System classes

System classes

Details

Classes with data and functionality describing systems of models.

Functions

• 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

Slots

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

$$\rho_{1} = \frac{1}{\sqrt{1 - \rho}}$$

rho2

$$\rho_{2} = \rho\rho_{1}$$

lh

Likelihood values for each observation.

gamma

Excess demand coefficient.

delta

$$\delta = \gamma + \alpha_{d} - \alpha_{s}$$

mu_P

$$\mu_{P} = \mathrm{E}P$$

var_P

$$V_{P} = \mathrm{Var}P$$

sigma_P

$$\sigma_{P} = \sqrt{V_{P}}$$

h_P

$$h_{P} = \frac{P - \mu_{P}}{\sigma_{P}}$$

lagged_price_vector

A vector with the system's observed prices lagged by one date.

mu_Q

$$\mu_{Q} = \mathrm{E}Q$$

var_Q

$$V_{Q} = \mathrm{Var}Q$$

sigma_Q

$$\sigma_{Q} = \sqrt{V_{Q}}$$

h_Q

$$h_{Q} = \frac{Q - \mu_{Q}}{\sigma_{Q}}$$

rho_QP

$$\rho_{QP} = \frac{\mathrm{Cov}(Q,P)}{\sqrt{\mathrm{Var}Q\mathrm{Var}P}}$$

rho_1QP

$$\rho_{1,QP} = \frac{1}{\sqrt{1 - \rho_{QP}^2}}$$

rho_2QP

$$\rho_{2,QP} = \rho_{QP}\rho_{1,QP}$$

z_QP

$$z_{QP} = \frac{h_{Q} - \rho_{QP}h_{P}}{\sqrt{1 - \rho_{QP}^2}}$$

z_PQ

$$z_{PQ} = \frac{h_{P} - \rho_{PQ}h_{Q}}{\sqrt{1 - \rho_{PQ}^2}}$$

price_equation

Price equation.

zeta

$$\zeta = \sqrt{1 - \rho_{DS}^2 - \rho_{DP}^2 - \rho_{SP}^2 + 2 \rho_DP \rho_DS \rho_SP}$$

zeta_DD

$$\zeta_{DD} = 1 - \rho_{SP}^2$$

zeta_DS

$$\zeta_{DS} = \rho_{DS} - \rho_{DP}\rho_{SP}$$

zeta_DP

$$\zeta_{DP} = \rho_{DP} - \rho_{DS}\rho_{SP}$$

zeta_SS

$$\zeta_{SS} = 1 - \rho_{DP}^2$$

zeta_SP

$$\zeta_{SP} = \rho_{SP} - \rho_{DS}\rho_{DP}$$

zeta_PP

$$\zeta_{PP} = 1 - \rho_{DS}^2$$

mu_D

$$\mu_{D} = \mathrm{E}D$$

var_D

$$V_{D} = \mathrm{Var}D$$

sigma_D

$$\sigma_{D} = \sqrt{V_{D}}$$

mu_S

$$\mu_{S} = \mathrm{E}S$$

var_S

$$V_{S} = \mathrm{Var}S$$

sigma_S

$$\sigma_{S} = \sqrt{V_{S}}$$

sigma_DP

$$\sigma_{DP} = \mathrm{Cov}(D, P)$$

sigma_DS

$$\sigma_{DS} = \mathrm{Cov}(D, S)$$

sigma_SP

$$\sigma_{SP} = \mathrm{Cov}(S, P)$$

rho_DS

$$\rho_{DS} = \frac{\mathrm{Cov}(D,S)}{\sqrt{\mathrm{Var}D\mathrm{Var}S}}$$

rho_DP

$$\rho_{DP} = \frac{\mathrm{Cov}(D,P)}{\sqrt{\mathrm{Var}D\mathrm{Var}P}}$$

rho_SP

$$\rho_{SP} = \frac{\mathrm{Cov}(S,P)}{\sqrt{\mathrm{Var}S\mathrm{Var}P}}$$

h_D

$$h_{D} = \frac{D - \mu_{D}}{\sigma_{D}}$$

h_S

$$h_{S} = \frac{S - \mu_{S}}{\sigma_{S}}$$

z_DP

$$z_{DP} = \frac{h_{D} - \rho_{DP}h_{P}}{\sqrt{1 - \rho_{DP}^2}}$$

z_PD

$$z_{PD} = \frac{h_{P} - \rho_{PD}h_{D}}{\sqrt{1 - \rho_{PD}^2}}$$

z_SP

$$z_{SP} = \frac{h_{S} - \rho_{SP}h_{P}}{\sqrt{1 - \rho_{SP}^2}}$$

z_PS

$$z_{PS} = \frac{h_{P} - \rho_{PS}h_{S}}{\sqrt{1 - \rho_{PS}^2}}$$

omega_D

$$\omega_{D} = \frac{h_{D}\zeta_{DD} - h_{S}\zeta_{DS} - h_{P}\zeta_{DP}}{\zeta_{DD}}$$

omega_S

$$\omega_{S} = \frac{h_{S}\zeta_{SS} - h_{S}\zeta_{SS} - h_{P}\zeta_{SP}}{\zeta_{SS}}$$

w_D

$$w_{D} = - \frac{h_{D}^2 - 2 h_{D} h_{P} \rho_{DP} + h_{P}^2}{2\zeta_{SS}}$$

w_S

$$w_{S} = - \frac{h_{S}^2 - 2 h_{S} h_{P} \rho_{SP} + h_{P}^2}{2\zeta_{DD}}$$

psi_D

$$\psi_{D} = \phi\left(\frac{\omega_{D}}{\zeta}\right)$$

psi_S

$$\psi_{S} = \phi\left(\frac{\omega_{S}}{\zeta}\right)$$

Psi_D

$$\Psi_{D} = 1 - \Phi\left(\frac{\omega_{D}}{\zeta}\right)$$

Psi_S

$$\Psi_{S} = 1 - \Phi\left(\frac{\omega_{S}}{\zeta}\right)$$

g_D

$$g_{D} = \frac{\psi_{D}}{\Psi_{D}}$$

g_S

$$g_{S} = \frac{\psi_{S}}{\Psi_{S}}$$

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.