Problems with model setting

Dear Professor Pfeifer,

I’ve got three questions about the model setting when learning the models. Would you please give any advice ? Thank you very much.

(1) I read that the net worth of entrepreneur is generally set as:
{{N}_{t}}=\gamma {{V}_{t}}+W_{t}^{e}
Bernanke et al. set W_{t}^{e} as entrepreneurial wage, and Christiano et al.(2010) set it as initial fund of entrepreneurs. While in the code this W_{t}^{e} is treated as a parameter. Why don’t they directly set it as a parameter in the content?

(2) The entrepreneurs’ objective function in BGG(1999) is
\underset{K,\bar{\omega }}{\mathop{\max }}\,\left[ 1-\Gamma \left( {\bar{\omega }} \right) \right]{{R}^{k}}QK
While after setting s={{R}^{k}}/R and k=QK/N, why the objective function become as
\underset{k,\bar{\omega }}{\mathop{\max }}\,\left[ 1-\Gamma \left( {\bar{\omega }} \right) \right]sk ?

(3) In the market clearing part of some papers, the agents are measured with parameters such like {{c}_{t}}=\gamma c_{t}^{P}+\left( 1-\gamma \right)c_{t}^{I}, while in some other papers(e.g. Iacoviello(2010)) the authors just set {{c}_{t}}= c_{t}^{P}+c_{t}^{I}. What is the difference in between?

Thank you for your precious time.

  1. The term W_t^e is stipulated to be exogenous. It being constant is a special case. Thus, they describe a generic model and then fix the process during calibration.
  2. Where did you get that transformation from? It’s not in the paperr.
  3. That depends on whether the total mass of agents is normalized to 1, with the respective shares being \gamma and 1-\gamma or whether each type of agents has mass 1 so that the weight is 1.

It’s on Page 1385, Appendix A.3

It seems they divide the whole problem (including the constraint) by R, which is strictly positive and not a control variable here. It holds that
\max\limits_x{} a\times f(x)=a\times \max\limits_x{} f(x). So the resulting x will be the same.

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