Allows government consumption and investment to come from multiple sectors

docs/book/content/intro/parameters.md

@@ -221,7 +221,7 @@ _Out-of-Range Action:_ error
 
 
 ####  `io_matrix`  
-_Description:_ Input-output matrix used to map production outputs into consumption goods using a fixed coefficient model.  This matrix has dimensions I x M, where I is the number of distinct consumption goods and M is the number of distinct production goods.  The sum each row of this matrix must be 1.  
+_Description:_ Input-output matrix used to map production outputs into consumption and government goods using a fixed coefficient model. It has dimensions (I+2) x M. The first I rows map consumption goods, row I+1 maps government consumption, and row I+2 maps infrastructure investment. Each row sums to 1.
 _Value Type:_ float  
 _Valid Range:_ min = 0.0 and max = 1.0  
 _Out-of-Range Action:_ error  

docs/book/content/theory/equilibrium.md

@@ -179,7 +179,7 @@ The computational algorithm for solving for the steady-state follows the steps b
        ```
 
         1. Make sure that steady-state government spending is nonnegative $\bar{G}\geq 0$. If steady-state government spending is negative, that means the government is getting resources to supply the debt from outside the economy each period to stabilize the debt-to-GDP ratio. $\bar{G}<0$ is a good indicator of unsustainable policies.
-	      1. Make sure that the resource constraint (goods market clearing) {eq}`EqStnrzMarkClrGoods_M` is satisfied. It is redundant, but this is a good check as to whether everything worked correctly.
+    1. Make sure that the industry resource constraints are satisfied, including the input-output demands for government consumption and infrastructure goods. One goods-market condition is redundant, but it provides a useful solution check.
 	      2. Make sure that the government budget constraint {eq}`EqStnrzGovBC` binds.
 	      3. Make sure that all the $2JS$ household Euler equations are solved to a satisfactory tolerance.
 
@@ -411,7 +411,7 @@ The stationary non-steady state (transition path) solution algorithm has followi
 
 24. If the maximum absolute error among the M-1+5 outer loop error terms is less-than-or-equal-to some small positive tolerance $toler_{tpi,out}$ in each period along the transition path, $\max\big|\left(error_{r_p}, error_r, error_w, error_p, error_{bq},error_{tr}\right)\bigr| \leq toler_{tpi,out}$ then the non-steady-state equilibrium has been found.
 
-    1. Make sure that the resource constraint for industry $M$ (goods market clearing) {eq}`EqStnrzMarkClrGoods_M` is satisfied in each period along the time path. It is redundant, but this is a good check as to whether everything worked correctly.
+    1. Make sure that every industry resource constraint, including the input-output demands for government consumption and infrastructure goods, is satisfied in each period. One condition is redundant, but it provides a useful solution check.
     2. Make sure that the government budget constraint {eq}`EqStnrzGovBC` binds in every period.
     3. Make sure that all the $(T+S)\times2JS$ household Euler equations are solved to a satisfactory tolerance in every period.
 

docs/book/content/theory/firms.md

@@ -26,7 +26,7 @@ The production side of the `OG-Core` model is populated by $M$ industries indexe
     Y_{m,t} = Z_{m,t} (K_{m,t})^{\gamma_m} (K_{g,m,t})^{\gamma_{g,m}}(e^{g_y t}L_{m,t})^{1-\gamma_m-\gamma_{g,m}} \quad\forall m,t \quad\text{for}\quad \varepsilon_m=1
   ```
 
-Industry $M$ in the model is unique in two respects.  First, we will define industry $M$ goods as the numeraire in OG_Core.  Therefore, all quantities are in terms of industry $M$ goods and all prices are relative to the price of a unit of industry $M$ goods.  Second, the model solution is greatly simplified if just one production industry produces capital goods.  The assumption in OG-Core is that industry $M$ is the only industry producing capital goods (though industry $M$ goods can also be used for consumption).
+Industry $M$ in the model is unique in two respects. First, we define industry $M$ goods as the numeraire in OG-Core. Therefore, all prices are relative to the price of a unit of industry $M$ goods. Second, industry $M$ is the only industry producing private capital goods. Household consumption goods, government consumption goods, and infrastructure investment goods may each combine output from all $M$ industries through the input-output matrix.
 
 (EqFirmsFOC)=
 ## Optimality Conditions

docs/book/content/theory/government.md

@@ -619,10 +619,10 @@ Note that the budget closure rule (described in Section ref{`SecUnbalGBCcloseRul
 
   ```{math}
   :label: EqUnbalGBCbudgConstr
-    D_{t+1} + Rev_t + FA_t = (1 + r_{gov,t})D_t + G_t + I_{g,t} + Pensions_t + TR_t + UBI_t  \quad\forall t
+    D_{t+1} + Rev_t + FA_t = (1 + r_{gov,t})D_t + p_{g,t}G_t + p_{I_g,t}I_{g,t} + Pensions_t + TR_t + UBI_t  \quad\forall t
   ```
 
-  where $r_{gov,t}$ is the interest rate paid by the government defined in equation {eq}`EqUnbalGBC_rate_wedge` below, $G_{t}$ is government spending on public goods, $I_{g,t}$ is total government spending on infrastructure investment, $TR_{t}$ are non-pension government transfers, and $UBI_t$ is the total UBI transfer outlays across households in time $t$. All variables in {eq}`EqUnbalGBCbudgConstr` are real variables denominated in units of current-period output in industry $M$ the numeraire ($p_{M,t}=1$ for all $t$).
+  where $G_t$ and $I_{g,t}$ are quantities of composite government consumption and infrastructure goods. Their prices are determined by the final two rows of the input-output matrix, $p_{g,t}=\sum_m\pi_{I+1,m}p_{m,t}$ and $p_{I_g,t}=\sum_m\pi_{I+2,m}p_{m,t}$. Other fiscal flows are denominated in units of industry $M$, the numeraire ($p_{M,t}=1$).
 
   We assume that government spending on public goods in terms of the numeraire good is a fixed fraction of GDP each period in the initial periods.
 

docs/book/content/theory/market_clearing.md

@@ -107,17 +107,17 @@
     C_{i,t} \equiv \sum_{s=E+1}^{E+S}\sum_{j=1}^{J}\omega_{s,t}\lambda_j c_{i,j,s,t} \quad\forall i,t
   ```
 
