R/gemIntertemporal_EndogenousEquilibriumInterestRate__ForeignExchangeRate.R

In GE: General Equilibrium Modeling

#' @export
#' @title An Example Illustrating Endogenous Equilibrium Interest Rates and Foreign Exchange Rates in a Two-country (Timeline) Transitional Equilibrium Path
#' @aliases gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate
#' @description This example illustrates (endogenous) equilibrium primitive interest rates and foreign exchange rates in a two-country transitional equilibrium path.
#' Assume that the velocity of money is equal to one, that is, money circulates once per period.
#' @param ... arguments to be passed to the function sdm2.
#' @seealso \code{\link{gemIntertemporal_EndogenousEquilibriumInterestRate}}
#' @examples
#' \donttest{
#' eis <- 0.8 # the elasticity of intertemporal substitution
#' Gamma.beta <- 10 / 11 # the subjective discount factor
#' gr <- 0 # the steady-state growth rate
#' money1.supply <- 600
#' money2.supply <- 100
#' np <- 20 # the number of economic periods
#'
#' sserr(eis, Gamma.beta, gr, prepaid = TRUE)
#'
#' f <- function(ir = rep(0.1, 2 * np - 2), return.ge = FALSE,
#'               y1.wheat = 10, # 49.24 #49.79 the wheat supply in the first period
#'               y1.iron = 5 # 41.32 #45.45 the iron supply in the first period
#' ) {
#'   ir1 <- head(ir, np - 1)
#'   ir2 <- tail(ir, np - 1)
#'
#'   n <- 2 * np + 2 * (np - 1) + 2 # the number of commodity kinds
#'   m <- 2 * (np - 1) + 4 # the number of agent kinds
#'
#'   names.commodity <- c(
#'     paste0("wheat", 1:np),
#'     paste0("lab1.", 1:(np - 1)),
#'     "money1",
#'     paste0("iron", 1:np),
#'     paste0("lab2.", 1:(np - 1)),
#'     "money2"
#'   )
#'
#'   names.agent <- c(
#'     paste0("firm.wheat", 1:(np - 1)),
#'     "laborer1", "moneyOwner1",
#'     paste0("firm.iron", 1:(np - 1)),
#'     "laborer2", "moneyOwner2"
#'   )
#'
#'   # the exogenous supply matrix.
#'   S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
#'   S0Exg[paste0("lab1.", 1:(np - 1)), "laborer1"] <- 100 * (1 + gr)^(0:(np - 2))
#'   S0Exg["money1", "moneyOwner1"] <- money1.supply
#'   S0Exg["wheat1", "laborer1"] <- y1.wheat
#'
#'   S0Exg[paste0("lab2.", 1:(np - 1)), "laborer2"] <- 100 * (1 + gr)^(0:(np - 2))
#'   S0Exg["money2", "moneyOwner2"] <- money2.supply
#'   S0Exg["iron1", "laborer2"] <- y1.iron
#'
#'   # the output coefficient matrix.
#'   B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
#'   for (k in 1:(np - 1)) {
#'     B[paste0("wheat", k + 1), paste0("firm.wheat", k)] <- 1
#'     B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1
#'   }
#'
#'   dstl.firm.wheat <- dstl.firm.iron <- list()
#'   for (k in 1:(np - 1)) {
#'     dstl.firm.wheat[[k]] <- node_new(
#'       "prod",
#'       type = "FIN", rate = c(1, ir1[k]),
#'       "cc1", "money1"
#'     )
#'     node_set(dstl.firm.wheat[[k]], "cc1",
#'       type = "CD", alpha = 1, beta = c(0.5, 0.5),
#'       paste0("iron", k), paste0("lab1.", k)
#'     )
#'
#'     dstl.firm.iron[[k]] <- node_new(
#'       "prod",
#'       type = "FIN", rate = c(1, ir2[k]),
#'       "cc1", "money2"
#'     )
#'     node_set(dstl.firm.iron[[k]], "cc1",
#'       type = "CD", alpha = 1, beta = c(0.5, 0.5),
#'       paste0("iron", k), paste0("lab2.", k)
#'     )
#'   }
#'
#'   dst.laborer1 <- node_new(
#'     "util",
#'     type = "CES", es = eis,
#'     alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
#'     paste0("cc", 1:(np - 1)), paste0("wheat", np)
#'   )
#'   for (k in 1:(np - 1)) {
#'     node_set(dst.laborer1, paste0("cc", k),
