| gemIntertemporal_5_5 {GE} | R Documentation |
Some Intertemporal (Timeline and Time-circle) Models with Land, Two Consumers, and Three Types of Firms
Description
Some intertemporal (timeline and time-circle) models with two consumers (i.e. a laborer and a landowner) and three types of firms (i.e. wheat producers, iron producers and iron leaser). Here the iron leasing firm is actually a quasi-firm, which does not require primary factors such as labor and land in its production process. There are four commodities in the model, namely wheat, iron, iron leased out as a capital good, labor and land.
Usage
gemIntertemporal_5_5(...)
Arguments
... |
arguments to be passed to the function sdm2. |
Examples
#### a timeline model.
np <- 15 # the number of economic periods
gr <- 0 # the growth rate in the steady state equilibrium
eis <- 1 # the elasticity of intertemporal substitution of consumers
Gamma.beta <- 0.97 # the subjective discount factor of consumers
last.beta.laborer <- 0
last.beta.landowner <- 0
depreciation.rate <- 0.06
alpha.firm.wheat <- rep(5, np - 1)
alpha.firm.iron <- rep(5, np - 1)
y1.wheat <- 200
y1.iron <- 100
names.commodity <- c(
paste0("wheat", 1:np),
paste0("iron", 1:np),
paste0("cap", 1:(np - 1)),
paste0("lab", 1:(np - 1)),
paste0("land", 1:(np - 1))
)
names.agent <- c(
paste0("firm.wheat", 1:(np - 1)), paste0("firm.iron", 1:(np - 1)),
paste0("quasifirm.cap", 1:(np - 1)), # a quasifirm
"laborer", "landowner"
)
n <- length(names.commodity) # the number of commodity kinds, i.e. 5 * np - 3
m <- length(names.agent) # the number of agent kinds, i.e. 3 * np - 1
# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg["wheat1", "laborer"] <- y1.wheat
S0Exg["iron1", "landowner"] <- y1.iron
S0Exg[paste0("lab", 1:(np - 1)), "laborer"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of labor
S0Exg[paste0("land", 1:(np - 1)), "landowner"] <- 100 * (1 + gr)^(0:(np - 2)) # the supply of land
# the output coefficient matrix.
B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
for (k in 1:(np - 1)) {
B[paste0("wheat", k + 1), paste0("firm.wheat", k)] <- 1
B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1
B[paste0("cap", k), paste0("quasifirm.cap", k)] <- 1
B[paste0("iron", k + 1), paste0("quasifirm.cap", k)] <- 1 - depreciation.rate
}
dstl.firm.wheat <- dstl.firm.iron <- dstl.quasifirm.cap <- list()
for (k in 1:(np - 1)) {
dstl.firm.wheat[[k]] <- node_new(
"prod",
type = "CES", es = 1,
alpha = alpha.firm.wheat[k], beta = c(0.2, 0.4, 0.4),
paste0("cap", k), paste0("lab", k), paste0("land", k)
)
dstl.firm.iron[[k]] <- node_new(
"prod",
type = "CES", es = 1,
alpha = alpha.firm.iron[k], beta = c(0.4, 0.4, 0.2),
paste0("cap", k), paste0("lab", k), paste0("land", k)
)
dstl.quasifirm.cap[[k]] <- node_new(
"output",
type = "Leontief", a = 1,
paste0("iron", k)
)
}
tmp.beta <- Gamma.beta^(1:(np - 1))
tmp.beta <- tmp.beta / tmp.beta[np - 1]
tmp.beta <- c(tmp.beta, last.beta.laborer)
dst.laborer <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(tmp.beta),
paste0("cc", 1:(np - 1)), paste0("wheat", np)
)
for (k in 1:(np - 1)) {
node_set(dst.laborer, paste0("cc", k),
type = "CES", es = 1,
alpha = 1, beta = c(0.4, 0.4, 0.2),
paste0("wheat", k), paste0("lab", k), paste0("land", k)
)
}
tmp.beta <- Gamma.beta^(1:(np - 1))
tmp.beta <- tmp.beta / tmp.beta[np - 1]
tmp.beta <- c(tmp.beta, last.beta.landowner)
dst.landowner <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(tmp.beta),
paste0("cc", 1:(np - 1)), paste0("iron", np)
)
for (k in 1:(np - 1)) {
node_set(dst.landowner, paste0("cc", k),
type = "CES", es = 1,
alpha = 1, beta = c(0.2, 0.4, 0.4),
paste0("wheat", k), paste0("lab", k), paste0("land", k)
)
}
ge <- sdm2(
A = c(
dstl.firm.wheat, dstl.firm.iron, dstl.quasifirm.cap,
dst.laborer, dst.landowner
),
B = B,
S0Exg = S0Exg,
names.commodity = names.commodity,
names.agent = names.agent,
numeraire = "lab1",
policy = makePolicyMeanValue(50),
ts = TRUE,
priceAdjustmentVelocity = 0.03
)
ge$p
ge$z
plot(ge$z[2 * (np - 1) + (1:(np - 1))], type = "b", pch = 20)
lines(1:(np - 1), ge$z[1:(np - 1)], type = "b", pch = 21)
lines(1:(np - 1), ge$z[np - 1 + (1:(np - 1))], type = "b", pch = 22)
legend("topleft", c("cap","wheat", "iron"), pch = 20:22)
