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#' @export
#' @title A Two-Country General Equilibrium Model with Money
#' @aliases gemInputOutputTable_2_8_4
#' @description A two-country general equilibrium model with money.
#' This general equilibrium model is based on a two-country (i.e. CHN and ROW) input-output table.
#' Each country contains four sectors and eight commodities (or subjects).
#' The four sectors are production, consumption, investment and foreign trade.
#' The eight commodities (or subjects) are product, labor, capital goods, bond, tax, dividend, imported product and money interest.
#' Hence the input-output table has 16 rows and 8 columns.
#' @param IT the input part of the input-output table (unit: trillion yuan).
#' @param product.output.CHN the product output of the production sector of CHN.
#' @param product.output.ROW the product output of the production sector of ROW.
#' @param labor.supply.CHN the labor supply of CHN.
#' @param labor.supply.ROW the labor supply of ROW.
#' @param capital.supply.CHN the capital supply of CHN.
#' @param capital.supply.ROW the capital supply of ROW.
#' @param money.interest.supply.CHN the money interest supply of CHN,
#' that is, the exogenous money supply multiplied by the exogenous interest rate.
#' @param money.interest.supply.ROW the money interest supply of ROW.
#' @param es.DIProduct.production.CHN the elasticity of substitution between
#' domestic product and imported product used by the production sector of CHN.
#' @param es.DIProduct.production.ROW the elasticity of substitution between
#' domestic product and imported product used by the production sector of ROW.
#' @param es.laborCapital.production.CHN the elasticity of substitution between
#' labor and capital goods used by the production sector of CHN.
#' @param es.laborCapital.production.ROW the elasticity of substitution between
#' labor and capital goods used by the production sector of ROW.
#' @param es.consumption.CHN the elasticity of substitution between
#' domestic product and imported product used by the consumption sector of CHN.
#' @param es.consumption.ROW the elasticity of substitution between
#' domestic product and imported product used by the consumption sector of ROW.
#' @param es.investment.CHN the elasticity of substitution between
#' domestic product and imported product used by the investment sector of CHN.
#' @param es.investment.ROW the elasticity of substitution between
#' domestic product and imported product used by the investment sector of ROW.
#' @param interest.rate.CHN the interest rate of CHN.
#' @param interest.rate.ROW the interest rate of ROW.
#' @param return.dstl If TRUE, the demand structure tree will be returned.
#' @param ... arguments to be transferred to the function \code{\link{sdm2}}.
#' @return A general equilibrium, which usually is a list with the following elements:
#' \itemize{
#' \item p - the price vector with CHN labor as numeraire, wherein
#' the price of a currency is the interest per unit of currency.
#' \item D - the demand matrix, also called the input table. Wherein the benchmark prices are used.
#' \item DV - the demand value matrix, also called the value input table. Wherein the current price is used.
#' \item SV - the supply value matrix, also called the value output table. Wherein the current price is used.
#' \item eri.CHN - the exchange rate index of CHN currency.
#' \item eri.ROW - the exchange rate index of ROW currency.
#' \item p.money - the price vector with CHN money as numeraire
#' if both interest.rate.CHN and interest.rate.CHN are not NA.
#' \item dstl - the demand structure tree list of sectors if return.dstl == TRUE.
#' \item ... - some elements returned by the function \code{\link{sdm2}}.
#' }
#' @details If interest.rate.CHN is NA or interest.rate.CHN is NA, they are assumed to be equal.
#' And in this case, the exchange rate is determined by the ratio of the interest of unit currency of the two countries.
#' In this model, the ratio of a sector's monetary interest expenditure to its transaction value may not be equal to the interest rate
#' because the ratio is not only affected by the interest rate,
#' but also by the sector's currency circulation velocity and other factors.
