gemTechnologyProgress_PopulationGrowth {GE}

Some General Equilibrium Models with Technology Progress and Population Growth

Description

Some examples illustrating technology Progress and population growth.

Usage

gemTechnologyProgress_PopulationGrowth(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

#### a financial sequential model
gr.e <- 0.03 # the population growth rate
tpr <- 0.02 # the rate of technological progress
gr <- (1 + gr.e) * (1 + tpr) - 1
eis <- 0.8 # the elasticity of intertemporal substitution
Gamma.beta <- 0.8 # the subjective discount factor
yield.rate <- (1 + gr)^(1 / eis - 1) / Gamma.beta - 1 # the dividend rate
y1 <- 143.18115 # the initial product supply

dst.firm <- node_new("output",
  type = "FIN",
  rate = c(1, dividend.rate = yield.rate),
  "cc1", "equity.share"
)
node_set(dst.firm, "cc1",
  type = "CD",
  alpha = 2, beta = c(0.5, 0.5),
  "prod", "cc1.1"
)
node_set(dst.firm, "cc1.1",
  type = "Leontief", a = 1,
  "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 / (1 + gr.e)
    S0Exg
  },
  names.commodity = c("prod", "lab", "equity.share"),
  names.agent = c("firm", "laborer", "shareholder"),
  numeraire = "prod",
  maxIteration = 1,
  numberOfPeriods = 20,
  policy = list(function(time, A) {
    node_set(A[[1]], "cc1.1", a = 1 / (1 + tpr)^(time - 1))
  }, policyMarketClearingPrice),
  z0 = c(y1, 0, 0),
  GRExg = gr.e,
  ts = TRUE
)

matplot(growth_rate(ge$ts.p), type = "l")
matplot(growth_rate(ge$ts.z), type = "l")
ge$ts.z

## a timeline model
np <- 5 # the number of economic periods.

n <- 2 * np - 1 # the number of commodity kinds
m <- np # the number of agent kinds

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

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

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

ge <- sdm2(
  A = c(dstl.firm, dst.consumer),
  B = B,
  S0Exg = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "prod1",
  maxIteration = 1,
  numberOfPeriods = 40,
  ts = TRUE,
  policy = list(
    makePolicyTailAdjustment(ind = c(np - 1, np), gr = gr),
    policyMarketClearingPrice
  )
)

ge$z
ge$D
ge$S
ge$p[1:3] / ge$p[2:4] - 1 # the steady-state equilibrium return rate
sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr) # the steady-state equilibrium return rate

## a financial time-circle model
zeta <- (1 + gr)^np # the ratio of repayments to loans

n <- 2 * np + 1 # the number of commodity kinds
m <- np + 1 # the number of agent kinds

names.commodity <- c(paste0("prod", 1:np), paste0("lab", 1:np), "claim")
names.agent <- c(paste0("firm", 1:np), "consumer")

# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:np), "consumer"] <- 100 * (1 + gr.e)^(0:(np - 1))
S0Exg["claim", "consumer"] <- 100

# 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
}
B["prod1", paste0("firm", np)] <- 1 / zeta

dstl.firm <- list()
for (k in 1:np) {
  dstl.firm[[k]] <- node_new("output",
                             type = "FIN", rate = c(1, yield.rate),
                             "cc1", "claim"
  )
  node_set(dstl.firm[[k]], "cc1",
           type = "CD", alpha = 2,
           beta = c(0.5, 0.5),
           paste0("prod", k), "cc1.1"
  )
  node_set(dstl.firm[[k]], "cc1.1",
           type = "Leontief", a = 1 / ((1 + tpr)^(k - 1)),
           paste0("lab", 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 = S0Exg,
  names.commodity = names.commodity,
  names.agent = names.agent,
  numeraire = "prod1",
  ts = TRUE
)

ge$z
growth_rate(ge$z)
ge$D
ge$S