(test) [cagan_adaptive] DRAFT report from tool-onboarding (action-translation)

Source:

Cagan_Adaptive = namedtuple("Cagan_Adaptive", 
                        ["α", "m0", "Eπ0", "T", "λ"])

def create_cagan_adaptive_model(α = 5, m0 = 1, Eπ0 = 0.5, T=80, λ = 0.9):
    return Cagan_Adaptive(α, m0, Eπ0, T, λ)

md = create_cagan_adaptive_model()

Target:

Cagan_Adaptive = namedtuple("Cagan_Adaptive", 
                        ["α", "m0", "Eπ0", "T", "λ"])

def create_cagan_model(α, m0, Eπ0, T, λ):
    return Cagan_Adaptive(α, m0, Eπ0, T, λ)

Source:

def solve_cagan_adaptive(model, μ_seq):
    " Solve the Cagan model in finite time. "
    α, m0, Eπ0, T, λ = model
    
    A = np.eye(T+2, T+2) - λ*np.eye(T+2, T+2, k=-1)
    B = np.eye(T+2, T+1, k=-1)
    C = -α*np.eye(T+1, T+2) + α*np.eye(T+1, T+2, k=1)
    Eπ0_seq = np.append(Eπ0, np.zeros(T+1))

    # Eπ_seq is of length T+2
    Eπ_seq = np.linalg.solve(A - (1-λ)*B @ C, (1-λ) * B @ μ_seq + Eπ0_seq)

    # π_seq is of length T+1
    π_seq = μ_seq + C @ Eπ_seq

    D = np.eye(T+1, T+1) - np.eye(T+1, T+1, k=-1) # D is the coefficient matrix in Equation (14.8)
    m0_seq = np.append(m0, np.zeros(T))

    # m_seq is of length T+2
    m_seq = np.linalg.solve(D, μ_seq + m0_seq)
    m_seq = np.append(m0, m_seq)

    # p_seq is of length T+2
    p_seq = m_seq + α * Eπ_seq

    return π_seq, Eπ_seq, m_seq, p_seq

Target:

# 参数
T = 80
T1 = 60
α = 5
λ = 0.9
m0 = 1

μ0 = 0.5
μ_star = 0

md = create_cagan_model(α=α, m0=m0, Eπ0=μ0, T=T, λ=λ)

Source:

def solve_and_plot(model, μ_seq):
    
    π_seq, Eπ_seq, m_seq, p_seq = solve_cagan_adaptive(model, μ_seq)
    
    T_seq = range(model.T+2)
    
    fig, ax = plt.subplots(5, 1, figsize=[5, 12], dpi=200)
    ax[0].plot(T_seq[:-1], μ_seq)
    ax[1].plot(T_seq[:-1], π_seq, label=r'$\pi_t$')
    ax[1].plot(T_seq, Eπ_seq, label=r'$\pi^{*}_{t}$')
    ax[2].plot(T_seq, m_seq - p_seq)
    ax[3].plot(T_seq, m_seq)
    ax[4].plot(T_seq, p_seq)
    
    y_labs = [r'$\mu$', r'$\pi$', r'$m - p$', r'$m$', r'$p$']
    subplot_title = [r'Money supply growth', r'Inflation', r'Real balances', r'Money supply', r'Price level']

    for i in range(5):
        ax[i].set_xlabel(r'$t$')
        ax[i].set_ylabel(y_labs[i])
        ax[i].set_title(subplot_title[i])

    ax[1].legend()
    plt.tight_layout()
    plt.show()
    
    return π_seq, Eπ_seq, m_seq, p_seq

Target:

def solve(model, μ_seq):
    "在求解有限视界的凯根模型"
    
    model_params = model.α, model.m0, model.Eπ0, model.T, model.λ
    α, m0, Eπ0, T, λ = model_params
    
    A = np.eye(T+2, T+2) - λ*np.eye(T+2, T+2, k=-1)
    B = np.eye(T+2, T+1, k=-1)
    C = -α*np.eye(T+1, T+2) + α*np.eye(T+1, T+2, k=1)
    Eπ0_seq = np.append(Eπ0, np.zeros(T+1))

    # Eπ_seq 的长度为 T+2
    Eπ_seq = np.linalg.inv(A - (1-λ)*B @ C) @ ((1-λ) * B @ μ_seq + Eπ0_seq)

    # π_seq 的长度为 T+1
    π_seq = μ_seq + C @ Eπ_seq

    D = np.eye(T+1, T+1) - np.eye(T+1, T+1, k=-1)
    m0_seq = np.append(m0, np.zeros(T))

    # m_seq 的长度为 T+2
    m_seq = np.linalg.inv(D) @ (μ_seq + m0_seq)
    m_seq = np.append(m0, m_seq)

    # p_seq 的长度为 T+2
    p_seq = m_seq + α * Eπ_seq

    return π_seq, Eπ_seq, m_seq, p_seq

Source:

print(np.abs((md.λ - md.α*(1-md.λ))/(1 - md.α*(1-md.λ))))

Target:

def solve_and_plot(model, μ_seq):
    
    π_seq, Eπ_seq, m_seq, p_seq = solve(model, μ_seq)
    
    T_seq = range(model.T+2)
    
    fig, ax = plt.subplots(5, 1, figsize=[5, 12], dpi=200)
    ax[0].plot(T_seq[:-1], μ_seq)
    ax[1].plot(T_seq[:-1], π_seq, label=r'$\pi_t$')
    ax[1].plot(T_seq, Eπ_seq, label=r'$\pi^{*}_{t}$')
    ax[2].plot(T_seq, m_seq - p_seq)
    ax[3].plot(T_seq, m_seq)
    ax[4].plot(T_seq, p_seq)
    
    y_labs = [r'$\mu$', r'$\pi$', r'$m - p$', r'$m$', r'$p$']

    for i in range(5):
        ax[i].set_xlabel(r'$t$')
        ax[i].set_ylabel(y_labs[i])

    ax[1].legend()
    plt.tight_layout()
    plt.show()
    
    return π_seq, Eπ_seq, m_seq, p_seq

Target:

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

# 求解并绘图
π_seq_1, Eπ_seq_1, m_seq_1, p_seq_1 = solve_and_plot(md, μ_seq_1)

This block exists only in target - not in source.

Source:

# Parameters for the experiment 1
T1 = 60
μ0 = 0.5
μ_star = 0

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

# solve and plot
π_seq_1, Eπ_seq_1, m_seq_1, p_seq_1 = solve_and_plot(md, μ_seq_1)

Target:

print(np.abs((λ - α*(1-λ))/(1 - α*(1-λ))))

Target:

# 参数
ϕ = 0.9
μ_seq_2 = np.array([ϕ**t * μ0 + (1-ϕ**t)*μ_star for t in range(T)])
μ_seq_2 = np.append(μ_seq_2, μ_star)


# 求解并绘图
π_seq_2, Eπ_seq_2, m_seq_2, p_seq_2 = solve_and_plot(md, μ_seq_2)

This block exists only in target - not in source.

Source:

# parameters
ϕ = 0.9
μ_seq_2 = np.array([ϕ**t * μ0 + (1-ϕ**t)*μ_star for t in range(md.T)])
μ_seq_2 = np.append(μ_seq_2, μ_star)


# solve and plot
π_seq_2, Eπ_seq_2, m_seq_2, p_seq_2 = solve_and_plot(md, μ_seq_2)

Target:

print(λ - α*(1-λ))