If you understand the title you understand the post. It's obvious really. Betas peg their exchange rate to alphas; alphas do not peg their exchange rates to betas. Beta's promise to redeem their liabilities for alpha liabilities at a fixed exchange rate; alphas make no such promise the other way. So alphas lead and betas follow. So if you want to understand where the pack is going, watch the alphas, not the betas. Central banks issue alpha currency; fiscal authorities issue beta bonds.

1. Suppose the US Fed decided to peg the exchange rate of the US Dollar to the Canadian Dollar. The Fed promises to redeem one US Dollar for (say) one Canadian Dollar. But the Bank of Canada makes no such commitment in return, and keeps on targeting 2% inflation in Canada. It's asymmetric redeemability.

US monetary policy would be set in Ottawa. Fed watchers would stop watching the Fed, and would watch the Bank of Canada instead. It does not matter whether the Fed is 10 times or 100 times bigger than the Bank of Canada. It would not matter if the Fed paid interest on its currency, and the Bank of Canada didn't. The Bank of Canada leads, and the Fed follows. The Fed would be targeting 2% Canadian inflation too. The Bank of Canada is alpha; the Fed is beta. Canadian dollars are the alpha money; US dollars are the beta money.

This is standard international finance theory.

2. The Bank of Montreal pegs the exchange rate of the Bank of Montreal dollar to the Bank of Canada dollar. Not the other way round. The Bank of Montreal promises to redeem its dollars at par with Bank of Canada dollars. Not the other way round. The Bank of Canada is alpha, and the Bank of Montreal is beta. It's the same for all the other commercial banks. It does not matter whether the commercial banks are bigger than the Bank of Canada. That's why Canadian monetary policy is set in Ottawa, not in Toronto.

3. I can issue bonds. If I write "IOU $100 payable December 2015 signed Nick Rowe" on a scrap of paper, and sell it, I have issued a bond. I promise to redeem my bond for Bank of Canada currency. The Bank of Canada does not promise to redeem its currency for Nick Rowe bonds. The Bank of Canada is alpha, and I am beta. The Bank of Canada sets Canadian monetary policy; I don't.

My local municipality can also issue bonds, just like I can. Chelsea promises to redeem its bonds for Bank of Canada money. The Bank of Canada does not promise to redeem its money for Chelsea's bonds. Chelsea is beta, to the Bank of Canada's alpha. Canadian monetary policy is set in Ottawa, not in Chelsea.

The province of Quebec can also issue bonds, just like I can. Quebec promises to redeem its bonds for Bank of Canada money. The Bank of Canada does not promise to redeem its money for Chelsea's bonds. Quebec is beta, to the Bank of Canada's alpha. Canadian monetary policy is set in Ottawa, not in Quebec.

The Federal government of Canada can also issue bonds, just like I can. The Department of Finance promises to redeem its bonds for Bank of Canada money. The Bank of Canada does not promise to redeem its money for Department of Finance bonds. It too is beta, to the Bank of Canada's alpha. Canadian monetary policy is set by the Bank of Canada, not by the Department of Finance.

4. It does not matter whether the stock of bonds is bigger than the stock of currency. It does not matter whether currency is printed on paper, on plastic, or on computer discs. It does not matter whether the net value of the stock of currency is positive, negative, or zero. It does not matter whether bonds are used as money or not. It does not matter whether currency is used as money or not. The only thing that matters is whether those who issue financial assets peg the exchange rate of their financial assets to the financial asset issued by the Bank of Canada, and not vice versa. That's what makes Bank of Canada currency the alpha, and every other financial asset the beta.

5. If the Bank of Canada gave all its seigniorage profits to the United Way (a charity), instead of to the Federal government, the only difference is that the United Way would have more revenue and the Federal government less revenue. The United Way would not set Canadian monetary policy. The Canadian price level would not be determined by the present value of the United Way's donations and expenditures.

Sure, if the United Way appointed the Governor of the Bank of Canada, that might matter. And if the United Way signed off on the Bank of Canada's 2% inflation target, that might matter. And if the Bank of Canada felt obliged to bail out the United Way if it risked defaulting on its bonds, that might matter too. But we would not in general say that the Canadian inflation rate is determined by the United Way's fiscal policy.