Exercise 4.13

An SOE-RBC Model with Cobb-Douglas Preferences

⬅ Return

Problem

Modify the period utility function of the EDEIR model as follows:

\[ U(c,h) = \frac{\left[ c^{1-\omega}(1-h)^{\omega} \right]^{1-\sigma}-1} {1-\sigma}. \]

All other features of the model are unchanged.

  1. Derive analytically the steady state of the model.

  2. Set all parameters of the model as in table~\(\ref{table:soe-rbc-calibration-SGU-JIE}\), except for \(\omega\). Calibrate \(\omega\) to ensure that in the deterministic steady state, hours equal 1/3 (i.e., ensure that in the steady state, households spend one-third of their time working). Calculate the implied value of \(\omega\).

  3. Produce a table of predicted second moments similar to table~\(\ref{table:soe-rbc-edeir}\). When performing this step, you might find it convenient to use as a starting point the Matlab programs for the EDEIR SOE-RBC model posted online.

  4. Compare the predictions of the present model with those of its GHH-preference counterpart.

Answer

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