Short-run dynamics in a search-theoretic model of monetary exchange

We study the short-run effects of monetary policy in a search-theoretic monetary model in which agents are subject to idiosyncratic liquidity shocks as well as aggregate monetary shocks. Namely, we analyze the role of the endogenous non-degenerate distribution of liquidity, liquidity constraints, and decentralized trade, for the transmission and propagation of monetary policy shocks. Money is injected through lump-sum transfers which have redistributive and persistent effects on output and prices. We propose a new numerical algorithm in the spirit of Algan et al. (2008) to solve the model. We find that a one-time expansionary monetary policy shock has persistent positive effects on output, prices, and welfare, even in the absence of nominal rigidities. Furthermore, the effects of positive and negative monetary shocks are typically asymmetric. Negative (contractionary) shocks have bigger effects than positive (expansionary) shocks. In addition, in an economy with larger shocks, the responses tend to be disproportionately larger than those in an economy with smaller shocks. Finally, the effectiveness of monetary shocks depends on the steady-state level of inflation. The higher the average level of inflation (money growth), the bigger the impact effect of a shock of a given size but the smaller its cumulative effect. These results are consistent with existing empirical evidence.