Skip to content

Commit

Permalink
Turning on some tests before redoing the expectations
Browse files Browse the repository at this point in the history
  • Loading branch information
@jlperla
jlperla committed Jan 3, 2024
1 parent b9ed62c commit 0df31a0
Showing 1 changed file with 58 additions and 48 deletions.
106 changes: 58 additions & 48 deletions lectures/multi_agent_models/lake_model.md
View file
Original file line number Diff line number Diff line change
Expand Up @@ -349,9 +349,9 @@ Let's look at the convergence of the unemployment and employment rate to steady

```{code-cell} julia
lm = LakeModel()
e_0 = 0.92 # initial employment rate
u_0 = 1 - e_0 # initial unemployment rate
T = 50 # simulation length
e_0 = 0.92 # initial employment rate
u_0 = 1 - e_0 # initial unemployment rate
T = 50 # simulation length
u_bar, e_bar = lm.x_bar
x_0 = [u_0; e_0]
Expand Down Expand Up @@ -621,7 +621,7 @@ function solve_mccall_model(mcm; U_iv = 1.0, V_iv = ones(length(mcm.w)), tol = 1
iter = 2_000)
(; alpha, beta, sigma, c, gamma, w, E, u) = mcm
# necessary objects
# pre-calculate utilities
u_w = u.(w, sigma)
u_c = u(c, sigma)
Expand Down Expand Up @@ -656,12 +656,12 @@ And the McCall object

```{code-cell} julia
function McCallModel(; alpha = 0.2,
beta = 0.98, # discount rate
beta = 0.98,
gamma = 0.7,
c = 6.0, # unemployment compensation
sigma = 2.0,
u = (c, sigma) -> c > 0 ? (c^(1 - sigma) - 1) / (1 - sigma) : -10e-6,
w = range(10, 20, length = 60), # w= wage values
w = range(10, 20, length = 60),
E = Expectation(BetaBinomial(59, 600, 400)))
return (; alpha, beta, gamma, c, sigma, u, w, E)
end
Expand All @@ -686,8 +686,7 @@ end
function compute_steady_state_quantities(c_pretax, tau; E, sigma, gamma, beta,
alpha, w_pretax, b, d)
w_bar, lambda, V, U = compute_optimal_quantities(c_pretax, tau; E, sigma, gamma,
beta, alpha, w_pretax)
w_bar, lambda, V, U = compute_optimal_quantities(c_pretax, tau; E, sigma, gamma, beta, alpha, w_pretax)
# compute steady state employment and unemployment rates
lm = LakeModel(; lambda, alpha, b, d)
Expand All @@ -705,9 +704,7 @@ end
function find_balanced_budget_tax(c_pretax; E, sigma, gamma, beta, alpha, w_pretax,
b, d)
function steady_state_budget(t)
u_rate, e_rate, w = compute_steady_state_quantities(c_pretax, t; E, sigma,
gamma, beta, alpha,
w_pretax, b, d)
u_rate, e_rate, w = compute_steady_state_quantities(c_pretax, t; E, sigma, gamma, beta, alpha, w_pretax, b, d)
return t - u_rate * c_pretax
end
Expand All @@ -716,7 +713,28 @@ function find_balanced_budget_tax(c_pretax; E, sigma, gamma, beta, alpha, w_pret
end
```

Using these functions with some parameters.
Helper function to calculate for various unemployment insurance levels

```{code-cell} julia
function calculate_equilibriums(c_pretax; E, sigma, gamma, beta, alpha, w_pretax, b, d)
tau_vec = similar(c_pretax)
u_vec = similar(c_pretax)
e_vec = similar(c_pretax)
welfare_vec = similar(c_pretax)
for (i, c_pre) in enumerate(c_pretax)
tau = find_balanced_budget_tax(c_pre; E, sigma, gamma, beta, alpha, w_pretax, b, d)
u_rate, e_rate, welfare = compute_steady_state_quantities(c_pre, tau; E, sigma, gamma, beta, alpha, w_pretax, b, d)
tau_vec[i] = tau
u_vec[i] = u_rate
e_vec[i] = e_rate
welfare_vec[i] = welfare
end
return tau_vec, u_vec, e_vec, welfare_vec
end
```

Parameters for our experiment

