Make interest rate on government debt a function of the debt to GDP ratio

CHANGELOG.md

@@ -5,6 +5,12 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## [0.15.2] - 2025-01-22 12:00:00
+
+### Added
+
+- A new parameters, `r_gov_DY` and `r_gov_DY2`, that allow the government interest rate to be a function of the debt-to-GDP ratio.  See PR [#1037](https://github.com/PSLmodels/OG-Core/pull/1037)
+
 ## [0.15.1] - 2026-01-19 12:00:00
 
 ### Added
@@ -493,6 +499,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Any earlier versions of OG-USA can be found in the [`OG-Core`](https://github.com/PSLmodels/OG-Core) repository [release history](https://github.com/PSLmodels/OG-Core/releases) from [v.0.6.4](https://github.com/PSLmodels/OG-Core/releases/tag/v0.6.4) (Jul. 20, 2021) or earlier.
 
 
+[0.15.2]: https://github.com/PSLmodels/OG-Core/compare/v0.15.1...v0.15.2
+[0.15.1]: https://github.com/PSLmodels/OG-Core/compare/v0.15.0...v0.15.1
 [0.15.0]: https://github.com/PSLmodels/OG-Core/compare/v0.14.14...v0.15.0
 [0.14.14]: https://github.com/PSLmodels/OG-Core/compare/v0.14.13...v0.14.14
 [0.14.13]: https://github.com/PSLmodels/OG-Core/compare/v0.14.12...v0.14.13

docs/book/content/theory/government.md

@@ -667,14 +667,14 @@ Note that the budget closure rule (described in Section ref{`SecUnbalGBCcloseRul
 (SecRateWedge)=
 ## Interest Rate on Government Debt and Household Savings
 
-  Despite the model having no aggregate risk, it may be helpful to build in an interest rate differential between the rate of return on private capital and the interest rate on government debt. Doing so helps to add realism by including a risk premium. `OG-Core` allows users to set an exogenous wedge between these two rates. The interest rate on government debt,
+  Despite the model having no aggregate risk, it may be helpful to build in an interest rate differential between the rate of return on private capital and the interest rate on government debt. Doing so helps to add realism by including a risk premium. `OG-Core` allows users to set an exogenous wedge between these two rates. `OG-Core` also allows for the risk premium on debt to be a quadratic function of the debt-to-GDP ratio. The interest rate on government debt is given by:
 
   ```{math}
     :label: EqUnbalGBC_rate_wedge
-    r_{gov, t} = (1 - \tau_{d, t})r_{t} - \mu_{d}
+    r_{gov, t} = (1 - \tau_{d, t})r_{t} - \mu_{d} + \beta_{1}\frac{D_t}{Y_t} + \beta_{2}\left(\frac{D_t}{Y_t}\right)^2
   ```
 
-  where $r_t$ is the marginal product of capital faced by firms. The two parameters, $\tau_{d,t}$ and $\mu_{d,t}$ can be used to allow for a government interest rate that is a percentage hair cut from the market rate or a government interest rate with a constant risk premium.
+  where $r_t$ is the marginal product of capital faced by firms. The two parameters, $\tau_{d,t}$ and $\mu_{d,t}$ can be used to allow for a government interest rate that is a percentage hair cut from the market rate or a government interest rate with a constant risk premium.  The parameters $\beta_1$ and $\beta_2$ can be used to allow for a quadratic risk premium on government debt that is a function of the debt-to-GDP ratio.
 
 
 (SecUnbalGBCcloseRule)=

ogcore/SS.py

@@ -444,7 +444,7 @@ def inner_loop(outer_loop_vars, p, client):
     B = aggr.get_B(bssmat, p, "SS", False)
 
     # Find gov't debt
-    r_gov = fiscal.get_r_gov(r, p, "SS")
+    r_gov = fiscal.get_r_gov(r, p.debt_ratio_ss, p, "scalar", t=-1)
     D, D_d, D_f, new_borrowing, _, new_borrowing_f = fiscal.get_D_ss(
         r_gov, Y, p
     )
@@ -495,7 +495,7 @@ def inner_loop(outer_loop_vars, p, client):
         new_r = firm.get_r(Y_vec[-1], K_vec[-1], p_m, p, "SS", -1)
     new_w = firm.get_w(Y_vec[-1], L_vec[-1], p_m, p, "SS")
 
