sdm_dstl: Structural Dynamic Model (alias Structural Growth Model) with...

In GE: General Equilibrium Modeling

Structural Dynamic Model (alias Structural Growth Model) with a Demand Structure Tree List

Description

This is a wrapper of the function CGE::sdm. The parameter A of CGE::sdm is replaced with a demand structure tree list. This function can be replaced by the more comprehensive function sdm2, so it is not recommended.

Usage

sdm_dstl(dstl, names.commodity, names.agent, ...)

Arguments

dstl	a demand structure tree list.
names.commodity	names of commodities.
names.agent	names of agents.
...	arguments to be passed to the function CGE::sdm.

Value

A general equilibrium, which is a list with the following elements:

• D - the demand matrix.

• DV - the demand value matrix.

• SV - the supply value matrix.

• ... - some elements returned by the CGE::sdm function

References

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

LI Wu (2010) A Structural Growth Model and its Applications to Sraffa's System. http://www.iioa.org/conferences/18th/papers/files/104_20100729011_AStructuralGrowthModelanditsApplicationstoSraffasSstem.pdf

Manuel Alejandro Cardenete, Ana-Isabel Guerra, Ferran Sancho (2012, ISBN: 9783642247453) Applied General Equilibrium: An Introduction. Springer-Verlag Berlin Heidelberg.

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

See Also

sdm2

Examples

#### a pure exchange economy with two agents and two commodities
dst.CHN <- node_new("util.CHN",
                    type = "SCES", alpha = 1, beta = c(0.8, 0.2), es = 2,
                    "lab.CHN", "lab.ROW"
)
node_plot(dst.CHN)

dst.ROW <- node_new("util.ROW",
                    type = "SCES", alpha = 1, beta = c(0.05, 0.95), es = 2,
                    "lab.CHN", "lab.ROW"
)

dstl <- list(dst.CHN, dst.ROW)

ge <- sdm_dstl(dstl,
               names.commodity = c("lab.CHN", "lab.ROW"),
               names.agent = c("CHN", "ROW"),
               B = matrix(0, 2, 2, TRUE),
               S0Exg = matrix(c(
                 100, 0,
                 0, 600
               ), 2, 2, TRUE)
)

## supply change
geSC <- sdm_dstl(dstl,
                 names.commodity = c("lab.CHN", "lab.ROW"),
                 names.agent = c("CHN", "ROW"),
                 B = matrix(0, 2, 2, TRUE),
                 S0Exg = matrix(c(
                   200, 0,
                   0, 600
                 ), 2, 2, TRUE)
)

geSC$p / ge$p

## preference change
dst.CHN$beta <- c(0.9, 0.1)
gePC <- sdm_dstl(dstl,
                 names.commodity = c("lab.CHN", "lab.ROW"),
                 names.agent = c("CHN", "ROW"),
                 B = matrix(0, 2, 2, TRUE),
                 S0Exg = matrix(c(
                   100, 0,
                   0, 600
                 ), 2, 2, TRUE)
)

gePC$p / ge$p


#### a pure exchange economy with two agents and four basic commodities
prod.CHN <- node_new("prod.CHN",
                     type = "SCES", alpha = 1, beta = c(0.5, 0.5), es = 0.75,
                     "lab.CHN", "cap.CHN"
)

node_plot(prod.CHN)

prod.ROW <- node_new("prod.ROW",
                     type = "SCES", alpha = 2, beta = c(0.4, 0.6), es = 0.75,
                     "lab.ROW", "cap.ROW"
)

dst.CHN <- node_new("CHN",
                    type = "SCES", alpha = 1, beta = c(0.8, 0.2), es = 2,
                    prod.CHN, prod.ROW
)

node_plot(dst.CHN)
node_print(dst.CHN)
p <- c("lab.CHN" = 1, "cap.CHN" = 1, "lab.ROW" = 1, "cap.ROW" = 1)
demand_coefficient(dst.CHN, p)


