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shlff committed Mar 5, 2024
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Expand Up @@ -5,10 +5,6 @@ jupytext:
format_name: myst
format_version: 0.13
jupytext_version: 1.15.2
<<<<<<< HEAD
jupytext_version: 1.15.2
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
kernelspec:
display_name: Python 3 (ipykernel)
language: python
Expand Down Expand Up @@ -374,7 +370,6 @@ We define a namedtuple to store parameters, grids and transition
probabilities.
```{code-cell} ipython3
<<<<<<< HEAD
ArellanoEconomy = namedtuple('ArellanoEconomy', ('β', # Time discount parameter
'γ', # Utility parameter
'r', # Lending rate
Expand All @@ -394,18 +389,6 @@ def create_arellano(B_size=251, # Grid size for bonds
B_min=-0.45, # Smallest B value
B_max=0.45, # Largest B value
y_size=51, # Grid size for income
=======
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
def create_arellano(B_size=251, # Grid size for bonds
B_min=-0.45, # Smallest B value
B_max=0.45, # Largest B value
y_size=51, # Grid size for income
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
β=0.953, # Time discount parameter
γ=2.0, # Utility parameter
r=0.017, # Lending rate
Expand All @@ -422,24 +405,16 @@ def create_arellano(B_size=251, # Grid size for bonds
B_grid = jax.device_put(B_grid)
y_grid = jax.device_put(y_grid)
P = jax.device_put(P)
<<<<<<< HEAD
# Put grids on the device
B_grid = jax.device_put(B_grid)
y_grid = jax.device_put(y_grid)
P = jax.device_put(P)
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
# Output received while in default, with same shape as y_grid
def_y = jnp.minimum(def_y_param * jnp.mean(y_grid), y_grid)
<<<<<<< HEAD
return ArellanoEconomy(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,
=======
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, \
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
def_y=def_y)
```
Expand Down Expand Up @@ -501,10 +476,7 @@ def T_d(v_c, v_d, params, sizes, arrays):
B_size, y_size = sizes
P, B_grid, y_grid, def_y = arrays
<<<<<<< HEAD
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
B0_idx = jnp.searchsorted(B_grid, 1e-10) # Index at which B is near zero
current_utility = u(def_y, γ)
Expand Down Expand Up @@ -589,11 +561,7 @@ def update_values_and_prices(v_c, v_d, params, sizes, arrays):
return new_v_c, new_v_d
```
<<<<<<< HEAD
We can now write a function that will use an instance of `ArellanoEconomy` and
=======
We can now write a function that will use an instance of `Arellano_Economy` and
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
the functions defined above to compute the solution to our model.
One of the jobs of this function is to take an instance of
Expand All @@ -605,11 +573,7 @@ down to more basic objects, which are then passed out to jitted functions.
def solve(model, tol=1e-8, max_iter=10_000):
"""
<<<<<<< HEAD
Given an instance of `ArellanoEconomy`, this function computes the optimal
=======
Given an instance of `Arellano_Economy`, this function computes the optimal
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
policy and value functions.
"""
# Unpack
Expand All @@ -619,15 +583,12 @@ def solve(model, tol=1e-8, max_iter=10_000):
params = β, γ, r, ρ, η, θ
sizes = B_size, y_size
arrays = P, B_grid, y_grid, def_y
<<<<<<< HEAD
β, γ, r, ρ, η, θ, B_size, y_size, P, B_grid, y_grid, def_y = model
params = β, γ, r, ρ, η, θ
sizes = B_size, y_size
arrays = P, B_grid, y_grid, def_y
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
# Initial conditions for v_c and v_d
v_c = jnp.zeros((B_size, y_size))
Expand Down Expand Up @@ -656,10 +617,6 @@ Let's try solving the model.
:hide-output: false
ae = create_arellano()
<<<<<<< HEAD
ae = create_arellano()
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
```
```{code-cell} ipython3
Expand Down Expand Up @@ -692,15 +649,8 @@ def simulate(model, T, v_c, v_d, q, B_star, key):
"""
# Unpack elements of the model
B_size, y_size = model.B_size, model.y_size
<<<<<<< HEAD
B_size, y_size = model.B_size, model.y_size
B_grid, y_grid, P = model.B_grid, model.y_grid, model.P
=======
B_grid, y_grid, P = model.B_grid, model.y_grid, model.P
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
B0_idx = jnp.searchsorted(B_grid, 1e-10) # Index at which B is near zero
# Set initial conditions
Expand Down Expand Up @@ -757,11 +707,7 @@ 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`.
<<<<<<< HEAD
In what follows, all results are computed using parameter values of `ArellanoEconomy` created by `create_arellano`.
=======
In what follows, all results are computed using parameter values of `Arellano_Economy` created by `create_arellano`.
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
For example, `r=0.017` matches the average quarterly rate on a 5 year US treasury over the period 1983–2001.
Expand All @@ -770,10 +716,6 @@ exercises.
The first figure shows the bond price schedule and replicates Figure 3 of
{cite}`Are08`, where $ y_L $ and $ Y_H $ are particular below average and above average
<<<<<<< HEAD
{cite}`Are08`, where $ y_L $ and $ Y_H $ are particular below average and above average
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
values of output $ y $.
```{figure} _static/lecture_specific/arellano/arellano_bond_prices.png
Expand All @@ -784,10 +726,6 @@ values of output $ y $.
The grid used to compute this figure was relatively fine (`y_size, B_size = 51, 251`), which explains the minor differences between this and
<<<<<<< HEAD
The grid used to compute this figure was relatively fine (`y_size, B_size = 51, 251`), which explains the minor differences between this and
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
Arrelano’s figure.
The figure shows that
Expand Down Expand Up @@ -834,11 +772,7 @@ Periods of relative stability are followed by sharp spikes in the discount rate
To the extent that you can, replicate the figures shown above
<<<<<<< HEAD
- Use the parameter values listed as defaults in `ArellanoEconomy` created by `create_arellano`.
=======
- Use the parameter values listed as defaults in `Arellano_Economy` created by `create_arellano`.
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
- The time series will of course vary depending on the shock draws.
```{exercise-end}
Expand All @@ -854,29 +788,17 @@ Compute the value function, policy and equilibrium prices
:hide-output: false
ae = create_arellano()
<<<<<<< HEAD
ae = create_arellano()
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
v_c, v_d, q, B_star = solve(ae)
```
Compute the bond price schedule as seen in figure 3 of {cite}`Are08`
<<<<<<< HEAD
Compute the bond price schedule as seen in figure 3 of {cite}`Are08`
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
```{code-cell} ipython3
:hide-output: false
# Unpack some useful names
B_grid, y_grid, P = ae.B_grid, ae.y_grid, ae.P
B_size, y_size = ae.B_size, ae.y_size
<<<<<<< HEAD
B_size, y_size = ae.B_size, ae.y_size
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
r = ae.r
# Create "Y High" and "Y Low" values as 5% devs from mean
Expand All @@ -892,10 +814,6 @@ q_low = []
q_high = []
for i, B in enumerate(B_grid):
if -0.35 <= B <= 0: # To match fig 3 of Arellano (2008)
<<<<<<< HEAD
if -0.35 <= B <= 0: # To match fig 3 of Arellano (2008)
=======
>>>>>>> ff86e0fd39571a8a7965cd8f9c588d44310d538e
x.append(B)
q_low.append(q[i, iy_low])
q_high.append(q[i, iy_high])
Expand Down

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