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I am working on macroeconomic model and I need to calibrate it. I am looking primarily for a statistically-founded estimate for the coefficient of relative risk aversion in the CRRA utility function based on macroeconomic US data (but also for the coefficient of absolute risk aversion for the case of a CARA utility function). Cannot seem to find it anywhere. Can anybody help?

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  • $\begingroup$ Is there a particular reason why you want to use CARA and not CRRA utility? $\endgroup$ – Alecos Papadopoulos Dec 14 '14 at 10:52
  • $\begingroup$ u(c)=(c^(1-σ))/(1-σ); I need an estimate for sigma $\endgroup$ – Zetway Kapinos Dec 14 '14 at 11:50
  • $\begingroup$ sorry, I ment CRRA $\endgroup$ – Zetway Kapinos Dec 14 '14 at 11:52
  • $\begingroup$ You just made my answer irrelevant. But since CRRA estimates are all over the place, maybe I will find something about it also. $\endgroup$ – Alecos Papadopoulos Dec 14 '14 at 12:01
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In Babcock, B. A., Choi, E. K., & Feinerman, E. (1993). Risk and probability premiums for CARA utility functions. Journal of Agricultural and Resource Economics, 17-24. (downloadable) we find the following table (the first column is the coefficient of absolute risk aversion)

enter image description here

You can download the paper and trace the papers which it summarizes in the table.

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  • $\begingroup$ This is micro data based on lottery picks, this is useful, but not exactly what I need, I need some estimates based on macro US data. $\endgroup$ – Zetway Kapinos Dec 14 '14 at 11:47
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There are many estimates in the literature. For example, Havranek (2013) does a meta-analysis of avalible results and argues for a value of intertemporal elasticity (inverse of sigma in your notation) around 0.3-0.4. But it might also depend on what your goal is - the single parameter in CRRA utility controls both risk aversion and intertemporal smoothing motive, so a calibration for asset-pricing model might need to differ from let's say a deterministic growth model.

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  • $\begingroup$ that Havranek paper is great. Lots of upward publication bias in the empirical EIS literature - which makes the contrast between the low estimates there and the high ones that Epstein-Zin finance guys need even more striking. $\endgroup$ – nominally rigid Dec 16 '14 at 1:05

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