GE (version 0.4.3)

gemIntertemporal_InterestRate: An Example Illustrating Endogenous Equilibrium Interest Rates in a (Timeline) Transitional Equilibrium Path

Description

This example illustrates (endogenous) equilibrium interest rates in a transitional equilibrium path, which is an intertemporal path distinct from a steady-state equilibrium. There are three types of economic agents in the model: firms, a laborer, and a money owner. Suppose the laborer and the money owner need to use money to buy products, and firms need to use money to buy products and labor. Formally, the money owner borrows money from himself and pays interest to himself.

Usage

gemIntertemporal_InterestRate(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

# \donttest{
vm <- 1 # the velocity of money
eis <- 0.8 # the elasticity of intertemporal substitution
Gamma.beta <- 0.8 # the subjective discount factor
gr <- 0 # the growth rate
y1 <- 10 # the product supply in the first period
np <- 20 # the number of economic periods

f <- function(ir = rep(0.25, np - 1), return.ge = FALSE) {
  n <- 2 * np # the number of commodity kinds
  m <- np + 1 # the number of agent kinds

  names.commodity <- c(
    paste0("prod", 1:np),
    paste0("lab", 1:(np - 1)),
    "money"
  )
  names.agent <- c(
    paste0("firm", 1:(np - 1)),
    "laborer", "moneyOwner"
  )

  # the exogenous supply matrix.
  S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
  S0Exg[paste0("lab", 1:(np - 1)), "laborer"] <- 100 * (1 + gr)^(0:(np - 2))
  S0Exg["money", "moneyOwner"] <- 100
  S0Exg["prod1", "laborer"] <- 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 = "FIN", rate = c(1, ir[k] / vm),
      "cc1", "money"
    )
    node_set(dstl.firm[[k]], "cc1",
             type = "CD", alpha = 2, beta = c(0.5, 0.5),
             paste0("prod", k), paste0("lab", k)
    )
  }

  dst.laborer <- node_new(
    "util",
    type = "CES", es = eis,
    alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
    paste0("cc", 1:(np - 1)), paste0("prod", np)
  )

  for (k in 1:(np - 1)) {
    node_set(dst.laborer, paste0("cc", k),
      type = "FIN", rate = c(1, ir[k] / vm),
      paste0("prod", k), "money"
    )
  }

  dst.moneyOwner <- 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.moneyOwner, paste0("cc", k),
             type = "FIN", rate = c(1, ir[k] / vm),
             paste0("prod", k), "money"
    )
  }

  ge <- sdm2(
    A = c(dstl.firm, dst.laborer, dst.moneyOwner),
    B = B,
    S0Exg = S0Exg,
    names.commodity = names.commodity,
    names.agent = names.agent,
    numeraire = "prod1",
    policy = makePolicyHeadTailAdjustment(gr = gr, np = np, type = c("tail"))
  )

  tmp <- rowSums(ge$SV)
  ts.supply.value <- tmp[paste0("prod", 1:(np - 1))] + tmp[paste0("lab", 1:(np - 1))]
  ir.new <- ts.supply.value[1:(np - 2)] / ts.supply.value[2:(np - 1)] - 1
  ir.new <- pmax(1e-6, ir.new)
  ir.new[np - 1] <- ir.new[np - 2]

  ir <- c(ir * ratio_adjust(ir.new / ir, 0.3))
  cat("ir: ", ir, "\n")

  if (return.ge) {
    return(ge)
  } else {
    return(ir)
  }
}

## Calculate equilibrium interest rates.
## Warning: Running the program below takes about several minutes.
# result <- iterate(rep(0.1, np - 1), f, times = 30)
# sserr(eis, Gamma.beta, gr, prepaid = TRUE)

## Below are the calculated equilibrium interest rates.
ir <- rep(0.25, np - 1)
ir[1:14] <- c(0.4301, 0.3443, 0.3007, 0.2776, 0.2652, 0.2584, 0.2546,
  0.2526, 0.2514, 0.2508, 0.2504, 0.2502, 0.2501, 0.2501)

ge <- f(ir, TRUE)

plot(ge$z[1:(np - 1)], type = "o")
tmp <- rowSums(ge$SV)
ts.supply.value <- tmp[paste0("prod", 1:(np - 1))] + tmp[paste0("lab", 1:(np - 1))]
ts.supply.value[1:(np - 2)] / ts.supply.value[2:(np - 1)] - 1
ir

## Calculate equilibrium interest rates.
## Warning: Running the program below takes about several minutes.
# gr <- 0.03
# result <- iterate(rep(0.1, np - 1), f, times = 30)
# sserr(eis, Gamma.beta, gr, prepaid = TRUE)
# }