dst.ROW <- node_new("ROW",
                    type = "SCES", alpha = 1, beta = c(0.05, 0.95), es = 2,
                    prod.CHN, prod.ROW
)

node_plot(dst.ROW)
node_print(dst.ROW)

dstl <- list(dst.CHN, dst.ROW)

ge <- sdm_dstl(dstl,
               names.commodity = c("lab.CHN", "cap.CHN", "lab.ROW", "cap.ROW"),
               names.agent = c("CHN", "ROW"),
               B = matrix(0, 4, 2, TRUE),
               S0Exg = matrix(c(
                 100, 0,
                 100, 0,
                 0, 600,
                 0, 800
               ), 4, 2, TRUE)
)


## Add currencies to the example above.
prod_money.CHN <- node_new("prod_money.CHN",
                           type = "FIN", rate = c(1, 0.1), # 0.1 is the interest rate.
                           prod.CHN, "money.CHN"
)

prod_money.ROW <- node_new("prod_money.ROW",
                           type = "FIN", rate = c(1, 0.1),
                           prod.ROW, "money.ROW"
)

dst.CHN <- node_new("util.CHN",
                    type = "SCES", alpha = 1, beta = c(0.8, 0.2), es = 2,
                    prod_money.CHN, prod_money.ROW
)

dst.ROW <- node_new("util.ROW",
                    type = "SCES", alpha = 1, beta = c(0.05, 0.95), es = 2,
                    prod_money.CHN, prod_money.ROW
)

dstl <- list(dst.CHN, dst.ROW)

ge <- sdm_dstl(dstl,
               names.commodity = c(
                 "lab.CHN", "cap.CHN", "money.CHN",
                 "lab.ROW", "cap.ROW", "money.ROW"
               ),
               names.agent = c("CHN", "ROW"),
               B = matrix(0, 6, 2, TRUE),
               S0Exg = matrix(c(
                 100, 0,
                 100, 0,
                 100, 0,
                 0, 600,
                 0, 800,
                 0, 100
               ), 6, 2, TRUE)
)

ge$p["money.ROW"] / ge$p["money.CHN"] # the exchange rate


#### Example 7.6 in Li (2019), which illustrates foreign exchange rates.
interest.rate.CHN <- 0.1
interest.rate.ROW <- 0.1

firm.CHN <- node_new("output.CHN",
                     type = "FIN", rate = c(1, interest.rate.CHN),
                     "cc1.CHN", "money.CHN"
)
node_set(firm.CHN, "cc1.CHN",
         type = "CD", alpha = 1, beta = c(0.5, 0.5),
         "lab.CHN", "iron"
)

household.CHN <- node_new("util",
                          type = "FIN", rate = c(1, interest.rate.CHN),
                          "wheat", "money.CHN"
)

moneylender.CHN <- Clone(household.CHN)


firm.ROW <- node_new("output.ROW",
                     type = "FIN", rate = c(1, interest.rate.ROW),
                     "cc1.ROW", "money.ROW"
)
node_set(firm.ROW, "cc1.ROW",
         type = "CD", alpha = 1, beta = c(0.5, 0.5),
         "iron", "lab.ROW"
)

household.ROW <- node_new("util",
                          type = "FIN", rate = c(1, interest.rate.ROW),
                          "wheat", "money.ROW"
)

moneylender.ROW <- Clone(household.ROW)


dstl <- list(
  firm.CHN, household.CHN, moneylender.CHN,
  firm.ROW, household.ROW, moneylender.ROW
)

ge <- sdm_dstl(dstl,
               names.commodity = c(
                 "wheat", "lab.CHN", "money.CHN",
                 "iron", "lab.ROW", "money.ROW"
               ),
               names.agent = c(
                 "firm.CHN", "household.CHN", "moneylender.CHN",
                 "firm.ROW", "household.ROW", "moneylender.ROW"
               ),
               B = {
                 tmp <- matrix(0, 6, 6)
                 tmp[1, 1] <- 1
                 tmp[4, 4] <- 1
                 tmp
               },
               S0Exg = {
                 tmp <- matrix(NA, 6, 6)
                 tmp[2, 2] <- 100
                 tmp[3, 3] <- 600
                 tmp[5, 5] <- 100
                 tmp[6, 6] <- 100
                 tmp
               }
)