#' @examples
#' \donttest{
#' ITExample <- matrix(0, 16, 8, dimnames = list(
#' c(
#' "product.CHN", "labor.CHN", "capital.CHN", "bond.CHN",
#' "tax.CHN", "dividend.CHN", "imported.product.CHN", "money.interest.CHN",
#' "product.ROW", "labor.ROW", "capital.ROW", "bond.ROW",
#' "tax.ROW", "dividend.ROW", "imported.product.ROW", "money.interest.ROW"
#' ),
#' c(
#' "production.CHN", "consumption.CHN", "investment.CHN", "foreign.trade.CHN",
#' "production.ROW", "consumption.ROW", "investment.ROW", "foreign.trade.ROW"
#' )
#' ))
#'
#' production.CHN <- c(
#' product.CHN = 140, labor.CHN = 40, capital.CHN = 10,
#' tax.CHN = 10, dividend.CHN = 20, imported.product.CHN = 5, money.interest.CHN = 5
#' )
#' production.ROW <- c(
#' product.ROW = 840, labor.ROW = 240, capital.ROW = 60,
#' tax.ROW = 60, dividend.ROW = 120, imported.product.ROW = 6, money.interest.ROW = 30
#' )
#'
#' consumption.CHN <- c(
#' product.CHN = 40, bond.CHN = 30, imported.product.CHN = 5, money.interest.CHN = 2
#' )
#'
#' consumption.ROW <- c(
#' product.ROW = 240, bond.ROW = 180, imported.product.ROW = 6, money.interest.ROW = 12
#' )
#'
#' investment.CHN <- c(
#' product.CHN = 30,
#' imported.product.CHN = 4, money.interest.CHN = 1,
#' bond.ROW = 1,
#' money.interest.ROW = 0.02
#' )
#'
#' investment.ROW <- c(
#' bond.CHN = 1,
#' money.interest.CHN = 0.02,
#' product.ROW = 180,
#' imported.product.ROW = 4, money.interest.ROW = 6
#' )
#'
#'
#' foreign.trade.CHN <- c(
#' product.ROW = 13,
#' tax.CHN = 0.65,
#' money.interest.ROW = 0.26
#' )
#'
#' foreign.trade.ROW <- c(
#' product.CHN = 15,
#' tax.ROW = 0.75,
#' money.interest.CHN = 0.3
#' )
#'
#' ITExample <- matrix_add_by_name(
#' ITExample, production.CHN, consumption.CHN, investment.CHN, foreign.trade.CHN,
#' production.ROW, consumption.ROW, investment.ROW, foreign.trade.ROW
#' )
#'
#' ge <- gemInputOutputTable_2_8_4(
#' IT = ITExample,
#' return.dstl = TRUE
#' )
#' ge$eri.CHN
#' ge$p
#' node_plot(ge$dstl[[4]], TRUE)
#'
#' ge2 <- gemInputOutputTable_2_8_4(
#' IT = ge$DV,
#' money.interest.supply.CHN = sum(ge$DV["money.interest.CHN", ]),
#' money.interest.supply.ROW = sum(ge$DV["money.interest.ROW", ]),
#' return.dstl = TRUE
#' )
#' ge2$eri.CHN
#' ge2$p
#'
#'
#' #### technology progress in CHN
#' ITTmp <- ITExample
#' ITTmp["labor.CHN", "production.CHN"] <- ITTmp["labor.CHN", "production.CHN"] * 0.8
#' geTmp <- gemInputOutputTable_2_8_4(
#' IT = ITTmp,
#' product.output.CHN = sum(ITExample[, "production.CHN"]),
#' return.dstl = TRUE
#' )
#' geTmp$eri.CHN
#'
#'
#' #### increased demand for imported product in CHN
#' ITTmp <- ITExample
#' ITTmp["imported.product.CHN", "production.CHN"] <-
#' ITTmp["imported.product.CHN", "production.CHN"] * 1.2
#' geTmp <- gemInputOutputTable_2_8_4(
#' IT = ITTmp,
#' return.dstl = TRUE
#' )
#' geTmp$eri.CHN
#'
#'
#' #### capital accumulation in CHN
#' geTmp <- gemInputOutputTable_2_8_4(
#' IT = ITExample,
#' capital.supply.CHN = sum(ITExample["capital.CHN", ]) * 1.2,
#' return.dstl = TRUE
#' )
#' geTmp$eri.CHN
#'
#' ##
#' geTmp <- gemInputOutputTable_2_8_4(
#' IT = ITExample,
#' capital.supply.CHN = sum(ITExample["capital.CHN", ]) * 1.2,
#' es.DIProduct.production.CHN = 0.3,
#' return.dstl = TRUE
#' )
#' geTmp$eri.CHN
#' }
#'
gemInputOutputTable_2_8_4 <- function(IT,
product.output.CHN = sum(IT[, "production.CHN"]),
product.output.ROW = sum(IT[, "production.ROW"]),
labor.supply.CHN = sum(IT["labor.CHN", ]),
