Update foreign private capital K^f specification

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Evaluación

Dificultad
5/5
Tiempo estimado
Más de una semana
Aptitud para principiantes
12/100
Tipo de issue
Refactorización
Claridad
Bastante claro
Estado de actividad
Estancado
Stack tecnológico
python
Área
backend, documentation

Línea de trabajo

The open question is the derivation of foreign private capital K^f in the market clearing chapter, equations (73)-(75) of the docs page linked in the issue. Read that section first, then the open-economy capital demand logic it describes. Choosing between the two proposed approaches needs maintainer input, since the issue has no comments yet. Done means a decided specification, with the docs equations and the code updated to match.

Escrito por el modelo de indexación a partir del texto del issue.

Descripción

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

Lenguaje dominante
Python
Estrellas
85
Forks
153
Merge medio
1 d 19 h
PR fusionados (30 d)
19

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