thorek1 · matyasfarkas · Apr 28, 2023 · Apr 30, 2023 · Apr 30, 2023 · May 1, 2023
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
@@ -13,8 +13,8 @@ jobs:
       fail-fast: false
       matrix:
         version:
-          - '1'
-          - '^1.9.0-0' #^1-0 and ^1.9-0 are not recognised
+          - '1.8'
+          - '1.9' #^1-0 and ^1.9-0 are not recognised
           # - 'nightly' # fails for zygote
         os:
           - ubuntu-latest
@@ -26,6 +26,10 @@ jobs:
         include:
           - os: ubuntu-latest
             prefix: xvfb-run
+          # - version: 'nightly'
+          #   os: ubuntu-latest
+          #   arch: x64
+          #   allow_failure: true
     steps:
       - uses: actions/checkout@v3
       - uses: julia-actions/setup-julia@latest

diff --git a/.gitignore b/.gitignore
@@ -50,3 +50,4 @@ fevd*.png
 solution*.png
 conditional_fcst*.png
 .CondaPkg/
+estimation__*
diff --git a/Project.toml b/Project.toml
@@ -1,15 +1,19 @@
 name = "MacroModelling"
 uuid = "687ffad2-3618-405e-ac50-e0f7b9c75e44"
 authors = ["Thore Kockerols <[email protected]>"]
-version = "0.1.19"
+version = "0.1.23"
 
 [deps]
+AbstractDifferentiation = "c29ec348-61ec-40c8-8164-b8c60e9d9f3d"
+AdvancedHMC = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
 AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
 BlockTriangularForm = "adeb47b7-70bf-415a-bb24-c358563e873a"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 ComponentArrays = "b0b7db55-cfe3-40fc-9ded-d10e2dbeff66"
 DataStructures = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
+DifferentiableStateSpaceModels = "beacd9db-9e5e-4956-9b09-459a4b2028df"
 DocStringExtensions = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
+DynamicHMC = "bbc10e6e-7c05-544b-b16e-64fede858acb"
 DynarePreprocessor_jll = "23afba7c-24e5-5ee2-bc2c-b42e07f0492a"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -21,6 +25,7 @@ LineSearches = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 LinearMaps = "7a12625a-238d-50fd-b39a-03d52299707e"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
+MuseInference = "43b88160-90c7-4f71-933b-9d65205cd921"
 Optim = "429524aa-4258-5aef-a3af-852621145aeb"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
@@ -38,6 +43,10 @@ Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
+[weakdeps]
+StatsPlots = "f3b207a7-027a-5e70-b257-86293d7955fd"
+Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
+
 [compat]
 AxisKeys = "^0.2"
 BlockTriangularForm = "^0.1"
@@ -60,9 +69,11 @@ Requires = "^1"
 RuntimeGeneratedFunctions = "^0.5"
 SpecialFunctions = "^2"
 SpeedMapping = "^0.3"
+StatsPlots = "^0.15"
 Subscripts = "^0.1"
 SymPy = "^1"
 Symbolics = "^5"
+Turing = "^0.21"
 julia = "1.8"
 
 [extras]

diff --git a/docs/src/tutorials/rbc.md b/docs/src/tutorials/rbc.md
@@ -175,7 +175,7 @@ For simulations this is possible by calling [`simulate`](@ref):
 simulate(RBC)
 ```
 
-which returns the simulated data in a 3-dimensional `KeyedArray` of the same structure as for the IRFs.
+which returns the simulated data in levels in a 3-dimensional `KeyedArray` of the same structure as for the IRFs.
 
 ## Conditional forecasts
 
@@ -206,17 +206,19 @@ Note that for the first 4 periods the shock has no predetermined value and is de
 Finally we can get the conditional forecast:
 
 ```@repl tutorial_1
-get_conditional_forecast(RBC, conditions, shocks = shocks)
+get_conditional_forecast(RBC, conditions, shocks = shocks, conditions_in_levels = false)
 ```
 
 The function returns a `KeyedArray` with the values of the endogenous variables and shocks matching the conditions exactly.
 
 We can also plot the conditional forecast. Please note that you need to import the `StatsPlots` packages once before the first plot. In order to plot we can use:
 
