GE (version 0.3.6)

gemIntertemporal_Money_Dividend_Example7.5.1: Three Equivalent Models with Money and Dividend

Description

Three equivalent models with money and dividend as follows: (1) a sequential model (Li, 2019, example 7.5); (2) a time-circle model; (3) a timeline model with head-tail adjustment.

Stocks, fiat currencies, bonds, and taxes, etc. can be collectively referred to as claims. Sometimes we do not need to differentiate between these financial instruments when modeling. Furthermore, sometimes we do not need to consider which period these financial instruments belong to.

Usage

gemIntertemporal_Money_Dividend_Example7.5.1(...)

Arguments

...

arguments to be passed to the function sdm2.

References

LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)

Examples

# \donttest{
#### (1) a sequential model. See the first part of example 7.5 in Li (2019).
dividend.rate <- 0.25
ir <- 0.25 # the interest rate.

dst.firm <- node_new(
  "output",
  type = "FIN", rate = c(1, dividend.rate),
  "cc1", "dividend"
)
node_set(dst.firm, "cc1",
         type = "FIN", rate = c(1, ir),
         "cc1.1", "money"
)
node_set(dst.firm, "cc1.1",
         type = "CD", alpha = 1, beta = c(0.5, 0.5),
         "prod", "lab"
)

dst.consumer <- node_new(
  "util",
  type = "FIN", rate = c(1, ir),
  "cc1", "money"
)
node_set(dst.consumer, "cc1",
         type = "CD", alpha = 1, beta = c(0.5, 0.5),
         "prod", "lab"
)

ge.seq <- sdm2(
  A = list(
    dst.firm, dst.consumer, dst.consumer, dst.consumer
  ),
  B = diag(c(1, 0, 0, 0)),
  S0Exg = {
    tmp <- matrix(NA, 4, 4)
    tmp[2, 2] <- tmp[3, 3] <- tmp[4, 4] <- 100
    tmp
  },
  names.commodity = c("prod", "lab", "money", "dividend"),
  names.agent = c("firm", "laborer", "money.owner", "shareholder"),
  numeraire = "prod",
  GRExg = 0.1,
  z0 = c(9.30909, 0, 0, 0),
  policy = policyMarketClearingPrice,
  maxIteration = 1,
  numberOfPeriods = 20,
  ts = TRUE
)

matplot(ge.seq$ts.z, type = "o", pch = 20)
ge.seq$D
ge.seq$S
ge.seq$ts.z[,1]
growth_rate(ge.seq$ts.z[,1])

#### (2) a time-circle model.
np <- 5 # the number of periods.
gr <- 0.1 # the growth rate.
dividend.rate <- 0.25
ir <- 0.25
zeta <- (1 + gr)^np

S <- matrix(NA, 2 * np+1, np + 1) # the exogenous supply matrix.
S[(np + 1):(2 * np), np + 1] <- 100 * (1 + gr)^(0:(np - 1)) # labor supply.
S[2* np + 1, np+1] <- np*100 # claim supply.

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(
    "prod",
    type = "FIN", rate = c(1, (1+ir)*(1+dividend.rate)-1),
    "cc1","claim"
  )
  node_set( dstl.firm[[k]], "cc1",
            type = "CD", alpha = 1, beta = c(0.5, 0.5),
            paste0("prod", k), paste0("lab", k)
  )
}

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

ge.tc <-  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"
)

ge.tc$D
ge.tc$z

#### (3) a timeline model with head-tail adjustment.
np <- 5 # the number of (internal) periods.
gr <- 0.1
dividend.rate <- 0.25
ir <- 0.25

S <- matrix(NA, 2 * np + 1, np) # exogenous supply matrix.
S[(np + 1):(2 * np), np] <- 100 * (1 + gr)^(0:(np - 1))
S[2 * np + 1, np] <- np * 100
S[1, np] <- 10 # 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 = "FIN", rate = c(1, (1 + ir) * (1 + dividend.rate) - 1),
    "cc1", "claim"
  )
  node_set(dstl.firm[[k]], "cc1",
           type = "CD", alpha = 1, beta = c(0.5, 0.5),
           paste0("prod", k), paste0("lab", k)
  )
}

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

ge.tl <- 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 - 1)), "consumer"),
  numeraire = "prod1",
  policy = makePolicyHeadTailAdjustment(gr = gr, np = np)
)

node_plot(dst.consumer, TRUE)
ge.tl$D
ge.tl$z
# }