Actually are there any differences for the central banks for these two things? If not, why bother to buy bonds?
Open market purchase vs helicopter drop
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First, nowadays the market is flush with reserves. So open market purchases are not how things are really done, at least at the moment. However, to your broader point, I have severe doubts about whether or not the helicopter drop as is traditionally understood really makes sense. A dirty secret of monetary policy is that we dont really have an accurate measure of money supply, and I would claim that this idea of 'money' as some special unique asset may be a bit naive. This is why the literature has begun to emphasize "moneyness" rather than money. Most monetary policy people dont really think in terms of money supply, but in terms of interest rates. Thats why OMOs are emphasized.