 ```@repl tutorial_1
-plot_conditional_forecast(RBC, conditions, shocks = shocks)
+plot_conditional_forecast(RBC, conditions, shocks = shocks, conditions_in_levels = false)
 ```
 
 ![RBC conditional forecast](../assets/conditional_fcst__RBC__conditional_forecast__1.png)
 
+and we need to set `conditions_in_levels = false` since the conditions are defined in deviations.
+
 Note that the stars indicate the values the model is conditioned on.
diff --git a/docs/src/tutorials/sw03.md b/docs/src/tutorials/sw03.md
@@ -308,7 +308,7 @@ For simulations this is possible by calling [`simulate`](@ref):
 simulate(SW03)
 ```
 
-which returns the simulated data in a 3-dimensional `KeyedArray` of the same structure as for the IRFs.
+which returns the simulated data in levels in a 3-dimensional `KeyedArray` of the same structure as for the IRFs.
 
 ## Conditional forecasts
 
@@ -340,19 +340,21 @@ The above shock `Matrix` means that for the first two periods shocks 1, 2, 3, 5,
 Finally we can get the conditional forecast:
 
 ```@repl tutorial_2
-get_conditional_forecast(SW03, conditions, shocks = shocks, variables = [:Y,:pi,:W])
+get_conditional_forecast(SW03, conditions, shocks = shocks, variables = [:Y,:pi,:W], conditions_in_levels = false)
 ```
 
 The function returns a `KeyedArray` with the values of the endogenous variables and shocks matching the conditions exactly.
 
 We can also plot the conditional forecast. Please note that you need to import the `StatsPlots` packages once before the first plot.
 
 ```@repl tutorial_2
-plot_conditional_forecast(SW03,conditions, shocks = shocks, plots_per_page = 6,variables = [:Y,:pi,:W])
+plot_conditional_forecast(SW03,conditions, shocks = shocks, plots_per_page = 6,variables = [:Y,:pi,:W],conditions_in_levels = false)
 ```
 
 ![SW03 conditional forecast 1](../assets/conditional_fcst__SW03__conditional_forecast__1.png)
 
 ![SW03 conditional forecast 2](../assets/conditional_fcst__SW03__conditional_forecast__2.png)
 
+and we need to set `conditions_in_levels = false` since the conditions are defined in deviations.
+
 Note that the stars indicate the values the model is conditioned on.
diff --git a/docs/src/unfinished_docs/todo.md b/docs/src/unfinished_docs/todo.md
@@ -3,8 +3,24 @@
 ## High priority
 
 - [ ] add balanced growth path handling
+- [ ] add JOSS article (see Makie.jl)
+- [ ] write docs for (non-linear) solution algorithms
+- [ ] for cond forecastind and kalman, get rid of observables input and use axis key of data input
+- [ ] for cond forecasting allow less shocks than conditions with a warning. should be svd then
+- [ ] have parser accept rss | (r[ss] - 1) * 400 = rss
+- [ ] when doing calibration with optimiser have better return values when he doesnt find a solution (probably NaN)
+- [ ] sampler returned negative std. investigate and come up with solution ensuring sampler can continue
+- [ ] automatically adjust plots for different legend widhts and heights
+- [ ] include weakdeps: https://pkgdocs.julialang.org/dev/creating-packages/#Weak-dependencies
+- [ ] write to mod file for unicode characters. have them take what you would type: \alpha\bar
+- [ ] have get_std take variables as an input
+- [ ] more informative errors when something goes wrong when writing a model
+- [ ] initial state accept keyed array
+- [ ] bring solution error into an object of the model so we dont have to pass it on as output
+- [ ] check that there is an error if he cant find SS
+- [ ] plot_model_estimates with unconditional forecast at the end
 - [ ] check if you can do analytic derivatives for higher order derivatives
-- [ ] kick out unsused parameters from m.parameters
+- [ ] kick out unused parameters from m.parameters
 - [ ] higher order solution derivs with Zygote
 - [ ] use cache for gradient calc in estimation (see DifferentiableStateSpaceModels)
 - [ ] use krylov instead of linearsolve and speed up sparse matrix calcs in implicit diff of higher order funcs
@@ -29,7 +45,10 @@
 - [ ] figure out combinations for inputs (parameters and variables in different formats for get_irf for example)
 - [ ] Find any SS by optimising over both SS guesses and parameter inputs
 - [ ] weed out SS solver and saved objects
-
+
+- [x] fix ss of pruned solution in plotsolution. seems detached
+- [x] get solution higher order with multidimensional array (states, 1 and 2 partial derivatives variables names as dimensions in 2order case)
+- [x] add pruning
 - [x] add other outputs from estimation (smoothed, filter states and shocks)
 - [x] shorten plot_irf (take inspiration from model estimate)
 - [x] fix solution plot
@@ -96,7 +115,6 @@
 - [ ] rewrite first order with riccati equation MatrixEquations.jl
 - [ ] exploit variable incidence and compression for higher order derivatives
 - [ ] for estimation use CUDA with st order: linear time iteration starting from last 1st order solution and then LinearSolveCUDA solvers for higher orders. this should bring benefits for large models and HANK models
-- [ ] test on highly [nonlinear model](https://www.sciencedirect.com/science/article/pii/S0165188917300970)
 - [ ] pull request in StatsFuns to have norminv... accept type numbers and add translation from matlab: norminv to StatsFuns norminvcdf
 - [ ] more informative errors when declaring equations/ calibration
 - [ ] unit equation errors
@@ -106,6 +124,7 @@
 - [ ] print legend for algorithm in last subplot of plot only
 - [ ] select variables for moments
 
