dle¶
- class quantecon.dle.DLE(information, technology, preferences)[source]¶
Bases:
objectThis class is for analyzing dynamic linear economies, as set out in Hansen & Sargent (2013). The planner’s problem is to choose {c_t, s_t, i_t, h_t, k_t, g_t}_{t=0}^infty to maximize
max -(1/2) mathbb{E} sum_{t=0}^{infty} beta^t [(s_t - b_t).(s_t-b_t) + g_t.g_t]
subject to the linear constraints
Phi_c c_t + Phi_g g_t + Phi_i i_t = Gamma k_{t-1} + d_t k_t = Delta_k k_{t-1} + Theta_k i_t h_t = Delta_h h_{t-1} + Theta_h c_t s_t = Lambda h_{t-1} + Pi c_t
and
z_{t+1} = A_{22} z_t + C_2 w_{t+1} b_t = U_b z_t d_t = U_d z_t
where h_{-1}, k_{-1}, and z_0 are given as initial conditions.
Section 5.5 of HS2013 describes how to map these matrices into those of a LQ problem.
HS2013 sort the matrices defining the problem into three groups:
Information: A_{22}, C_2, U_b , and U_d characterize the motion of information sets and of taste and technology shocks
Technology: Phi_c, Phi_g, Phi_i, Gamma, Delta_k, and Theta_k determine the technology for producing consumption goods
Preferences: Delta_h, Theta_h, Lambda, and Pi determine the technology for producing consumption services from consumer goods. A scalar discount factor beta determines the preference ordering over consumption services.
- Parameters:
- Informationtuple
Information is a tuple containing the matrices A_{22}, C_2, U_b, and U_d
- Technologytuple
Technology is a tuple containing the matrices Phi_c, Phi_g, Phi_i, Gamma, Delta_k, and Theta_k
- Preferencestuple
Preferences is a tuple containing the scalar beta and the matrices Lambda, Pi, Delta_h, and Theta_h
Methods
Compute canonical preference representation Uses auxiliary problem of 9.4.2, with the preference shock process reintroduced Calculates pihat, llambdahat and ubhat for the equivalent canonical household technology
compute_sequence(x0[, ts_length, Pay])Simulate quantities and prices for the economy
compute_steadystate([nnc])Computes the non-stochastic steady-state of the economy.
irf([ts_length, shock])Create Impulse Response Functions
- canonical()[source]¶
Compute canonical preference representation Uses auxiliary problem of 9.4.2, with the preference shock process reintroduced Calculates pihat, llambdahat and ubhat for the equivalent canonical household technology
- compute_sequence(x0, ts_length=None, Pay=None)[source]¶
Simulate quantities and prices for the economy
- Parameters:
- x0array_like(float)
The initial state
- ts_lengthscalar(int)
Length of the simulation
- Payarray_like(float)
Vector to price an asset whose payout is Pay*xt