Do open market operations matter? Theory and evidence from the Second Bank of the United States

Modigliani-Miller theorems for open market operations describe conditions under which central bank portfolio rearrangements will have no consequences for allocations, relative prices, or the time path of the price level. Such theorems for government owned central banks have limited applicability, and hence are difficult to test. We develop a Modigliani-Miller theorem for privately owned central banks, and test its implications using data from the Second Bank of the United States. The data are consistent with an absence of price level effects due to open market operations, and are inconsistent with standard versions of the quantity theory of money.