-LM framework, there is no mystery. The answer to their question is obvious: the source of the trouble is the existence of the euro that pegs the exchange rate in Italy and Spain. If speculators come to think that the exchange rate is overvalued at its euro parity ε--probably because it is overvalued at its euro parity ε--that dictates what the long-term real interest rate has to be:

• rL = (ε* - εo)/εr

The central bank does not lose control over rL, rather, the central bank acts to maintain the euro parity. But does this have any application to floating-rate sovereigns--to Japan or the U.S. or Britain or to the eurozone itself in 2013? I would say not: they are not at all close to any phase transition in which the financial markets break down at the margins so much as to set the long-term real interest rate rL free from whatever the central bank does in the present and commits to for the future of the short-term safe real interest rate.

The rubber hits the road here because this sudden phase change of the economy to a sudden-stop regime is what Blanchard and Leigh use when they make the case for more austerity now even in the exorbitant privilege-possessing floating-rate sovereigns of the global north. They write:

the risk of multiple equilibria. When debt levels are high, but not so high that default is certain, there are likely to be two, self-fulfilling, equilibria: “good” and “bad.” The “good” equilibrium is where investors believe that the probability of default is low and ask for a low interest rate. The “bad” equilibrium is where investors believe the probability of default is higher and ask for a higher interest rate to compensate for the risk, making it harder for the government to avoid default, and thus justifying their initial beliefs. The higher the level of debt, the closer the two equilibria, and the more likely that, at some point, the economy suddenly shifts to the bad equilibrium.... Since it is nearly impossible to know what will make investors shift their beliefs, the situation policymakers face here is one of “Knightian uncertainty.” The prudent approach to dealing with such “unknown unknowns,” to use former US defence secretary Donald Rumsfeld’s expression, is to move away from the danger zone...

In the model, these "unknown unknowns", this "danger zone", is a rapid phase transition from the case in which rL is a policy level that determines the exchange rate via:

• ε = εo + εr * rL

to one in which rL is completely disconnected from domestic monetary policy, and instead driven to whatever level makes for:

• IM(Y) = GX + IMF

Is that the risk we should be guarding against? Aren't there many real, urgent problems of low production and employment that it is more important not to guard against the risk of but to correct right now?