R/diseq_deterministic_adjustment.R

In diseq: Estimation Methods for Markets in Equilibrium and Disequilibrium

#' @include disequilibrium_model.R

#' @describeIn market_models Disequilibrium model with deterministic price dynamics.
#'
#' @description
#' \subsection{diseq_deterministic_adjustment}{
#' The disequilibrium model with deterministic price adjustment consists
#' of four equations. The two market equations, the short side rule and price
#' evolution equation. The first two equations are stochastic. The price
#' equation is deterministic. The sample is separated based on the sign of
#' the price changes as in the \code{\linkS4class{diseq_directional}} model.
#' The model is estimated using full information maximum likelihood.
#'
#' \deqn{D_{nt} = X_{d,nt}'\beta_{d} + P_{nt}\alpha_{d} + u_{d,nt},}
#' \deqn{S_{nt} = X_{s,nt}'\beta_{s} + P_{nt}\alpha_{s} + u_{s,nt},}
#' \deqn{Q_{nt} = \min\{D_{nt},S_{nt}\},}
#' \deqn{\Delta P_{nt} = \frac{1}{\gamma} \left( D_{nt} - S_{nt} \right).}
#' }
#' @export
setClass(
  "diseq_deterministic_adjustment",
  contains = "disequilibrium_model",
  representation(),
  prototype()
)

#' @describeIn initialize_market_model Disequilibrium model with deterministic price
#'   adjustment constructor
#' @examples
#' simulated_data <- simulate_data(
#'   # model type, observed entities and time points
#'   "diseq_deterministic_adjustment", 500, 3,
#'   # demand coefficients
#'   -0.9, 8.9, c(0.03, -0.02), c(-0.03, -0.01),
#'   # supply coefficients
#'   0.9, 4.2, c(0.03), c(0.05, 0.02),
#'   # price adjustment coefficient
#'   1.4
#' )
#'
#' # initialize the model
#' model <- new(
#'   "diseq_deterministic_adjustment", # model type
#'   subject = id, time = date, quantity = Q, price = P,
#'   demand = P + Xd1 + Xd2 + X1 + X2, supply = P + Xs1 + X1 + X2,
#'   simulated_data, # data
#'   correlated_shocks = TRUE # allow shocks to be correlated
#' )
#'
#' show(model)
setMethod(
  "initialize", "diseq_deterministic_adjustment",
  function(.Object,
           quantity, price, demand, supply, subject, time,
           data,
           correlated_shocks = TRUE, verbose = 0) {
    specification <- make_specification(
      data, quantity, price, demand, supply, subject, time
    )
    .Object <- callNextMethod(
      .Object,
      "Deterministic Adjustment", verbose,
      specification,
      correlated_shocks,
      data,
      function(...) new("system_deterministic_adjustment", ...)
    )

    print_info(
      .Object@logger,
      "Sample separated with ", sum(.Object@system@demand@separation_subset),
      " rows in excess supply and ",
      sum(.Object@system@supply@separation_subset), " in excess demand state."
    )

    .Object
  }
)

#' @describeIn single_call_estimation Disequilibrium model with deterministic
#' price adjustments.
#' @export
setGeneric(
  "diseq_deterministic_adjustment",
  function(specification, data,
           correlated_shocks = TRUE, verbose = 0,
           estimation_options = list()) {
    standardGeneric("diseq_deterministic_adjustment")
  }
)

#' @rdname single_call_estimation
setMethod(
  "diseq_deterministic_adjustment", signature(specification = "formula"),
  function(specification, data, correlated_shocks, verbose,
           estimation_options) {
    initialize_from_formula(
      "diseq_deterministic_adjustment", specification, data,
      correlated_shocks, verbose, estimation_options
    )
  }
)

#' @rdname minus_log_likelihood
setMethod(
  "minus_log_likelihood", signature(object = "diseq_deterministic_adjustment"),
  function(object, parameters) {
    object@system <- set_parameters(object@system, parameters)
    -sum(calculate_system_loglikelihood(object@system))
  }
)

#' @rdname gradient
setMethod(
  "gradient", signature(object = "diseq_deterministic_adjustment"),
  function(object, parameters) {
    object@system <- set_parameters(object@system, parameters)
    gradient <- as.matrix(colSums(calculate_system_scores(object@system)))
    -gradient
  }
)

#' @rdname scores
setMethod(
  "scores", signature(object = "diseq_deterministic_adjustment"),
  function(object, parameters) {
    object@system <- set_parameters(object@system, parameters)
    -calculate_system_scores(object@system)
  }
)

setMethod(
  "calculate_initializing_values",
  signature(object = "diseq_deterministic_adjustment"),
  function(object) {
    demand <- stats::lm(
      object@system@demand@dependent_vector ~
      object@system@demand@independent_matrix - 1
    )
    names(demand$coefficients) <- colnames(
      object@system@demand@independent_matrix
    )
    var_d <- var(demand$residuals)
    names(var_d) <- prefixed_variance_variable(object@system@demand)

    supply <- stats::lm(
      object@system@supply@dependent_vector ~
      object@system@supply@independent_matrix - 1
    )
    names(supply$coefficients) <- colnames(
      object@system@supply@independent_matrix
    )
    var_s <- var(supply$residuals)
    names(var_s) <- prefixed_variance_variable(object@system@supply)

    dp <- object@model_tibble[, price_differences_variable(object@system)] %>%
      dplyr::pull()
    xd <- demand$fitted.values - supply$fitted.values
    prices <- stats::lm(dp ~ xd - 1)
    names(prices$coefficients) <- price_differences_variable(object@system)

    start <- c(
      demand$coefficients, supply$coefficients,
      prices$coefficients, var_d, var_s
    )

    if (object@system@correlated_shocks) {
      rho <- 0.0
      names(rho) <- correlation_variable(object@system)

      start <- c(start, rho)
    }

    start
  }
)