#### a time-circle model.
np <- 5 # the number of economic periods
gr <- 0.03 # the growth rate in the steady state equilibrium
eis <- 0.5 # the elasticity of intertemporal substitution of consumers
Gamma.beta <- 0.97 # the subjective discount factor of consumers
es.firm <- 1
depreciation.rate <- 0.06
zeta <- (1 + gr)^np # the ratio of repayments to loans
yield.rate <- sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr, prepaid = TRUE)
captial.share.laborer <- 0.7795
captial.share.landowner <- 1 - captial.share.laborer
alpha.firm.wheat <- rep(5, np)
alpha.firm.iron <- rep(5, np)
names.commodity <- c(
paste0("wheat", 1:np),
paste0("iron", 1:np),
paste0("cap", 1:np),
paste0("lab", 1:np),
paste0("land", 1:np),
"claim"
)
names.agent <- c(
paste0("firm.wheat", 1:np), paste0("firm.iron", 1:np),
paste0("quasifirm.cap", 1:np), # a quasifirm
"laborer", "landowner"
)
n <- length(names.commodity) # the number of commodity kinds
m <- length(names.agent) # the number of agent kinds
# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab", 1:np), "laborer"] <- 100 * (1 + gr)^(0:(np - 1)) # the supply of labor
S0Exg[paste0("land", 1:np), "landowner"] <- 100 * (1 + gr)^(0:(np - 1)) # the supply of land
S0Exg["claim", "laborer"] <- 100 * captial.share.laborer
S0Exg["claim", "landowner"] <- 100 * captial.share.landowner
# the output coefficient matrix.
B <- matrix(0, n, m, dimnames = list(names.commodity, names.agent))
for (k in 1:(np - 1)) {
B[paste0("wheat", k + 1), paste0("firm.wheat", k)] <- 1
B[paste0("iron", k + 1), paste0("firm.iron", k)] <- 1
B[paste0("cap", k), paste0("quasifirm.cap", k)] <- 1
B[paste0("iron", k + 1), paste0("quasifirm.cap", k)] <- 1 - depreciation.rate
}
B[paste0("wheat", 1), paste0("firm.wheat", np)] <- 1 / zeta
B[paste0("iron", 1), paste0("firm.iron", np)] <- 1 / zeta
B[paste0("cap", np), paste0("quasifirm.cap", np)] <- 1
B[paste0("iron", 1), paste0("quasifirm.cap", np)] <- (1 - depreciation.rate) / zeta
dstl.firm.wheat <- dstl.firm.iron <- dstl.quasifirm.cap <- list()
for (k in 1:(np - 1)) {
dstl.firm.wheat[[k]] <- node_new(
"prod",
type = "CES", es = es.firm,
alpha = alpha.firm.wheat[k], beta = c(0.2, 0.4, 0.4),
paste0("cap", k), paste0("lab", k), paste0("land", k)
)
dstl.firm.iron[[k]] <- node_new(
"prod",
type = "CES", es = es.firm,
alpha = alpha.firm.iron[k], beta = c(0.4, 0.4, 0.2),
paste0("cap", k), paste0("lab", k), paste0("land", k)
)
dstl.quasifirm.cap[[k]] <- node_new(
"output",
type = "Leontief", a = 1,
paste0("iron", k)
)
}
dstl.firm.wheat[[np]] <- node_new(
"prod",
type = "FIN", rate = c(1, (1 + yield.rate)^np - 1),
"cc1", "claim"
)
node_set(dstl.firm.wheat[[np]], "cc1",
type = "CES", es = es.firm,
alpha = alpha.firm.wheat[k], beta = c(0.2, 0.4, 0.4),
paste0("cap", np), paste0("lab", np), paste0("land", np)
)
dstl.firm.iron[[np]] <- node_new(
"prod",
type = "FIN", rate = c(1, (1 + yield.rate)^np - 1),
"cc1", "claim"
)
node_set(dstl.firm.iron[[np]], "cc1",
type = "CES", es = es.firm,
alpha = alpha.firm.wheat[k], beta = c(0.4, 0.4, 0.2),
paste0("cap", np), paste0("lab", np), paste0("land", np)
)
return.rate <- sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr)
fund.occupancy.rate <- (1 - depreciation.rate) / (1 + return.rate)
