gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate: An Example Illustrating Endogenous Equilibrium Interest Rates...
In GE: General Equilibrium Modeling
gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate R Documentation
An Example Illustrating Endogenous Equilibrium Interest Rates and Foreign Exchange Rates in a Two-country (Timeline) Transitional Equilibrium Path
Description
This example illustrates (endogenous) equilibrium primitive interest rates and foreign exchange rates in a two-country transitional equilibrium path.
Usage
gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate(...)
Arguments
...
arguments to be passed to the function sdm2.
See Also
gemIntertemporal_EndogenousEquilibriumInterestRate
Examples
vm <- 1 # the velocity of money
eis <- 0.8 # the elasticity of intertemporal substitution
Gamma.beta <- 10 / 11 # the subjective discount factor
gr <- 0 # the growth rate
money1.supply <- 600
money2.supply <- 100
np <- 20 # the number of economic periods
sserr(eis, Gamma.beta, gr, prepaid = TRUE)
f <- function(ir = rep(0.1, 2 * np - 2), return.ge = FALSE,
y1.wheat = 10, # 49.24 #49.79 the wheat supply in the first period
y1.iron = 5 # 41.32 #45.45 the iron supply in the first period
) {
ir1 <- head(ir, np - 1)
ir2 <- tail(ir, np - 1)
n <- 2 * np + 2 * (np - 1) + 2 # the number of commodity kinds
m <- 2 * (np - 1) + 4 # the number of agent kinds
names.commodity <- c(
paste0("wheat", 1:np),
paste0("lab1.", 1:(np - 1)),
"money1",
paste0("iron", 1:np),
paste0("lab2.", 1:(np - 1)),
"money2"
)
names.agent <- c(
paste0("firm.wheat", 1:(np - 1)),
"laborer1", "moneyOwner1",
paste0("firm.iron", 1:(np - 1)),
"laborer2", "moneyOwner2"
)
# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab1.", 1:(np - 1)), "laborer1"] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg["money1", "moneyOwner1"] <- money1.supply
S0Exg["wheat1", "laborer1"] <- y1.wheat
S0Exg[paste0("lab2.", 1:(np - 1)), "laborer2"] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg["money2", "moneyOwner2"] <- money2.supply
S0Exg["iron1", "laborer2"] <- y1.iron
# 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
}
dstl.firm.wheat <- dstl.firm.iron <- list()
for (k in 1:(np - 1)) {
dstl.firm.wheat[[k]] <- node_new(
"prod",
type = "FIN", rate = c(1, ir1[k] / vm),
"cc1", "money1"
)
node_set(dstl.firm.wheat[[k]], "cc1",
type = "CD", alpha = 1, beta = c(0.5, 0.5),
paste0("iron", k), paste0("lab1.", k)
)
dstl.firm.iron[[k]] <- node_new(
"prod",
type = "FIN", rate = c(1, ir2[k] / vm),
"cc1", "money2"
)
node_set(dstl.firm.iron[[k]], "cc1",
type = "CD", alpha = 1, beta = c(0.5, 0.5),
paste0("iron", k), paste0("lab2.", k)
)
}
dst.laborer1 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
paste0("cc", 1:(np - 1)), paste0("wheat", np)
)
for (k in 1:(np - 1)) {
node_set(dst.laborer1, paste0("cc", k),
type = "FIN", rate = c(1, ir1[k] / vm),
paste0("wheat", k), "money1"
)
}
dst.moneyOwner1 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:(np - 1))),
paste0("cc", 1:(np - 1))
)
for (k in 1:(np - 1)) {
node_set(dst.moneyOwner1, paste0("cc", k),
type = "FIN", rate = c(1, ir1[k] / vm),
paste0("wheat", k), "money1"
)
}
dst.laborer2 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
paste0("cc", 1:(np - 1)), paste0("iron", np)
)
for (k in 1:(np - 1)) {
node_set(dst.laborer2, paste0("cc", k),
type = "FIN", rate = c(1, ir2[k] / vm),
paste0("wheat", k), "money2"
)
}
dst.moneyOwner2 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:(np - 1))),
paste0("cc", 1:(np - 1))
)
for (k in 1:(np - 1)) {
node_set(dst.moneyOwner2, paste0("cc", k),
type = "FIN", rate = c(1, ir2[k] / vm),
paste0("wheat", k), "money2"
