The Effect of Monetary Policy on Consumption Inequality: An Analysis of Transmission Channels through TANK Models

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.