Economic Aggregates Equations

Aggregates

open_cge.aggregates

open_cge.aggregates.eqKd(g, Sp, lam, pq)[source]

Domestic capital holdings.

\[K^{d} = \frac{S^{p}}{g\sum_{i}\lambda_{i}pq_{i}}\]
Parameters

  • g (float) – Exogenous long run growth rate of the economy

  • Sp (float) – Total household savings

  • lam (1D numpy array) – Fixed shares of investment for each good i

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

Returns

Domestically owned capital

Return type

Kd (float)

open_cge.aggregates.eqKf(Kk, Kd)[source]

Foreign holdings of domestically used capital.

\[K^{f} = KK - K^{d}\]
Parameters

  • Kk (float) – Total capital stock

  • Kd (float) – Domestically owned capital

Returns

Foreign owned domestic capital

Return type

Kf (float)

open_cge.aggregates.eqKk(pf, Ff, R, lam, pq)[source]

Capital market clearing equation.

\[KK = \frac{pf * Ff}{R \sum_{i}\lambda_{i}pq_{i}}\]
Parameters

  • pf (1D numpy array) – The price of factor h

  • Ff (1D numpy array) – Endowment of factor h

  • R (float) – Real return on capital

  • lam (1D numpy array) – Fixed shares of investment for each good i

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

Returns

Total capital stock

Return type

Kk (float)

open_cge.aggregates.eqSf(g, lam, pq, Kf)[source]

Net foreign investment/savings.

\[Sf = g Kf \sum_{i} \lambda_{i} pq_{i}\]
Parameters

  • g (float) – Exogenous long run growth rate of the economy

  • lam (1D numpy array) – Fixed shares of investment for each good i

  • pq (1D numpy array) – price of the Armington good (domestic + imports) for each good i

  • Kf (float) – Foreign owned domestic capital

Returns

Total foreign savings (??)

Return type

Sf (float)

open_cge.aggregates.eqSp(ssp, pf, Ff, Fsh, Trf)[source]

Total household savings.

\[Sp = ssp \cdot \left(\sum_{h}pf_{h}Ff_{h} \right)\]
Parameters

  • ssp (float) – Fixed household savings rate

  • pf (1D numpy array) – The price of factor h

  • Ff (1D numpy array) – Endowment of factor h

  • Fsh (float) – Repatriated profits

  • Trf (float) – Total transfers to households

Returns

Total household savings

Return type

Sp (float)

open_cge.aggregates.eqXXv(g, Kk)[source]

Total investment.

\[XXv = g \cdot KK\]
Parameters

  • g (float) – Exogenous long run growth rate of the economy

  • Kk (float) – Total capital stock

Returns

Total investment.

Return type

XXv (float)

open_cge.aggregates.eqbop(pWe, pWm, E, M, Sf, Fsh, er)[source]

Balance of payments.

\[\sum_{i}pWe_{i}E_{i} + \frac{Sf}{\varepsilon} = \sum_{i}pWm_{i}M_{i} + \frac{Fsh}{\varepsilon}\]
Parameters

  • pWe (1D numpy array) – The world export price of good i in foreign currency

  • pWm (1D numpy array) – The world import price of good i in foreign currency.

  • E (1D numpy array) – Exports of good i

  • M (1D numpy array) – Imports of good i

  • Sf (float) – Total foreign savings

  • Fsh (float) – Repatriated profits

  • er (float) – The real exchange rate

Returns

Error in balance of payments equation.

Return type

bop_error (float)

open_cge.aggregates.eqpf(F, Ff0)[source]

Comparing labor demand from the model to that in the data.

..math::

F_{h} - sum_{i}F_{h,i}

Parameters

  • F (2D numpy array) – The use of factor h in the production of good i

  • Ff0 (float) – Total demand for factor h from SAM

Returns

Error in aggregate labor demand

Return type

pf_error (float)

open_cge.aggregates.eqpk(F, Kk, Kk0, Ff0)[source]

Comparing capital demand in the model and data.

..math:: sum_{i}F_{h,i} - frac{Kk}{Kk0} cdot Ff0

Parameters

  • F (2D numpy array) – The use of factor h in the production of good i

  • Kk (float) – Total capital stock

  • Kk0 (float) – Total capital stock from SAM

  • Ff0 (float) – Total labor demand from SAM

Returns

Error in aggregate capital demand

Return type

pk_error (float)

open_cge.aggregates.eqpqerror(Q, Xp, Xg, Xv, X)[source]

Resource constraint.

\[Q(i) = X^{p}_{i} + X^{g}_{i} + X^{v}_{i} + \sum_{i}X_{i,j}\]
Parameters

  • Q (1D numpy array) – The domestic supply of good Q(i), the Armington good

  • Xp (1D numpy array) – Demand for production good i by consumers

  • Xg (1D numpy array) – Government expenditures on good i

  • Xv (1D numpy array) – Investment demand for each good i

  • X (2D numpy array) – Demand for factor h used in the production of good i

Returns

Error in resource constraint for each good i

Return type

pq_error (1D numpy array)