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[FIX] Minor bug fixes #587

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[FIX] Minor bug fixes #587

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268225a
minor bug fixes
HumphreyYang May 28, 2025
263f52e
minor update
HumphreyYang May 28, 2025
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35 changes: 19 additions & 16 deletions lectures/cagan_ree.md
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ jupytext:
extension: .md
format_name: myst
format_version: 0.13
jupytext_version: 1.16.1
jupytext_version: 1.17.1
kernelspec:
display_name: Python 3 (ipykernel)
language: python
Expand Down Expand Up @@ -267,6 +267,7 @@ def solve(model, T):
A1 = np.eye(T+1, T+1) - δ * np.eye(T+1, T+1, k=1)
A2 = np.eye(T+1, T+1) - np.eye(T+1, T+1, k=-1)

# Assume γ* = 1
b1 = (1-δ) * μ_seq + np.concatenate([np.zeros(T), [δ * π_end]])
b2 = μ_seq + np.concatenate([[m0], np.zeros(T)])

Expand Down Expand Up @@ -326,7 +327,7 @@ T1 = 60
μ_star = 0
T = 80

μ_seq_1 = np.append(μ0*np.ones(T1+1), μ_star*np.ones(T-T1))
μ_seq_1 = np.append(μ0*np.ones(T1), μ_star*np.ones(T-T1+1))

cm = create_cagan_model(μ_seq=μ_seq_1)

Expand Down Expand Up @@ -493,32 +494,34 @@ cm1 = create_cagan_model(μ_seq=μ_seq_2_path1)
π_seq_2_path1, m_seq_2_path1, p_seq_2_path1 = solve(cm1, T)

# continuation path
μ_seq_2_cont = μ_star * np.ones(T-T1)
μ_seq_2_cont = μ_star * np.ones(T-T1+1)

cm2 = create_cagan_model(m0=m_seq_2_path1[T1+1],
cm2 = create_cagan_model(m0=m_seq_2_path1[T1],
μ_seq=μ_seq_2_cont)
π_seq_2_cont, m_seq_2_cont1, p_seq_2_cont1 = solve(cm2, T-1-T1)
π_seq_2_cont, m_seq_2_cont1, p_seq_2_cont1 = solve(cm2, T-T1)


# regime 1 - simply glue π_seq, μ_seq
μ_seq_2 = np.concatenate((μ_seq_2_path1[:T1+1],
μ_seq_2 = np.concatenate((μ_seq_2_path1[:T1],
μ_seq_2_cont))
π_seq_2 = np.concatenate((π_seq_2_path1[:T1+1],
π_seq_2 = np.concatenate((π_seq_2_path1[:T1],
π_seq_2_cont))
m_seq_2_regime1 = np.concatenate((m_seq_2_path1[:T1+1],
m_seq_2_regime1 = np.concatenate((m_seq_2_path1[:T1],
m_seq_2_cont1))
p_seq_2_regime1 = np.concatenate((p_seq_2_path1[:T1+1],
p_seq_2_regime1 = np.concatenate((p_seq_2_path1[:T1],
p_seq_2_cont1))

π_seq_2[T1-1] = p_seq_2_regime1[T1] - p_seq_2_regime1[T1-1]

# regime 2 - reset m_T1
m_T1 = (m_seq_2_path1[T1] + μ0) + cm2.α*(μ0 - μ_star)
m_T1 = (m_seq_2_path1[T1-1] + μ0) + cm2.α*(μ0 - μ_star)

cm3 = create_cagan_model(m0=m_T1, μ_seq=μ_seq_2_cont)
π_seq_2_cont2, m_seq_2_cont2, p_seq_2_cont2 = solve(cm3, T-1-T1)
π_seq_2_cont2, m_seq_2_cont2, p_seq_2_cont2 = solve(cm3, T-T1)

