# Wage rigidity

Hi, I’m trying to introduce real wage rigidity in the (usual) model. In its simplest form, w=w(-1)=steady_state(w). However, by replacing w with steady_state(w) in the FOC for labour and in the Euler equation (2), the zero lower bound on nominal interest rate doesn’t bind anymore, since the int. rate becomes negative. How is that possible ?

Your model does not solve at all when the real wage is not allowed to change at. Unfortunately, Dynare does not provide an explicit warning. To change this, use the attached files in Dynare 4.4.3

Currently, you are plotting a path that does not solve the model. This is why the interest rate goes below 0.

Intuitively, I think you cannot completely fix the real wage as you are making the wage completely exogenous and the labor market will not clear in this case.
sim1_purely_backward.m (2.2 KB)
sim1_purely_forward.m (1.89 KB)

Moreover, my final goal is to introduce downward nominal wage rigidity, which is even more problematic. I set Pw=P(-1)w(-1), where w is the real wage. Given that P is not defined, I rearrange terms and obtain w=1/(1+pi)w(-1), where pi is the net inflation rate. Replacing this formula in the two equations with w results in an error since the rank condition is not verified. How else can I introduce this constraint on wages ? Thanks in advance.

Hi, running the attached mod file results in the usual error ‘The rank condition ISN’T verified!’. So far, I’ve tried different versions of this model but I’m not succeeding in introducing the constraint on nominal wages. What should I change in this setting ? Thanks.

Hello, I’ve tried another specification for the cost of nominal wage adjustment. The rank condition is verified, but there is another problem here:

Error using sim1 (line 144)
Simulation terminated with NaN or Inf in the
residuals or endogenous variables. There is
most likely something wrong with your model

In a previous post, I read that this problem might be due to the impossibility of the deterministic simulation to converge. Is there anything I can do with this specification, or should I change it again ? By the way, I cannot find anything that works, which is really weird given the simplicity of such constraint.

As always, start with a simple version that works. That is, use a small deviation from steady state and check whether the model converges back. Only then increase the shocks size/initial deviation. In this regard, you might want to add a parameter to your model that governs the strength of the rigidity. Start out with full flexibility and then slowly increase the rigidity to see when the problem occurs.

Hi, I’m following your suggestion to add a parameter that governs the degree of nominal rigidity and start out with full flexibility. So the simple idea (which does not imply downward rigidity) is to impose w_tilde=rho/(1+pi)*w(-1)+(1-rho)*w, where w is the real wage and (1+pi) is the net inflation rate. I start with rho=0 but I do not get the same dynamics I would obtain with w_tilde=w, why ?

Hello,

I am trying myself to introduce downward wage rigidity (as in Schmitt-Grohe and Uribe (2013) - DNWR) in an otherwise very simple model. In particular, I want to have a condition where w=gamma*w(-1), where gamma>=0. For values of gamma~=1, I cannot find the steady-state, which makes me think that I am overlooking something fundamental.

Any help is much appreciated. Eta, have you found a way to implement this?

many thanks

r
dnwr.mod (685 Bytes)