ge$p.money <- ge$p
ge$p.money["money.CHN"] <- ge$p["money.CHN"] / interest.rate.CHN
ge$p.money["money.ROW"] <- ge$p["money.ROW"] / interest.rate.ROW
ge$p.money <- ge$p.money / ge$p.money["money.CHN"]

ge$p.money["money.ROW"] / ge$p.money["money.CHN"] # the exchange rate


#### the example (see Table 2.1 and 2.2) of the canonical dynamic
#### macroeconomic general equilibrium model in Torres (2016).
discount.factor <- 0.97
return.rate <- 1 / discount.factor - 1
depreciation.rate <- 0.06

production.firm <- node_new("output",
                            type = "CD", alpha = 1, beta = c(0.65, 0.35),
                            "labor", "capital.goods"
)

household <- node_new("util",
                      type = "CD", alpha = 1, beta = c(0.4, 0.6),
                      "product", "labor"
)

leasing.firm <- node_new("output",
                         type = "FIN", rate = c(1, return.rate),
                         "product", "dividend"
)

dstl <- list(
  production.firm, household, leasing.firm
)

ge <- sdm_dstl(dstl,
               names.commodity = c("product", "labor", "capital.goods", "dividend"),
               names.agent = c("production.firm", "household", "leasing.firm"),
               B = matrix(c(
                 1, 0, 1 - depreciation.rate,
                 0, 1, 0,
                 0, 0, 1,
                 0, 1, 0
               ), 4, 3, TRUE),
               S0Exg = {
                 tmp <- matrix(NA, 4, 3)
                 tmp[2, 2] <- 1
                 tmp[4, 2] <- 1
                 tmp
               },
               priceAdjustmentVelocity = 0.03,
               maxIteration = 1,
               numberOfPeriods = 15000,
               ts = TRUE
)

ge$D # the demand matrix
ge$p / ge$p[1]

plot(ge$ts.z[, 1], type = "l")


#### an example of applied general equilibrium (see section 3.4, Cardenete et al., 2012).
dst.consumer1 <- node_new("util",
                          type = "CD", alpha = 1, beta = c(0.3, 0.7),
                          "prod1", "prod2"
)

dst.consumer2 <- node_new("util",
                          type = "CD", alpha = 1, beta = c(0.6, 0.4),
                          "prod1", "prod2"
)

dst.firm1 <- node_new("output",
                      type = "Leontief", a = c(0.5, 0.2, 0.3),
                      "VA", "prod1", "prod2"
)
node_set(dst.firm1, "VA",
         type = "CD",
         alpha = 0.8^-0.8 * 0.2^-0.2, beta = c(0.8, 0.2),
         "lab", "cap"
)

dst.firm2 <- Clone(dst.firm1)
dst.firm2$a <- c(0.25, 0.5, 0.25)
node_set(dst.firm2, "VA",
         alpha = 0.4^-0.4 * 0.6^-0.6, beta = c(0.4, 0.6)
)

node_print(dst.firm2)

dstl <- list(dst.firm1, dst.firm2, dst.consumer1, dst.consumer2)

ge <- sdm_dstl(dstl,
               names.commodity = c("prod1", "prod2", "lab", "cap"),
               names.agent = c("firm1", "firm2", "consumer1", "consumer2"),
               B = {
                 tmp <- matrix(0, 4, 4)
                 tmp[1, 1] <- 1
                 tmp[2, 2] <- 1
                 tmp
               },
               S0Exg = {
                 tmp <- matrix(NA, 4, 4)
                 tmp[3, 3] <- 30
                 tmp[4, 3] <- 20
                 tmp[3, 4] <- 20
                 tmp[4, 4] <- 5
                 tmp
               }
)

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