Hours worked vs Employed persons

Dear modelers,

I would like to know how would you define labor in DSGE models for households and firm. My first hint would be hours worked for a representative household and labor force (in person) for firms. But I encounter problems when I want to pose an equilibrium condition for the labor market, since I do not define labor the same way for both agents.

Hence, the second hint would be only considering hours worked for the representative household and the representative firm, with n being standardly equal to 1/3. My issue is the following. I am estimating the macroeconomic elasticity of substitution (not with dynare) between capital and labor, using data on capital (in billion euros) and labor (in thousand persons). Should the estimation of the elasticity be coherent with the model; meaning estimating the production function with hours worked and not employed persons? Cause I don’t see myself estimating the model with hours worked (or should I?).

Thank you!


If so, How do I incorporate population growth?

The guiding principle is that you need to be consistent. If your are estimating an extensive margin elasticity in the data, you can’t say anything about the intensive margin (hours). In practice, labor elasticities are the sum of the intensive and extensive margin. See e.g. https://www.aeaweb.org/articles?id=10.1257/aer.101.3.471

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Thank you.

I don’t really care about employment in my model. I am only incorporating it because I have a firm that uses capital and labor as factors of production. Hence I incorporate labor supply (therefor leisure and hours worked…) for households as well. Can I just incorporate labor supply as being the number of employees and not hours worked per person ? Such as,


L(t) being the number of employed persons, C(t) total consumption
l(t) number of worked hours, and c(t) consumption per worker

Note that I’m in a growth model framework, not a DSGE one ; which is why fluctuations of hours worked at business cycle frequencies are not key for my model.

Thank you again.