```{code-cell} julia
alpha_base = 0.013
Expand All @@ -730,41 +748,23 @@ sigma = 2.0
# the default wage distribution: a discretized log normal
log_wage_mean, wage_grid_size, max_wage = 20, 200, 170
w_pretax = range(1e-3, max_wage, length = wage_grid_size + 1)
logw_dist = Normal(log(log_wage_mean), 1)
cdf_logw = cdf.(logw_dist, log.(w_pretax))
pdf_logw = cdf_logw[2:end] - cdf_logw[1:(end - 1)]
p_vec = pdf_logw ./ sum(pdf_logw)
w_pretax = (w_pretax[1:(end - 1)] + w_pretax[2:end]) / 2
E = expectation(Categorical(p_vec)) # expectation object
# levels of unemployment insurance we wish to study
Nc = 60
c_pretax = range(5, 140, length = Nc)
tax_vec = zeros(Nc)
unempl_vec = similar(tax_vec)
empl_vec = similar(tax_vec)
welfare_vec = similar(tax_vec)
for i in 1:Nc
t = find_balanced_budget_tax(c_pretax[i]; E, sigma, gamma, beta, alpha,
w_pretax, b, d)
u_rate, e_rate, welfare = compute_steady_state_quantities(c_pretax[i], t; E,
sigma, gamma, beta,
alpha, w_pretax, b, d)
tax_vec[i] = t
unempl_vec[i] = u_rate
empl_vec[i] = e_rate
welfare_vec[i] = welfare
end
c_pretax = range(5, 140, length = 60)
tau_vec, u_vec, e_vec, welfare_vec = calculate_equilibriums(c_pretax;E, sigma,gamma, beta,alpha, w_pretax, b, d)
plt_unemp = plot(title = "Unemployment", c_pretax, unempl_vec, color = :blue,
# plots
plt_unemp = plot(title = "Unemployment", c_pretax, u_vec, color = :blue,
lw = 2, alpha = 0.7, label = "", grid = true)
plt_tax = plot(title = "Tax", c_pretax, tax_vec, color = :blue, lw = 2, alpha = 0.7,
plt_tax = plot(title = "Tax", c_pretax, tau_vec, color = :blue, lw = 2, alpha = 0.7,
label = "", grid = true)
plt_emp = plot(title = "Employment", c_pretax, empl_vec, color = :blue, lw = 2,
plt_emp = plot(title = "Employment", c_pretax, e_vec, color = :blue, lw = 2,
alpha = 0.7, label = "", grid = true)
plt_welf = plot(title = "Welfare", c_pretax, welfare_vec, color = :blue, lw = 2,
alpha = 0.7, label = "", grid = true)
Expand All @@ -776,6 +776,17 @@ Welfare first increases and then decreases as unemployment benefits rise.

The level that maximizes steady state welfare is approximately 62.

```{code-cell} julia
---
tags: [remove-cell]
---
@testset begin
@test tau_vec[2] ≈ 0.859664806251665
@test u_vec[10] ≈ 0.22587607040020583
@test e_vec[4] ≈ 0.8527180941230578
end
```

## Exercises

### Exercise 1
Expand Down Expand Up @@ -864,9 +875,8 @@ plot(plt_unemp, plt_emp, plt_labor, layout = (3, 1), size = (800, 600))
tags: [remove-cell]
---
@testset begin
#test x1[1] ≈ 8.266626766923284
#test x2[2] ≈ 91.43632870031433
#test x3[3] ≈ 100.83774723999996
@test x3[21] ≈ 108.70045145781441
@test x2[12] ≈ 93.05432951806618
end
```

Expand All @@ -890,8 +900,8 @@ plot(plt_unemp, plt_emp, layout = (2, 1), size = (800, 600))
tags: [remove-cell]
---
@testset begin
#test x_path[1,3] ≈ 0.09471014989625384
#test x_path[2,7] ≈ 0.8936171021324064
@test x_path[1,3] ≈ 0.09471014989625384
@test x_path[2,7] ≈ 0.8936171021324064
end
```

Expand All @@ -918,7 +928,7 @@ x0 = lm.x_bar
tags: [remove-cell]
---
@testset begin
#test x0[1] ≈ 0.08266626766923285
@test x0[1] ≈ 0.08266626766923285
end
```

Expand Down Expand Up @@ -978,9 +988,9 @@ plot(plt_unemp, plt_emp, plt_labor, layout = (3, 1), size = (800, 600))
tags: [remove-cell]
---
@testset begin
#test x1[1] ≈ 8.266626766923284
#test x2[2] ≈ 92.11681873319097
#test x3[3] ≈ 98.95872483999996
@test x1[1] ≈ 8.266626766923284
@test x2[2] ≈ 92.11681873319097
@test x3[3] ≈ 98.95872483999996
end
```

Expand All @@ -1004,8 +1014,8 @@ plot(plt_unemp, plt_emp, layout = (2, 1), size = (800, 600))
tags: [remove-cell]
---
@testset begin
#test x_path[1,3] ≈ 0.06791408368459205
#test x_path[2,7] ≈ 0.9429334437639298
@test x_path[1,3] ≈ 0.06791408368459205
@test x_path[2,7] ≈ 0.9429334437639298
end
```

0 comments on commit 0df31a0

Please sign in to comment.