R/gemIntertemporal_EndogenousEquilibriumInterestRate__ForeignExchangeRate.R

In GE: General Equilibrium Modeling

#' @export
#' @title Some Examples Illustrating Endogenous Equilibrium Interest Rates and Foreign Exchange Rates in an Intertemporal Pure Exchange Economy with Two Currencies
#' @aliases gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate
#' @description These examples illustrate (endogenous) equilibrium primitive interest rates and foreign exchange rates in an intertemporal pure exchange economy with two currencies.
#' 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{
#' f <- function(ir, es = 1, beta, beta_prime = beta, return.ge = FALSE) {
#'   np <- length(beta) / 2
#'   n <- 4 * np # the number of commodity kinds
#'   m <- 2 # the number of agent kinds
#'
#'   ir[c(np, 2 * np)] <- last.ir <- 1000
#'   dst.consumer1 <- node_new(
#'     "util",
#'     type = "SCES", alpha = 1, es = es,
#'     beta = beta,
#'     paste0("cc", 1:(2 * np))
#'   )
#'   for (k in 1:(2 * np)) {
#'     node_set(
#'       dst.consumer1,
#'       paste0("cc", k),
#'       type = "FIN", rate = ir[k],
#'       paste0("lab", k), paste0("money", k)
#'     )
#'   }
#'
#'   dst.consumer2 <- Clone(dst.consumer1)
#'   dst.consumer2$beta <- beta_prime
#'
#'   names.commodity <- c(
#'     paste0("lab", 1:(2 * np)),
#'     paste0("money", 1:(2 * np))
#'   )
#'   names.agent <- paste0("consumer", 1:m)
#'
#'   ## the exogenous supply matrix.
#'   S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
#'   S0Exg[paste0("lab", 1:np), "consumer1"] <-
#'     S0Exg[paste0("lab", (np + 1):(2 * np)), "consumer2"] <- 100
#'   S0Exg[paste0("money", 1:np), "consumer1"] <-
#'     S0Exg[paste0("money", (np + 1):(2 * np)), "consumer2"] <- 1
#'
#'   # the output coefficient matrix.
#'   B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
#'
#'   ge <- sdm2(
#'     A = list(dst.consumer1, dst.consumer2),
#'     B = B,
#'     S0Exg = S0Exg,
#'     names.commodity = names.commodity,
#'     names.agent = names.agent,
#'     numeraire = "lab1",
#'     ts = TRUE
#'   )
#'
#'   tmp <- rowSums(ge$SV)
#'   ts.trading.value <- tmp[paste0("lab", 1:(2 * np))] * (1 + ir)
#'
#'   ir[1:(np - 1)] <- ts.trading.value[1:(np - 1)] / ts.trading.value[2:np] - 1
#'   ir[(np + 1):(2 * np - 1)] <- ts.trading.value[(np + 1):(2 * np - 1)] /
#'     ts.trading.value[(np + 2):(2 * np)] - 1
#'   ir <- pmax(1e-6, ir)
#'
#'   cat("ir: ", ir, "\n")
#'   cat("foreign.exchange.rate: ", ts.trading.value[(np + 1):(2 * np)] / ts.trading.value[1:np], "\n")
#'   if (return.ge) {
#'     ge$ts.trading.value <- ts.trading.value
#'     return(ge)
#'   } else {
#'     return(ir)
#'   }
#' }
#'
#'
#' ##
#' np <- 4 # the number of economic periods
#' beta <- proportions(c(0.4, 0.3, 0.2, 0.1, 0.5, 0.25, 0.15, 0.1))
#' mat.ir <- iterate(rep(0.1, 2 * np), f, tol = 1e-4, beta = beta)
#' beta[1:(np - 1)] / beta[2:np] - 1 # domestic interest rates
#' beta[(np + 1):(2 * np - 1)] / beta[(np + 2):(2 * np)] - 1 # foreign interest rates
#' beta[(np + 1):(2 * np)] / beta[1:np] # foreign exchange rates
#'
#' ge <- f(ir = tail(mat.ir, 1), es = 1.1, beta = beta, return.ge = TRUE)
#'
#' ## Assume that the two consumers have different preferences.
#' random.beta <- function(np) {
#'   beta <- runif(np, 0.9, 1) |>
#'   cumprod() |>
#'   proportions()
#' }
#'
#' set.seed(1)
#' np <- 5
#' beta <- proportions(c(random.beta(np), random.beta(np)))
#' beta_prime <- proportions(c(random.beta(np), random.beta(np)))
#' mat.ir <- iterate(rep(0.1, 2 * np), f, tol = 1e-4, beta = beta, beta_prime = beta_prime)
#'
#' # Calculate the equilibrium exchange rates and
#' # interest rates based on closed-form solutions.
#' compute_fx_ir <- function(beta, beta_prime) {
#'   np <- length(beta) / 2
#'   xi1 <- sum(beta_prime[1:np])
#'   xi2 <- sum(beta[(np + 1):(2 * np)])
#'
#'   v_tilde <- xi2 * beta_prime + xi1 * beta
#'   names(v_tilde) <- paste0("v", seq_len(2 * np))
#'
#'   foreign.exchange.rate <- v_tilde[(np + 1):(2 * np)] / v_tilde[1:np]
#'   names(foreign.exchange.rate) <- paste0("epsilon", 1:np)
#'
#'   r <- rep(NA_real_, 2 * np)
#'   for (i in 1:(2 * np - 1)) r[i] <- v_tilde[i] / v_tilde[i + 1] - 1
#'   r[np] <- Inf
#'   r[2 * np] <- Inf
#'   names(r) <- paste0("r", 1:(2 * np))
#'
#'   list(
#'     ir = r,
#'     foreign.exchange.rate = foreign.exchange.rate
#'   )
#' }
#'
#' compute_fx_ir(beta, beta_prime)
#' }

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