#'       type = "FIN", rate = c(1, ir1[k]),
#'       paste0("wheat", k), "money1"
#'     )
#'   }
#'
#'   dst.moneyOwner1 <- node_new(
#'     "util",
#'     type = "CES", es = eis,
#'     alpha = 1, beta = prop.table(Gamma.beta^(1:(np - 1))),
#'     paste0("cc", 1:(np - 1))
#'   )
#'   for (k in 1:(np - 1)) {
#'     node_set(dst.moneyOwner1, paste0("cc", k),
#'       type = "FIN", rate = c(1, ir1[k]),
#'       paste0("wheat", k), "money1"
#'     )
#'   }
#'
#'   dst.laborer2 <- node_new(
#'     "util",
#'     type = "CES", es = eis,
#'     alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
#'     paste0("cc", 1:(np - 1)), paste0("iron", np)
#'   )
#'
#'   for (k in 1:(np - 1)) {
#'     node_set(dst.laborer2, paste0("cc", k),
#'       type = "FIN", rate = c(1, ir2[k]),
#'       paste0("wheat", k), "money2"
#'     )
#'   }
#'
#'   dst.moneyOwner2 <- node_new(
#'     "util",
#'     type = "CES", es = eis,
#'     alpha = 1, beta = prop.table(Gamma.beta^(1:(np - 1))),
#'     paste0("cc", 1:(np - 1))
#'   )
#'   for (k in 1:(np - 1)) {
#'     node_set(dst.moneyOwner2, paste0("cc", k),
#'       type = "FIN", rate = c(1, ir2[k]),
#'       paste0("wheat", k), "money2"
#'     )
#'   }
#'
#'   ge <- sdm2(
#'     A = c(
#'       dstl.firm.wheat, dst.laborer1, dst.moneyOwner1,
#'       dstl.firm.iron, dst.laborer2, dst.moneyOwner2
#'     ),
#'     B = B,
#'     S0Exg = S0Exg,
#'     names.commodity = names.commodity,
#'     names.agent = names.agent,
#'     numeraire = "wheat1",
#'     policy = makePolicyTailAdjustment(
#'       ind = rbind(
#'         c(np - 1, np),
#'         c(2 * np, 2 * (np - 1) + 3)
#'       ),
#'       gr = gr
#'     )
#'   )
#'
#'   tmp <- rowSums(ge$SV)
#'
#'   ts1.exchange.value <- tmp[paste0("wheat", 1:(np - 1))] + tmp[paste0("lab1.", 1:(np - 1))]
#'   ir1.new <- ts1.exchange.value[1:(np - 2)] / ts1.exchange.value[2:(np - 1)] - 1
#'   ir1.new <- pmax(1e-6, ir1.new)
#'   ir1.new[np - 1] <- ir1.new[np - 2]
#'
#'   ir1 <- c(ir1 * ratio_adjust(ir1.new / ir1, 0.3))
#'   cat("ir1: ", ir1, "\n")
#'
#'
#'   ts2.exchange.value <- tmp[paste0("iron", 1:(np - 1))] + tmp[paste0("lab2.", 1:(np - 1))]
#'   ir2.new <- ts2.exchange.value[1:(np - 2)] / ts2.exchange.value[2:(np - 1)] - 1
#'   ir2.new <- pmax(1e-6, ir2.new)
#'   ir2.new[np - 1] <- ir2.new[np - 2]
#'
#'   ir2 <- c(ir2 * ratio_adjust(ir2.new / ir2, 0.3))
#'   cat("ir2: ", ir2, "\n")
#'
#'   if (return.ge) {
#'     ge$ts1.exchange.value <- unname(ts1.exchange.value)
#'     ge$ts2.exchange.value <- unname(ts2.exchange.value)
#'     ge$ts.forex <- unname((ge$ts2.exchange.value / money2.supply) /
#'       (ge$ts1.exchange.value / money1.supply))
#'     return(ge)
#'   } else {
#'     return(c(ir1, ir2))
#'   }
#' }
#'
#' ## Calculate equilibrium interest rates.
#' ## Warning: Running the program below takes about several minutes.
#' # mat.ir <- iterate(rep(0.1, 2*np - 2), f, tol = 1e-4)
#' # sserr(eis, Gamma.beta, gr, prepaid = TRUE)
#'
#' ## Below are the calculated equilibrium interest rates.
#' ir1 <- c(
#'   0.2218, 0.1888, 0.1455, 0.1228, 0.1115, 0.1058, 0.1029, 0.1015, 0.1008,
#'   0.1004, 0.1002, 0.1001, 0.1001, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000
#' )
#' ir2 <- c(
#'   0.1292, 0.1080, 0.1037, 0.1019, 0.1010, 0.1005, 0.1003, 0.1001, 0.1001,
#'   0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000
#' )
#'
#' ge <- f(c(ir1, ir2), return.ge = TRUE)
#' plot(ge$z[1:(np - 1)], type = "o", ylab = "wheat output")
#' ge$ts.forex
#'
#' ## the corresponding sequential model with the same steady-state equilibrium.
