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Update foreign private capital K^f specification #801

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rickecon opened this issue Apr 11, 2022 · 0 comments
Open

Update foreign private capital K^f specification #801

rickecon opened this issue Apr 11, 2022 · 0 comments

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@rickecon
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With the addition of government capital K_g to the model, I am worried about our derivation and specification in the OG-Core master branch of foreign capital inflow to the country K^f. In the documentation, the current specification is derived in equations (73), (74), and (75) in the Private capital market clearing section of the Market Clearing chapter.

Currently, the open-economy domestic private capital demand K^{d,r*} is determined by (i) using the open-economy interest rate r* to solve for (ii) the open-economy capital-labor ratio, then (iii) multiply the open-economy capital-labor ratio by L to get the implied open-economy capital demand.

This approach of deriving a capital-labor ratio from r* only works in the model without government capital K_g=0. Furthermore, in this approach in step (iii), the L multiplied by the capital-labor ratio is based off of the market determined interest rate and not the open-economy rate.

I propose two alternative approaches, and I favor the latter approach (2).

  1. In the presence of government capital, we could calculate K^{d,r*} by calculating (a) the open-economy Y/K given r*, then back out the open economy K^{d,r*} as Y / (Y/K).
  2. We could assume that K^f is a fixed percent zeta_K of total capital K. This means the private capital market clearing condition K = K^d + K^f is equivalent to saying K^f = zeta_K * K and K^d = (1 - zeta_K) * K.

I think that both approaches (1) and (2) will work. Approach (1) is most analogous to what we are currently doing, and it incorporates K_g > 0 into the solution. However, approach (2) is more simple. And its specification is more closely connected to the way we would calibrate zeta_K.

cc: @jdebacker

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