gemSkill {GE}

Some General Equilibrium Models with Skill (i.e. Human Capital)

Description

Some general equilibrium models with skill (i.e. human capital).

Usage

gemSkill(...)

Arguments

...

arguments to be passed to the function sdm2.

Examples

depreciation.rate <- 0.05 # the depreciation rate of skill
skill.density <- 10
relative.efficiency.coef <- 2
efficiency.coef <- skill.density * relative.efficiency.coef

dst.efficiency.unit <- node_new("efficiency unit",
  type = "Leontief",
  a =  1 / efficiency.coef,
  "complex labor"
)

dst.firm <- node_new(
  "product",
  type = "SCES", alpha = 1,
  beta = c(0.4, 0.6), es = 0.5,
  "product", "labor"
)
node_set(dst.firm, "labor",
  type = "SCES", alpha = 1,
  beta = c(0.5, 0.5), es = 1.5,
  "simple labor", dst.efficiency.unit
)

dst.school <- node_new(
  "skill",
  type = "Leontief",
  a = c(0.1, 1, 0.1),
  "product", "simple labor", dst.efficiency.unit
)

dst.complex.laborer <- node_new(
  "complex labor",
  type = "Leontief", a = c(skill.density, 1),
  "skill", "simple labor"
)

dst.simple.laborer <- node_new(
  "util",
  type = "Leontief", a = 1,
  "product"
)

ge <- sdm2(
  A = list(dst.firm, dst.school, dst.complex.laborer, dst.simple.laborer),
  B = matrix(c(
    1, 0, 0, 0,
    0, 1, skill.density * (1 - depreciation.rate), 0,
    0, 0, 1, 0,
    0, 0, 0, 0
  ), 4, 4, TRUE),
  S0Exg = {
    tmp <- matrix(NA, 4, 4)
    tmp[4, 4] <- 100
    tmp
  },
  names.commodity = c("product", "skill", "complex labor", "simple labor"),
  names.agent = c("firm", "school", "complex laborer", "simple laborer"),
  numeraire = "simple labor",
  policy = makePolicyMeanValue(50),
  priceAdjustmentVelocity = 0.05,
  maxIteration = 1,
  numberOfPeriods = 1000,
  ts = TRUE
)

ge$p
ge$z
addmargins(ge$D, 2)
addmargins(ge$S, 2)
matplot(ge$ts.p, type = "l")

#### Assumed that the amount of education and training purchased by laborers is
## determined primarily by their preferences rather than their investment motives.
depreciation.rate <- 0.05
skill.density <- 10
relative.efficiency.coef <- 2
efficiency.coef <- skill.density * relative.efficiency.coef

dst.efficiency.unit <- node_new("efficiency unit",
  type = "Leontief",
  a = c(skill.density / efficiency.coef, 1 / efficiency.coef),
  "skill service", "simple labor"
)

dst.firm <- node_new(
  "product",
  type = "SCES", alpha = 1,
  beta = c(0.4, 0.6), es = 0.5,
  "product", "labor"
)
node_set(dst.firm, "labor",
  type = "SCES", alpha = 1,
  beta = c(0.5, 0.5), es = 1.5,
  "simple labor", dst.efficiency.unit
)

dst.school <- node_new(
  "skill",
  type = "Leontief",
  a = c(0.1, 1, 0.1),
  "product", "simple labor", dst.efficiency.unit
)

dst.laborer <- node_new(
  "util",
  type = "CD", alpha = 1,
  beta = c(0.7887, 0.2113),
  # beta <- c(0.9, 0.1),
  # beta <- c(0.6, 0.4),
  "product", "skill",
  skill.stock = 0
)

ge <- sdm2(
  A = list(dst.firm, dst.school, dst.laborer),
  B = matrix(c(
    1, 0, 0,
    0, 1, 0,
    0, 0, 0,
    0, 0, 0
  ), 4, 3, TRUE),
  S0Exg = {
    tmp <- matrix(NA, 4, 3)
    tmp[4, 3] <- 100
    tmp
  },
  names.commodity = c("product", "skill", "skill service", "simple labor"),
  names.agent = c("firm", "school", "laborer"),
  numeraire = "simple labor",
  policy = function(A, state) {
    last.D <- state$last.A %*% dg(state$last.z)
    new.skill <- last.D[2, 3]
    state$S[3, 3] <- A[[3]]$skill.stock <-
      A[[3]]$skill.stock * (1 - depreciation.rate) + new.skill
    state
  },
  priceAdjustmentVelocity = 0.05,
  maxIteration = 1,
  numberOfPeriods = 1000,
  ts = TRUE
)

ge$p
ge$z
addmargins(ge$D, 2)
addmargins(ge$S, 2)
matplot(log(ge$ts.p), type = "l")