# Problems with model solving

Dear Professor Pfeifer,

I have got three unrelated problems when solving the model. Would you please give any advice ? Thank you very much.

(1) When I was running dynare code, it says “The Jacobian of the static model contains Inf or NaN”. I searched the forum while still cannot find the solution. Would you please take a look ? The code files have been sent through message.

(2) When using CES production function in the model, there are two types of formula:
{{Z}_{t}}={{\left[ \theta {{\left( {{X}_{t}} \right)}^{\frac{\varepsilon -1}{\varepsilon }}}+\left( 1-\theta \right){{\left( {{Y}_{t}} \right)}^{\frac{\varepsilon -1}{\varepsilon }}} \right]}^{\frac{\varepsilon }{\varepsilon -1}}}
or
{{Z}_{t}}={{\left[ {{\theta }^{\frac{1}{\varepsilon }}}{{\left( {{X}_{t}} \right)}^{\frac{\varepsilon -1}{\varepsilon }}}+{{\left( 1-\theta \right)}^{\frac{1}{\varepsilon }}}{{\left( {{Y}_{t}} \right)}^{\frac{\varepsilon -1}{\varepsilon }}} \right]}^{\frac{\varepsilon }{\varepsilon -1}}}

How should I choose the better one ? And also, is there any limitation on the value range of parameter \varepsilon or it could be any value larger than 0 ?

(3) The land variable {l}_{t} in Iacviello and Neri(2010) is fixed and always equal to 1, then why agents in the model could still make decision on it ? How should I understand this behavior ?

1. model_diagnostics should be after steady. It returns information on a collinearity problem between equations 35 and 36.
2. For appropriate values of \theta, the two are isomorphic. For a given \epsilon you can always choose a corresponding value. \epsilon is the elasticity of substitution. It needs to be bigger or equal to 0.
3. Land supply is fixed at 1. Agents decide on labor demand. In equilibrium, of course demand has to equal supply.

Dear Professor Pfeifer,

For the first question, I check that equations 35 and 36 are just like equations 32 and 33, which are first-order conditions of similar agents. It is very strange that 35 and 36 have collinearity problem while 32 and 33 do not. And also, these equations work well in another model code with same agents. I totally have no idea where the collinearity comes out.