Skip to content

Commit

Permalink
Updated aggregate remittances in resource constraint
Browse files Browse the repository at this point in the history
  • Loading branch information
rickecon committed Sep 18, 2024
1 parent ca46d5f commit abad20e
Show file tree
Hide file tree
Showing 3 changed files with 10 additions and 8 deletions.
6 changes: 3 additions & 3 deletions docs/book/content/theory/market_clearing.md
Original file line number Diff line number Diff line change
Expand Up @@ -117,7 +117,7 @@

```{math}
:label: EqMarkClrGoods_M
Y_{M,t} = C_{M,t} + I_{M,t} + I_{g,t} + G_t + r_{p,t} K^f_t + r_{p,t}D^f_t - (K^f_{t+1} - K^f_t) - \bigl(D^f_{t+1} - D^f_t\bigr) \quad\forall t
Y_{M,t} = C_{M,t} + I_{M,t} + I_{g,t} + G_t + r_{p,t} K^f_t + r_{p,t}D^f_t - (K^f_{t+1} - K^f_t) - \bigl(D^f_{t+1} - D^f_t\bigr) - RM_t \quad\forall t
```
where
```{math}
Expand All @@ -129,9 +129,9 @@

In the partially open economy, we must add to the right-hand-side of {eq}`EqMarkClrGoods_M` the output paid to the foreign owners of capital $r_{p,t} K^f_t$ and to the foreign holders of government debt $r_{p,t}D^f_t$. And we must subtract off the foreign inflow component $K^f_{t+1} - K^f_t$ from private capital investment as shown in the first term in parentheses on the right-hand-side of {eq}`EqMarkClrGoods_M`. You can see in the definition of private investment {eq}`EqMarkClrGoods_IMt` where this amount of foreign capital is part of $I_{M,t}$.

Similarly, we must subtract off the foreign purchases of new government debt $D^f_{t+1} - D^f_t$ as shown in the second term in parentheses on the right-hand-side of {eq}`EqMarkClrGoods_M`. These new foreign purchases of government debt are part of $I_{g,t}$ and $G_t$, as they are functions of GDP $p_tY_t$, as shown in {eq}`EqUnbalGBC_Gt`, {eq}`EqUnbalGBC_Igt`, and the government budget constraint {eq}`EqUnbalGBCbudgConstr`. Foreign lending relaxes the resource constraint.
Similarly, we must subtract off the foreign purchases of new government debt $D^f_{t+1} - D^f_t$ and aggregate remittances $RM_t$ as shown in the second term in parentheses and the last term, respectively, on the right-hand-side of {eq}`EqMarkClrGoods_M`. The new foreign purchases of government debt are part of $I_{g,t}$ and $G_t$, as they are functions of GDP $Y_t$, as shown in {eq}`EqUnbalGBC_Gt`, {eq}`EqUnbalGBC_Igt`, and the government budget constraint {eq}`EqUnbalGBCbudgConstr`. Foreign lending relaxes the resource constraint. And aggregate remittances are part of aggregate consumption $C_t$ and also relax the resource constraint.

Net exports (imports) of capital in the form of foreign private capital inflows $K^f_t$ and foreign holdings of government debt $D^f_t$ are clearly accounted for in {eq}`EqMarkClrGoods_M`. Foreign remittances described in Section {ref}`SecHHremit` of Chapter {ref}`Chap_House` are indirectly accounted for in these goods market clearing equations by domestic household consumption and savings, which are augmented by this income from abroad.
Net exports (imports) of capital in the form of foreign private capital inflows $K^f_t$, foreign holdings of government debt $D^f_t$, and remittances $RM_t$ are clearly accounted for in {eq}`EqMarkClrGoods_M`. Foreign remittances received by domestic households are described in Section {ref}`SecHHremit` of Chapter {ref}`Chap_House`.


(SecMarkClrBQ)=
Expand Down
4 changes: 2 additions & 2 deletions docs/book/content/theory/stationarization.md
Original file line number Diff line number Diff line change
Expand Up @@ -333,7 +333,7 @@ The usual definition of equilibrium would be allocations and prices such that ho
```


### Stationarized Pension System Equations
### Stationarized Pension System Equations

#### Stiationarized Notional Defined Contributions Equations

Expand Down Expand Up @@ -492,7 +492,7 @@ Stationarized pension amount derivative:
```{math}
:label: EqStnrzMarkClrGoods_M
\hat{Y}_{M,t} &= \hat{C}_{M,t} + \hat{I}_{M,t} + \hat{I}_{g,t} + \hat{G}_t + r_{p,t} \hat{K}^f_t + r_{p,t}\hat{D}^f_t ... \\
&\quad - \Bigl(e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{K}^f_{t+1} - \hat{K}^f_t\Bigr) - \Bigl(e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{D}^f_{t+1} - \hat{D}^f_t\Bigr) \quad\forall t
&\quad - \Bigl(e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{K}^f_{t+1} - \hat{K}^f_t\Bigr) - \Bigl(e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{D}^f_{t+1} - \hat{D}^f_t\Bigr) - \hat{RM}_t \quad\forall t
```
where
```{math}
Expand Down
8 changes: 5 additions & 3 deletions ogcore/aggregates.py
Original file line number Diff line number Diff line change
Expand Up @@ -522,10 +522,12 @@ def resource_constraint(Y, C, G, I_d, I_g, net_capital_flows, RM):
Compute the error in the resource constraint.
.. math::
\text{rc_error} = \hat{Y}_t - \hat{C}_t -
\begin{split}
\text{rc_error} &= \hat{Y}_t - \hat{C}_t -
\Bigl(e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{K}^d_{t+1} -
\hat{K}^d_t\Bigr) - \delta\hat{K}_t - \hat{G}_t - \hat{I}_{g,t} -
\text{net capital outflows}_t - RM_t
\hat{K}^d_t\Bigr) - \delta\hat{K}_t - \hat{G}_t - \hat{I}_{g,t} ... \\
&\qquad -\: \hat{\text{net capital outflows}}_t - \hat{RM}_t
\end{split}
Args:
Y (array_like): aggregate output by industry
Expand Down

0 comments on commit abad20e

Please sign in to comment.