Returns the estimated effect of a variable. The effect accounts for both sides of the market. If the given variable belongs only to the demand side, the name of result is prefixed by "D_". If the given variable belongs only to the supply side, the name of result is prefixed by "S_". If the variable can be found both sides, the result name is prefixed by "B_".

## Usage

shortage_marginal(fit, variable, model, parameters)

shortage_probability_marginal(
fit,
variable,
aggregate = "mean",
model,
parameters
)

# S4 method for missing,ANY,market_model,ANY
shortage_marginal(variable, model, parameters)

# S4 method for missing,ANY,ANY,market_model,ANY
shortage_probability_marginal(variable, aggregate, model, parameters)

# S4 method for missing,ANY,market_model,ANY
shortage_marginal(variable, model, parameters)

# S4 method for market_fit,ANY,missing,missing
shortage_marginal(fit, variable)

# S4 method for market_fit,ANY,ANY,missing,missing
shortage_probability_marginal(fit, variable, aggregate)

## Arguments

fit

A fitted market model.

variable

Variable name for which the effect is calculated.

model

A market model object.

parameters

A vector of parameters.

aggregate

Mode of aggregation. Valid options are "mean" (the default) and "at_the_mean".

## Value

The estimated effect of the passed variable.

## Functions

• shortage_marginal(): Marginal effect on market system

Returns the estimated marginal effect of a variable on the market system. For a system variable $$x$$ with demand coefficient $$\beta_{d, x}$$ and supply coefficient $$\beta_{s, x}$$, the marginal effect on the market system is given by $$M_{x} = \frac{\beta_{d, x} - \beta_{s, x}}{\sqrt{\sigma_{d}^{2} + \sigma_{s}^{2} - 2 \rho_{ds} \sigma_{d} \sigma_{s}}}.$$

• shortage_probability_marginal(): Marginal effect on shortage probabilities

Returns the estimated marginal effect of a variable on the probability of observing a shortage state. The mean marginal effect (aggregate = "mean") on the shortage probability is given by $$M_{x} \mathrm{E} \phi\left(\frac{D - S}{\sqrt{\sigma_{d}^2 + \sigma_{s}^2 - 2 rho \sigma_{d} \sigma_{s}}}\right)$$. and the marginal effect at the mean (aggregate = "at_the_mean") by $$M_{x} \phi\left(\mathrm{E}\frac{D - S}{\sqrt{\sigma_{d}^2 + \sigma_{s}^2 - 2 rho \sigma_{d} \sigma_{s}}}\right)$$ where $$M_{x}$$ is the marginal effect on the system, $$D$$ is the demanded quantity, $$S$$ the supplied quantity, and $$\phi$$ is the standard normal density.

## Examples

# \donttest{
# estimate a model using the houses dataset
HS | RM | ID | TREND ~
RM + TREND + W + CSHS + L1RM + L2RM + MONTH |
RM + TREND + W + L1RM + MA6DSF + MA3DHF + MONTH,
fair_houses(),
correlated_shocks = FALSE,
estimation_options = list(control = list(maxit = 1e+5))
)

# mean marginal effect of variable "RM" on the shortage probabilities
#' shortage_probability_marginal(fit, "RM")

# marginal effect at the mean of variable "RM" on the shortage probabilities
shortage_probability_marginal(fit, "CSHS", aggregate = "at_the_mean")
#>       D_CSHS
#> 0.0003055982

# marginal effect of variable "RM" on the system
shortage_marginal(fit, "RM")
#>       B_RM
#> -0.1830798
# }