system_classes | R Documentation |
System classes
Classes with data and functionality describing systems of models.
system_base-class
: System base class
system_basic-class
: Basic model's system class
system_deterministic_adjustment-class
: Deterministic adjustment model's system class
system_directional-class
: Directional system class
system_equilibrium-class
: Equilibrium model's system class
system_stochastic_adjustment-class
: Stochastic adjustment model's system class
demand
Demand equation.
supply
Supply equation.
correlated_shocks
Boolean indicating whether the shock of the equations of the system are correlated.
sample_separation
Boolean indicating whether the sample of the system is separated.
quantity_vector
A vector with the system's observed quantities.
price_vector
A vector with the system's observed prices.
rho
Correlation coefficient of demand and supply shocks.
rho1
ρ_{1} = \frac{1}{√{1 - ρ}}
rho2
ρ_{2} = ρρ_{1}
lh
Likelihood values for each observation.
gamma
Excess demand coefficient.
delta
δ = γ + α_{d} - α_{s}
mu_P
μ_{P} = \mathrm{E}P
var_P
V_{P} = \mathrm{Var}P
sigma_P
σ_{P} = √{V_{P}}
h_P
h_{P} = \frac{P - μ_{P}}{σ_{P}}
lagged_price_vector
A vector with the system's observed prices lagged by one date.
mu_Q
μ_{Q} = \mathrm{E}Q
var_Q
V_{Q} = \mathrm{Var}Q
sigma_Q
σ_{Q} = √{V_{Q}}
h_Q
h_{Q} = \frac{Q - μ_{Q}}{σ_{Q}}
rho_QP
ρ_{QP} = \frac{\mathrm{Cov}(Q,P)}{√{\mathrm{Var}Q\mathrm{Var}P}}
rho_1QP
ρ_{1,QP} = \frac{1}{√{1 - ρ_{QP}^2}}
rho_2QP
ρ_{2,QP} = ρ_{QP}ρ_{1,QP}
z_QP
z_{QP} = \frac{h_{Q} - ρ_{QP}h_{P}}{√{1 - ρ_{QP}^2}}
z_PQ
z_{PQ} = \frac{h_{P} - ρ_{PQ}h_{Q}}{√{1 - ρ_{PQ}^2}}
price_equation
Price equation.
zeta
ζ = √{1 - ρ_{DS}^2 - ρ_{DP}^2 - ρ_{SP}^2 + 2 ρ_DP ρ_DS ρ_SP}
zeta_DD
ζ_{DD} = 1 - ρ_{SP}^2
zeta_DS
ζ_{DS} = ρ_{DS} - ρ_{DP}ρ_{SP}
zeta_DP
ζ_{DP} = ρ_{DP} - ρ_{DS}ρ_{SP}
zeta_SS
ζ_{SS} = 1 - ρ_{DP}^2
zeta_SP
ζ_{SP} = ρ_{SP} - ρ_{DS}ρ_{DP}
zeta_PP
ζ_{PP} = 1 - ρ_{DS}^2
mu_D
μ_{D} = \mathrm{E}D
var_D
V_{D} = \mathrm{Var}D
sigma_D
σ_{D} = √{V_{D}}
mu_S
μ_{S} = \mathrm{E}S
var_S
V_{S} = \mathrm{Var}S
sigma_S
σ_{S} = √{V_{S}}
sigma_DP
σ_{DP} = \mathrm{Cov}(D, P)
sigma_DS
σ_{DS} = \mathrm{Cov}(D, S)
sigma_SP
σ_{SP} = \mathrm{Cov}(S, P)
rho_DS
ρ_{DS} = \frac{\mathrm{Cov}(D,S)}{√{\mathrm{Var}D\mathrm{Var}S}}
rho_DP
ρ_{DP} = \frac{\mathrm{Cov}(D,P)}{√{\mathrm{Var}D\mathrm{Var}P}}
rho_SP
ρ_{SP} = \frac{\mathrm{Cov}(S,P)}{√{\mathrm{Var}S\mathrm{Var}P}}
h_D
h_{D} = \frac{D - μ_{D}}{σ_{D}}
h_S
h_{S} = \frac{S - μ_{S}}{σ_{S}}
z_DP
z_{DP} = \frac{h_{D} - ρ_{DP}h_{P}}{√{1 - ρ_{DP}^2}}
z_PD
z_{PD} = \frac{h_{P} - ρ_{PD}h_{D}}{√{1 - ρ_{PD}^2}}
z_SP
z_{SP} = \frac{h_{S} - ρ_{SP}h_{P}}{√{1 - ρ_{SP}^2}}
z_PS
z_{PS} = \frac{h_{P} - ρ_{PS}h_{S}}{√{1 - ρ_{PS}^2}}
omega_D
ω_{D} = \frac{h_{D}ζ_{DD} - h_{S}ζ_{DS} - h_{P}ζ_{DP}}{ζ_{DD}}
omega_S
ω_{S} = \frac{h_{S}ζ_{SS} - h_{S}ζ_{SS} - h_{P}ζ_{SP}}{ζ_{SS}}
w_D
w_{D} = - \frac{h_{D}^2 - 2 h_{D} h_{P} ρ_{DP} + h_{P}^2}{2ζ_{SS}}
w_S
w_{S} = - \frac{h_{S}^2 - 2 h_{S} h_{P} ρ_{SP} + h_{P}^2}{2ζ_{DD}}
psi_D
ψ_{D} = φ≤ft(\frac{ω_{D}}{ζ}\right)
psi_S
ψ_{S} = φ≤ft(\frac{ω_{S}}{ζ}\right)
Psi_D
Ψ_{D} = 1 - Φ≤ft(\frac{ω_{D}}{ζ}\right)
Psi_S
Ψ_{S} = 1 - Φ≤ft(\frac{ω_{S}}{ζ}\right)
g_D
g_{D} = \frac{ψ_{D}}{Ψ_{D}}
g_S
g_{S} = \frac{ψ_{S}}{Ψ_{S}}
rho_ds
Shadows rho
in the diseq_stochastic_adjustment model
rho_dp
Correlation of demand and price equations' shocks.
rho_sp
Correlation of supply and price equations' shocks.
L_D
Likelihood conditional on excess supply.
L_S
Likelihood conditional on excess demand.
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