Merge pull request #4 from BASEforHANK/dev_Christian

Dev christian

src/Model/IncomesETC/fcn_incomes.jl

@@ -67,7 +67,7 @@ function incomes!(
     unionprofits,
     av_tax_rate,
 )
-    tax_prog_scale = (m_par.γ + m_par.τ_prog) / ((m_par.γ + τprog))
+    tax_prog_scale = (m_par.γ + m_par.τprog ) / ((m_par.γ + τprog))
     labor_inc = mcw .* w .* N ./ Ht .* (n_par.mesh_y / H) .^ tax_prog_scale
     net_labor_inc = τlev .* labor_inc .^ (1.0 - τprog)
     net_u_profits = unionprofits .* (1.0 .- av_tax_rate) .* n_par.HW

src/Model/IncomesETC/fcn_utils_product_prices_etc.jl

@@ -0,0 +1,136 @@
+##----------------------------------------------------------------------------
+## Basic Functions: Utility, marginal utility and its inverse, 
+##                  Return on capital, Wages, Employment, Output, etc
+##---------------------------------------------------------------------------
+
+## Utility functions and margnal utility
+function util(c::AbstractArray, m_par)
+    if m_par.ξ == 1.0
+        util = log.(c)
+    elseif m_par.ξ == 2.0
+        util = 1.0 - 1.0 ./ c
+    elseif m_par.ξ == 4.0
+        util = (1.0 - 1.0 ./ (c .* c .* c)) ./ 3.0
+    else
+        util = (c .^ (1.0 .- m_par.ξ) .- 1.0) ./ (1.0 .- m_par.ξ)
+    end
+    return util
+end
+
+function mutil(c::AbstractArray, m_par)
+    if m_par.ξ == 1.0
+        mutil = 1.0 ./ c
+    elseif m_par.ξ == 2.0
+        mutil = 1.0 ./ (c .^ 2)
+    elseif m_par.ξ == 4.0
+        mutil = 1.0 ./ ((c .^ 2) .^ 2)
+    else
+        mutil = c .^ (-m_par.ξ)
+    end
+    return mutil
+end
+
+function mutil!(mu::AbstractArray, c::AbstractArray, m_par)
+    if m_par.ξ == 1.0
+        mu .= 1.0 ./ c
+    elseif m_par.ξ == 2.0
+        mu .= 1.0 ./ (c .^ 2)
+    elseif m_par.ξ == 4.0
+        mu .= 1.0 ./ ((c .^ 2) .^ 2)
+    else
+        mu .= c .^ (-m_par.ξ)
+    end
+    return mu
+end
+
+function invmutil(mu, m_par)
+    if m_par.ξ == 1.0
+        c = 1.0 ./ mu
+    elseif m_par.ξ == 2.0
+        c = 1.0 ./ (sqrt.(mu))
+    elseif m_par.ξ == 4.0
+        c = 1.0 ./ (sqrt.(sqrt.(mu)))
+    else
+        c = 1.0 ./ mu .^ (1.0 ./ m_par.ξ)
+    end
+    return c
+end
+
+function invmutil!(c, mu, m_par)
+    if m_par.ξ == 1.0
+        c .= 1.0 ./ mu
+    elseif m_par.ξ == 2.0
+        c .= 1.0 ./ (sqrt.(mu))
+    elseif m_par.ξ == 4.0
+        c .= 1.0 ./ (sqrt.(sqrt.(mu)))
+    else
+        c .= 1.0 ./ mu .^ (1.0 ./ m_par.ξ)
+    end
+    return c
+end
+
+## Production functions and factor incomes
+# Incomes (K:capital, Z: TFP): Interest rate = MPK.-δ, Wage = MPL, profits = Y-wL-(r+\delta)*K
+
+output(z::Vector, m_par) = z[2] .* (z[1] .^ (m_par.α)) .* (z[3] .^ (1 - m_par.α)) #   Z .* K .^ (m_par.α) .* N .^ (1 - m_par.α)
+output(K::Number, Z::Number, N::Number, m_par) = output([K; Z; N], m_par)
+
+# Factor incomes as marginal products
+interest(K::Number, Z::Number, N::Number, m_par) = Z .* m_par.α .* (K ./ N) .^ (m_par.α - 1.0) .- m_par.δ_0
+wage(K::Number, Z::Number, N::Number, m_par) = Z .* (1 - m_par.α) .* (K ./ N) .^ m_par.α 
+
+# Alternatively, using ForwardDiff instead of analytical derivatives. 
+# Yields small differences in the results due to numerical precision differences. 
+# interest(K::Number, Z::Number, N::Number, m_par) = ForwardDiff.gradient(z -> output(z, m_par), [K; Z; N])[1] - m_par.δ_0 # derivative instead of gradient leads to perturbation confusion
+# wage(K::Number, Z::Number, N::Number, m_par) = ForwardDiff.gradient(z -> output(z, m_par), [K; Z; N])[3] # derivative instead of gradient leads to perturbation confusion
+
+## Labor supply given wages (paid to households), resulting from leisure preferences
+labor_supply(w, τlev, τprog, Ht, m_par) = ((1.0 .- τprog ) .* τlev .* w^(1.0 .- τprog)).^
+                                            (1.0 ./ (m_par.γ .+ τprog)) .* Ht
+
+labor_supply(w, m_par) = labor_supply(w, m_par.τlev, m_par.τprog, 1.0, m_par) # steady state version
+
+## Asset markets
+# price of tradable stock in steady state
+qΠSS_fnc(Y::Number, RB, m_par) =
+        m_par.ωΠ .* (1.0 .- 1.0 ./ m_par.μ) .* Y ./ 
+        (RB ./ m_par.π .- 1 .+ m_par.ιΠ) + 1.0
+
+# steady state payout to entrepreneurs
+profitsSS_fnc(Y::Number, RB, m_par) =
+        (1.0 - m_par.ωΠ) .* (1.0 .- 1.0 ./ m_par.μ) .* Y .+
+        m_par.ιΠ .* (qΠSS_fnc(Y, RB, m_par) .- 1.0)
+
+# Valuation of liquid wealth (stock)
+value_liquid(B, qΠ, qΠlag) = 1.0 .+ (qΠ .- qΠlag) ./ B
+
+##--------------------------------------------------------------------------------------
+## Functions only used in the steady state calculations
+##--------------------------------------------------------------------------------------
+# Employment given labor supply = labor demand at a given capital stock and productivity
+# This is used in the steady state calculations.
+employment(K::Number, Z::Number, m_par) =
+    (
+        Z .* (1.0 - m_par.α) .*
+        (m_par.τlev .* (1.0 - m_par.τprog )) .^ (1.0 / (1.0 - m_par.τprog )) .*
+        K .^ (m_par.α)
+    ) .^
+    ((1.0 - m_par.τprog ) ./ (m_par.γ + m_par.τprog  + (m_par.α) .* (1 - m_par.τprog )))
+
+# Capital intensity (K/N) given interest rate and productivity, 
+# used for starting guesses in the steady state calculations
+# Optimal capital intensity under Cobb Douglas
+capital_intensity(r, m_par) = ((r + m_par.δ_0) ./ m_par.α .* m_par.μ)^(1.0 ./ (m_par.α .- 1))
+
+# Capital used in production (in complete markets) at a given interest rate, taking labor supply into account
+CompMarketsCapital(r, m_par) = capital_intensity(r, m_par) .* 
+                               labor_supply(
+                                        wage(
+                                            capital_intensity(r, m_par), 1.0 ./ m_par.μ, 1.0, m_par
+                                            ) ./ m_par.μw # wage markup needs to be taken into account
+                                    , m_par)
+
+
+
+
+