-    new_r_gov = fiscal.get_r_gov(new_r, p, "SS")
+    new_r_gov = fiscal.get_r_gov(new_r, p.debt_ratio_ss, p, "scalar", t=-1)
     # now get accurate measure of debt service cost
     (
         D,
@@ -829,7 +829,7 @@ def SS_solver(
     K_vec_ss = new_K_vec
     L_vec_ss = new_L_vec
     Y_vec_ss = new_Y_vec
-    r_gov_ss = fiscal.get_r_gov(rss, p, "SS")
+    r_gov_ss = fiscal.get_r_gov(rss, p.debt_ratio_ss, p, "scalar", t=-1)
     p_m_ss = new_p_m
     p_i_ss = np.dot(p.io_matrix, p_m_ss)
     p_tilde_ss = aggr.get_ptilde(p_i_ss, p.tau_c[-1, :], p.alpha_c)

ogcore/TPI.py

@@ -715,7 +715,8 @@ def run_TPI(p, client=None):
     total_tax_revenue = np.ones(p.T + p.S) * ss_vars["total_tax_revenue"]
 
     # Compute other interest rates
-    r_gov = fiscal.get_r_gov(r, p, "TPI")
+    r_gov = np.ones_like(r) * ss_vars["r_gov"]
+    r_gov[: p.T] = fiscal.get_r_gov(r[: p.T], D[: p.T] / Y[: p.T], p, "TPI")
     r_p = np.ones_like(r) * ss_vars["r_p"]
     MPKg = np.zeros((p.T, p.M))
     for m in range(p.M):
@@ -1082,6 +1083,11 @@ def run_TPI(p, client=None):
             "TPI",
         )
         total_tax_revenue[: p.T] = total_tax_rev
+        if not p.baseline_spending:
+            I_g = fiscal.get_I_g(Y[: p.T], None, p, "TPI")
+        if p.baseline:
+            K_g0 = p.initial_Kg_ratio * Y[0]
+        K_g = fiscal.get_K_g(K_g0, I_g, p, "TPI")
         dg_fixed_values = (
             Y,
             total_tax_revenue,
@@ -1097,18 +1103,12 @@ def run_TPI(p, client=None):
             G[: p.T],
             D_d[: p.T],
             D_f[: p.T],
+            r_gov_new,
             new_borrowing,
             debt_service,
             new_borrowing_f,
-        ) = fiscal.D_G_path(r_gov, dg_fixed_values, p)
-        K[: p.T], K_d[: p.T], K_f[: p.T] = aggr.get_K_splits(
-            B[: p.T], K_demand_open_vec.sum(-1), D_d[: p.T], p.zeta_K[: p.T]
-        )
-        if not p.baseline_spending:
-            I_g = fiscal.get_I_g(Y[: p.T], None, p, "TPI")
-        if p.baseline:
-            K_g0 = p.initial_Kg_ratio * Y[0]
-        K_g = fiscal.get_K_g(K_g0, I_g, p, "TPI")
+        ) = fiscal.D_G_path(r, dg_fixed_values, p)
+
         rnew = r.copy()
         rnew[: p.T] = np.squeeze(
             firm.get_r(
@@ -1117,14 +1117,20 @@ def run_TPI(p, client=None):
         )
         # For case where economy is small open econ
         rnew[p.zeta_K == 1] = p.world_int_rate[p.zeta_K == 1]
-        r_gov_new = fiscal.get_r_gov(rnew, p, "TPI")
         MPKg_vec = np.zeros((p.T, p.M))
         for m in range(p.M):
             MPKg_vec[:, m] = np.squeeze(
                 firm.get_MPx(
                     Y_vec[: p.T, m], K_g[: p.T], p.gamma_g[m], p, "TPI", m
                 )
             )
+
+        K[: p.T], K_d[: p.T], K_f[: p.T] = aggr.get_K_splits(
+            B[: p.T], K_demand_open_vec.sum(-1), D_d[: p.T], p.zeta_K[: p.T]
+        )
+        r_gov_new = fiscal.get_r_gov(
+            rnew[: p.T], Dnew[: p.T] / Y[: p.T], p, "TPI"
+        )
         r_p_new = aggr.get_r_p(
             rnew[: p.T],
             r_gov_new[: p.T],

ogcore/__init__.py

@@ -20,4 +20,4 @@
 from ogcore.txfunc import *
 from ogcore.utils import *
 
-__version__ = "0.15.1"
+__version__ = "0.15.2"

ogcore/default_parameters.json

@@ -1010,6 +1010,42 @@
             }
         }
     },
+    "r_gov_DY": {
+        "title": "Linear effect of debt to GDP ratio on government interest rate",
+        "section_1": "Fiscal Policy Parameters",
+        "description": "Parameter summarizing the linear effect of the debt to GDP ratio on the government interest rate.",
+        "notes": "",
+        "type": "float",
+        "value": [
+            {
+                "value": 0.0
+            }
+        ],
+        "validators": {
+            "range": {
+                "min": -0.3,
+                "max": 0.3
+            }
+        }
+    },
+    "r_gov_DY2": {
+        "title": "Quadratic effect of debt to GDP ratio on government interest rate",
+        "section_1": "Fiscal Policy Parameters",
+        "description": "Parameter summarizing the quadratic effect of the debt to GDP ratio on the government interest rate.",
+        "notes": "",
+        "type": "float",
+        "value": [
+            {
+                "value": 0.0
+            }
+        ],
+        "validators": {
+            "range": {
+                "min": -0.3,
+                "max": 0.3
+            }
+        }
+    },
     "cit_rate": {
         "title": "Corporate income tax rate",
         "description": "Corporate income tax rate.  Set value for base year, click '+' to add value for next year.  All future years not specified are set to last value entered.",

ogcore/fiscal.py

@@ -17,7 +17,7 @@
 """
 
