Monday, November 12, 2012

The Name's Bond, Vigilante Bond

I don't see where exactly the line is drawn with respect to bond vigilantism. After all, what it comes down to is the premise that investors can have an impact on economic policy by selling off bonds and refusing to buy them, thus sending prices plummeting and yields soaring.

That's been the fear from a significant portion of the think tank and it hasn't really garnered enough opposition as far as I've noticed. Let's be clear though, do 'vigilantes' set bond prices? I would say no, Cullen Roche at Seeking Alpha plays it safer with an 'it depends'. In fact, he likens the situation to a person walking an untrained dog. The dog tries to lead the walker (investors/traders) lead the Fed (front-running), but the Fed "as supplier of reserves to the banking system, can ALWAYS control the price of bonds".

In any case, Krugman is most vocal about this and he brings us back to basic macro and the IS-LM model. He seems to insinuate that the chorus coming from the fearful ones is clouded by the impression that the US has a fixed exchange rate and a simple macro model illustrates the difference.

The key here, as mentioned above, is the difference in the floating and constant exchange rate. Krugman goes on to argue that if the exchange rate is free to float, a 'vigilante attack' is in fact, expansionary.
Here are the basics (though it's hard to explain it easier than he does!):

The first equation is a simple linear function relating the demand for domestically produced goods and services to the interest rate and the exchange rate. Thus,

y = -ai + be (where y is real GDP, i is the interest rate, and e is the log(exch. rate) in terms of foreign currency - rise = depreciation (expansionary)

Immediately, one would point out the use of nominal terms and the convenient inflation ignoring that goes on here but simplicity is the key here and inflationary expectations...well...don't make things simpler.

If the exchange rate is fixed, then the second term of the equation above is constant and i is automatically a function of the willingness of international investors to hold securities. If i* is a riskless foreign security, then the domestic i = i* + p where p is the risk premium demanded.

On a downward sloping curve of real GDP versus interest rate, a rise in i automatically leads to a drop in y - i.e: economic contraction. But this is with a fixed exchange rate. 

If i is set by Fed policy (according to a phantom Taylor-rule for example) - i = r*y, then there will be expected arbitrage across borders that can be expressed by:

i = i* + d(e*-e) + p; where d(e*-e) [think of d as delta] expresses the expected 
depreciation. Rearranging gives us:

e = e* + (i* - i + p)/d.

It's simple now, put this expression for e back into the original linear function and you get:

y = -ai + be* + (b/d)(i* - i + p)

Clearly, the interest rate changes AD by:
a) raising domestic demand
b) depreciating the exchange rate and increasing net exports

On the IS graph with a constant policy-rule upward sloping curve, the IS curve shifts to the right outward over a loss of confidence, increasing the risk premium, depreciating the exchange rate and increasing demand - there's the expansion. 

Summarily, a loss of confidence wouldn't cause a rise in rates but a fall in the dollar (better competitiveness). That's not an easy sell but it's an undeniable factor when looking at the bond market. What about the distinction in short and long-term rates? Take a guess. 

Krugman thinks it's still difficult to imagine a contraction. Moreover, there's no issue of foreign denominated debt so it's hard to see where the fear comes from. 

Of course there are numerous other factors at play here (depreciation isn't the end-all solution to economic woe!) but first instinct would tell anyone with common sense that vigilante fears are almost unwarranted in the short-term. 

Fear in the long-run however, is a different matter altogether.

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