@@ -23,16 +23,28 @@ def D_G_path(r, dg_fixed_values, p):
2323
2424 .. math::
2525 \begin{split}
26- &e^{g_y}\left(1 + \tilde{g}_{n,t+1}\right)\hat{D}_{t+1} + \hat{Rev}_t = (1 + r_{gov,t})\hat{D}_t + \hat{G}_t + \hat{TR}_t + \hat{UBI}_t \quad\forall t \\
26+ &e^{g_y}\left(1 + \tilde{g}_{n,t+1}\right)\hat{D}_{t+1}
27+ + \hat{Rev}_t = (1 + r_{gov,t})\hat{D}_t + \hat{G}_t
28+ + \hat{TR}_t + \hat{UBI}_t \quad\forall t \\
2729 &\hat{G}_t = g_{g,t}\:\alpha_{g}\: \hat{Y}_t \\
2830 &\text{where}\quad g_{g,t} =
2931 \begin{cases}
30- 1 \qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\:\:\text{if}\quad t < T_{G1} \\
31- \frac{e^{g_y}\left(1 + \tilde{g}_{n,t+1}\right)\left[\rho_{d}\alpha_{D}\hat{Y}_{t} + (1-\rho_{d})\hat{D}_{t}\right] - (1+r_{gov,t})\hat{D}_{t} - \hat{TR}_{t} - \hat{UBI}_t + \hat{Rev}_{t}}{\alpha_g \hat{Y}_t} \quad\text{if}\quad T_{G1}\leq t<T_{G2} \\
32- \frac{e^{g_y}\left(1 + \tilde{g}_{n,t+1}\right)\alpha_{D}\hat{Y}_{t} - (1+r_{gov,t})\hat{D}_{t} - \hat{TR}_{t} - \hat{UBI}_t + \hat{Rev}_{t}}{\alpha_g \hat{Y}_t} \qquad\qquad\quad\,\text{if}\quad t \geq T_{G2}
32+ 1 \quad\text{if}\quad t < T_{G1} \\
33+ \frac{e^{g_y}(1+\tilde{g}_{n,t+1})[\rho_{d}\alpha_{D}
34+ \hat{Y}_{t}+(1-\rho_{d})\hat{D}_{t}]-(1+r_{gov,t})
35+ \hat{D}_{t}-\hat{TR}_{t}-\hat{UBI}_t+\hat{Rev}_{t}}
36+ {\alpha_g \hat{Y}_t}
37+ \quad\text{if}\quad T_{G1}\leq t<T_{G2} \\
38+ \frac{e^{g_y}(1+\tilde{g}_{n,t+1})\alpha_{D}\hat{Y}_{t}
39+ -(1+r_{gov,t})\hat{D}_{t}-\hat{TR}_{t}-\hat{UBI}_t
40+ +\hat{Rev}_{t}}{\alpha_g \hat{Y}_t}
41+ \quad\text{if}\quad t \geq T_{G2}
3342 \end{cases} \\
3443 &\text{and}\quad g_{tr,t} = 1 \quad\forall t \\
35- &e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{D}^{f}_{t+1} = \hat{D}^{f}_{t} + \zeta_{D}\Bigl(e^{g_y}\bigl[1 + \tilde{g}_{n,t+1}\bigr]\hat{D}_{t+1} - \hat{D}_{t}\Bigr) \quad\forall t
44+ &e^{g_y}\bigl[1+\tilde{g}_{n,t+1}\bigr]\hat{D}^{f}_{t+1}
45+ = \hat{D}^{f}_{t} + \zeta_{D}\Bigl(e^{g_y}
46+ \bigl[1+\tilde{g}_{n,t+1}\bigr]\hat{D}_{t+1}
47+ - \hat{D}_{t}\Bigr) \quad\forall t
3648 \end{split}
3749
3850 Args:
@@ -203,7 +215,8 @@ def get_D_ss(r_gov, Y, p):
203215 \bar{D} &= \alpha_D \bar{Y}\\
204216 \bar{D_d} &= \bar{D} - \bar{D}^{f}\\
205217 \bar{D_f} &= \zeta_{D}\bar{D} \\
206- \overline{\text{new borrowing}} &= (e^{g_{y}}(1 + \bar{g}_n) - 1)\bar{D}\\
218+ \overline{\text{new borrowing}} &=
219+ (e^{g_{y}}(1 + \bar{g}_n) - 1)\bar{D}\\
207220 \overline{\text{debt service}} &= \bar{r}_{gov}\bar{D} \\
208221 \overline{\text{new foreign borrowing}} &=
209222 (e^{g_{y}}(1 + \bar{g}_n) - 1)\bar{D_f}\\
@@ -361,14 +374,17 @@ def get_r_gov(r, DY_ratio, p, method, t=0):
361374 Determine the interest rate on government debt
362375
363376 .. math::
364- 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\}
377+ r_{gov,t} = \max\{(1-\tau_{d,t}r_{t} - \mu_d
378+ + \beta_1 \frac{D_t}{Y_t}
379+ + \beta_2 \left(\frac{D_t}{Y_t}\right)^2, 0.0\}
365380
366381 Args:
367382 r (array_like): interest rate on private capital debt over the
368383 time path or in the steady state
369384 DY_ratio (array_like): ratio of government debt to GDP
370385 p (OG-Core Specifications object): model parameters
371- method (str): either 'scalar' for one period or 'TPI' for transition path
386+ method (str): either 'scalar' for one period or 'TPI' for
387+ transition path
372388 t (int): time period index, used only if method is 'scalar'
373389
374390 Returns:
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