Log utility and normalization in Dynare

Good morning everyone,

I have a normalized utility function that is log in consumption and hours worked in my model. Does it complicate computations in Dynare since C(t)/C is less than 1 for some years ? C being the point of normalization. The same issue would apply to hours worked since (1-l(t)) is less than 1.

Thank you.

Best,

You need to explain this in more detail. What is C (without any index) in your context?

C is the point of normalisation. I have a normalised consumption function because I have CES functions for consumption ( one between non durable goods and energy services, another one between energy and durable goods). I want to perform robustness test on elasticities , which is why I have to normalise my consumption functions. That is why I normalised utility.

Is it clear enough ?

Thank you

I see. But why should it be a problem if the ratio is less than 1?

Oops I forgot to mention that I have a log utility in consumption. A log with a value less than 1 is a problem, isn’t it?

Thanks

No, a log with a negative value below 0 is a problem.

Thank you.

One last question: for the construction of total hours worked, should I take (employed persons x average annual hours worked) or (workforce x average annual hours worked). Since I do not model any unemployment in my growth model, my first hint would be to use workforce data.

Usually, in models without extensive margin and explicit population growth, you want hours per person in the workforce. That is, you take
(employed persons x average annual hours worked)/workforce

Thank you.

I actually have population growth in my model. Should I still apply your response to my data ?

Best

I mean can I estimate (not from Dynare) my elasticity of substitution between capital and labor, with capital in billion euros and labor from workforce in person without taking into account average hours worked (even if my model has labour hours in the production function)? I get better estimates that way than with data on total hours worked (workforce x average hours worked).

I actually have a growth model assessing long run impacts (2050), so hours worked should not really matter in such a model. Should I erase hours worked from my model?

Thank you

That is a question that cannot be generally answered without a knowing lot more details. But generally, if your model is built for the long-run and therefore only has implications for the workforce, then you should not use hours worked. Of course, you need to be consistent with your parameterization. Estimating a substitution elasticity for the short run using hours worked would not be advisable. But as you are estimating the elasticity using the workforce, this should be fine.

Thank you

I get better estimates with number of employed persons than workforce. Can I use employed persons instead of workforce for the estimation of capital-labor elasticity, even if I do not model unemployment ?

Best

The most important things it to approach this with some economics. You are trying to estimate the substitution elasticity in a production function. What enters the production function is usually the people that actually work, not the ones that could work. The workforce is not a production factor. So unless you identification is based on the workforce for some reason, I don’t see how you could use it for estimation.