Commercial banks are typically beta banks, and central banks are typically alpha banks. Beta banks promise to convert their money into the money of alpha banks at a fixed exchange rate. Alpha banks make no such promise the other way. It's asymmetric redeemability. This means there cannot be an excess supply of beta money in terms of alpha money. (Nor can there be an excess demand for alpha money in terms of beta money.) Because people would convert their beta money into alpha money if there were. But there can be an excess supply of beta money in terms of goods, just as there can be an excess supply of alpha money in terms of goods. If beta money is in excess supply in terms of goods, so is alpha money, and vice versa. If commercial and central bank monies are perfect or imperfect substitutes, an increased supply of commercial bank money will create an excess supply of both monies against goods. The Law of Reflux will not prevent this.
This is in response to David Glasner's good post. David has forced me to be much clearer about what it means to say there is an excess supply of commercial bank money.
Money, the medium of exchange, is not like other goods, because if there are n goods plus one money, there are n markets in which money is traded, and n different excess supplies of money. Money might be in excess supply in the apple market, and in excess demand in the banana market.
If there are two monies, and n other goods, there are n markets in which money is traded against goods, plus one market in which the two monies are traded for each other. If beta money is convertible into alpha money, there can never be an excess supply of beta money in the one market where beta money is traded for alpha money. But there can be an excess supply of both beta and alpha money in each or all of the other n markets.
Start in equilibrium, where the existing stocks of both alpha and beta money are willingly held. Hold constant the stock of alpha money. Now suppose the issuers of beta money create more beta money. Could this cause an excess supply of money and an increase in the price level?
If alpha and beta money were perfect substitutes for each other, people would be indifferent about the proportions of alpha to beta monies they held. The desired share or ratio of alpha/beta money would be indeterminate, but the desired total of alpha+beta money would still be well-defined. If beta banks issued more beta money, holding constant the stock of alpha money, the total stock of money would be higher than desired, and there would be an excess supply of both monies against all other goods. But no individual would choose to go to the beta bank to convert his beta money into alpha money, because, by assumption, he doesn't care about the share of alpha/beta money he holds. The Law of Reflux will not work to eliminate the excess supply of alpha+beta money against all other goods.
Now suppose that alpha and beta money are close but imperfect substitutes. If beta banks want to prevent the Law of Reflux from reducing the stock of beta money, they would need to make beta money slightly more attractive to hold relative to alpha money. Suppose they do that, by paying slightly higher interest on beta money. This ensures that the desired share of alpha/beta money equals the actual share. No individual wants to reduce his share of beta/alpha money. But there will be an excess supply of both alpha and beta monies against all other goods. If apples and pears are substitutes, an increased supply of pears reduces the demand for apples.
Now suppose that alpha and beta money are neither substitutes nor complements. Only in this case would an increased stock of beta money, plus a large enough increase in the rate of interest paid on beta money to ensure that nobody wants to convert beta money into alpha money, mean that there is no excess supply of alpha and beta money in terms of goods. If Canadians use only alpha money, and Americans use only beta money, and the Fed promises to convert US beta dollars into Canadian alpha dollars at a fixed exchange rate, the Fed could not create inflation by increasing the supply of beta money and making it more attractive to hold.
Purely for completeness, if alpha and beta monies were complements, if beta banks increased the stock of beta money, and increased the rate of interest paid on beta money to ensure nobody wanted to convert beta money into alpha money, this would create an excess demand for both alpha and beta money against all other goods.
Commercial banks are beta banks. They fix the exchange rates of their monies against central bank alpha money. It seems reasonable to assume that commercial bank money is an imperfect substitute for central bank money. Chequing accounts are an imperfect substitute for currency. If so, an increase in the supply of commercial bank money, with commercial banks taking actions to ensure that people want to hold a larger share of commercial bank money relative to central bank money, will create an excess supply of both monies against all other goods.
The Law of Reflux would work very well for any good except money. If producers of refrigerators stand ready to convert refrigerators into money or vice versa at a fixed exchange rate, there could never be an excess supply or demand of refrigerators in terms of money. Nor could there ever be an excess demand or supply of money in terms of refrigerators. But refrigerators are traded in one market, for money. Money is traded in all markets, for all other goods. There could never be an excess supply or demand of money in terms of refrigerators; but there could still be an excess supply or demand of money in terms of everything else.