| gemCanonicalDynamicMacroeconomic_Timeline_2_2 {GE} | R Documentation |
A Canonical Dynamic Macroeconomic General Equilibrium Model in Timeline Form (see Torres, 2016)
Description
A canonical dynamic macroeconomic general equilibrium model in timeline form (see Torres, 2016, Table 2.1 and 2.2). The firm has a CESAK production function.
Usage
gemCanonicalDynamicMacroeconomic_Timeline_2_2(
alpha.firm = rep(1, 4),
es.prod.lab.firm = 1,
beta.prod.firm = 0.35,
depreciation.rate = 0.06,
eis = 1,
Gamma.beta = 0.97,
beta.prod.consumer = 0.4,
es.prod.lab.consumer = 1,
gr = 0,
initial.product.supply = 200,
head.tail.adjustment = "both",
wage.payment = "post",
beta.consumer = NULL,
...
)
Arguments
alpha.firm |
a positive vector, indicating the efficiency parameters of the firm for each economic period. The number of economic periods will be set to length(alpha.firm) + 1. |
es.prod.lab.firm |
the elasticity of substitution between product and labor in the production function of the firm. |
beta.prod.firm |
the share parameter of the product in the production function. |
depreciation.rate |
the physical depreciation rate of capital stock. |
eis |
a positive scalar indicating the elasticity of intertemporal substitution of the consumer. |
Gamma.beta |
the subjective discount factor of the consumer. |
beta.prod.consumer |
the share parameter of the product in the period utility function. |
es.prod.lab.consumer |
the elasticity of substitution between product and labor in the CES-type period utility function of the consumer. |
gr |
the growth rate of the labor supply. |
initial.product.supply |
the initial product supply. |
head.tail.adjustment |
a character string specifying the type of the head-tail-adjustment policy, must be one of "both" (default), "head", "tail" or "none". |
wage.payment |
a character string specifying the wage payment method, must be one of "pre" or "post". |
beta.consumer |
NULL (the default) or a positive vector containing length(alpha.firm) + 1 elements specifying the consumer's intertemporal share parameter. If beta.consumer is not NULL, Gamma.beta will be ignored. |
... |
arguments to be passed to the function sdm2. |
References
Torres, Jose L. (2016, ISBN: 9781622730452) Introduction to Dynamic Macroeconomic General Equilibrium Models (Second Edition). Vernon Press.
See Also
gemCanonicalDynamicMacroeconomic_TimeCircle_2_2,
gemCanonicalDynamicMacroeconomic_Sequential_3_2,
gemCanonicalDynamicMacroeconomic_Sequential_WagePostpayment_4_3.
Examples
#### Take the wage postpayment assumption.
ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2()
np <- 5
eis <- 1
Gamma.beta <- 0.97
gr <- 0
ge$p
ge$p[1:(np - 1)] / ge$p[2:np] - 1
ge$p[(np + 1):(2 * np - 2)] / ge$p[(np + 2):(2 * np - 1)] - 1
sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr) # the steady-state equilibrium return rate
ge$z
ge$D
node_plot(ge$dst.consumer, TRUE)
#### Take the wage postpayment assumption.
eis <- 0.8
Gamma.beta <- 0.97
gr <- 0.03
ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(
es.prod.lab.firm = 0.8,
eis = eis, Gamma.beta = Gamma.beta, es.prod.lab.consumer = 0.8,
gr = gr
)
np <- 5
ge$p
growth_rate(ge$p[1:np])
1 / (1 + sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr)) - 1
ge$z
growth_rate(ge$z[1:(np - 1)])