labor.supply.ROW = sum(IT["labor.ROW", ]),
capital.supply.CHN = sum(IT["capital.CHN", ]),
capital.supply.ROW = sum(IT["capital.ROW", ]),
money.interest.supply.CHN = 5,
money.interest.supply.ROW = 30,
es.DIProduct.production.CHN = 0.5,
es.DIProduct.production.ROW = 0.5,
es.laborCapital.production.CHN = 0.75,
es.laborCapital.production.ROW = 0.75,
es.consumption.CHN = 0.5,
es.consumption.ROW = 0.5,
es.investment.CHN = 0.9,
es.investment.ROW = 0.9,
interest.rate.CHN = NA,
interest.rate.ROW = NA,
return.dstl = FALSE,
...) {
# exogenous supply --------------------------------------------------------
SExg <- IT * NA
SExg[c("labor.CHN", "dividend.CHN", "tax.CHN", "money.interest.CHN", "capital.CHN"), "consumption.CHN"] <-
c(
labor.supply.CHN,
sum(IT["dividend.CHN", ]),
sum(IT["tax.CHN", ]),
money.interest.supply.CHN,
capital.supply.CHN
)
SExg[c("labor.ROW", "dividend.ROW", "tax.ROW", "money.interest.ROW", "capital.ROW"), "consumption.ROW"] <-
c(
labor.supply.ROW,
sum(IT["dividend.ROW", ]),
sum(IT["tax.ROW", ]),
money.interest.supply.ROW,
capital.supply.ROW
)
SExg["bond.CHN", "investment.CHN"] <- sum(IT["bond.CHN", ])
SExg["bond.ROW", "investment.ROW"] <- sum(IT["bond.ROW", ])
# demand structure tree ---------------------------------------------------
# production.CHN ----------------------------------------------------------
dst.production.CHN <- node_new(
"production.CHN",
type = "FIN",
beta = prop.table(c((sum(IT[, "production.CHN"]) - IT["money.interest.CHN", "production.CHN"]), IT["money.interest.CHN", "production.CHN"])),
"cc1.production.CHN", "money.interest.CHN"
)
node_set(
dst.production.CHN,
"cc1.production.CHN",
type = "Leontief",
a = prop.table(c(sum(IT[
c("product.CHN", "imported.product.CHN"),
"production.CHN"
]), sum(IT[c(
"labor.CHN", "capital.CHN",
"tax.CHN", "dividend.CHN"
), "production.CHN"]))),
"cc1.1.production.CHN",
"cc1.2.production.CHN"
)
node_set(
dst.production.CHN,
"cc1.1.production.CHN",
type = "SCES",
es = es.DIProduct.production.CHN,
alpha = 1,
beta = prop.table(IT[
c("product.CHN", "imported.product.CHN"),
"production.CHN"
]),
"product.CHN",
"imported.product.CHN"
)
node_set(
dst.production.CHN,
"cc1.2.production.CHN",
type = "FIN",
beta = prop.table(c(
sum(IT[c(
"labor.CHN",
"capital.CHN"
), "production.CHN"]),
tax.CHN = IT[
"tax.CHN",
"production.CHN"
],
dividend.CHN = IT[
"dividend.CHN",
"production.CHN"
]
)),
"cc1.2.1.production.CHN",
"tax.CHN",
"dividend.CHN"
)
node_set(
dst.production.CHN,
"cc1.2.1.production.CHN",
type = "SCES",
es = es.laborCapital.production.CHN,
alpha = 1,
beta = prop.table(IT[
c("labor.CHN", "capital.CHN"),
"production.CHN"
]),
"labor.CHN",
"capital.CHN"
)
# production.ROW ----------------------------------------------------------
dst.production.ROW <- node_new("production.ROW",
type = "FIN",
beta = prop.table(c((sum(IT[, "production.ROW"]) - IT[
"money.interest.ROW",
"production.ROW"
]), IT["money.interest.ROW", "production.ROW"])),
"cc1.production.ROW", "money.interest.ROW"
)
node_set(dst.production.ROW, "cc1.production.ROW",
type = "Leontief",
a = prop.table(c(sum(IT[
c("product.ROW", "imported.product.ROW"),
"production.ROW"
]), sum(IT[c(
"labor.ROW", "capital.ROW",
"tax.ROW", "dividend.ROW"
), "production.ROW"]))),
"cc1.1.production.ROW", "cc1.2.production.ROW"
)
node_set(
dst.production.ROW,
"cc1.1.production.ROW",
type = "SCES",
es = es.DIProduct.production.ROW,
