I am trying to write a model of collateral constraint with inelastic labor supply and fixed wages.
The basis for this is the model by Jermann and Quadrini, 2012, “macroeconomic effects of financial shocks” (in which there is an enforcement constraint, and following them I assume this is always binding). I want to see what happen if (real) wages are fully rigid, and labor supply is inelastic (households supply all work needed by firms, e.g as in Shimer 2010), so that the response of unemployment is determined by the demand side.
Dynare can find the steady state, but then there is a unit root, which leads the IRF to never return to steady state. In addition, when I try to include the technology shock, BK condition is no more satisfied.
Has someone an idea of the origin of the unit root in my model?
Maybe the problem is basically my model itself… but I would appreciate if someone can help in finding what is wrong with it.
The reason is that you fixed the real wage at wbar, but left the labor supply from the firm side endogenous, while the households labor FOC is missing.
thank you for your answer.
my point was precisely to write a model in which the labor market equilibrium is fully determined by the labor demand from firms, when the wage is completely rigid (so exogenously fixed to wbar):
thus I assumed that households supply labor needed by firms, but this is exogenous for them, they don’t choose how much they work. This is why I dropped the labor choice by HH.
Is my idea not feasible?
An other question: my view is that this non-stationarity is a problem. But is it possible that it does make sense from an economic point of view?
Working more after a shock does not pay off permanently due to the decreasing marginal returns to labor. Thus, the real wage decreases when people work. In your model, this does not happen and people permanently work more, resulting in the unit root. I haven’t looked closely enough at your model to be able to judge whether this mechanism makes sense. You have to check whether the resource constraints hold on whether firms do not make negative profits on average when they have to pay wages that differ from the marginal product.