 
-def D_G_path(r_gov, dg_fixed_values, p):
+def D_G_path(r, dg_fixed_values, p):
     r"""
     Calculate the time paths of debt and government spending
 
@@ -87,11 +87,14 @@ def D_G_path(r_gov, dg_fixed_values, p):
         G = p.alpha_G[: p.T] * Y[: p.T]
         D_f = np.zeros(p.T)
         D_d = np.zeros(p.T)
+        r_gov = get_r_gov(r[: p.T], np.zeros(p.T), p, method="TPI")
         new_borrowing = np.zeros(p.T)
         debt_service = np.zeros(p.T)
         new_borrowing_f = np.zeros(p.T)
     else:
         t = 1
+        r_gov = np.zeros_like(r)
+        r_gov[0] = get_r_gov(r[0], D[0] / Y[0], p, method="scalar", t=0)
         while t < p.T - 1:
             D[t] = (1 / growth[t]) * (
                 (1 + r_gov[t - 1]) * D[t - 1]
@@ -102,6 +105,7 @@ def D_G_path(r_gov, dg_fixed_values, p):
                 + agg_pension_outlays[t - 1]
                 - total_tax_revenue[t - 1]
             )
+            r_gov[t] = get_r_gov(r[t], D[t] / Y[t], p, method="scalar", t=t)
             if (t >= p.tG1) and (t < p.tG2):
                 G[t] = (
                     growth[t + 1]
@@ -137,6 +141,7 @@ def D_G_path(r_gov, dg_fixed_values, p):
             + agg_pension_outlays[t - 1]
             - total_tax_revenue[t - 1]
         )
+        r_gov[t] = get_r_gov(r[t], D[t] / Y[t], p, method="scalar", t=t)
         G[t] = (
             growth[t] * (p.debt_ratio_ss * Y[t])
             - (1 + r_gov[t]) * D[t]
@@ -182,6 +187,7 @@ def D_G_path(r_gov, dg_fixed_values, p):
         G,
         D_d,
         D_f[: p.T],
+        r_gov[: p.T],
         new_borrowing,
         debt_service,
         new_borrowing_f,
@@ -350,27 +356,42 @@ def get_TR(
     return new_TR
 
 
-def get_r_gov(r, p, method):
+def get_r_gov(r, DY_ratio, p, method, t=0):
     r"""
     Determine the interest rate on government debt
 
     .. math::
-        r_{gov,t} = \max\{(1-\tau_{d,t}r_{t} - \mu_d, 0.0\}
+        r_{gov,t} = \max\{(1-\tau_{d,t}r_{t} - \mu_d + \beta_1 \frac{D_t}{Y_t} + \beta_2 \left(\frac{D_t}{Y_t}\right)^2, 0.0\}
 
     Args:
         r (array_like): interest rate on private capital debt over the
             time path or in the steady state
+        DY_ratio (array_like): ratio of government debt to GDP
         p (OG-Core Specifications object): model parameters
+        method (str): either 'scalar' for one period or 'TPI' for transition path
+        t (int): time period index, used only if method is 'scalar'
 
     Returns:
         r_gov (array_like): interest rate on government debt over the
             time path or in the steady-state
 
     """
-    if method == "SS":
-        r_gov = np.maximum(p.r_gov_scale[-1] * r - p.r_gov_shift[-1], 0.00)
+    if method == "scalar":
+        r_gov = np.maximum(
+            p.r_gov_scale[t] * r
+            - p.r_gov_shift[t]
+            + p.r_gov_DY * DY_ratio
+            + p.r_gov_DY2 * DY_ratio**2,
+            0.00,
+        )
     else:
-        r_gov = np.maximum(p.r_gov_scale * r - p.r_gov_shift, 0.00)
+        r_gov = np.maximum(
+            p.r_gov_scale[: p.T] * r[: p.T]
+            - p.r_gov_shift[: p.T]
+            + p.r_gov_DY * DY_ratio[: p.T]
+            + p.r_gov_DY2 * DY_ratio[: p.T] ** 2,
+            0.00,
+        )
 
     return r_gov
 

setup.py

@@ -5,7 +5,7 @@
 
 setuptools.setup(
     name="ogcore",
-    version="0.15.1",
+    version="0.15.2",
     author="Jason DeBacker and Richard W. Evans",
     license="CC0 1.0 Universal (CC0 1.0) Public Domain Dedication",
     description="A general equilibrium overlapping generations model for fiscal policy analysis",