alpha = 1,
beta = prop.table(IT[
c("product.ROW", "imported.product.ROW"),
"production.ROW"
]),
"product.ROW", "imported.product.ROW"
)
node_set(
dst.production.ROW,
"cc1.2.production.ROW",
type = "FIN",
beta = prop.table(c(
sum(IT[c(
"labor.ROW",
"capital.ROW"
), "production.ROW"]),
tax.ROW = IT[
"tax.ROW",
"production.ROW"
], dividend.ROW = IT[
"dividend.ROW",
"production.ROW"
]
)),
"cc1.2.1.production.ROW",
"tax.ROW",
"dividend.ROW"
)
node_set(
dst.production.ROW,
"cc1.2.1.production.ROW",
type = "SCES",
es = es.laborCapital.production.ROW,
alpha = 1,
beta = prop.table(IT[
c("labor.ROW", "capital.ROW"),
"production.ROW"
]),
"labor.ROW",
"capital.ROW"
)
# consumption.CHN ---------------------------------------------------------
dst.consumption.CHN <- node_new("consumption.CHN",
type = "FIN",
beta = prop.table(c(sum(IT[, "consumption.CHN"]) - IT[
"money.interest.CHN",
"consumption.CHN"
], IT["money.interest.CHN", "consumption.CHN"])),
"cc1.consumption.CHN", "money.interest.CHN"
)
node_set(dst.consumption.CHN, "cc1.consumption.CHN",
type = "FIN",
beta = prop.table(c(sum(IT[
c("product.CHN", "imported.product.CHN"),
"consumption.CHN"
]), IT["bond.CHN", "consumption.CHN"])),
"cc1.1.consumption.CHN", "bond.CHN"
)
node_set(
dst.consumption.CHN,
"cc1.1.consumption.CHN",
type = "SCES",
es = es.consumption.CHN,
alpha = 1,
beta = prop.table(IT[c(
"product.CHN",
"imported.product.CHN"
), "consumption.CHN"]),
"product.CHN", "imported.product.CHN"
)
# consumption.ROW ---------------------------------------------------------
dst.consumption.ROW <- node_new("consumption.ROW",
type = "FIN",
beta = prop.table(c(sum(IT[, "consumption.ROW"]) - IT[
"money.interest.ROW",
"consumption.ROW"
], IT["money.interest.ROW", "consumption.ROW"])),
"cc1.consumption.ROW", "money.interest.ROW"
)
node_set(dst.consumption.ROW, "cc1.consumption.ROW",
type = "FIN",
beta = prop.table(c(sum(IT[
c("product.ROW", "imported.product.ROW"),
"consumption.ROW"
]), IT["bond.ROW", "consumption.ROW"])),
"cc1.1.consumption.ROW", "bond.ROW"
)
node_set(
dst.consumption.ROW,
"cc1.1.consumption.ROW",
type = "SCES",
es = es.consumption.ROW,
alpha = 1,
beta = prop.table(IT[c(
"product.ROW",
"imported.product.ROW"
), "consumption.ROW"]),
"product.ROW", "imported.product.ROW"
)
# investment.CHN ----------------------------------------------------------
dst.investment.CHN <- node_new("investment.CHN",
type = "FIN",
beta = prop.table(c(sum(IT[c(
"product.CHN", "imported.product.CHN",
"money.interest.CHN"
), "investment.CHN"]), sum(IT[c(
"bond.ROW",
"money.interest.ROW"
), "investment.CHN"]))),
"cc1.investment.CHN", "cc2"
)
node_set(dst.investment.CHN, "cc1.investment.CHN",
type = "FIN",
beta = prop.table(c(sum(IT[
c("product.CHN", "imported.product.CHN"),
"investment.CHN"
]), IT["money.interest.CHN", "investment.CHN"])),
"cc1.1.investment.CHN", "money.interest.CHN"
)
node_set(
dst.investment.CHN,
"cc1.1.investment.CHN",
type = "SCES",
es = es.investment.CHN,
alpha = 1,
beta = prop.table(IT[c(
"product.CHN",
"imported.product.CHN"
), "investment.CHN"]),
"product.CHN", "imported.product.CHN"
)
node_set(dst.investment.CHN,
"cc2",
type = "FIN",
beta = prop.table(c(IT[
"bond.ROW",
"investment.CHN"
], IT["money.interest.ROW", "investment.CHN"])),
"bond.ROW", "money.interest.ROW"
)
# investment.ROW ----------------------------------------------------------
dst.investment.ROW <- node_new("investment.ROW",
