We analyze the effects on inflation and output of unconventional open-market operations due to the possible income losses on the central bank's balance sheet. We first state a general Neutrality Property, and characterize the theoretical conditions supporting it. We then discuss three non-neutrality cases. First, with no treasury's support, sizeable (current or expected) balance sheet losses can undermine the central bank's solvency and should be resolved through an increase in inflation. Second, a central bank might also engineer higher inflation in the case it wants to limit or reduce losses because of political constraints or to seek more financial independence. Third, if the treasury is unable or unwilling to tax households to cover the central bank's losses, the wealth transfer to the private sector also leads to higher inflation.
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