168 lines
4.6 KiB
R
168 lines
4.6 KiB
R
|
# ========================================================== #
|
|||
|
|
# scenario1 #
|
|||
|
|
# ========================================================== #
|
|||
|
|
# Description:
|
|||
|
|
|
|||
|
|
## Variables
|
|||
|
|
η = 1.1
|
|||
|
|
ρ = -0.5
|
|||
|
|
δ = 0.005
|
|||
|
|
r_1 = 0.06
|
|||
|
|
r_2 = -0.02
|
|||
|
|
### r_1_paper = 0.06 ## yearly
|
|||
|
|
### r_1 = 1+log(1+r_1_paper) ## instantaneous
|
|||
|
|
### r_2_paper = -0.02 ## yearly
|
|||
|
|
### r_2 = 1+log(1+r_2_paper) ## instantaneous
|
|||
|
|
γ_1 = 0.03
|
|||
|
|
γ_2 = 0.01
|
|||
|
|
w_2 = 5000
|
|||
|
|
β_2 = 1
|
|||
|
|
λ_1 = 0.5
|
|||
|
|
λ_2 = 0.5
|
|||
|
|
δ_2 = 0.44
|
|||
|
|
q=0.5
|
|||
|
|
|
|||
|
|
## Initial conditions. Correspond to "year 0".
|
|||
|
|
K_init = 10^13
|
|||
|
|
L_init = 10^4
|
|||
|
|
|
|||
|
|
## Integration constant
|
|||
|
|
c1_forward_shooting = 10^(-8) # 10^10 ## 2*10^(-6)
|
|||
|
|
|
|||
|
|
## Stepsize
|
|||
|
|
stepsize = 0.1
|
|||
|
|
r1_stepsize = ((1+r_1)^stepsize)-1
|
|||
|
|
r2_stepsize = ((1+r_2)^stepsize)-1
|
|||
|
|
|
|||
|
|
## Notes time it takes to run the simulations
|
|||
|
|
### stepsize = 0.1 => seconds (7s).
|
|||
|
|
### stepsize = 0.01 => minutes (3 mins).
|
|||
|
|
|
|||
|
|
## Knife-edge constant
|
|||
|
|
knife_edge_constant = (γ_1/(ρ-1)) + ((r_1 - δ)/η) + max(0,(γ_1*(1-η-ρ)/(η*(ρ-1)))) - max(r_2,(γ_2+γ_1*δ_2*λ_2)/(1-δ_2))
|
|||
|
|
|
|||
|
|
## Interval
|
|||
|
|
first = 0
|
|||
|
|
last = 1000
|
|||
|
|
times_forward_shooting = seq(from=first, to=last, by=stepsize)
|
|||
|
|
times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
|
|||
|
|
|
|||
|
|
# ========================================================== #
|
|||
|
|
# scenario2 #
|
|||
|
|
# ========================================================== #
|
|||
|
|
# Description: Knife edge constant = 0
|
|||
|
|
|
|||
|
|
## Variables
|
|||
|
|
η = 1.1
|
|||
|
|
ρ = -0.5
|
|||
|
|
### δ = 0.005
|
|||
|
|
r_1 = 0.06
|
|||
|
|
r_2 = -0.02
|
|||
|
|
### r_1_paper = 0.06 ## yearly
|
|||
|
|
### r_1 = 1+log(1+r_1_paper) ## instantaneous
|
|||
|
|
### r_2_paper = -0.02 ## yearly
|
|||
|
|
### r_2 = 1+log(1+r_2_paper) ## instantaneous
|
|||
|
|
γ_1 = 0.03
|
|||
|
|
γ_2 = 0.01
|
|||
|
|
w_2 = 5000
|
|||
|
|
β_2 = 1
|
|||
|
|
λ_1 = 0.5
|
|||
|
|
λ_2 = 0.5
|
|||
|
|
δ_2 = 0.44
|
|||
|
|
q=0.5
|
|||
|
|
δ = r_1 + η*( (γ_1/(ρ-1)) + max(0,(γ_1*(1-η-ρ)/(η*(ρ-1)))) - max(r_2,(γ_2+γ_1*δ_2*λ_2)/(1-δ_2)) )
|
|||
|
|
|
|||
|
|
## Initial conditions. Correspond to "year 0".
|
|||
|
|
K_init = 10^13 ## 10^13 to afford movement building. 10^14 to have a reasonable amount of direct investment as well. This is close to the net discounted value of US GDP.