+- [x] test on highly [nonlinear model](https://www.sciencedirect.com/science/article/pii/S0165188917300970) # caldara et al is actually epstein zin wiht stochastic vol
 - [x] conditional forecasting
 - [x] find way to recover from failed SS solution which is written to init guess
 - [x] redo ugly solution for selecting parameters to differentiate for

diff --git a/models/SW03.jl b/models/SW03.jl
@@ -1,105 +1,162 @@
 @model SW03 begin
     -q[0] + beta * ((1 - tau) * q[1] + epsilon_b[1] * (r_k[1] * z[1] - psi^-1 * r_k[ss] * (-1 + exp(psi * (-1 + z[1])))) * (C[1] - h * C[0])^(-sigma_c))
+
     -q_f[0] + beta * ((1 - tau) * q_f[1] + epsilon_b[1] * (r_k_f[1] * z_f[1] - psi^-1 * r_k_f[ss] * (-1 + exp(psi * (-1 + z_f[1])))) * (C_f[1] - h * C_f[0])^(-sigma_c))
+
     -r_k[0] + alpha * epsilon_a[0] * mc[0] * L[0]^(1 - alpha) * (K[-1] * z[0])^(-1 + alpha)
+
     -r_k_f[0] + alpha * epsilon_a[0] * mc_f[0] * L_f[0]^(1 - alpha) * (K_f[-1] * z_f[0])^(-1 + alpha)
+
     -G[0] + T[0]
+
     -G[0] + G_bar * epsilon_G[0]
+
     -G_f[0] + T_f[0]
+
     -G_f[0] + G_bar * epsilon_G[0]
+
     -L[0] + nu_w[0]^-1 * L_s[0]
+
     -L_s_f[0] + L_f[0] * (W_i_f[0] * W_f[0]^-1)^(lambda_w^-1 * (-1 - lambda_w))
+
     L_s_f[0] - L_f[0]
+
     L_s_f[0] + lambda_w^-1 * L_f[0] * W_f[0]^-1 * (-1 - lambda_w) * (-W_disutil_f[0] + W_i_f[0]) * (W_i_f[0] * W_f[0]^-1)^(-1 + lambda_w^-1 * (-1 - lambda_w))
+
     Pi_ws_f[0] - L_s_f[0] * (-W_disutil_f[0] + W_i_f[0])
+
     Pi_ps_f[0] - Y_f[0] * (-mc_f[0] + P_j_f[0]) * P_j_f[0]^(-lambda_p^-1 * (1 + lambda_p))
+
     -Q[0] + epsilon_b[0]^-1 * q[0] * (C[0] - h * C[-1])^(sigma_c)
+
     -Q_f[0] + epsilon_b[0]^-1 * q_f[0] * (C_f[0] - h * C_f[-1])^(sigma_c)
+
     -W[0] + epsilon_a[0] * mc[0] * (1 - alpha) * L[0]^(-alpha) * (K[-1] * z[0])^alpha
+
     -W_f[0] + epsilon_a[0] * mc_f[0] * (1 - alpha) * L_f[0]^(-alpha) * (K_f[-1] * z_f[0])^alpha
+
     -Y_f[0] + Y_s_f[0]
+
     Y_s[0] - nu_p[0] * Y[0]
+
     -Y_s_f[0] + Y_f[0] * P_j_f[0]^(-lambda_p^-1 * (1 + lambda_p))
+
     beta * epsilon_b[1] * (C_f[1] - h * C_f[0])^(-sigma_c) - epsilon_b[0] * R_f[0]^-1 * (C_f[0] - h * C_f[-1])^(-sigma_c)
+
     beta * epsilon_b[1] * pi[1]^-1 * (C[1] - h * C[0])^(-sigma_c) - epsilon_b[0] * R[0]^-1 * (C[0] - h * C[-1])^(-sigma_c)
+
     Y_f[0] * P_j_f[0]^(-lambda_p^-1 * (1 + lambda_p)) - lambda_p^-1 * Y_f[0] * (1 + lambda_p) * (-mc_f[0] + P_j_f[0]) * P_j_f[0]^(-1 - lambda_p^-1 * (1 + lambda_p))
+
     epsilon_b[0] * W_disutil_f[0] * (C_f[0] - h * C_f[-1])^(-sigma_c) - omega * epsilon_b[0] * epsilon_L[0] * L_s_f[0]^sigma_l
