describe r_gov params

docs/book/OGZAF_references.bib

@@ -738,3 +738,18 @@ @ARTICLE{Zhang:1997
   month = {December},
   pages = {2187-2209},
 }
+
+@Article{LMW2023,
+  author={Li, Delong and Magud, Nicolas E. and Werner, Alejandro},
+  title={{The long-run impact of sovereign yields on corporate yields in emerging markets}},
+  journal={Journal of International Money and Finance},
+  year=2023,
+  volume={130},
+  number={C},
+  pages={},
+  month={},
+  keywords={Bonds; Emerging markets; Sovereign risk; Transfer risk; Liquidity premium; JEL Classification Number},
+  doi={10.1016/j.jimonfin.2022.1},
+  abstract={We analyze the long-run impact of sovereign yields on corporate yields of the same country, finding that, for emerging markets, the average pass-through is around one. The pass-through is larger in countries with greater sovereign risk and where sovereign bonds are more liquid. The pass-through is also greater for corporate bonds with lower ratings, shorter maturities, and those issued by financial companies and government-related firms. Our results support theoretical arguments that corporate and sovereign yields are linked together through credit risk and liquidity premiums. Consequently, high sovereign risk can slowdown growth by persistently increasing private sector borrowing costs.},
+  url={https://ideas.repec.org/a/eee/jimfin/v130y2023ics0261560622001516.html}
+}

docs/book/content/calibration/macro.md

@@ -25,6 +25,18 @@ We set $\zeta_K = 0.9$. Note, this parameter is harder to pin down from the data
 
 The path of government debt is endogenous.  But the initial value is exogenous.  To avoid converting between model units and dollars, we calibrate the initial debt to GDP ratio, rather than the dollar value of the debt.  This is the model parameter $\alpha_D$.  We compute this from the ratio of publicly held debt outstanding to GDP.  Based on 2023 values, this gives us a ratio of 0.59.
 
+
+#### Interest rates on government debt
+
+We assume that there is a wedge between the real rate of return on private capital and the real interest rate on government debt.  We model this wedge a scale and level shift.  Specifically, we assume that the real interest rate on government debt, $r_{gov,t}$, is related to the real rate of return on private capital, $r_{t}$, by the following equation:
+
+```{math}
+:label: eqn:r_gov
+    r_{gov,t} = (1-\tau_{d,t})r_t + \mu_d
+```
+
+where $\tau_d$ is the scale parameter and $\mu_d$ is the level shift parameter.  We set the values of these two parameters to 0.245 and -0.034, respectively.  These are found by using the estimated relationship between corporate and sovereign yields in {cite}`LMW2023` (Table 8, Column 2) and simulating a series of corporate yields given a series of sovereign yields between 2% and 12%.  We then estimate the scale and level shift parameters that best fit these simulated data using ordinary least squares.
+
 ### Aggregate transfers
 
 Aggregate (non-Social Security) transfers to households are set as a share of GDP with the parameter $\alpha_T$. We exclude Social Security from transfers since it is modeled specifically. With this definition, the share of transfers to GDP in 2015 is 0.04 according to [IMF data](https://data.imf.org/?sk=b052f0f0-c166-43b6-84fa-47cccae3e219&hide_uv=1).
@@ -34,3 +46,4 @@ Aggregate (non-Social Security) transfers to households are set as a share of GD
 Government spending on goods and services are also set as a share of GDP with the parameter $\alpha_G$. We define government spending as:
     <center>Government Spending = Total Outlays - Transfers - Net Interest on Debt - Social Security</center>
 With this definition, the share of government expenditure to GDP is 0.267 based on [data from the IMF](https://data.imf.org/?sk=b052f0f0-c166-43b6-84fa-47cccae3e219&hide_uv=1).
+