# Credit as an observed variable in Christiano, Trabandt, Walentin (2011)

1. I would like to include credit as an observed variable in CTW model (paper here), so I understand I should include the next two equations:

\begin{split} B_{t}^{obs} =& B_{t}\\ &+\nu^{f}W_{t}H_{t} \\ &+\nu^{x}q_{t}p_{t}^{c}p_{t}^{x}x_{t}\\ &+\nu^{*}q_{t}p_{t}^{c} \left( c_{t}^{m}(\mathring{p}_{t}^{m,c})^\frac{\lambda_{m,c}}{1-\lambda_{m,c}} + i_{t}^{m}(\mathring{p}_{t}^{m,i})^\frac{\lambda_{m,i}}{1-\lambda_{m,i}} + x_{t}^{m}(\mathring{p}_{t}^{m,x})^\frac{\lambda_{m,x}}{1-\lambda_{m,x}} \right) \end{split}

data\_bdiffU = 100(log(B_{t}^{obs}) - log(B_{t-1}^{obs}) ) % measurement equation

Where:

• B_{t} : loan the entrepreneur requires

• \nu^{f}W_{t}H_{t} : fraction of the wage bill that firms must borrow.

• \nu^{x}q_{t}p_{t}^{c}p_{t}^{x}x_{t} : fraction of exports that firms must borrow

• \nu^{*}q_{t}p_{t}^{c} \left( c_{t}^{m}(\mathring{p}_{t}^{m,c})^\frac{\lambda_{m,c}}{1-\lambda_{m,c}} + i_{t}^{m}(\mathring{p}_{t}^{m,i})^\frac{\lambda_{m,i}}{1-\lambda_{m,i}} + x_{t}^{m}(\mathring{p}_{t}^{m,x})^\frac{\lambda_{m,x}}{1-\lambda_{m,x}} \right)
: fraction of expenses on imports that firms must borrow

• data\_bdiffU : observed variable, business loans

1. What would it be happen if I include loans to household for house purchase. Would it modify the previou equation?

Thanks a lot

Aldo

That depends on your data. If data\_bdiffU already includes housing loans, then you need to adjust B_t^{obs} to include it as well. Most probably, you would add a term like B_t.

Sidenote: Are you sure there are no brackets missing around the 1-\lambda?

Thanks a lot for your time and answer dear jpfeifer. I just edited my question. Yes, there must be brackets.

My data about data_bdiffU solely includes business loans (I have another measurement equation for housing loans and its respective data).