GE (version 0.3.8)

gemIntertemporal_Dividend: The Identical Steady-state Equilibrium: Four Models Illustrating Dividend

Description

Four models are presented to illustrate dividend, which have the same steady-state equilibrium.

These models are as follows: (1) a real timeline model with head-tail adjustment; (2) a financial timeline model with dividend and head-tail adjustment; (3) a financial sequential model with dividend; (4) a financial time-circle model with dividend.

Usage

gemIntertemporal_Dividend(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

# \donttest{
#### (1) a real timeline model with head-tail adjustment.
eis <- 0.8 # the elasticity of intertemporal substitution
rho.beta <- 0.8 # the subjective discount factor
gr <- 0.03 # the growth rate
np <- 5 # the number of internal periods
S0Exg <- matrix(NA, 2 * np - 1, np)
S0Exg[(np + 1):(2 * np - 1), np] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg[1, np] <- 140 # the product supply in the first period, which will be adjusted.

B <- matrix(0, 2 * np - 1, np)
B[2:np, 1:(np - 1)] <- diag(np - 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 = eis,
  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 = c(paste0("prod", 1:np), paste0("lab", 1:(np - 1))),
  names.agent = c(paste0("firm", 1:(np - 1)), "consumer"),
  numeraire = "prod1",
  policy = makePolicyHeadTailAdjustment(gr = gr, np = np)
)

((1 + gr))^(1 / eis) / rho.beta - 1 # the real interest rate.
ge$p[1:(np - 1)] / ge$p[2:np] - 1
ge$z

## (2) a financial timeline model with dividend and head-tail adjustment.
yield <- 0.2593 # (1 + gr)^(1 / eis - 1) / rho.beta - 1

S0Exg <- matrix(NA, 2 * np, np)
S0Exg[(np + 1):(2 * np - 1), np] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg[2 * np, np] <- 100
S0Exg[1, np] <- 140 # the product supply in the first period, which will be adjusted.

B <- matrix(0, 2 * np, np)
B[2:np, 1:(np - 1)] <- diag(np - 1)

dstl.firm <- list()
for (k in 1:(np - 1)) {
  dstl.firm[[k]] <- node_new(
    "prod",
    type = "FIN", rate = c(1, yield),
    "cc1", "claim"
  )
  node_set(dstl.firm[[k]], "cc1",
           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(rep(1, np)), # prop.table(rho.beta^(1:np)),
  paste0("prod", 1:np)
)

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S0Exg,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:(np - 1)), "claim"),
  names.agent = c(paste0("firm", 1:(np - 1)), "consumer"),
  numeraire = "prod1",
  policy = makePolicyHeadTailAdjustment(gr = gr, np = np)
)

#### (3) a financial sequential model with dividend.
gr <- 0.03 # the growth rate.
yield <- 0.2593 # (1 + gr)^(1 / eis - 1) / rho.beta - 1

dst.firm <- node_new("output",
  type = "FIN",
  rate = c(1, dividend.rate = yield),
  "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",
  GRExg = gr
)

ge$z

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 = gr,
  maxIteration = 1,
  numberOfPeriods = 20,
  z0 = c(154.20, 0, 0),
  policy = policyMarketClearingPrice,
  ts = TRUE
)

ge$ts.z[, 1]
growth_rate(ge$ts.z[, 1])

#### (4) a financial time-circle model with dividend.
np <- 5
gr <- 0.03
yield <- 0.2593

zeta <- (1 + gr)^np # the ratio of repayments to loans
S <- matrix(NA, 2 * np + 1, np + 1)
S[(np + 1):(2 * np + 1), np + 1] <- c(100 * (1 + gr)^(0:(np - 1)), 100)

B <- matrix(0, 2 * np + 1, np + 1)
B[1:np, 1:np] <- diag(np)[, c(2:np, 1)]
B[1, np] <- 1 / zeta

dstl.firm <- list()
for (k in 1:np) {
  dstl.firm[[k]] <- node_new("output",
    type = "FIN", rate = c(1, yield),
    "cc1", "claim"
  )
  node_set(dstl.firm[[k]], "cc1",
    type = "CD", alpha = 2,
    beta = c(0.5, 0.5),
    paste0("lab", k), paste0("prod", k)
  )
}

dst.consumer <- node_new(
  "util",
  type = "CES", es = 1,
  alpha = 1, beta = prop.table(rep(1, np)),
  paste0("prod", 1:np)
)

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:np), "claim"),
  names.agent = c(paste0("firm", 1:np), "consumer"),
  numeraire = "prod1",
  ts = TRUE
)

ge$z
# }