# The prepaid rent rate (i.e. the prepaid-rent-to-price ratio) of
# the capital good is equal to 1 minus fund.occupancy.rate.
dstl.quasifirm.cap[[np]] <- node_new(
"prod",
type = "FIN", rate = c(1, ((1 + yield.rate)^np - 1) * fund.occupancy.rate),
"cc1", "claim"
)
node_set(dstl.quasifirm.cap[[np]], "cc1",
type = "Leontief", a = 1,
paste0("iron", np)
)
dst.laborer <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
paste0("cc", 1:np)
)
for (k in 1:np) {
node_set(dst.laborer, paste0("cc", k),
type = "CES", es = 1,
alpha = 1, beta = c(0.4, 0.4, 0.2),
paste0("wheat", k), paste0("lab", k), paste0("land", k)
)
}
dst.landowner <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
paste0("cc", 1:np)
)
for (k in 1:np) {
node_set(dst.landowner, paste0("cc", k),
type = "CES", es = 1,
alpha = 1, beta = c(0.2, 0.4, 0.4),
paste0("wheat", k), paste0("lab", k), paste0("land", k)
)
}
ge.tc <- sdm2(
A = c(
dstl.firm.wheat, dstl.firm.iron, dstl.quasifirm.cap,
dst.laborer, dst.landowner
),
B = B,
S0Exg = S0Exg,
names.commodity = names.commodity,
names.agent = names.agent,
numeraire = "lab1",
numberOfPeriods = 1000,
priceAdjustmentVelocity = 0.03
)
ge.tc$p
growth_rate(ge.tc$p)
ge.tc$z
growth_rate(ge.tc$z)
## the corresponding sequential model with the same steady-state equilibrium.
dst.firm.wheat <- node_new("prod",
type = "FIN", rate = c(1, yield.rate),
"cc1", "equity.share.wheat"
)
node_set(dst.firm.wheat, "cc1",
type = "CES", es = es.firm,
alpha = 5, beta = c(0.2, 0.4, 0.4),
"cap", "lab", "land"
)
dst.firm.iron <- node_new("prod",
type = "FIN", rate = c(1, yield.rate),
"cc1", "equity.share.iron"
)
node_set(dst.firm.iron, "cc1",
type = "CES", es = es.firm,
alpha = 5, beta = c(0.4, 0.4, 0.2),
"cap", "lab", "land"
)
dst.quasifirm.cap <- node_new("prod",
type = "FIN", rate = c(1, yield.rate * fund.occupancy.rate),
"cc1", "equity.share.cap"
)
node_set(dst.quasifirm.cap, "cc1",
type = "Leontief", a = 1,
"iron"
)
dst.laborer <- node_new("util",
type = "CES", es = 1,
alpha = 1, beta = c(0.4, 0.4, 0.2),
"wheat", "lab", "land"
)
dst.landowner <- node_new("util",
type = "CES", es = 1,
alpha = 1, beta = c(0.2, 0.4, 0.4),
"wheat", "lab", "land"
)
ge.seq <- sdm2(
A = list(
dst.firm.wheat, dst.firm.iron, dst.quasifirm.cap,
dst.laborer, dst.landowner
),
B = matrix(c(
1, 0, 0, 0, 0,
0, 1, 1 - depreciation.rate, 0, 0,
0, 0, 1 + gr, 0, 0,
0, 0, 0, 0, 0,
0, 0, 0, 0, 0,
0, 0, 0, 0, 0,
0, 0, 0, 0, 0,
0, 0, 0, 0, 0
), 8, 5, TRUE),
S0Exg = matrix(c(
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, NA, NA,
NA, NA, NA, 100, NA,
NA, NA, NA, NA, 100,
NA, NA, NA, 100 * captial.share.laborer, 100 * captial.share.landowner,
NA, NA, NA, 100 * captial.share.laborer, 100 * captial.share.landowner,
NA, NA, NA, 100 * captial.share.laborer, 100 * captial.share.landowner
), 8, 5, TRUE),
names.commodity = c(
"wheat", "iron", "cap", "lab", "land",
"equity.share.wheat", "equity.share.iron", "equity.share.cap"
),
names.agent = c("firm.wheat", "firm.iron", "quasifirm.cap", "laborer", "landowner"),
numeraire = "lab",
numberOfPeriods = 2000,
priceAdjustmentVelocity = 0.03,
GRExg = gr
)
ge.seq$p
ge.seq$z
ge.tc$z
[Package GE version 0.4.5 Index]