m_seq_2_regime2 = np.concatenate((m_seq_2_path1[:T1+1],
m_seq_2_regime2 = np.concatenate((m_seq_2_path1[:T1],
m_seq_2_cont2))
p_seq_2_regime2 = np.concatenate((p_seq_2_path1[:T1+1],
p_seq_2_regime2 = np.concatenate((p_seq_2_path1[:T1],
p_seq_2_cont2))
```

Expand All @@ -539,8 +542,8 @@ plot_configs = [
{'data': [(T_seq, m_seq_2_regime1, 'Smooth $m_{T_1}$'),
(T_seq, m_seq_2_regime2, 'Jumpy $m_{T_1}$')],
'ylabel': r'$m$'},
{'data': [(T_seq, p_seq_2_regime1, 'Smooth $p_{T_1}$'),
(T_seq, p_seq_2_regime2, 'Jumpy $p_{T_1}$')],
{'data': [(T_seq, p_seq_2_regime1, 'Jumpy $m_{T_1}$'),
(T_seq, p_seq_2_regime2, 'Smooth $m_{T_1}$')],
'ylabel': r'$p$'}
]

Expand Down Expand Up @@ -591,7 +594,7 @@ fig, ax = plt.subplots(5, figsize=(5, 12), dpi=200)
plot_configs = [
{'data': [(T_seq[:-1], μ_seq_2)], 'ylabel': r'$\mu$'},
{'data': [(T_seq, π_seq_2, 'Unforeseen'),
(T_seq, π_seq_1, 'Foreseen')], 'ylabel': r'$p$'},
(T_seq, π_seq_1, 'Foreseen')], 'ylabel': r'$\pi$'},
{'data': [(T_seq, m_seq_2_regime1 - p_seq_2_regime1, 'Unforeseen'),
(T_seq, m_seq_1 - p_seq_1, 'Foreseen')], 'ylabel': r'$m - p$'},
{'data': [(T_seq, m_seq_2_regime1, 'Unforeseen (Smooth $m_{T_1}$)'),
Expand Down
6 changes: 3 additions & 3 deletions lectures/cons_smooth.md
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ jupytext:
extension: .md
format_name: myst
format_version: 0.13
jupytext_version: 1.16.4
jupytext_version: 1.17.1
kernelspec:
display_name: Python 3 (ipykernel)
language: python
Expand Down Expand Up @@ -279,7 +279,7 @@ def compute_optimal(model, a0, y_seq):
b = y_seq - c_seq
b[0] = b[0] + a0

a_seq = np.linalg.inv(A) @ b
a_seq = np.linalg.inv(A) @ (R * b)
a_seq = np.concatenate([[a0], a_seq])

return c_seq, a_seq, h0
Expand Down Expand Up @@ -361,7 +361,7 @@ def plot_cs(model, # consumption-smoothing model
c_seq, a_seq, h0 = compute_optimal(model, a0, y_seq)

# Sequence length
T = cs_model.T
T = model.T

fig, axes = plt.subplots(1, 2, figsize=(12,5))

Expand Down
8 changes: 4 additions & 4 deletions lectures/tax_smooth.md
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,7 @@ jupytext:
extension: .md
format_name: myst
format_version: 0.13
jupytext_version: 1.16.4
jupytext_version: 1.17.1
kernelspec:
display_name: Python 3 (ipykernel)
language: python
Expand Down Expand Up @@ -283,7 +283,7 @@ def compute_optimal(model, B0, G_seq):
A = np.diag(-R*np.ones(S), k=-1) + np.eye(S+1)
b = G_seq - T_seq
b[0] = b[0] + B0
B_seq = np.linalg.inv(A) @ b
B_seq = np.linalg.inv(A) @ (R * b)
B_seq = np.concatenate([[B0], B_seq])

return T_seq, B_seq, h0
Expand Down Expand Up @@ -368,7 +368,7 @@ def plot_ts(model, # tax-smoothing model
T_seq, B_seq, h0 = compute_optimal(model, B0, G_seq)

# Sequence length
S = tax_model.S
S = model.S

fig, axes = plt.subplots(1, 2, figsize=(12,5))

Expand Down Expand Up @@ -656,4 +656,4 @@ plt.plot(ξ1_arr, cost_grad)
plt.ylabel('derivative of cost')
plt.xlabel(r'$\phi$')
plt.show()
```
```
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