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I'm not sure I follow your formal analysis.

Specifically, I find it confusing that your rows do not sum to zero because their elements can be denominated in different currencies under your notation. The whole thing would be much clearer (if also somewhat more cumbersome) if you had each of the three sectors hold both dollar assets and liabilities and reals assets and liabilities, and explicitly settled the FX transactions implied by the foreign and domestic sectors' willingness to hold non-native currency.

To this end, I prefer to treat all foreign trade as being transacted in either the currency of the trade bloc hegemon (for unspecified trade with RoW) or in the currency of the higher-ranking party (in the case of specific bilateral relationships). I believe that this better reflects the actual constraints imposed by the international trade and tribute system than the symmetric treatment you impose here.

However, qualitatively I believe your conclusion rests upon the key assumption that the private sector's FX reserves operate broadly similarly to the strategic FX reserve. This is false: The private sector FX reserve is largely inaccessible during a national solvency crisis, and the strategic FX reserve is largely inaccessible in the daily operations of a non-crisis economy.

This is why prudent central banks should maintain strategic FX reserves on the order of the gross, rather than the net FX debt of their private sector (plus the net FX debt of any other branches of government).

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sat Jan 18th, 2014 at 03:21:37 AM EST
Specifically, I find it confusing that your rows do not sum to zero because their elements can be denominated in different currencies under your notation.
You can just multiply the entire RoW column by φ before adding row-wise.
The whole thing would be much clearer (if also somewhat more cumbersome) if you had each of the three sectors hold both dollar assets and liabilities and reals assets and liabilities, and explicitly settled the FX transactions implied by the foreign and domestic sectors' willingness to hold non-native currency.
Well, it's already the case that the domestic sector holds both Real and dollar assets and liabilities. I'm also assuming the foreign sector has negligible willingness to hold non-dollar liabilities. Those assumptions are easiy relaxed by adding a couple of lines to the matrix.

I also have not exhibited explicitly the balance sheet. Maybe I should do that.

However, qualitatively I believe your conclusion rests upon the key assumption that the private sector's FX reserves operate broadly similarly to the strategic FX reserve. This is false: The private sector FX reserve is largely inaccessible during a national solvency crisis, and the strategic FX reserve is largely inaccessible in the daily operations of a non-crisis economy.
The only simplifying assumption is that the private sector's only foreign asset is cash, but the private sector does hold a foreign asset.

However, the stability condition involves only the domestic dollar liabilities, not the assets. So I am not assuming the domestic dollar cash is accessible in a solvency crisis.

What I am saying is that, if the domestic sector has a demand for foreign assets (cash), "clever" domestic-denominated derivatives won't fool them. So you cannot control the exchnge rate with derivatives.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 04:30:27 AM EST
[ Parent ]
But they aren't doing domestic-denominated derivatives, are they? They're net short dollars, which they must presumably settle at some future date, no? Or are these options merely side bets settled in Reals rather than dollars?

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sat Jan 18th, 2014 at 06:59:13 AM EST
[ Parent ]
That's precisely the point: the swaps have one leg denominated in dollars, but they are settled in reals.

FT.com: Brazil: net debtor to the world

When the bank uses such a swap to limit the depreciation of the real, it offers to pay the difference between the initial exchange rate and the final exchange rate during the period of the contract, plus a dollar-linked rate of interest (known to traders as the cupom cambial). In return, it receives the cumulative interbank interest rate (currently about 10 per cent a year) on the amount of the contract in Brazilian reals. Crucially, the contracts are settled entirely in reals. No dollars exchange hands and there is no obvious impact on the country's ability to pay its foreign debts.


A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 10:12:48 AM EST
[ Parent ]
That's still a dollar liability for the purpose of the internal stability condition (which is external stability plus no index-linked gov't obligations).

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sat Jan 18th, 2014 at 11:16:22 AM EST
[ Parent ]
I'm not seeing it. The balance sheet is (assuming the BCB has the "wrong" side of the swaps, so the S stocks have to opposite sign from the body of the diary):

Balance SheetBRA (BRL)BCB (BRL)RoW (USD)
BRA $ Liabilities-λL$φ+λL$
BCB $ Reserves+ρR$φ-ρR$
BRA BRL Debt-βBR+βBR
Cash+CR+C$φ-CR-C$
Swaps $ Leg+σS$φ-σS$φ
Swaps BRL Leg-σ'SR+σ'SR

Suppose the domestic sector's $ liabilities of -λL$φ come suddenly due. Because the external stability condition ρR$ > λL$ is being maintained, the BCB can settle the liability with the external creditors in exchange for domestic BRL debt. The result is

Balance SheetBRA (BRL)BCB (BRL)RoW (USD)
BRA $ Liabilities00
BCB $ Reserves(+ρR$-λL$)φ+λL$-ρR$
BRA BRL Debt-βBR-λL$φT+βBR+λL$φT
Cash+CR+C$φ-CR-C$
Swaps $ Leg+σS$φ-σS$φ
Swaps BRL Leg-σ'SR+σ'SR

The subscript T is in case we want to be generous to the domestic sector and not index the new debt to the dollar exchange rate but just vaue it at the exchange rate at the time of the rescue. In that case, the stock of new debt might well be written as
β[BR+(λL$φ/β)T]

