Investment, matching and persistence in a modified cash-in-advance economy

We simulate and estimate a new Keynesian search and matching model with sticky wages in which capital has to be financed with cash, at least partially. Our objective is to assess the ability of this framework to account for the persistence of output and inflation observed in the data. We find that our setup generates enough output and inflation persistence with standard stickiness parameters. The key factor driving these results is the inclusion of investment in the CIA constraint, rather than any other nominal or real rigidity. The model reproduces labor market dynamics after a positive increase in productivity: hours fall, nominal wages hardly react, and real wages go up with some delay. Regarding money supply shocks, we investigate the conditions under which our model specification generates the liquidity effect, a fact which is absent in most sticky price models.