)
}
ge <- sdm2(
A = c(
dstl.firm.wheat, dst.laborer1, dst.moneyOwner1,
dstl.firm.iron, dst.laborer2, dst.moneyOwner2
),
B = B,
S0Exg = S0Exg,
names.commodity = names.commodity,
names.agent = names.agent,
numeraire = "wheat1",
policy = makePolicyTailAdjustment(
ind = rbind(
c(np - 1, np),
c(2 * np, 2 * (np - 1) + 3)
),
gr = gr
)
)
tmp <- rowSums(ge$SV)
ts1.exchange.value <- tmp[paste0("wheat", 1:(np - 1))] + tmp[paste0("lab1.", 1:(np - 1))]
ir1.new <- ts1.exchange.value[1:(np - 2)] / ts1.exchange.value[2:(np - 1)] - 1
ir1.new <- pmax(1e-6, ir1.new)
ir1.new[np - 1] <- ir1.new[np - 2]
ir1 <- c(ir1 * ratio_adjust(ir1.new / ir1, 0.3))
cat("ir1: ", ir1, "\n")
ts2.exchange.value <- tmp[paste0("iron", 1:(np - 1))] + tmp[paste0("lab2.", 1:(np - 1))]
ir2.new <- ts2.exchange.value[1:(np - 2)] / ts2.exchange.value[2:(np - 1)] - 1
ir2.new <- pmax(1e-6, ir2.new)
ir2.new[np - 1] <- ir2.new[np - 2]
ir2 <- c(ir2 * ratio_adjust(ir2.new / ir2, 0.3))
cat("ir2: ", ir2, "\n")
if (return.ge) {
ge$ts1.exchange.value <- unname(ts1.exchange.value)
ge$ts2.exchange.value <- unname(ts2.exchange.value)
ge$ts.forex <- unname((ge$ts2.exchange.value / money2.supply) /
(ge$ts1.exchange.value / money1.supply))
return(ge)
} else {
return(c(ir1, ir2))
}
}
## Calculate equilibrium interest rates.
## Warning: Running the program below takes about several minutes.
# mat.ir <- iterate(rep(0.1, 2*np - 2), f, tol = 1e-4)
# sserr(eis, Gamma.beta, gr, prepaid = TRUE)
## Below are the calculated equilibrium interest rates.
ir1 <- c(
0.2218, 0.1888, 0.1455, 0.1228, 0.1115, 0.1058, 0.1029, 0.1015, 0.1008,
0.1004, 0.1002, 0.1001, 0.1001, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000
)
ir2 <- c(
0.1292, 0.1080, 0.1037, 0.1019, 0.1010, 0.1005, 0.1003, 0.1001, 0.1001,
0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000
)
ge <- f(c(ir1, ir2), return.ge = TRUE)
plot(ge$z[1:(np - 1)], type = "o", ylab = "wheat output")
ge$ts.forex
## the corresponding sequential model with the same steady-state equilibrium.
np <- 5
ge.ss <- f(return.ge = TRUE, y1.wheat = 49.24, y1.iron = 41.32)
ir <- dividend.rate <- 0.1
dst.firm.wheat <- node_new("output",
type = "FIN", rate = c(1, ir / vm, (1 + ir) * dividend.rate),
"cc1", "money1", "equity.share.wheat"
)
node_set(dst.firm.wheat, "cc1",
type = "CD", alpha = 1,
beta = c(0.5, 0.5),
"iron", "lab1"
)
dst.firm.iron <- node_new("output",
type = "FIN", rate = c(1, ir / vm, (1 + ir) * dividend.rate),
"cc1", "money2", "equity.share.iron"
)
node_set(dst.firm.iron, "cc1",
type = "CD", alpha = 1,
beta = c(0.5, 0.5),
"iron", "lab2"
)
dst.laborer1 <- node_new("util",
type = "FIN", rate = c(1, interest.rate = 0.1),
"cc1", "money1"
)
node_set(dst.laborer1, "cc1",
type = "Leontief", a = 1,
"wheat"
)
dst.moneyOwner1 <- Clone(dst.laborer1)
dst.laborer2 <- Clone(dst.laborer1)
node_replace(dst.laborer2, "money1", "money2")
dst.moneyOwner2 <- Clone(dst.laborer2)
ge <- sdm2(
A = list(
dst.firm.wheat, dst.laborer1, dst.moneyOwner1,
dst.firm.iron, dst.laborer2, dst.moneyOwner2
),
B = matrix(c(
1, 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, 1, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0
), 8, 6, TRUE),
S0Exg = matrix(c(
NA, NA, NA, NA, NA, NA,
NA, 100, NA, NA, NA, NA,
NA, NA, 600, NA, NA, NA,
NA, 100, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, 100, NA,
NA, NA, NA, NA, NA, 100,
NA, NA, NA, NA, 100, NA
), 8, 6, TRUE),
names.commodity = c(
"wheat", "lab1", "money1", "equity.share.wheat",
"iron", "lab2", "money2", "equity.share.iron"
),
names.agent = c(
"firm1", "laborer1", "moneyOwner1",
"firm2", "laborer2", "moneyOwner2"
),
numeraire = c("money1" = 0.1) # interest.rate
)
