I try to build a very basic New Keynesian 2-country DSGE model (here I work with the non-linearized form) with households and firms as well as price rigidities (Calvo) but I cannot find the steady-state.

Setting:

Each country has a final firm (aggregates home and foreign intermediate goods) and an intermediate firm (producing intermediate goods). Therefore, each country’s price index is a CES aggregate of foreign and domestic good’s prices. There is a domestic and a foreign bond. There is no govermnemt but there exists a monetary authority.

In this first version of the model, there are no habit persistence preferences and no kind of adjustment costs. Preferences depend on consumption and on labor effort.

There is a single shock: a technology shock.

I assume no growth in the model.

The entire model is deflated by domestic and foreign’s total price level.

Inflation is always gross inflation.

I think there is (at least) a problem with home/foreign NK Phillips Curves…

When you are using a steady_state_model-block, you need to set all non-zero variables. Dynare says

WARNING: in the 'steady_state_model' block, variable 'x_H' is not assigned a value
WARNING: in the 'steady_state_model' block, variable 'x_F' is not assigned a value
WARNING: in the 'steady_state_model' block, variable 'price_dispersion_H' is not assigned a value
WARNING: in the 'steady_state_model' block, variable 'price_dispersion_F' is not assigned a value

MODEL_DIAGNOSTICS: The Jacobian of the static model is singular
MODEL_DIAGNOSTICS: there is 1 colinear relationships between the variables and the equations
Colinear variables:
w_H
P_H
R_H
mc_H
p_Xstar_H
Colinear equations
4 6 7 8
MODEL_DIAGNOSTICS: The presence of a singularity problem typically indicates that there is one
MODEL_DIAGNOSTICS: redundant equation entered in the model block, while another non-redundant equation
MODEL_DIAGNOSTICS: is missing. The problem often derives from Walras Law.