Capital-Labor substitution and housing stock

General DSGE Modeling
1

Dear members,

I was wondering if I needed to take out of total capital stock the housing stock to estimate the elasticity of substitution between labor and capital. My first hint would be yes. However, I have a very aggregated economy, with one sole producer, meaning that its GVA includes also the GVA from the housing market and its the capital factor includes the housing stock.

Besty regards

2

People usually do not distinguish between structures and equipment.

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3

Thanks a lot.

I often see aggregated growth models that take micro-estimates (not at the aggregate level, but for the private non-residential sector) of substitution elasticities. I find this odd as the elasticity is not coherent with the aggregated model.

Best regards

4

Strictly speaking, it is not consistent. But the question is whether the numbers would differ. Most models assume that the elasticity is the same, regardless of the type of capital considered.

5

Thanks.

Well it differs. I have an estimation of 0.5 if I take out the public sector and the housing market. And I have an estimate of 0.75 if I don’t take out theses sectors from Y, K and L…

6

But those are point estimates. Chirinko (2008) surveys the literature and reports a range between 0.4 and 0.6 and Oberfield/Raval (2019) now report a range of 0.5 to 0.7. So you could most probably not distinguish between the values.

7

Thanks for the references.

Do you mean that 0.75 ou 0.5, this does not matter much?

8

I don’t know whether the difference matters qualitatively. But empirically, you can’t tell for sure whether the correct value is 0.5 or 0.75.

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