+
     -1 + xi_p * (pi[0]^-1 * pi[-1]^gamma_p)^(-lambda_p^-1) + (1 - xi_p) * pi_star[0]^(-lambda_p^-1)
+
     -1 + (1 - xi_w) * (w_star[0] * W[0]^-1)^(-lambda_w^-1) + xi_w * (W[-1] * W[0]^-1)^(-lambda_w^-1) * (pi[0]^-1 * pi[-1]^gamma_w)^(-lambda_w^-1)
+
     -Phi - Y_s[0] + epsilon_a[0] * L[0]^(1 - alpha) * (K[-1] * z[0])^alpha
+
     -Phi - Y_f[0] * P_j_f[0]^(-lambda_p^-1 * (1 + lambda_p)) + epsilon_a[0] * L_f[0]^(1 - alpha) * (K_f[-1] * z_f[0])^alpha
+
     std_eta_b * eta_b[x] - log(epsilon_b[0]) + rho_b * log(epsilon_b[-1])
+
     -std_eta_L * eta_L[x] - log(epsilon_L[0]) + rho_L * log(epsilon_L[-1])
+
     std_eta_I * eta_I[x] - log(epsilon_I[0]) + rho_I * log(epsilon_I[-1])
+
     std_eta_w * eta_w[x] - f_1[0] + f_2[0]
+
     std_eta_a * eta_a[x] - log(epsilon_a[0]) + rho_a * log(epsilon_a[-1])
+
     std_eta_p * eta_p[x] - g_1[0] + g_2[0] * (1 + lambda_p)
+
     std_eta_G * eta_G[x] - log(epsilon_G[0]) + rho_G * log(epsilon_G[-1])
+
     -f_1[0] + beta * xi_w * f_1[1] * (w_star[0]^-1 * w_star[1])^(lambda_w^-1) * (pi[1]^-1 * pi[0]^gamma_w)^(-lambda_w^-1) + epsilon_b[0] * w_star[0] * L[0] * (1 + lambda_w)^-1 * (C[0] - h * C[-1])^(-sigma_c) * (w_star[0] * W[0]^-1)^(-lambda_w^-1 * (1 + lambda_w))
+
     -f_2[0] + beta * xi_w * f_2[1] * (w_star[0]^-1 * w_star[1])^(lambda_w^-1 * (1 + lambda_w) * (1 + sigma_l)) * (pi[1]^-1 * pi[0]^gamma_w)^(-lambda_w^-1 * (1 + lambda_w) * (1 + sigma_l)) + omega * epsilon_b[0] * epsilon_L[0] * (L[0] * (w_star[0] * W[0]^-1)^(-lambda_w^-1 * (1 + lambda_w)))^(1 + sigma_l)
+
     -g_1[0] + beta * xi_p * pi_star[0] * g_1[1] * pi_star[1]^-1 * (pi[1]^-1 * pi[0]^gamma_p)^(-lambda_p^-1) + epsilon_b[0] * pi_star[0] * Y[0] * (C[0] - h * C[-1])^(-sigma_c)
+
     -g_2[0] + beta * xi_p * g_2[1] * (pi[1]^-1 * pi[0]^gamma_p)^(-lambda_p^-1 * (1 + lambda_p)) + epsilon_b[0] * mc[0] * Y[0] * (C[0] - h * C[-1])^(-sigma_c)
+
     -nu_w[0] + (1 - xi_w) * (w_star[0] * W[0]^-1)^(-lambda_w^-1 * (1 + lambda_w)) + xi_w * nu_w[-1] * (W[-1] * pi[0]^-1 * W[0]^-1 * pi[-1]^gamma_w)^(-lambda_w^-1 * (1 + lambda_w))
+
     -nu_p[0] + (1 - xi_p) * pi_star[0]^(-lambda_p^-1 * (1 + lambda_p)) + xi_p * nu_p[-1] * (pi[0]^-1 * pi[-1]^gamma_p)^(-lambda_p^-1 * (1 + lambda_p))
+
     -K[0] + K[-1] * (1 - tau) + I[0] * (1 - 0.5 * varphi * (-1 + I[-1]^-1 * epsilon_I[0] * I[0])^2)
+
     -K_f[0] + K_f[-1] * (1 - tau) + I_f[0] * (1 - 0.5 * varphi * (-1 + I_f[-1]^-1 * epsilon_I[0] * I_f[0])^2)
+