src/Model/Parameters.jl

@@ -44,8 +44,8 @@ julia> priors = collect(metaflatten(m_par, prior))
 
     # Further steady-state parameters
     ψ::T = 0.1 | "psi" | L"\psi" | _ | false # steady-state bond to capital ratio
-    τ_lev::T = 0.8225 | "tau_lev" | L"\tau^L" | _ | false # steady-state income tax rate level
-    τ_prog::T = 0.1022 | "tau_pro" | L"\tau^P" | _ | false # steady-state income tax rate progressivity
+    τlev::T = 0.8225 | "tau_lev" | L"\tau^L" | _ | false # steady-state income tax rate level
+    τprog ::T = 0.1022 | "tau_pro" | L"\tau^P" | _ | false # steady-state income tax rate progressivity
 
     R::T = 1.01 | "R" | L"R" | _ | false # steady state rate of return capital (unused)
     K::T = 40.0 | "K" | L"K" | _ | false # steady state quantity of capital (unused)

src/Model/input_aggregate_model.jl

@@ -30,7 +30,7 @@ MPKSS = exp(XSS[indexes.rSS]) - 1.0 + m_par.δ_0       # stationary equil. margi
 δ_2 = δ_1 .* m_par.δ_s                              # express second utilization coefficient in relative terms
 # Auxiliary variables
 Kserv = K * u                                         # Effective capital
-MPKserv = mc .* Z .* m_par.α .* (Kserv ./ N) .^ (m_par.α - 1.0)      # marginal product of Capital
+MPKserv = interest(Kserv, mc.*Z, N, m_par) .+ m_par.δ_0 # mc .* Z .* m_par.α .* (Kserv ./ N) .^ (m_par.α - 1.0)      # marginal product of Capital
 depr = m_par.δ_0 + δ_1 * (u - 1.0) + δ_2 / 2.0 * (u - 1.0)^2.0   # depreciation
 