#' np <- 5
#' ge.ss <- f(return.ge = TRUE, y1.wheat = 49.24, y1.iron = 41.32)
#'
#' ir <- dividend.rate <- 0.1
#'
#' dst.firm.wheat <- node_new("output",
#'   type = "FIN", rate = c(1, ir, (1 + ir) * dividend.rate),
#'   "cc1", "money1", "equity.share.wheat"
#' )
#' node_set(dst.firm.wheat, "cc1",
#'   type = "CD", alpha = 1,
#'   beta = c(0.5, 0.5),
#'   "iron", "lab1"
#' )
#'
#' dst.firm.iron <- node_new("output",
#'   type = "FIN", rate = c(1, ir, (1 + ir) * dividend.rate),
#'   "cc1", "money2", "equity.share.iron"
#' )
#' node_set(dst.firm.iron, "cc1",
#'   type = "CD", alpha = 1,
#'   beta = c(0.5, 0.5),
#'   "iron", "lab2"
#' )
#'
#' dst.laborer1 <- node_new("util",
#'   type = "FIN", rate = c(1, interest.rate = 0.1),
#'   "cc1", "money1"
#' )
#' node_set(dst.laborer1, "cc1",
#'   type = "Leontief", a = 1,
#'   "wheat"
#' )
#'
#' dst.moneyOwner1 <- Clone(dst.laborer1)
#'
#' dst.laborer2 <- Clone(dst.laborer1)
#' node_replace(dst.laborer2, "money1", "money2")
#'
#' dst.moneyOwner2 <- Clone(dst.laborer2)
#'
#' ge <- sdm2(
#'   A = list(
#'     dst.firm.wheat, dst.laborer1, dst.moneyOwner1,
#'     dst.firm.iron, dst.laborer2, dst.moneyOwner2
#'   ),
#'   B = matrix(c(
#'     1, 0, 0, 0, 0, 0,
#'     0, 0, 0, 0, 0, 0,
#'     0, 0, 0, 0, 0, 0,
#'     0, 0, 0, 0, 0, 0,
#'     0, 0, 0, 1, 0, 0,
#'     0, 0, 0, 0, 0, 0,
#'     0, 0, 0, 0, 0, 0,
#'     0, 0, 0, 0, 0, 0
#'   ), 8, 6, TRUE),
#'   S0Exg = matrix(c(
#'     NA, NA, NA, NA, NA, NA,
#'     NA, 100, NA, NA, NA, NA,
#'     NA, NA, 600, NA, NA, NA,
#'     NA, 100, NA, NA, NA, NA,
#'     NA, NA, NA, NA, NA, NA,
#'     NA, NA, NA, NA, 100, NA,
#'     NA, NA, NA, NA, NA, 100,
#'     NA, NA, NA, NA, 100, NA
#'   ), 8, 6, TRUE),
#'   names.commodity = c(
#'     "wheat", "lab1", "money1", "equity.share.wheat",
#'     "iron", "lab2", "money2", "equity.share.iron"
#'   ),
#'   names.agent = c(
#'     "firm1", "laborer1", "moneyOwner1",
#'     "firm2", "laborer2", "moneyOwner2"
#'   ),
#'   numeraire = c("money1" = 0.1) # interest.rate
#' )
#'
#' ge.ss$ts.forex
#' ge$p["money2"] / ge$p["money1"] # the foreign exchange rate
#'
#' ## Calculate equilibrium interest rates.
#' ## Warning: Running the program below takes about several minutes.
#' # np <- 20
#' # gr <- 0.03
#' # mat.ir <- iterate(rep(0.1, 2*np - 2), f, tol = 1e-4)
#' # sserr(eis, Gamma.beta, gr, prepaid = TRUE)
#'
#' ## a steady-state equilibrium with an exogenous interest rate 0.1.
#' ## The endogenous equilibrium interest rate and dividend rate are 0.
#' ## See also CGE::Example7.6.
#' eis <- 1 # the elasticity of intertemporal substitution
#' Gamma.beta <- 1 # the subjective discount factor
#' gr <- 0 # the steady-state growth rate
#' money1.supply <- 600
#' money2.supply <- 100
#' np <- 20 # the number of economic periods
#'
#' np <- 5
#' ge.ss <- f(return.ge = TRUE, y1.wheat = 49.79, y1.iron = 45.45)
#' ge.ss$z
#' ge.ss$ts.forex
#' }

gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate <- function(...) sdm2(...)