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

General DSGE Modeling
1

Please, I have two questions.

  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

2

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?

3

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).

Now my question about housing loans is solved. But I would like some confirmation I am doing well about measurement equation about business loans. Please.

By including working capital loans, I am following Christiano, Motto and Rostagno (2010) , equation 23. There, firm must finance a constant fraction \nu of its wage bill and of its rental cost of capital but it is a closed economy model, so there are not exports neither imports. In CTW(2011) there is not financing of rental cost of capital and it is an open economy model but credit is not an observed variable.

4

I don’t really understand what your last question is. But generally, accounting for working capital loans is tricky. The fundamental question is whether they are intra-period loans and whether they therefore show up in the statistics or not. That is a question that cannot generally be answered.