|
|||
|
|
L_init = 10^4
|
|||
|
|
|
|||
|
|
## Integration constant
|
|||
|
|
c1_forward_shooting = 10^(-8) # 10^10 ## 2*10^(-6)
|
|||
|
|
|
|||
|
|
## Stepsize
|
|||
|
|
stepsize = 0.1
|
|||
|
|
r1_stepsize = ((1+r_1)^stepsize)-1
|
|||
|
|
r2_stepsize = ((1+r_2)^stepsize)-1
|
|||
|
|
|
|||
|
|
## Notes time it takes to run the simulations
|
|||
|
|
### stepsize = 0.1 => seconds (7s).
|
|||
|
|
### stepsize = 0.01 => minutes (3 mins).
|
|||
|
|
|
|||
|
|
## Knife-edge constant
|
|||
|
|
knife_edge_constant = (γ_1/(ρ-1)) + ((r_1 - δ)/η) + max(0,(γ_1*(1-η-ρ)/(η*(ρ-1)))) - max(r_2,(γ_2+γ_1*δ_2*λ_2)/(1-δ_2))
|
|||
|
|
|
|||
|
|
## Interval
|
|||
|
|
first = 0
|
|||
|
|
last = 1000
|
|||
|
|
times_forward_shooting = seq(from=first, to=last, by=stepsize)
|
|||
|
|
times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
|
|||
|
|
|
|||
|
|
|
|||
|
|
# ========================================================== #
|
|||
|
|
# scenario3 #
|
|||
|
|
# ========================================================== #
|
|||
|
|
# Description: Knife edge constant < 0
|
|||
|
|
|
|||
|
|
## Variables
|
|||
|
|
η = 1.1
|
|||
|
|
ρ = -0.5
|
|||
|
|
δ = 0.00578572
|
|||
|
|
r_1 = 0.06
|
|||
|
|
r_2 = -0.02
|
|||
|
|
### r_1_paper = 0.06 ## yearly
|
|||
|
|
### r_1 = 1+log(1+r_1_paper) ## instantaneous
|
|||
|
|
### r_2_paper = -0.02 ## yearly
|
|||
|
|
### r_2 = 1+log(1+r_2_paper) ## instantaneous
|
|||
|
|
γ_1 = 0.03
|
|||
|
|
γ_2 = 0.01
|
|||
|
|
w_2 = 5000
|
|||
|
|
β_2 = 1
|
|||
|
|
λ_1 = 0.5
|
|||
|
|
λ_2 = 0.5
|
|||
|
|
δ_2 = 0.44
|
|||
|
|
q=0.5
|
|||
|
|
|
|||
|
|
## Initial conditions. Correspond to "year 0".
|
|||
|
|
K_init = 10^13 ## 10^13 to afford movement building. 10^14 to have a reasonable amount of direct investment as well. This is close to the net discounted value of US GDP.
|
|||
|
|
L_init = 10^4
|
|||
|
|
|
|||
|
|
## Integration constant
|
|||
|
|
c1_forward_shooting = 10^(-8) # 10^10 ## 2*10^(-6)
|
|||
|
|
|
|||
|
|
## Stepsize
|
|||
|
|
stepsize = 0.1
|
|||
|
|
r1_stepsize = ((1+r_1)^stepsize)-1
|
|||
|
|
r2_stepsize = ((1+r_2)^stepsize)-1
|
|||
|
|
|
|||
|
|
## Notes time it takes to run the simulations
|
|||
|
|
### stepsize = 0.1 => seconds (7s).
|
|||
|
|
### stepsize = 0.01 => minutes (3 mins).
|
|||
|
|
|
|||
|
|
## Knife-edge constant
|
|||
|
|
knife_edge_constant = (γ_1/(ρ-1)) + ((r_1 - δ)/η) + max(0,(γ_1*(1-η-ρ)/(η*(ρ-1)))) - max(r_2,(γ_2+γ_1*δ_2*λ_2)/(1-δ_2))
|
|||
|
|
knife_edge_constant
|
|||
|
|
## Interval
|
|||
|
|
first = 0
|
|||
|
|
last = 1000
|
|||
|
|
times_forward_shooting = seq(from=first, to=last, by=stepsize)
|
|||
|
|
times_reverse_shooting = seq(from=last, to=first, by=-stepsize)
|
|||
|
|
|
|||
|
|
# ========================================================== #
|
|||
|
|
# scenarios 4 to 14 #
|
|||
|
|
# ========================================================== #
|
|||
|
|
|
|||
|
|
δ_array = seq(from=0.0044, to=0.0064, by=0.0002)
|
|||
|
|
δ = δ_array[1]
|
|||
|
|
δ = δ_array[2]
|
|||
|
|
δ = δ_array[3]
|
|||
|
|
δ = δ_array[4]
|
|||
|
|
δ = δ_array[5]
|
|||
|
|
δ = δ_array[6]
|
|||
|
|
δ = δ_array[7]
|
|||
|
|
δ = δ_array[8]
|
|||
|
|
δ = δ_array[9]
|
|||
|
|
δ = δ_array[10]
|
|||
|
|
δ = δ_array[11]
|
|||
|
|
|
|||
|
|
knife_edge_constant = (γ_1/(ρ-1)) + ((r_1 - δ)/η) + max(0,(γ_1*(1-η-ρ)/(η*(ρ-1)))) - max(r_2,(γ_2+γ_1*δ_2*λ_2)/(1-δ_2))
|