# Log-linearization and bonds which are zero in steady state

Hi,

I have what is a relatively simple problem about log-linearization.

I have a NK model, which features bonds which are zero in steady state and has a Phillips curve. I want to use Dynare, so I am trying to work out what are my options.

I figure log-linearizing the entire model is out (bonds - can’t take the log of zero). I gather I can’t use a combination of log-linearization and linearization. So how then to deal with the Phillips Curve? Can I simply interpret the Phillips Curve as:

pi_t = BetaE_t((pi_t+1 - pi_bar) / pi_bar) + kappa*((mc_t-mc_bar) / mc_bar)?

It doesn’t feel right. But otherwise, how can I reconcile the use of an equation in percentage deviations from steady state and other equations in levels which feature variables with steady states of zero?

How is this commonly accommodated?

Hi. I was wondering whether this generates any bias or problem since you are not performing the same operation in some equations. For instance: you will have `phi_t=1/2(exp(I_t)/exp(I_t(-1))-1)^2`. Since in steady state phi_t must be zero you write the code without the “exp” but i_t is a variable you would like to log-linearize so it is accompanied by the “exp”. To me, it looks inconsistent. What is the advantage of this over redefining variables? let’s say, `exp(phi_t)=1+1/2(exp(I_t)/exp(I_t(-1))-1)^2`, and the where-ever phi_t is on the FOC you write `(exp(phi_t)-1)`?