gemCanonicalDynamicMacroeconomic_4_3: A Canonical Dynamic Macroeconomic General Equilibrium Model...

In GE: General Equilibrium Modeling

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

Description

This is a function used to calculate the steady state of a canonical dynamic macroeconomic general equilibrium model (see Torres, 2016, Table 2.1 and Table 2.2). The model consists of four commodities (i.e., product, labor, capital, and equity shares) and three agents (i.e., a production firm, a consumer, and a capital-leasing firm). It can also compute the spot equilibrium path based on the steady-state return rate.

Usage

gemCanonicalDynamicMacroeconomic_4_3(
  discount.factor = 0.97,
  depreciation.rate = 0.06,
  beta.prod.firm = 0.35,
  beta.prod.consumer = 0.4,
  ...
)

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 of the production firm.
beta.prod.consumer	the share parameter of the product in the Cobb-Douglas period utility function of the consumer.
...	arguments to be passed to the function sdm2.

Value

A general equilibrium (see sdm2)

References

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

Examples

#### (A) A spot equilibrium path that converges to the steady-state equilibrium.
ge <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = 100,
  policy = policyMarketClearingPrice
)

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

## population growth: a spot equilibrium path
## that converges to a balanced growth path
ge <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = 100,
  GRExg = 0.01,
  policy = policyMarketClearingPrice
)

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

#### (B) A disequilibrium path and the steady-state equilibrium.
ge <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = 5000,
  priceAdjustmentVelocity = 0.03,
)

ge$p
ge$z
matplot(ge$ts.z, type = "l")
node_plot(ge$dstl[[3]], param = TRUE)

## a small disturbance to the product supply
ge <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = 4000,
  priceAdjustmentVelocity = 0.03,
  policy = function(time, state) {
    if (time == 1500) {
      state$S[1, 1] <- state$S[1, 1] * 0.999
    }
    state
  }
)

#### (C) Business cycles.
de <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = 1000,
  priceAdjustmentVelocity = 0.15
)

## A tax rate policy is implemented from the 600th period to stabilize the economy.
ge <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = 1500,
  priceAdjustmentVelocity = 0.15,
  policy = Example9.10.policy.tax
)

matplot(ge$ts.z, type = "l")
plot(ge$policy.data, type = "l") # tax rates

#### (D) A spot equilibrium path with a productivity shock.
nPeriod <- 100 # the number of periods of the spot equilibrium path
set.seed(1)
alpha.shock <- rep(1, nPeriod)
alpha.shock[11] <- exp(0.01)
for (t in 12:nPeriod) {
  alpha.shock[t] <- exp(0.95 * log(alpha.shock[t - 1]))
}
plot(alpha.shock)

ge <- gemCanonicalDynamicMacroeconomic_4_3(
  numberOfPeriods = nPeriod,
  p0 = c(1, 1.34312, 0.09093, 0.08865),
  z0 = c(74.47, 61.20, 286.65),
  policy = list(
    function(time, A) {
      A[[1]]$alpha <- alpha.shock[time]
    },
    policyMarketClearingPrice
  )
)

matplot(ge$ts.z[, 1], type = "o", pch = 20)

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