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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).
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).
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.
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 countryK^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 rater*
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 capitalK_g=0
. Furthermore, in this approach in step (iii), theL
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).
K^{d,r*}
by calculating (a) the open-economyY/K
givenr*
, then back out the open economyK^{d,r*}
asY / (Y/K)
.K^f
is a fixed percentzeta_K
of total capitalK
. This means the private capital market clearing conditionK = K^d + K^f
is equivalent to sayingK^f = zeta_K * K
andK^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 calibratezeta_K
.cc: @jdebacker
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