gemstStructuralMultipleEquilibria_2_2: Structural Multiple Equilibria and Structural Transition...

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Structural Multiple Equilibria and Structural Transition Policy

Description

Some examples of structural multiple equilibria and structural transition policy. In these examples it is assumed that the firm has a structural production function (see Li, Fu, 2020), e.g.

structural_function(last.output, c(0.3, 0.4), 1, 2) * x1^0.35 * x2^0.65

wherein last.output is the output of the firm in the previous period.

Usage

gemstStructuralMultipleEquilibria_2_2(...)

Arguments

...	arguments to be passed to the function sdm2.

References

Li Wu, Fu Caihui (2020) A Simulation Study on the Economic Structure Transition Policy. Journal of Shanghai University (Social Sciences). 37(2), pp: 33-45. (In Chinese)

Examples

dst.firm <- node_new("output",
  type = "CD", alpha = 1,
  beta = c(0.35, 0.65),
  "prod", "lab"
)

dst.consumer <- node_new("utility",
  type = "CD", alpha = 1,
  beta = c(0.4, 0.6),
  "prod", "lab"
)

policy.technology <- function(time, state, A) {
  # state$last.z[1] is the previous output.
  A[[1]]$alpha <- structural_function(state$last.z[1], c(0.3, 0.4), 1, 2)
}

policy.tax <- function(time, state) {
  if ((time >= 15) && state$last.z[1] < 0.4) {
    state$S[2, 2] <- 0.8
    state$S[2, 1] <- 0.2
  } else {
    state$S[2, 2] <- 1
    state$S[2, 1] <- 0
  }

  state
}

f <- function(z0 = c(0.1, 1),
              policy = list(
                policy.technology,
                policyMarketClearingPrice
              )) {
  ge <- sdm2(
    A = list(dst.firm, dst.consumer),
    B = matrix(c(
      1, 0,
      0, 0
    ), 2, 2, TRUE),
    S0Exg = matrix(c(
      NA, NA,
      NA, 1
    ), 2, 2, TRUE),
    names.commodity = c("prod", "lab"),
    names.agent = c("firm", "consumer"),
    numeraire = "lab",
    z0 = z0,
    p0 = c(1, 1),
    maxIteration = 1,
    numberOfPeriods = 30,
    policy = policy,
    ts = TRUE
  )

  matplot(ge$ts.z, type = "o", pch = 20)
  invisible(ge)
}

geLow <- f()
geLow$z

geHigh <- f(z0 = c(0.5, 1))
geHigh$z

f(policy = list(
  policy.technology,
  policy.tax,
  policyMarketClearingPrice
))

#### structural transition: disequilibrium path and
## a market-clearing path (instantaneous equilibrium path)
dst.firm <- node_new("output",
  type = "CD", alpha = 5,
  beta = c(0.5, 0.5),
  "prod", "lab"
)

dst.consumer <- node_new("utility",
  type = "Leontief", a = 1,
  "prod"
)

policy.technology <- function(time, state, A) {
  # state$last.z[1] is last output.
  A[[1]]$alpha <- structural_function(state$last.z[1], c(15, 20), 5, 15)
  return(NULL)
}

policy.tax <- function(time, state) {
  if ((time >= 100) && (time <= 109)) {
    state$S[2, 2] <- 0.6
    state$S[2, 1] <- 0.4
  } else {
    state$S[2, 2] <- 1
    state$S[2, 1] <- 0
  }

  state
}

f <- function(z0 = c(1, 1),
              p0 = c(1, 1),
              policy = policy.technology) {
  ge <- sdm2(
    A = list(dst.firm, dst.consumer),
    B = matrix(c(
      1, 0,
      0, 1
    ), 2, 2, TRUE),
    S0Exg = matrix(c(
      NA, NA,
      NA, 1
    ), 2, 2, TRUE),
    names.commodity = c("prod", "lab"),
    names.agent = c("firm", "consumer"),
    numeraire = "lab",
    z0 = z0,
    p0 = p0,
    maxIteration = 1,
    numberOfPeriods = 200,
    policy = policy,
    priceAdjustmentVelocity = 0.4,
    ts = TRUE
  )

  matplot(ge$ts.z, type = "l", pch = 20)
  invisible(ge)
}

geLow <- f()
geLow$z

geHigh <- f(z0 = c(18, 1), p0 = c(1, 9))
geHigh$z

## structural transition: a disequilibrium path
f(policy = list(
  policy.technology,
  policy.tax
))$z


## structural transition: a market-clearing path
f(policy = list(
  policy.technology,
  policy.tax,
  policyMarketClearingPrice
))$z

## structural transition through foreign aid
policy.foreign_aid <- function(time, state) {
  if ((time >= 100) && (time <= 109)) {
    state$S[2, 2] <- 3
  } else {
    state$S[2, 2] <- 1
  }

  state
}

f(policy = list(
  function(time, state, A) { # technology policy
    # state$last.z[1] is last output.
    A[[1]]$alpha <- structural_function(state$last.z[1], c(30, 35), 5, 15)
  },
  policy.foreign_aid
))

#### another example
dst.firm <- node_new("prod",
  type = "CD", alpha = 2,
  beta = c(0.5, 0.5),
  "prod", "lab"
)

dst.consumer <- node_new("util",
  type = "Leontief", a = 1,
  "prod"
)

policy.technology <- function(time, state, A) {
  # state$last.z[1] is the previous output.
  A[[1]]$alpha <- structural_function(state$last.z[1], c(220, 250), 2, 4)
}

policy.tax <- function(time, state) {
  if ((time >= 15) && state$last.z[1] < 240) {
    state$S[2, 2] <- 80
    state$S[2, 1] <- 20
  } else {
    state$S[2, 2] <- 100
    state$S[2, 1] <- 0
  }

  state
}

ge <- sdm2(
  A = list(dst.firm, dst.consumer),
  B = matrix(c(
    1, 0,
    0, 0
  ), 2, 2, TRUE),
  S0Exg = matrix(c(
    NA, NA,
    NA, 100
  ), 2, 2, TRUE),
  names.commodity = c("prod", "lab"),
  names.agent = c("firm", "consumer"),
  numeraire = "lab",
  z0 = c(100, 100),
  maxIteration = 1,
  numberOfPeriods = 30,
  policy = list(
    policy.technology,
    policy.tax,
    policyMarketClearingPrice
  ),
  ts = TRUE
)

matplot(ge$ts.z, type = "b", pch = 20)

GE documentation built on Nov. 8, 2023, 9:07 a.m.