ge.ss$ts.forex
ge$p["money2"] / ge$p["money1"] # the foreign exchange rate
## Calculate equilibrium interest rates.
## Warning: Running the program below takes about several minutes.
# np <- 20
# gr <- 0.03
# mat.ir <- iterate(rep(0.1, 2*np - 2), f, tol = 1e-4)
# sserr(eis, Gamma.beta, gr, prepaid = TRUE)
## a steady-state equilibrium with an exogenous interest rate 0.1.
## The endogenous equilibrium interest rate and dividend rate are 0.
## See also CGE::Example7.6.
eis <- 1 # the elasticity of intertemporal substitution
Gamma.beta <- 1 # the subjective discount factor
gr <- 0 # the growth rate
money1.supply <- 600
money2.supply <- 100
np <- 20 # the number of economic periods
np <- 5
ge.ss <- f(return.ge = TRUE, y1.wheat = 49.79, y1.iron = 45.45)
ge.ss$z
ge.ss$ts.forex
GE documentation built on May 29, 2024, 2:52 a.m.
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| gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate | R Documentation |
An Example Illustrating Endogenous Equilibrium Interest Rates and Foreign Exchange Rates in a Two-country (Timeline) Transitional Equilibrium Path
Description
This example illustrates (endogenous) equilibrium primitive interest rates and foreign exchange rates in a two-country transitional equilibrium path.
Usage
gemIntertemporal_EndogenousEquilibriumInterestRate_ForeignExchangeRate(...)
Arguments
... |
arguments to be passed to the function sdm2. |
See Also
gemIntertemporal_EndogenousEquilibriumInterestRate
Examples
vm <- 1 # the velocity of money
eis <- 0.8 # the elasticity of intertemporal substitution
Gamma.beta <- 10 / 11 # the subjective discount factor
gr <- 0 # the growth rate
money1.supply <- 600
money2.supply <- 100
np <- 20 # the number of economic periods
sserr(eis, Gamma.beta, gr, prepaid = TRUE)
f <- function(ir = rep(0.1, 2 * np - 2), return.ge = FALSE,
y1.wheat = 10, # 49.24 #49.79 the wheat supply in the first period
y1.iron = 5 # 41.32 #45.45 the iron supply in the first period
) {
ir1 <- head(ir, np - 1)
ir2 <- tail(ir, np - 1)
n <- 2 * np + 2 * (np - 1) + 2 # the number of commodity kinds
m <- 2 * (np - 1) + 4 # the number of agent kinds
names.commodity <- c(
paste0("wheat", 1:np),
paste0("lab1.", 1:(np - 1)),
"money1",
paste0("iron", 1:np),
paste0("lab2.", 1:(np - 1)),
"money2"
)
names.agent <- c(
paste0("firm.wheat", 1:(np - 1)),
"laborer1", "moneyOwner1",
paste0("firm.iron", 1:(np - 1)),
"laborer2", "moneyOwner2"
)
