We analyze how the level of monetary policy rates affects the relevance of deposit market competition for the transmission of monetary policy. We find that following a monetary policy tightening when interest rates are sufficiently low (high), banks’ branches located in concentrated deposit markets experience an increase (decrease) in deposit quantities relative to branches of the same bank located in competitive markets. We also find how this differential effect translates partially into the lending markets, but do not find a differential effect in the labour market (wages and employment). These results suggest that monetary policy transmission channels may work differently when interest rates are low consistent with the presence of zero lower bound constraints in the deposit market.