     U[0] - beta * U[1] - epsilon_b[0] * ((1 - sigma_c)^-1 * (C[0] - h * C[-1])^(1 - sigma_c) - omega * epsilon_L[0] * (1 + sigma_l)^-1 * L_s[0]^(1 + sigma_l))
+
     U_f[0] - beta * U_f[1] - epsilon_b[0] * ((1 - sigma_c)^-1 * (C_f[0] - h * C_f[-1])^(1 - sigma_c) - omega * epsilon_L[0] * (1 + sigma_l)^-1 * L_s_f[0]^(1 + sigma_l))
+
     -epsilon_b[0] * (C[0] - h * C[-1])^(-sigma_c) + q[0] * (1 - 0.5 * varphi * (-1 + I[-1]^-1 * epsilon_I[0] * I[0])^2 - varphi * I[-1]^-1 * epsilon_I[0] * I[0] * (-1 + I[-1]^-1 * epsilon_I[0] * I[0])) + beta * varphi * I[0]^-2 * epsilon_I[1] * q[1] * I[1]^2 * (-1 + I[0]^-1 * epsilon_I[1] * I[1])
+
     -epsilon_b[0] * (C_f[0] - h * C_f[-1])^(-sigma_c) + q_f[0] * (1 - 0.5 * varphi * (-1 + I_f[-1]^-1 * epsilon_I[0] * I_f[0])^2 - varphi * I_f[-1]^-1 * epsilon_I[0] * I_f[0] * (-1 + I_f[-1]^-1 * epsilon_I[0] * I_f[0])) + beta * varphi * I_f[0]^-2 * epsilon_I[1] * q_f[1] * I_f[1]^2 * (-1 + I_f[0]^-1 * epsilon_I[1] * I_f[1])
-    std_eta_pi * eta_pi[x] - log(pi_obj[0]) + rho_pi_bar * log(pi_obj[-1]) + log(calibr_pi_obj) * (1 - rho_pi_bar)
+
     -C[0] - I[0] - T[0] + Y[0] - psi^-1 * r_k[ss] * K[-1] * (-1 + exp(psi * (-1 + z[0])))
-    -calibr_pi + std_eta_R * eta_R[x] - log(R[ss]^-1 * R[0]) + r_Delta_pi * (-log(pi[ss]^-1 * pi[-1]) + log(pi[ss]^-1 * pi[0])) + r_Delta_y * (-log(Y[ss]^-1 * Y[-1]) + log(Y[ss]^-1 * Y[0]) + log(Y_f[ss]^-1 * Y_f[-1]) - log(Y_f[ss]^-1 * Y_f[0])) + rho * log(R[ss]^-1 * R[-1]) + (1 - rho) * (log(pi_obj[0]) + r_pi * (-log(pi_obj[0]) + log(pi[ss]^-1 * pi[-1])) + r_Y * (log(Y[ss]^-1 * Y[0]) - log(Y_f[ss]^-1 * Y_f[0])))
+
     -C_f[0] - I_f[0] + Pi_ws_f[0] - T_f[0] + Y_f[0] + L_s_f[0] * W_disutil_f[0] - L_f[0] * W_f[0] - psi^-1 * r_k_f[ss] * K_f[-1] * (-1 + exp(psi * (-1 + z_f[0])))
+
     epsilon_b[0] * (K[-1] * r_k[0] - r_k[ss] * K[-1] * exp(psi * (-1 + z[0]))) * (C[0] - h * C[-1])^(-sigma_c)
+
     epsilon_b[0] * (K_f[-1] * r_k_f[0] - r_k_f[ss] * K_f[-1] * exp(psi * (-1 + z_f[0]))) * (C_f[0] - h * C_f[-1])^(-sigma_c)
+
+
+    # Perceived inflation objective
+    std_eta_pi * eta_pi[x] - log(pi_obj[0]) + rho_pi_bar * log(pi_obj[-1]) + log(calibr_pi_obj) * (1 - rho_pi_bar)
+
+    # Taylor rule
+    -calibr_pi + std_eta_R * eta_R[x] - log(R[ss]^-1 * R[0]) + r_Delta_pi * (-log(pi[ss]^-1 * pi[-1]) + log(pi[ss]^-1 * pi[0])) + r_Delta_y * (-log(Y[ss]^-1 * Y[-1]) + log(Y[ss]^-1 * Y[0]) + log(Y_f[ss]^-1 * Y_f[-1]) - log(Y_f[ss]^-1 * Y_f[0])) + rho * log(R[ss]^-1 * R[-1]) + (1 - rho) * (log(pi_obj[0]) + r_pi * (-log(pi_obj[0]) + log(pi[ss]^-1 * pi[-1])) + r_Y * (log(Y[ss]^-1 * Y[0]) - log(Y_f[ss]^-1 * Y_f[0])))
+
 end
 
