GE (version 0.3.8)

gemIntertemporal_FinancialClaim: Some Intertemporal Models with Financial Claim

Description

Some intertemporal models with financial claim (or long-term held securities). Financial claims may be equities, bonds, ad valorem taxation rights (ad valorem tax receipt), fiat money etc, which can be treated in the same way in models.

Usage

gemIntertemporal_FinancialClaim(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

# \donttest{
#### a model with tax.
np <- 5 # the number of (internal) periods.
gr.lab <- 0.03 # the growth rate of the labor supply.
tax.rate <- 0.25

S <- matrix(NA, 2 * np + 1, np + 1) # the exogenous supply matrix.
S[(np + 1):(2 * np), np] <- 100 * (1 + gr.lab)^(0:(np - 1)) # the labor supply.
S[1, np] <- 10 # the product supply in the first period.
S[2 * np + 1, np + 1] <- np * 100 # the supply of tax receipt

B <- matrix(0, 2 * np + 1, np + 1)
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, tax.rate),
    "cc1", "tax receipt"
  )
  node_set(dstl.firm[[k]], "cc1",
    type = "CD",
    alpha = 1, beta = c(0.5, 0.5),
    paste0("prod", k), paste0("lab", k)
  )
}

dst.laborer <- node_new(
  "util",
  type = "FIN", rate = c(1, tax.rate),
  "cc1", "tax receipt"
)
node_set(dst.laborer, "cc1",
  type = "CES", es = 0.5,
  alpha = 1, beta = rep(1 / np, np),
  paste0("cc1.", 1:np)
)
for (k in 1:np) {
  node_set(dst.laborer, paste0("cc1.", k),
    type = "CD", alpha = 1, beta = c(0.5, 0.5),
    paste0("prod", k), paste0("lab", k)
  )
}

dst.government <- node_new(
  "util",
  type = "CD",
  alpha = 1, beta = rep(1 / np, np),
  paste0("cc1.", 1:np)
)
for (k in 1:np) {
  node_set(dst.government, paste0("cc1.", k),
    type = "CD", alpha = 1, beta = c(0.5, 0.5),
    paste0("prod", k), paste0("lab", k)
  )
}
node_plot(dst.government, TRUE)

ge <- sdm2(
  A = c(dstl.firm, dst.laborer, dst.government),
  B = B,
  S0Exg = S,
  names.commodity = c(paste0("prod", 1:np), paste0("lab", 1:np), "tax receipt"),
  names.agent = c(paste0("firm", 1:(np - 1)), "laborer", "government"),
  numeraire = "prod1",
  # policy = makePolicyHeadTailAdjustment(gr = gr.lab, np = np)
)

ge$D
ge$z
ge$DV

#### a pure exchange model with money.
np <- 3 # the number of (internal) periods.
gr.lab <- 0.03 # the growth rate of endowments (i.e. labor supply)
eis <- 0.8 # the elasticity of intertemporal substitution
rho.beta <- 0.8 # the subjective discount factor
interest.rate <- 0.2593 # (1 + gr.lab)^(1 / eis - 1) / rho.beta - 1

dst.laborer <- node_new(
  "util",
  type = "CES", es = eis,
  alpha = 1, beta = rho.beta^(0:(np - 1)),
  paste0("cc", 1:np)
)

for (k in 1:np) {
  node_set(dst.laborer, paste0("cc", k),
    type = "FIN",
    rate = c(1, interest.rate),
    paste0("lab", k), paste0("money", k)
  )
}

node_plot(dst.laborer, TRUE)

dst.money.owner <- Clone(dst.laborer)

ge <- sdm2(
  A = list(dst.laborer, dst.money.owner),
  B = matrix(0, 2 * np, 2),
  S0Exg = {
    tmp <- matrix(0, 2 * np, 2)
    tmp[1:np, 1] <- 100 * (1 + gr.lab)^(0:(np - 1))
    tmp[(np + 1):(2 * np), 2] <- 200
    tmp
  },
  names.commodity = c(paste0("lab", 1:np), paste0("money", 1:np)),
  names.agent = c("laborer", "money.owner"),
  numeraire = c(money1 = interest.rate)
)

#### a two-period model with production and money.
interest.rate1 <- 0.25
interest.rate2 <- 0.1

dst.firm <- node_new(
  "prod",
  type = "FIN",
  rate = c(1, interest.rate1),
  "cc1", "money1"
)
node_set(dst.firm, "cc1",
  type = "CES",
  es = 1, alpha = 2, beta = c(0.5, 0.5),
  "prod1", "lab1"
)

dst.laborer <- node_new(
  "util",
  type = "CES",
  es = 0.5, alpha = 1, beta = c(2 / 3, 1 / 3),
  "cc1", "cc2"
)
node_set(dst.laborer, "cc1",
  type = "FIN",
  rate = c(1, interest.rate1),
  "prod1", "money1"
)

node_set(dst.laborer, "cc2",
  type = "FIN",
  rate = c(1, interest.rate2),
  "prod2", "money2"
)

dst.money.owner <- Clone(dst.laborer)

ge <- sdm2(
  A = list(dst.firm, dst.laborer, dst.money.owner),
  B = matrix(c(
    0, 0, 0,
    0, 0, 0,
    0, 0, 0,
    1, 0, 0,
    0, 0, 0
  ), 5, 3, TRUE),
  S0Exg = matrix(c(
    NA, 200, NA,
    NA, 100, NA,
    NA, NA, 100,
    NA, NA, NA,
    NA, NA, 100
  ), 5, 3, TRUE),
  names.commodity = c("prod1", "lab1", "money1", "prod2", "money2"),
  names.agent = c("firm", "laborer", "money.owner"),
  numeraire = c(money1 = interest.rate1)
)

ge$p
ge$DV
# }