-  Because we make a simplifying assumption that only the $M$th industry output can be used as investment, government spending, or government debt, consumption demand equals total output of good $m$ in the first $M-1$ industries.
+  Government consumption and infrastructure investment are also fixed-coefficient composites. Let $\pi_{I+1,m}$ and $\pi_{I+2,m}$ be the shares of industry $m$ used in one unit of those goods. Because private capital goods and net international financial flows remain assigned to industry $M$, the first $M-1$ goods-market conditions are
   ```{math}
   :label: EqMarkClrGoods_Mm1
-    Y_{m,t} = C_{m,t} \quad\forall t \quad\text{and}\quad m=1,2,...M-1
+    Y_{m,t} = C_{m,t} + \pi_{I+1,m}G_t + \pi_{I+2,m}I_{g,t} \quad\forall t \quad\text{and}\quad m=1,2,...M-1
   ```
 
-  The output of the $M$th industry can be used for private investment, infrastructure investment, government spending, and government debt.[^M_ind] As such, the market clearing condition in the $M$th industry will look more like the traditional $Y=C+I+G+NX$ expression.[^RCrates_note]
+  Industry $M$ additionally produces all private capital goods and absorbs the modeled net international financial flows.[^M_ind]
 
   ```{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) - RM_t \quad\forall t
+    Y_{M,t} = C_{M,t} + \pi_{I+1,M}G_t + \pi_{I+2,M}I_{g,t} + I_{M,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}

docs/book/content/theory/stationarization.md

@@ -244,7 +244,7 @@ The usual definition of equilibrium would be allocations and prices such that ho
 
   ```{math}
   :label: EqStnrzGovBC
-    e^{g_y}\left(1 + \tilde{g}_{n,t+1}\right)\hat{D}_{t+1} + \hat{Rev}_t + \hat{FA}_t = (1 + r_{gov,t})\hat{D}_t + \hat{G}_t + \hat{I}_{g,t} + \hat{Pensions}_t + \hat{TR}_t + \hat{UBI}_t \quad\forall t
+    e^{g_y}\left(1 + \tilde{g}_{n,t+1}\right)\hat{D}_{t+1} + \hat{Rev}_t + \hat{FA}_t = (1 + r_{gov,t})\hat{D}_t + p_{g,t}\hat{G}_t + p_{I_g,t}\hat{I}_{g,t} + \hat{Pensions}_t + \hat{TR}_t + \hat{UBI}_t \quad\forall t
   ```
 
   The stationarized versions of the rule for total government infrastructure investment spending $I_{g,t}$ in {eq}`EqUnbalGBC_Igt` and the rule for government investment spending in each industry in {eq}`EqUnbalGBC_Igt` are found by dividing both sides of the respective equations by $e^{g_y t}\tilde{N}_t$.

examples/multi_industry_example.py

@@ -68,7 +68,9 @@ def main():
         "debt_ratio_ss": 1.5,
         "alpha_T": alpha_T.tolist(),
         "alpha_G": alpha_G.tolist(),
-        "io_matrix": np.eye(3).tolist(),
+        "io_matrix": np.vstack(
+            [np.eye(3), np.array([[0.0, 0.0, 1.0]] * 2)]
+        ).tolist(),
         "tau_c": [[0]],
     }