What transmission channels drive the effect of monetary policy on consumption inequality? This paper investigates this question with tractable Two-Agent New Keynesian models with search-and-matching frictions and wage rigidities. I make a distinction between credit-constrained households and unconstrained households and find that an expansionary monetary policy shock decreases consumption inequality between those two households through three channels: (ⅰ) the income composition channel, through fluctuations in labor and profit income; (ⅱ) the savings redistribution channel, through fluctuations in real interest rate; and (ⅲ) the earnings heterogeneity channel, through fluctuations in unemployment. The results are in line with the empirical evidence.
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