Marginal effects

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
fit <- diseq_deterministic_adjustment(
  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 
# }