gemCanonicalDynamicMacroeconomic_3_2 {GE}

A Canonical Dynamic Macroeconomic General Equilibrium Model (see Torres, 2016)

Description

A canonical dynamic macroeconomic general equilibrium model (see Torres, 2016, Table 2.1 and 2.2).

Usage

gemCanonicalDynamicMacroeconomic_3_2(
  discount.factor = 0.97,
  depreciation.rate = 0.06,
  beta.prod.firm = 0.35,
  beta.prod.consumer = 0.4,
  policy.supply = NULL,
  policy.technology = NULL,
  policy.price = NULL,
  ...
)

Arguments

discount.factor

the intertemporal discount factor.

depreciation.rate

the physical depreciation rate of capital stock.

beta.prod.firm

the share parameter of the product in the Cobb-Douglas production function.

beta.prod.consumer

the share parameter of the product in the Cobb-Douglas period utility function. This parameter represents the individual's preferences regarding consumption-leisure decisions.

policy.supply

a policy function or a policy function list which adjusts the supplies.

policy.technology

a policy function or a policy function list which adjusts the technology.

policy.price

a policy function or a policy function list which adjusts the prices.

...

arguments to be to be passed to the function sdm2.

Details

A general equilibrium model with 3 commodities (i.e. product, labor and equity shares) and 2 agents (i.e. a firm and a consumer). Labor is the numeraire.

Value

A general equilibrium (see sdm2).

References

Torres, Jose L. (2016, ISBN: 9781622730452) Introduction to Dynamic Macroeconomic General Equilibrium Models (Second Edition). Vernon Press.

Li Xiangyang (2018, ISBN: 9787302497745) Dynamic Stochastic General Equilibrium (DSGE) Model: Theory, Methodology, and Dynare Practice. Tsinghua University Press. (In Chinese)

See Also

The spot market clearing path (alias instantaneous equilibrium path) can be computed with the function policyMarketClearingPrice.

Examples

gemCanonicalDynamicMacroeconomic_3_2()

#### a spot market clearing path (alias instantaneous equilibrium path)
ge <- gemCanonicalDynamicMacroeconomic_3_2(
  policy.price = policyMarketClearingPrice,
  ts = TRUE,
  maxIteration = 1,
  numberOfPeriods = 100,
  z0 = c(50, 100)
)

par(mfrow = c(1, 2))
matplot(ge$ts.z, type = "o", pch = 20)
matplot(ge$ts.p, type = "o", pch = 20)

#### technology change in a market-clearing path
policyTechnologyChange <- function(time, A) {
  alpha <- 1.2 # The original value is 1.
  time.win <- c(50, 50)
  discount.factor <- 0.97
  depreciation.rate <- 0.06
  beta.prod.firm  <- 0.35
  return.rate <- 1 / discount.factor - 1

  if (time >= time.win[1] && time <= time.win[2]) {
    A[[1]]$func <- function(p) {
      result <- CD_A(
        alpha, rbind(beta.prod.firm , 1 - beta.prod.firm , 0),
        c(p[1] * (return.rate + depreciation.rate), p[2:3])
      )
      result[3] <- p[1] * result[1] * return.rate / p[3]
      result
    }
  }
}

ge <- gemCanonicalDynamicMacroeconomic_3_2(
  policy.technology = policyTechnologyChange,
  policy.price = policyMarketClearingPrice,
  ts = TRUE,
  maxIteration = 1,
  numberOfPeriods = 100,
  z0 = c(50, 100)
)

par(mfrow = c(1, 2))
matplot(ge$ts.z, type = "o", pch = 20)
matplot(ge$ts.p, type = "o", pch = 20)

#### an example on page 46 of Li Xiangyang (2018)
ge <- gemCanonicalDynamicMacroeconomic_3_2(
  discount.factor = 0.99,
  depreciation.rate = 0.025,
  beta.prod.firm  = 0.36,
  beta.prod.consumer = 1
)