# the exogenous supply matrix.
S0Exg <- matrix(NA, n, m, dimnames = list(names.commodity, names.agent))
S0Exg[paste0("lab1.", 1:(np - 1)), "laborer1"] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg["money1", "moneyOwner1"] <- money1.supply
S0Exg["wheat1", "laborer1"] <- y1.wheat
S0Exg[paste0("lab2.", 1:(np - 1)), "laborer2"] <- 100 * (1 + gr)^(0:(np - 2))
S0Exg["money2", "moneyOwner2"] <- money2.supply
S0Exg["iron1", "laborer2"] <- y1.iron
# 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
}
dstl.firm.wheat <- dstl.firm.iron <- list()
for (k in 1:(np - 1)) {
dstl.firm.wheat[[k]] <- node_new(
"prod",
type = "FIN", rate = c(1, ir1[k] / vm),
"cc1", "money1"
)
node_set(dstl.firm.wheat[[k]], "cc1",
type = "CD", alpha = 1, beta = c(0.5, 0.5),
paste0("iron", k), paste0("lab1.", k)
)
dstl.firm.iron[[k]] <- node_new(
"prod",
type = "FIN", rate = c(1, ir2[k] / vm),
"cc1", "money2"
)
node_set(dstl.firm.iron[[k]], "cc1",
type = "CD", alpha = 1, beta = c(0.5, 0.5),
paste0("iron", k), paste0("lab2.", k)
)
}
dst.laborer1 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
paste0("cc", 1:(np - 1)), paste0("wheat", np)
)
for (k in 1:(np - 1)) {
node_set(dst.laborer1, paste0("cc", k),
type = "FIN", rate = c(1, ir1[k] / vm),
paste0("wheat", k), "money1"
)
}
dst.moneyOwner1 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:(np - 1))),
paste0("cc", 1:(np - 1))
)
for (k in 1:(np - 1)) {
node_set(dst.moneyOwner1, paste0("cc", k),
type = "FIN", rate = c(1, ir1[k] / vm),
paste0("wheat", k), "money1"
)
}
dst.laborer2 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:np)),
paste0("cc", 1:(np - 1)), paste0("iron", np)
)
for (k in 1:(np - 1)) {
node_set(dst.laborer2, paste0("cc", k),
type = "FIN", rate = c(1, ir2[k] / vm),
paste0("wheat", k), "money2"
)
}
dst.moneyOwner2 <- node_new(
"util",
type = "CES", es = eis,
alpha = 1, beta = prop.table(Gamma.beta^(1:(np - 1))),
paste0("cc", 1:(np - 1))
)
for (k in 1:(np - 1)) {
node_set(dst.moneyOwner2, paste0("cc", k),
type = "FIN", rate = c(1, ir2[k] / vm),
paste0("wheat", k), "money2"
)
}
ge <- sdm2(
A = c(
dstl.firm.wheat, dst.laborer1, dst.moneyOwner1,
dstl.firm.iron, dst.laborer2, dst.moneyOwner2
),
B = B,
S0Exg = S0Exg,
names.commodity = names.commodity,
names.agent = names.agent,
numeraire = "wheat1",
policy = makePolicyTailAdjustment(
ind = rbind(
c(np - 1, np),
c(2 * np, 2 * (np - 1) + 3)
),
gr = gr
)
)
tmp <- rowSums(ge$SV)
ts1.exchange.value <- tmp[paste0("wheat", 1:(np - 1))] + tmp[paste0("lab1.", 1:(np - 1))]
ir1.new <- ts1.exchange.value[1:(np - 2)] / ts1.exchange.value[2:(np - 1)] - 1
ir1.new <- pmax(1e-6, ir1.new)
ir1.new[np - 1] <- ir1.new[np - 2]
ir1 <- c(ir1 * ratio_adjust(ir1.new / ir1, 0.3))
cat("ir1: ", ir1, "\n")
ts2.exchange.value <- tmp[paste0("iron", 1:(np - 1))] + tmp[paste0("lab2.", 1:(np - 1))]
ir2.new <- ts2.exchange.value[1:(np - 2)] / ts2.exchange.value[2:(np - 1)] - 1
ir2.new <- pmax(1e-6, ir2.new)
ir2.new[np - 1] <- ir2.new[np - 2]
ir2 <- c(ir2 * ratio_adjust(ir2.new / ir2, 0.3))
cat("ir2: ", ir2, "\n")
if (return.ge) {
ge$ts1.exchange.value <- unname(ts1.exchange.value)
ge$ts2.exchange.value <- unname(ts2.exchange.value)
ge$ts.forex <- unname((ge$ts2.exchange.value / money2.supply) /
(ge$ts1.exchange.value / money1.supply))
return(ge)
} else {
return(c(ir1, ir2))
