policyMarketClearingPrice: Market-Clearing-Price Policy Function

In GE: General Equilibrium Modeling

Market-Clearing-Price Policy Function

Description

This policy is to make the market clear every period. In this case, the path of the economy is the market clearing path (alias instantaneous equilibrium path, temporary equilibrium path). Generally, this function is passed to the function sdm2 as an argument to compute the market clearing path.

Usage

policyMarketClearingPrice(time, A, state, ...)

Arguments

time	the current time.
A	a demand structure tree list (i.e. dstl, see demand_coefficient), a demand coefficient n-by-m matrix (alias demand structure matrix) or a function A(state) which returns an n-by-m matrix.
state	the current state.
...	optional arguments to be passed to the function sdm2.

Value

A list consisting of p, S and B which specify the prices, supplies and supply coefficient matrix after adjustment.

References

LI Wu (2019, ISBN: 9787521804225) General Equilibrium and Structural Dynamics: Perspectives of New Structural Economics. Beijing: Economic Science Press. (In Chinese)

Grandmont, J.M. (1977). Temporary General Equilibrium Theory. Econometrica 45, 535-572.

See Also

CGE::iep and sdm2, gemTemporaryEquilibriumPath. The market clearing prices are the prices with a stickiness value equal to zero. Therefore, this function can actually be replaced by makePolicyStickyPrice in the calculation.

Examples

#### an iep of the example (see Table 2.1 and 2.2) of the canonical dynamic
#### macroeconomic general equilibrium model in Torres (2016).
ge <- gemCanonicalDynamicMacroeconomic_3_2(
  policy.price = policyMarketClearingPrice,
  ts = TRUE,
  maxIteration = 1,
  numberOfPeriods = 50,
  z0 = c(0.5, 1)
)

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

#### the same as above
ge <- gemCanonicalDynamicMacroeconomic_3_2(
  policy.price = makePolicyStickyPrice(stickiness = 0),
  ts = TRUE,
  maxIteration = 1,
  numberOfPeriods = 50,
  z0 = c(0.5, 1)
)

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

#### TFP shock in the economy above (see Torres, 2016, section 2.8).
numberOfPeriods <- 200

discount.factor <- 0.97
depreciation.rate <- 0.06
beta1.firm <- 0.35
return.rate <- 1 / discount.factor - 1

set.seed(1)
alpha.shock <- rep(1, 100)
alpha.shock[101] <- exp(0.01)
for (t in 102:numberOfPeriods) {
  alpha.shock[t] <- exp(0.95 * log(alpha.shock[t - 1]))
}

policyTechnologyChange <- function(time, A) {
  A[[1]]$func <- function(p) {
    result <- CD_A(
      alpha.shock[time], rbind(beta1.firm, 1 - beta1.firm, 0),
      c(p[1] * (return.rate + depreciation.rate), p[2:3])
    )
    result[3] <- p[1] * result[1] * return.rate / p[3]
    result
  }
}

InitialEndowments <- {
  tmp <- matrix(0, 3, 2)
  tmp[1, 1] <- tmp[2, 2] <- tmp[3, 2] <- 1
  tmp
}

ge <- gemCanonicalDynamicMacroeconomic_3_2(
  policy.supply = makePolicySupply(InitialEndowments),
  policy.technology = policyTechnologyChange,
  policy.price = policyMarketClearingPrice,
  ts = TRUE,
  maxIteration = 1,
  numberOfPeriods = 200
)

c <- ge$A[1, 2] * ge$ts.z[, 2] # consumption
par(mfrow = c(2, 2))
matplot(ge$ts.z, type = "l")
x <- 100:140
plot(x, ge$ts.z[x, 1] / ge$ts.z[x[1], 1], type = "o", pch = 20)
plot(x, ge$ts.z[x, 2] / ge$ts.z[x[1], 2], type = "o", pch = 20)
plot(x, c[x] / c[x[1]], type = "o", pch = 20)

#### an iep of example 7.2 (a monetary economy) in Li (2019). See CGE::Example7.2.
interest.rate <- 0.25
dst.firm <- node_new("cc", #composite commodity
                     type = "FIN",
                     rate = c(1, interest.rate),
                     "cc1", "money"
)
node_set(dst.firm, "cc1",
         type = "CD", alpha = 1, beta = c(0.5, 0.5),
         "wheat", "labor"
)

dst.laborer <- Clone(dst.firm)
dst.money.lender <- Clone(dst.firm)

dstl <- list(dst.firm, dst.laborer, dst.money.lender)

B <- matrix(0, 3, 3)
B[1, 1] <- 1

S0Exg <- matrix(NA, 3, 3)
S0Exg[2, 2] <- 100
S0Exg[3, 3] <- 100

InitialEndowments <- {
  tmp <- matrix(0, 3, 3)
  tmp[1, 1] <- 10
  tmp[2, 2] <- tmp[3, 3] <- 100
  tmp
}

ge <- sdm2(
  A = dstl, B = B, S0Exg = S0Exg,
  names.commodity = c("wheat", "labor", "money"),
  names.agent = c("firm", "laborer", "money.lender"),
  numeraire = c(money = interest.rate),
  numberOfPeriods = 20,
  maxIteration = 1,
  ts = TRUE,
  policy = list(
    makePolicySupply(S = InitialEndowments),
    policyMarketClearingPrice
  )
)

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

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