gemOLG_StochasticSpotEquilibrium_3_3: An Example Illustrating OLG Stochastic Spot Equilibrium Paths

In GE: General Equilibrium Modeling

An Example Illustrating OLG Stochastic Spot Equilibrium Paths

Description

An example illustrating OLG stochastic spot equilibrium paths. The economy includes consumers with a lifespan of two periods and a type of spot-trading firm (i.e., a spot-trading enterprise). The economy features three types of commodities: products, labor, and public bonds, with the latter serving as a means of storing value.

Consumers in the economy live for two periods: youth and old age. Consumers only consume the product.

Young people save by purchasing public bonds. The savings rate of young consumers is an exogenous variable. This savings rate determines how each young person's income is distributed between their youth and old age.

Young people supply a total of 100 units of labor each period; old people supply a total of 100 units of public bonds each period.

The spot-trading enterprise operates independent of consumers, requiring products and labor for production, with a production function of \alpha\sqrt{x_1 x_2}. Assume \alpha follows a first-order autoregressive process. The enterprise's objective is to maximize current profits, without making forecasts for the future.

Usage

gemOLG_StochasticSpotEquilibrium_3_3(...)

Arguments

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

Note

The savings rate of the youth in the program is set to 0.5, meaning the savings-to-consumption ratio is 1.

Public bonds are used as the numeraire.

The initial output (i.e., initial product supply) is set to 20 in the parameter z0.

Examples

set.seed(1)
dst.firm <- node_new(
  "prod",
  type = "CD", alpha = 1,
  beta = c(0.5, 0.5),
  "prod", "lab"
)

dst.age1 <- node_new(
  "util",
  type = "FIN",
  rate = c(1, ratio.saving.consumption = 1),
  "prod", "publicBond"
)

dst.age2 <- node_new(
  "util",
  type = "Leontief", a = 1,
  "prod"
)

policy.technology <- function(time, A) {
  A[[1]]$alpha <- exp(0.95 * log(A[[1]]$alpha) +
                        rnorm(1, sd = 0.01))
}

set.seed(1)
ge <- sdm2(
  A = list(
    dst.firm, dst.age1, dst.age2
  ),
  B = matrix(c(
    1, 0, 0,
    0, 0, 0,
    0, 0, 0
  ), 3, 3, TRUE),
  S0Exg = matrix(c(
    NA, NA, NA,
    NA, 100, NA,
    NA, NA, 100
  ), 3, 3, TRUE),
  names.commodity = c("prod", "lab", "publicBond"),
  names.agent = c("firm", "age1", "age2"),
  numeraire = "publicBond",
  maxIteration = 1,
  numberOfPeriods = 20,
  policy = list(
    policy.technology,
    policyMarketClearingPrice
  ),
  z0 = c(20, 1, 1),
  ts = TRUE
)

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

GE documentation built on April 4, 2025, 5:33 a.m.