Equation classes

## Details

Classes with data and functionality describing equations of model systems.

## Functions

• equation_base-class: Equation base class

• equation_basic-class: Basic disequilibrium model equation class

• equation_deterministic_adjustment-class: Deterministic adjustment disequilibrium model equation class

• equation_directional-class: Directional disequilibrium model equation class

• equation_stochastic_adjustment-class: Stochastic adjustment disequilibrium model equation class

## Slots

formula

The equation formula using prefixed variables.

name

The name of the equation.

variable_prefix

A prefix string for the variables of the equation.

dependent_vector

The vector of the response.

independent_matrix

A model data matrix with columns corresponding to the set of independent variables.

price_vector

The vector of prices.

control_matrix

A model data matrix with columns corresponding to the set of independent variables without prices.

alpha_beta

A vector of right hand side coefficients.

alpha

The price coefficient.

beta

A vector of right hand side coefficient without the price coefficient.

var

The variance of the equation's shock.

sigma

The standard deviation of the equation's shock.

h

$$h_{x} = \frac{x - \mathrm{E} x}{\sqrt{\mathrm{Var} x}}$$

z

$$z_{xy} = \frac{h_{x} - \rho_{xy}h_{y}}{\sqrt{1 - \rho_{xy}^2}}$$

psi

$$\psi_{x} = \phi(h_{x})$$

Psi

$$\Psi_{x} = 1 - \Phi(z_{xy})$$

mu_Q

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

var_Q

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

sigma_Q

$$\sigma_{Q} = \sqrt{\mathrm{Var}Q}$$

rho_QP

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

rho_1QP

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

rho_2QP

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

sigma_QP

$$\sigma_{QP} = \mathrm{Cov}(Q,P)$$

h_Q

As in slot h

z_PQ

As in slot z

z_QP

As in slot z

separation_subset

A vector of indicators specifying the observations of the sample described by this equation according to the separation rule of the model.