R/gemEquityShare_3_3.R

In GE: General Equilibrium Modeling

#' @export
#' @title A General Equilibrium Model with Equity Shares
#' @aliases gemEquityShare_3_3
#' @description A general equilibrium model with equity shares and dividend.
#' @param ... arguments to be passed to the function sdm2.
#' @examples
#' \donttest{
#' dst.firm <- node_new("output",
#'                      type = "FIN",
#'                      rate = c(1, dividend.rate = 0.25),
#'                      "cc1", "equity.share"
#' )
#' node_set(dst.firm, "cc1",
#'          type = "CD",
#'          alpha = 2, beta = c(0.5, 0.5),
#'          "prod", "lab"
#' )
#'
#' dst.laborer <- node_new("util",
#'                         type = "Leontief",  a = 1,
#'                         "prod"
#' )
#'
#' dst.shareholder <- Clone(dst.laborer)
#'
#' ge <- sdm2(
#'   A = list(dst.firm, dst.laborer, dst.shareholder),
#'   B = diag(c(1, 0, 0)),
#'   S0Exg = {
#'     S0Exg <- matrix(NA, 3, 3)
#'     S0Exg[2, 2] <- S0Exg[3, 3] <- 100
#'     S0Exg
#'   },
#'   names.commodity = c("prod", "lab", "equity.share"),
#'   names.agent = c("firm", "laborer", "shareholder"),
#'   numeraire = "prod"
#' )
#'
#' ge$p # The third component is the dividend per unit of share.
#' ge$DV
#' ge$SV
#'
#' ## Set the growth rate to 0.03.
#' ge <- sdm2(
#'   A = list(dst.firm, dst.laborer, dst.shareholder),
#'   B = diag(c(1, 0, 0)),
#'   S0Exg = {
#'     S0Exg <- matrix(NA, 3, 3)
#'     S0Exg[2, 2] <- S0Exg[3, 3] <- 100
#'     S0Exg
#'   },
#'   names.commodity = c("prod", "lab", "equity.share"),
#'   names.agent = c("firm", "laborer", "shareholder"),
#'   numeraire = "prod",
#'   GRExg = 0.03
#' )
#'
#' ge$z
#' ge$p
#'
#' #### an equivalent intertemporal model.
#' gr <- 0.03
#' rho.beta <- 0.8
#' np <- 5 # the number of economic periods
#' y1 <- 100 # the initial product supply
#'
#' n <- 2 * np - 1 # the number of commodity kinds
#' m <- np # the number of agent kinds
#'
#' names.commodity <- c(paste0("prod", 1:np), paste0("lab", 1:(np - 1)))
#' names.agent <- c(paste0("firm", 1:(np - 1)), "consumer")
#'
#' # the exogenous supply matrix.
#' S0Exg <- S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
#' S0Exg[paste0("lab", 1:(np - 1)), "consumer"] <- 100 * (1 + gr)^(0:(np - 2))
#' S0Exg["prod1", "consumer"] <- y1
#'
#' # the output coefficient matrix.
#' B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
#' for (k in 1:(np - 1)) {
#'   B[paste0("prod", k + 1), paste0("firm", k)] <- 1
#' }
#'
#' dstl.firm <- list()
#' for (k in 1:(np - 1)) {
#'   dstl.firm[[k]] <- node_new(
#'     "prod",
#'     type = "CD",
#'     alpha = 2, beta = c(0.5, 0.5),
#'     paste0("prod", k), paste0("lab", k)
#'   )
#' }
#'
#' dst.consumer <- node_new(
#'   "util",
#'   type = "CES", es = 1,
#'   alpha = 1,  beta = prop.table(rho.beta^(1:np)),
#'   paste0("prod", 1:np)
#' )
#'
#' ge <- sdm2(
#'   A = c(dstl.firm, dst.consumer),
#'   B = B,
#'   S0Exg = S0Exg,
#'   names.commodity = names.commodity,
#'   names.agent = names.agent,
#'   numeraire = "prod1",
#'   policy = makePolicyHeadTailAdjustment(gr = gr, np = np)
#' )
#'
#' ge$z
#' growth_rate(ge$z[1:4])
#' ge$p[6:9] / ge$p[1:4]
#' addmargins(ge$D, 2)
#' addmargins(ge$S, 2)
#' }

gemEquityShare_3_3 <- function(...) sdm2(...)