But, in any case, to be able to rescue the domestic economy from its foreign entanglements, the swaps position is irrelevant. It is true that the swap legs indexed to the dollar are a potentially domestically destabilising after a "successful" external rescue.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman

by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 12:51:48 PM EST
[ Parent ]
You're right that they don't by themselves trigger a hyperinflationary debt-devaluation spiral. But if someone were to engage in unfriendly currency movements aimed at Reals depreciation, then they would adversely affect the ability of the BCB to maintain domestic stability.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sat Jan 18th, 2014 at 12:57:25 PM EST
[ Parent ]
Well, the fact that the BCB is attempting to prop up its exchange rate with derivatives is an indication that it's more interested in preserving the comprador class' access to foreign consumer goods than in domestic stability. If the Real is sliding it should let it slide, precisely because it needs to preserve its reserve buffer. It is possible that this all has something to do with the 2014 football world cup and the 2016 olympics. After that, all hell might break loose in the domestic market and the swaps might explode in the BCB's face.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 01:09:24 PM EST
[ Parent ]
I suppose that's the point the FT article is trying to make:
... Gersztein and Alday at BNP Paribas think a reasonable indication of the cost is to net out the central bank's short dollar position through currency swaps from its foreign reserves. After all, it is not only the stock of reserves but also the broader health of the Brazilian economy that affects its ability to pay its debts.
(my emphasis)
That is something investors may wish to keep a close eye on if, as widely predicted, the real continues to weaken and Brazil's fiscal position continues to deteriorate during 2014 and 2015.


A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 02:14:18 PM EST
[ Parent ]
I suppose that's the point the FT article is trying to make.

Clumsily and without focus.  It appears the BCB is attempting to manage currency by playing with financial markets (which it can do) instead of dealing with the actual foundation of the currency, the domestic economy (which it can't), and is doing so with the acquiescence of the government, which doesn't want to deal with the economy either.  Which supports your conclusion that they are simply manipulating money for the benefit of the moneyed.

by rifek on Thu Jan 30th, 2014 at 11:59:31 AM EST
[ Parent ]
I have added explicit balance sheet and reconciliation (capital gains) tables to all this to hopefully clear some of the confusion.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 05:16:12 AM EST
[ Parent ]
explicitly settled the FX transactions implied by the foreign and domestic sectors' willingness to hold non-native currency
How do you suggest to make the FX settlement explicit? I've been raking my brain abuot that all week and I can't see how to make that visible.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 06:01:39 AM EST
[ Parent ]
You use 6 columns:
Domestic nongov't domestic currency account
Domestic nongov't foreign currency account
Gov't domestic currency account
Gov't foreign currency account
Foreign domestic currency account
Foreign foreign currency account

An export transaction would then be (assuming the foreign trade is transacted in foreign currency):
Domestic nongov't domestic currency account
+Xphi Domestic nongov't foreign currency account
Gov't domestic currency account
Gov't foreign currency account
Foreign domestic currency account
-Xphi Foreign foreign currency account

And since the domestic sector does not wish to hold foreign currency, it will engage in an FX transaction with the domestic CB:

An export transaction would then be (assuming the foreign trade is transacted in foreign currency):
+X Domestic nongov't domestic currency account
-Xphi Domestic nongov't foreign currency account
-X Gov't domestic currency account
+Xphi Gov't foreign currency account
Foreign domestic currency account
Foreign foreign currency account

Similarly, if the gov't wants to build strategic currency reserves, it will engage with the foreign sector:
Domestic nongov't domestic currency account
Domestic nongov't foreign currency account
-X Gov't domestic currency account
+Xphi Gov't foreign currency account
+X Foreign domestic currency account
-Xphi Foreign foreign currency account

But since the foreign sector does not wish to hold domestic currency in non-negligible amounts, it will close out its transaction by dealing with the domestic private sector:
+X Domestic nongov't domestic currency account
-Xphi Domestic nongov't foreign currency account
Gov't domestic currency account
Gov't foreign currency account
-X Foreign domestic currency account
+Xphi Foreign foreign currency account

This picture represents the net positions. You can further split each column into a full balance sheet. Which you should if you want to discuss foreign stability, because the (strong) foreign account stability condition for a non-hegemonic economy is that neg gov't long FX position exceeds the private sector's gross short FX position and that the current account is not in deficit.

- Jake

Friends come and go. Enemies accumulate.

by JakeS (JangoSierra 'at' gmail 'dot' com) on Sat Jan 18th, 2014 at 06:44:15 AM EST
[ Parent ]
And since the domestic sector does not wish to hold foreign currency, it will engage in an FX transaction with the domestic CB
It makes much more sense that the foreign (hegemonic) sector does not wish to hold domestic currency. If is a fact that the domestic sector does want to hod dollars. Brazilian banks offer dollar deposit and there is even a specific interest rate (cupom cambial) in Brazil for that purpose. In fact, the dollar leg of the government's currency swaps not only has its notional denominated in dollars but the coupons are indexed to the cupom cambial.
FT.com: Brazil: net debtor to the world
When the bank uses such a swap to limit the depreciation of the real, it offers to pay the difference between the initial exchange rate and the final exchange rate during the period of the contract, plus a dollar-linked rate of interest (known to traders as the cupom cambial). In return, it receives the cumulative interbank interest rate (currently about 10 per cent a year) on the amount of the contract in Brazilian reals. Crucially, the contracts are settled entirely in reals. No dollars exchange hands and there is no obvious impact on the country's ability to pay its foreign debts.
(already quoted elsewhere in this thread, but okay...)
You use 6 columns:
Domestic nongov't domestic currency account
Domestic nongov't foreign currency account
Gov't domestic currency account
Gov't foreign currency account
Foreign domestic currency account
Foreign foreign currency account
Well, that's equivalent to using three columns and keeping the dollar and real assets separate, which is what I do in my balance sheet.

A society committed to the notion that government is always bad will have bad government. And it doesn't have to be that way. — Paul Krugman
by Carrie (migeru at eurotrib dot com) on Sat Jan 18th, 2014 at 01:11:23 PM EST
[ Parent ]

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