dle¶
Provides a class called DLE to convert and solve dynamic linear economies (as set out in Hansen & Sargent (2013)) as LQ problems.
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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_tand
z_{t+1} = A_{22} z_t + C_2 w_{t+1} b_t = U_b z_t d_t = U_d z_twhere 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: - Information : tuple
Information is a tuple containing the matrices A_{22}, C_2, U_b, and U_d
- Technology : tuple
Technology is a tuple containing the matrices Phi_c, Phi_g, Phi_i, Gamma, Delta_k, and Theta_k
- Preferences : tuple
Preferences is a tuple containing the matrices Delta_h, Theta_h, Lambda, Pi, and the scalar beta
Methods
canonical()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
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compute_sequence(x0, ts_length=None, Pay=None)[source]¶ Simulate quantities and prices for the economy
Parameters: - x0 : array_like(float)
The initial state
- ts_length : scalar(int)
Length of the simulation
- Pay : array_like(float)
Vector to price an asset whose payout is Pay*xt