 @parameters SW03 begin  
-    lambda_p = .368
-    G_bar = .362
+    lambda_p = 0.368
+    G_bar    = 0.362
     lambda_w = 0.5
-    Phi = .819
+    Phi      = 0.819
 
-    alpha = 0.3
-    beta = 0.99
+    alpha   = 0.3
+    beta    = 0.99
     gamma_w = 0.763
     gamma_p = 0.469
-    h = 0.573
-    omega = 1
-    psi = 0.169
+    h       = 0.573
+    omega   = 1
+    psi     = 0.169
 
-    r_pi = 1.684
-    r_Y = 0.099
-    r_Delta_pi = 0.14
-    r_Delta_y = 0.159
+    r_pi        = 1.684
+    r_Y         = 0.099
+    r_Delta_pi  = 0.14
+    r_Delta_y   = 0.159
 
     sigma_c = 1.353
     sigma_l = 2.4
-    tau = 0.025
-    varphi = 6.771
-    xi_w = 0.737
-    xi_p = 0.908
+    tau     = 0.025
+    varphi  = 6.771
+    xi_w    = 0.737
+    xi_p    = 0.908
 
-    rho = 0.961
-    rho_b = 0.855
-    rho_L = 0.889
-    rho_I = 0.927
-    rho_a = 0.823
-    rho_G = 0.949
-    rho_pi_bar = 0.924
+    rho         = 0.961
+    rho_b       = 0.855
+    rho_L       = 0.889
+    rho_I       = 0.927
+    rho_a       = 0.823
+    rho_G       = 0.949
+    rho_pi_bar  = 0.924
 
     std_scaling_factor = 10
 
-    std_eta_b = 0.336 / std_scaling_factor
-    std_eta_L = 3.52 / std_scaling_factor
-    std_eta_I = 0.085 / std_scaling_factor
-    std_eta_a = 0.598 / std_scaling_factor
-    std_eta_w = 0.6853261 / std_scaling_factor
-    std_eta_p = 0.7896512 / std_scaling_factor
-    std_eta_G = 0.325 / std_scaling_factor
-    std_eta_R = 0.081 / std_scaling_factor
-    std_eta_pi = 0.017 / std_scaling_factor
+    std_eta_b   = 0.336     / std_scaling_factor
+    std_eta_L   = 3.52      / std_scaling_factor
+    std_eta_I   = 0.085     / std_scaling_factor
+    std_eta_a   = 0.598     / std_scaling_factor
+    std_eta_w   = 0.6853261 / std_scaling_factor
+    std_eta_p   = 0.7896512 / std_scaling_factor
+    std_eta_G   = 0.325     / std_scaling_factor
+    std_eta_R   = 0.081     / std_scaling_factor
+    std_eta_pi  = 0.017     / std_scaling_factor
 
     calibr_pi_obj | 1 = pi_obj[ss]
     calibr_pi | pi[ss] = pi_obj[ss]