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