Log-linearization and bons which are zero in steady state

[Duke]

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 = Beta*E_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?

Thanks in advance.

[jpfeifer]

1. There is no reason to not perform a log-linearization for all variables except for bonds and then only do a linearization for bonds. See Remark 19 (Variables with Negative Steady States or already in Percent) in Pfeifer(2013): "A Guide to Specifying Observation Equations for the Estimation of DSGE Models" https://sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf.
2. If bonds must always be 0, this market clearing is typically imposed so that bonds do not even appear in the model.

You could check out Gali's textbook. There private bonds are also in 0 net supply and the model is log-linearized. An example mod-file is on my homepage.