further_edits

lectures/arellano.md

@@ -4,7 +4,7 @@ jupytext:
     extension: .md
     format_name: myst
     format_version: 0.13
-    jupytext_version: 1.14.5
+    jupytext_version: 1.15.2
 kernelspec:
   display_name: Python 3 (ipykernel)
   language: python
@@ -370,9 +370,9 @@ We define a namedtuple to store parameters, grids and transition
 probabilities.
 
 ```{code-cell} ipython3
-Arellano = namedtuple('Arellano', ('β', 'γ', 'r', 'ρ', 'η', 'θ', \
-                                  'B_size', 'y_size', \
-                                  'P', 'B_grid', 'y_grid', 'def_y'))
+Arellano_Economy = namedtuple('Arellano_Economy', ('β', 'γ', 'r', 'ρ', 'η', 'θ', \
+                                                  'B_size', 'y_size', \
+                                                  'P', 'B_grid', 'y_grid', 'def_y'))
 ```
 
 ```{code-cell} ipython3
@@ -400,9 +400,9 @@ def create_arellano(B_size=251,   # Grid size for bonds
     # Output received while in default, with same shape as y_grid
     def_y = jnp.minimum(def_y_param * jnp.mean(y_grid), y_grid)
     
-    return Arellano(β=β, γ=γ, r=r, ρ=ρ, η=η, θ=θ, B_size=B_size, \
-                    y_size=y_size, P=P, B_grid=B_grid, y_grid=y_grid, \
-                    def_y=def_y)
+    return Arellano_Economy(β=β, γ=γ, r=r, ρ=ρ, η=η, θ=θ, B_size=B_size, \
+                            y_size=y_size, P=P, B_grid=B_grid, y_grid=y_grid, \
+                            def_y=def_y)
 ```
 
 Here is the utility function.
@@ -462,6 +462,7 @@ def T_d(v_c, v_d, params, sizes, arrays):
     β, γ, r, ρ, η, θ = params
     B_size, y_size = sizes
     P, B_grid, y_grid, def_y = arrays
+
     B0_idx = jnp.searchsorted(B_grid, 1e-10)  # Index at which B is near zero
 
     current_utility = u(def_y, γ)
@@ -546,19 +547,19 @@ def update_values_and_prices(v_c, v_d, params, sizes, arrays):
     return new_v_c, new_v_d
 ```
 
-We can now write a function that will use the `Arellano` namedtuple and the
-functions defined above to compute the solution to our model.
+We can now write a function that will use an instance of `Arellano_Economy` and 
+the functions defined above to compute the solution to our model.
 
 One of the jobs of this function is to take an instance of
-`Arellano`, which is hard for the JIT compiler to handle, and strip it
+`Arellano_Economy`, which is hard for the JIT compiler to handle, and strip it
 down to more basic objects, which are then passed out to jitted functions.
 
 ```{code-cell} ipython3
 :hide-output: false
 
 def solve(model, tol=1e-8, max_iter=10_000):
     """
-    Given an instance of Arellano, this function computes the optimal
+    Given an instance of `Arellano_Economy`, this function computes the optimal
     policy and value functions.
     """
     # Unpack
@@ -621,14 +622,15 @@ def simulate(model, T, v_c, v_d, q, B_star, key):
     """
     Simulates the Arellano 2008 model of sovereign debt
 
-    Here `model` is an instance of `Arellano` and `T` is the length of
+    Here `model` is an instance of `Arellano_Economy` and `T` is the length of
     the simulation.  Endogenous objects `v_c`, `v_d`, `q` and `B_star` are
     assumed to come from a solution to `model`.
 
     """
     # Unpack elements of the model
     B_size, y_size = model.B_size, model.y_size
     B_grid, y_grid, P = model.B_grid, model.y_grid, model.P
+
     B0_idx = jnp.searchsorted(B_grid, 1e-10)  # Index at which B is near zero
 
     # Set initial conditions
@@ -685,17 +687,15 @@ def simulate(model, T, v_c, v_d, q, B_star, key):
 
 Let’s start by trying to replicate the results obtained in {cite}`Are08`.
 
-In what follows, all results are computed using Arellano’s parameter values.
-
-The values can be seen in the `create_arellano` method shown above.
+In what follows, all results are computed using parameter values of `Arellano_Economy` created by `create_arellano`.
 
 For example, `r=0.017` matches the average quarterly rate on a 5 year US treasury over the period 1983–2001.
 
 Details on how to compute the figures are reported as solutions to the
 exercises.
 
 The first figure shows the bond price schedule and replicates Figure 3 of
-Arellano, where $ y_L $ and $ Y_H $ are particular below average and above average
+{cite}`Are08`, where $ y_L $ and $ Y_H $ are particular below average and above average
 values of output $ y $.
 
 ![https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_bond_prices.png](https://python-advanced.quantecon.org/_static/lecture_specific/arellano/arellano_bond_prices.png)
@@ -755,7 +755,7 @@ Periods of relative stability are followed by sharp spikes in the discount rate
 
 To the extent that you can, replicate the figures shown above
 
-- Use the parameter values listed as defaults in `Arellano`.
+- Use the parameter values listed as defaults in `Arellano_Economy` created by `create_arellano`.
 - The time series will of course vary depending on the shock draws.
 
 ```{exercise-end}
@@ -778,7 +778,7 @@ ae = create_arellano()
 v_c, v_d, q, B_star = solve(ae)
 ```
 
-Compute the bond price schedule as seen in figure 3 of Arellano (2008)
+Compute the bond price schedule as seen in figure 3 of {cite}`Are08`
 
 ```{code-cell} ipython3
 :hide-output: false
@@ -800,7 +800,7 @@ x = []
 q_low = []
 q_high = []
 for i, B in enumerate(B_grid):
-    if -0.35 <= B <= 0:  # To match fig 3 of Arellano
+    if -0.35 <= B <= 0:  # To match fig 3 of Arellano (2008)
         x.append(B)
         q_low.append(q[i, iy_low])
         q_high.append(q[i, iy_high])