ge$D
ge$S
##### a fully anticipated technology shock.
## Warning: Running the program below takes several minutes.
# np <- 120
# alpha.firm <- rep(1, np - 1)
# alpha.firm[40] <- 1.05
# ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(alpha.firm = alpha.firm)
#
## The steady state product supply is 343.92.
## the (economic) time series of product supply.
# plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20)
## The steady state product consumption is 57.27.
## the (economic) time series of product consumption.
# plot(ge$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20)
# plot(growth_rate(ge$p[1:(np)]), type = "o", pch = 20)
# plot(growth_rate(ge$p[(np + 1):(2 * np)]), type = "o", pch = 20)
#
##### an unanticipated technology shock.
# np <- 50
# alpha.firm <- rep(1, np - 1)
# alpha.firm[1] <- 1.05
# ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(
# alpha.firm = alpha.firm,
# initial.product.supply = 286.6341, # the steady state value
# head.tail.adjustment = "tail"
# )
#
## The steady state product supply is 343.92.
## the (economic) time series of product supply.
# plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20)
## The steady state product consumption is 57.27.
## the (economic) time series of product consumption.
# plot(ge$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20)
# plot(growth_rate(ge$p[1:(np)]), type = "o", pch = 20)
# plot(growth_rate(ge$p[(np + 1):(2 * np)]), type = "o", pch = 20)
#
### a technology shock anticipated several periods in advance.
# np <- 50
# alpha.firm <- rep(1, np - 1)
# alpha.firm[5] <- 1.05
# ge5 <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(
# alpha.firm = alpha.firm,
# initial.product.supply = 286.6341, # the steady state value
# head.tail.adjustment = "tail"
# )
#
## The steady state product supply is 343.92.
## the (economic) time series of product supply
# plot(ge5$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20)
## The steady state product consumption is 57.27.
## the (economic) time series of product consumption
# plot(ge5$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20)
# plot(growth_rate(ge5$p[1:(np)]), type = "o", pch = 20)
# plot(growth_rate(ge5$p[(np + 1):(2 * np)]), type = "o", pch = 20)
#
# alpha.firm <- rep(1, np - 1)
# alpha.firm[10] <- 1.05
# ge10 <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(
# alpha.firm = alpha.firm,
# initial.product.supply = 286.6341, # the steady state value
# head.tail.adjustment = "tail"
# )
# plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20, ylim = c(-0.005, 0.017))
# lines(ge5$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 21)
# lines(ge10$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 22)
##### an unanticipated technology shock.
## Warning: Running the program below takes several minutes.
# np <- 100
# alpha.firm <- exp(0.01)
# for (t in 2:(np - 1)) {
# alpha.firm[t] <- exp(0.9 * log(alpha.firm[t - 1]))
# }
# plot(alpha.firm)
#
# ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(
# alpha.firm = alpha.firm,
# initial.product.supply = 286.6341, # the steady state value
# head.tail.adjustment = "tail"
# )
#
## The steady state product supply is 343.92.
## the (economic) time series of product supply
# plot(ge$z[1:(np - 1)] / 343.92 - 1, type = "o", pch = 20)
## The steady state product consumption is 57.27.
## the (economic) time series of product consumption
# plot(ge$D[2:(np - 1), np] / 57.27 - 1, type = "o", pch = 20)
# plot(growth_rate(ge$p[1:(np)]), type = "o", pch = 20)
# plot(growth_rate(ge$p[(np + 1):(2 * np)]), type = "o", pch = 20)
#### Take the wage prepayment assumption.
ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(wage.payment = "pre")
np <- 5
eis <- 1
Gamma.beta <- 0.97
gr <- 0
ge$p
ge$p[1:(np - 1)] / ge$p[2:np] - 1
ge$p[(np + 1):(2 * np - 2)] / ge$p[(np + 2):(2 * np - 1)] - 1
sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr) # the steady-state equilibrium return rate
ge$z
ge$D
node_plot(ge$dst.consumer, TRUE)
#### Take the wage prepayment assumption.
np <- 5
eis <- 0.8
Gamma.beta <- 0.97
gr <- 0.03
ge <- gemCanonicalDynamicMacroeconomic_Timeline_2_2(
es.prod.lab.firm = 0.8,
eis = eis, Gamma.beta = Gamma.beta, es.prod.lab.consumer = 0.8,
gr = gr,
wage.payment = "pre"
)
ge$p
growth_rate(ge$p[1:np])
1 / (1 + sserr(eis = eis, Gamma.beta = Gamma.beta, gr = gr)) - 1
ge$z
growth_rate(ge$z[1:(np - 1)])
ge$D
ge$S