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This might be a very basic question, but I am a beginner in macro models. I would appreciate help with my doubt.

In different papers I have read about the elasticity of labor supply or the inverse of the Frisch elasticity of labor supply. However, Thoenissen & Benigno (2008) talk about the elasticity of substitution in leisure, displaying the following utility function:

$ \begin{gather} U_t = E_t \sum_{s=t}^\infty \beta ^{s-t}\bigg[ \frac{1}{1-\rho}C_s^{1-\rho} (1-L_s)^\eta\bigg] \end{gather} $

where $\eta$ is the inverse of the intertemporal elasticity of substitution in leisure.

My question is, is there a difference between the elasticity of labor supply and the elasticity of substitution in leisure? If yes, is it possible to go from the elasticity of labor supply to the (inverse) of the intertemporal elasticty of substitution in leisure?

Thank you very much for your help.

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