GE (version 0.4.8)

gemCanonicalDynamicMacroeconomic_Timeline_2_2: 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

# \donttest{
#### 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
# }