}
}
## Calculate equilibrium interest rates.
## Warning: Running the program below takes about several minutes.
# mat.ir <- iterate(rep(0.1, 2*np - 2), f, tol = 1e-4)
# sserr(eis, Gamma.beta, gr, prepaid = TRUE)
## Below are the calculated equilibrium interest rates.
ir1 <- c(
0.2218, 0.1888, 0.1455, 0.1228, 0.1115, 0.1058, 0.1029, 0.1015, 0.1008,
0.1004, 0.1002, 0.1001, 0.1001, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000
)
ir2 <- c(
0.1292, 0.1080, 0.1037, 0.1019, 0.1010, 0.1005, 0.1003, 0.1001, 0.1001,
0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000, 0.1000
)
ge <- f(c(ir1, ir2), return.ge = TRUE)
plot(ge$z[1:(np - 1)], type = "o", ylab = "wheat output")
ge$ts.forex
## the corresponding sequential model with the same steady-state equilibrium.
np <- 5
ge.ss <- f(return.ge = TRUE, y1.wheat = 49.24, y1.iron = 41.32)
ir <- dividend.rate <- 0.1
dst.firm.wheat <- node_new("output",
type = "FIN", rate = c(1, ir / vm, (1 + ir) * dividend.rate),
"cc1", "money1", "equity.share.wheat"
)
node_set(dst.firm.wheat, "cc1",
type = "CD", alpha = 1,
beta = c(0.5, 0.5),
"iron", "lab1"
)
dst.firm.iron <- node_new("output",
type = "FIN", rate = c(1, ir / vm, (1 + ir) * dividend.rate),
"cc1", "money2", "equity.share.iron"
)
node_set(dst.firm.iron, "cc1",
type = "CD", alpha = 1,
beta = c(0.5, 0.5),
"iron", "lab2"
)
dst.laborer1 <- node_new("util",
type = "FIN", rate = c(1, interest.rate = 0.1),
"cc1", "money1"
)
node_set(dst.laborer1, "cc1",
type = "Leontief", a = 1,
"wheat"
)
dst.moneyOwner1 <- Clone(dst.laborer1)
dst.laborer2 <- Clone(dst.laborer1)
node_replace(dst.laborer2, "money1", "money2")
dst.moneyOwner2 <- Clone(dst.laborer2)
ge <- sdm2(
A = list(
dst.firm.wheat, dst.laborer1, dst.moneyOwner1,
dst.firm.iron, dst.laborer2, dst.moneyOwner2
),
B = matrix(c(
1, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 1, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0
), 8, 6, TRUE),
S0Exg = matrix(c(
NA, NA, NA, NA, NA, NA,
NA, 100, NA, NA, NA, NA,
NA, NA, 600, NA, NA, NA,
NA, 100, NA, NA, NA, NA,
NA, NA, NA, NA, NA, NA,
NA, NA, NA, NA, 100, NA,
NA, NA, NA, NA, NA, 100,
NA, NA, NA, NA, 100, NA
), 8, 6, TRUE),
names.commodity = c(
"wheat", "lab1", "money1", "equity.share.wheat",
"iron", "lab2", "money2", "equity.share.iron"
),
names.agent = c(
"firm1", "laborer1", "moneyOwner1",
"firm2", "laborer2", "moneyOwner2"
),
numeraire = c("money1" = 0.1) # interest.rate
)
ge.ss$ts.forex
ge$p["money2"] / ge$p["money1"] # the foreign exchange rate
## Calculate equilibrium interest rates.
## Warning: Running the program below takes about several minutes.
# np <- 20
# gr <- 0.03
# mat.ir <- iterate(rep(0.1, 2*np - 2), f, tol = 1e-4)
# sserr(eis, Gamma.beta, gr, prepaid = TRUE)
## a steady-state equilibrium with an exogenous interest rate 0.1.
## The endogenous equilibrium interest rate and dividend rate are 0.
## See also CGE::Example7.6.
eis <- 1 # the elasticity of intertemporal substitution
Gamma.beta <- 1 # the subjective discount factor
gr <- 0 # the growth rate
money1.supply <- 600
money2.supply <- 100
np <- 20 # the number of economic periods
np <- 5
ge.ss <- f(return.ge = TRUE, y1.wheat = 49.79, y1.iron = 45.45)
ge.ss$z
ge.ss$ts.forex
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