# Capital-Labor substitution and housing stock

**URL:** <https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483>\
**Category:** General DSGE Modeling\
**Created:** [2 April 2020 17:49 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483 "2020-04-02T17:49:57Z")\
**Posts on this page:** 8\
**Page:** 1

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**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\
**Post date:** [2 April 2020 17:49 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/1 "2020-04-02T17:49:58Z")

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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

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [3 April 2020 09:22 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/2 "2020-04-03T09:22:49Z")

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People usually do not distinguish between structures and equipment.

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**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\
**Post date:** [3 April 2020 09:38 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/3 "2020-04-03T09:38:34Z")

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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

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [3 April 2020 09:57 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/4 "2020-04-03T09:57:41Z")

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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.

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**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\
**Post date:** [3 April 2020 09:59 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/5 "2020-04-03T09:59:08Z")

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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…

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [3 April 2020 10:16 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/6 "2020-04-03T10:16:33Z")

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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.

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**Author:** ![dacorb](https://forum.dynare.org/letter_avatar_proxy/v4/letter/d/bb73d2/32.png) [@dacorb](https://forum.dynare.org/u/dacorb)\
**Post date:** [3 April 2020 10:17 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/7 "2020-04-03T10:17:56Z")

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Thanks for the references.

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

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**Author:** ![jpfeifer](https://forum.dynare.org/user_avatar/forum.dynare.org/jpfeifer/32/5044_2.png) [@jpfeifer](https://forum.dynare.org/u/jpfeifer)\
**Post date:** [3 April 2020 10:38 UTC](https://forum.dynare.org/t/capital-labor-substitution-and-housing-stock/15483/8 "2020-04-03T10:38:37Z")

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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.