type = "FIN",
beta = prop.table(c(sum(IT[c(
"product.ROW", "imported.product.ROW",
"money.interest.ROW"
), "investment.ROW"]), sum(IT[c(
"bond.CHN",
"money.interest.CHN"
), "investment.ROW"]))),
"cc1.investment.ROW", "cc2"
)
node_set(dst.investment.ROW,
"cc1.investment.ROW",
type = "FIN",
beta = prop.table(c(sum(IT[
c("product.ROW", "imported.product.ROW"),
"investment.ROW"
]), IT["money.interest.ROW", "investment.ROW"])),
"cc1.1.investment.ROW", "money.interest.ROW"
)
node_set(
dst.investment.ROW,
"cc1.1.investment.ROW",
type = "SCES",
es = es.investment.ROW,
alpha = 1,
beta = prop.table(IT[c(
"product.ROW",
"imported.product.ROW"
), "investment.ROW"]),
"product.ROW", "imported.product.ROW"
)
node_set(dst.investment.ROW,
"cc2",
type = "FIN",
beta = prop.table(c(IT[
"bond.CHN",
"investment.ROW"
], IT["money.interest.CHN", "investment.ROW"])),
"bond.CHN", "money.interest.CHN"
)
# foreign.trade.CHN -------------------------------------------------------
dst.foreign.trade.CHN <-
node_new(
"foreign.trade.CHN",
type = "FIN",
beta = prop.table(c(sum(IT[
c("product.ROW", "tax.CHN"),
"foreign.trade.CHN"
]), IT[
"money.interest.ROW",
"foreign.trade.CHN"
])),
"cc1.foreign.trade.CHN",
"money.interest.ROW"
)
node_set(
dst.foreign.trade.CHN,
"cc1.foreign.trade.CHN",
type = "FIN",
beta = prop.table(c(IT[
"product.ROW",
"foreign.trade.CHN"
], IT["tax.CHN", "foreign.trade.CHN"])),
"product.ROW",
"tax.CHN"
)
# foreign.trade.ROW -------------------------------------------------------
dst.foreign.trade.ROW <-
node_new("foreign.trade.ROW",
type = "FIN",
beta = prop.table(c(sum(IT[
c("product.CHN", "tax.ROW"),
"foreign.trade.ROW"
]), IT[
"money.interest.CHN",
"foreign.trade.ROW"
])),
"cc1.foreign.trade.ROW", "money.interest.CHN"
)
node_set(
dst.foreign.trade.ROW,
"cc1.foreign.trade.ROW",
type = "FIN",
beta = prop.table(c(IT[
"product.CHN",
"foreign.trade.ROW"
], IT["tax.ROW", "foreign.trade.ROW"])),
"product.CHN", "tax.ROW"
)
dstl <- list(
dst.production.CHN,
dst.consumption.CHN,
dst.investment.CHN,
dst.foreign.trade.CHN,
dst.production.ROW,
dst.consumption.ROW,
dst.investment.ROW,
dst.foreign.trade.ROW
)
# run sdm2 -----------------------------------------------------------------
ge <- sdm2(
A = dstl,
B = {
B <- IT * 0
B["product.CHN", "production.CHN"] <-
B["imported.product.CHN", "foreign.trade.CHN"] <-
B["product.ROW", "production.ROW"] <-
B["imported.product.ROW", "foreign.trade.ROW"] <- 1
B
},
S0Exg = SExg,
names.commodity = rownames(IT),
names.agent = colnames(IT),
numeraire = "labor.CHN",
priceAdjustmentVelocity = 0.05,
...
)
ge$eri.ROW <- unname(ge$p["money.interest.ROW"] / ge$p["money.interest.CHN"]) # exchange rate index
ge$eri.CHN <- unname(ge$p["money.interest.CHN"] / ge$p["money.interest.ROW"])
if (!is.na(interest.rate.CHN) & !is.na(interest.rate.ROW)) {
money.value.CHN <- ge$p["money.interest.CHN"] / interest.rate.CHN
money.value.ROW <- ge$p["money.interest.ROW"] / interest.rate.ROW
ge$p.money <- ge$p
ge$p.money["money.interest.CHN"] <- money.value.CHN
ge$p.money["money.interest.ROW"] <- money.value.ROW
ge$p.money <- ge$p.money / ge$p.money["money.interest.CHN"]
ge$eri.ROW <- unname(ge$p.money["money.interest.ROW"] / ge$p.money["money.interest.CHN"])
ge$eri.CHN <- unname(ge$p.money["money.interest.CHN"] / ge$p.money["money.interest.ROW"])
}
if (return.dstl) ge$dstl <- dstl
return(ge)
}
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