Merge pull request #1100 from MahadevBalla/docs/infra-investment-leakage

Update docs for infra investment leakage parameter

Author: jdebacker

docs/book/content/intro/parameters.md

@@ -433,6 +433,13 @@ _Valid Range:_ min = 0.0 and max = 0.3
 _Out-of-Range Action:_ error  
 
 
+####  `infra_investment_leakage_rate`  
+_Description:_ Fraction of government infrastructure investment lost to leakage (e.g., corruption or other frictions) and treated as deadweight loss. Only $(1 - \phi_g)$ of investment enters the public capital stock.  
+_Value Type:_ float  
+_Valid Range:_ min = 0.0 and max = 1.0  
+_Out-of-Range Action:_ error  
+
+
 ####  `alpha_bs_T`  
 _Description:_ Proportional adjustment to government transfers relative to baseline amount when budget balance is true. Set value for base year, click '+' to add value for next year.  All future years not specified are set to last value entered.  
 _Value Type:_ float  

docs/book/content/theory/government.md

@@ -651,10 +651,10 @@ Note that the budget closure rule (described in Section ref{`SecUnbalGBCcloseRul
 
   ```{math}
   :label: EqUnbalGBC_Kgmt
-    K_{g,m,t+1} = (1 - \delta_g) K_{g,m,t} + I_{g,m,t} \quad\forall m,t
+    K_{g,m,t+1} = (1 - \delta_g) K_{g,m,t} + (1 - \phi_g) I_{g,m,t} \quad\forall m,t
   ```
 
-  where $\delta_g$ is the depreciation rate on infrastructure. The stock of public capital in each industry $m$ complements labor and private capital in the production function of the representative firm, in Equation {eq}`EqFirmsCESprodfun`.
+  where $\delta_g$ is the depreciation rate on infrastructure and $\phi_g$ (`infra_investment_leakage_rate`) is the fraction of infrastructure investment lost to leakage (e.g., corruption or other frictions). The stock of public capital in each industry $m$ complements labor and private capital in the production function of the representative firm, in Equation {eq}`EqFirmsCESprodfun`.
 
   Aggregate spending on UBI at time $t$ is the sum of UBI payments across all households at time $t$:
 

docs/book/content/theory/stationarization.md

@@ -261,7 +261,7 @@ The usual definition of equilibrium would be allocations and prices such that ho
 
   ```{math}
   :label: EqStnrz_Kgmt
-    \hat{K}_{g,m,t+1} = \frac{(1 - \delta_g)\hat{K}_{g,m,t} + \hat{I}_{g,m,t}}{e^{g_y}(1 + \tilde{g}_{n,t+1})}  \quad\forall m,t
+    \hat{K}_{g,m,t+1} = \frac{(1 - \delta_g)\hat{K}_{g,m,t} + (1 - \phi_g)\hat{I}_{g,m,t}}{e^{g_y}(1 + \tilde{g}_{n,t+1})}  \quad\forall m,t
   ```
 
   Stationary aggregate universal basic income expenditure is found in one of two ways depending on how the individual UBI payments $ubi_{j,s,t}$ are modeled. In Section {ref}`SecUBI` of Chapter {ref}`Chap_UnbalGBC`, we discuss how UBI payments to households $ubi_{j,s,t}$ can be growth adjusted so that they grow over time at the rate of productivity growth or non-growth adjusted such that they are constant overtime. In the first case, when UBI benefits are growth adjusted and growing over time, the stationary aggregate government UBI payout $\hat{UBI}_t$ is found by dividing {eq}`EqUnbalGBC_UBI` by $e^{g_y t}\tilde{N}_t$. In the second case, when UBI benefits are constant over time and not growing with productivity, the stationary aggregate government UBI payout $\hat{UBI}_t$ is found by dividing {eq}`EqUnbalGBC_UBI` by only $\tilde{N}_t$.