# Structural Dynamic Model (alias Structural Growth Model) with a Demand Structure Tree List 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. ```r 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. ## Returns 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 ## Examples ```r #### 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 } ) ``` ## 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`

sdm_dstl function