 Wagesum = N * w                                         # Total wages in economy t
@@ -41,7 +41,7 @@ YREACTION = Ygrowth                                  # Policy reaction function
 distr_y = sum(distrSS, dims = (1, 2))
 
 # tax progressivity variabels used to calculate e.g. total taxes
-tax_prog_scale = (m_par.γ + m_par.τ_prog) / ((m_par.γ + τprog))                        # scaling of labor disutility including tax progressivity
+tax_prog_scale = (m_par.γ + m_par.τprog ) / ((m_par.γ + τprog))                        # scaling of labor disutility including tax progressivity
 incgross = ((n_par.grid_y ./ n_par.H) .^ tax_prog_scale .* mcw .* w .* N ./ Ht)  # capital liquidation Income (q=1 in steady state)
 incgross[end] = (n_par.grid_y[end] .* profits)                         # gross profit income
 inc = τlev .* (incgross .^ (1.0 .- τprog))                                 # capital liquidation Income (q=1 in steady state)
@@ -52,7 +52,7 @@ IncAux = dot(distr_y, incgross)
 
 Htact = dot(
     distr_y[1:end-1],
-    (n_par.grid_y[1:end-1] / n_par.H) .^ ((m_par.γ + m_par.τ_prog) / (m_par.γ + τprog)),
+    (n_par.grid_y[1:end-1] / n_par.H) .^ ((m_par.γ + m_par.τprog ) / (m_par.γ + τprog)),
 )
 ############################################################################
 #           Error term calculations (i.e. model starts here)          #
@@ -189,13 +189,13 @@ F[indexes.LPXA] = log.(LPXA) - (log((qPrime + rPrime - 1.0) / q) - log(RBPrime /
 F[indexes.I] =
     KPrime .- K .* (1.0 .- depr) .-
     ZI .* I .* (1.0 .- m_par.ϕ ./ 2.0 .* (Igrowth - 1.0) .^ 2.0)           # Capital accumulation equation
-F[indexes.N] =
-    log.(N) -
-    log.(
-        ((1.0 - τprog) * τlev * (mcw .* w) .^ (1.0 - τprog)) .^ (1.0 / (m_par.γ + τprog)) .*
-        Ht
-    )   # labor supply
-F[indexes.Y] = log.(Y) - log.(Z .* N .^ (1.0 .- m_par.α) .* Kserv .^ m_par.α)                                          # production function
+
+F[indexes.N] = log.(N) - log.(labor_supply(w.*mcw, τlev, τprog, Ht, m_par))
+    # log.(
+    #     ((1.0 - τprog) * τlev * (mcw .* w) .^ (1.0 - τprog)) .^ (1.0 / (m_par.γ + τprog)) .*
+    #     Ht
+    # )   # labor supply
+F[indexes.Y] = log.(Y) - log.(output(Kserv, Z, N, m_par))    #log.(Z .* N .^ (1.0 .- m_par.α) .* Kserv .^ m_par.α) # Z .* N .^ (1.0 .- m_par.α) .* Kserv .^ m_par.α                                      # production function
 F[indexes.C] = log.(Y .- G .- I .- BD * m_par.Rbar .+ (A .- 1.0) .* RL .* B ./ π) .- log(C)                            # Resource constraint
 
 # Error Term on prices/aggregate summary vars (logarithmic, controls), here difference to SS value averages

src/Model/input_aggregate_steady_state.jl

@@ -4,8 +4,8 @@ ZSS = 1.0
 ZISS = 1.0
 μSS = m_par.μ
 μwSS = m_par.μw
-τprogSS = m_par.τ_prog
-τlevSS = m_par.τ_lev
+τprogSS = m_par.τprog 
+τlevSS = m_par.τlev
 
 σSS = 1.0
 τprog_obsSS = 1.0

src/Preprocessor/generated_fcns/FSYS_agg_generated.jl

@@ -73,7 +73,7 @@ MPKSS = exp(XSS[indexes.rSS]) - 1.0 + m_par.δ_0       # stationary equil. margi
 δ_2 = δ_1 .* m_par.δ_s                              # express second utilization coefficient in relative terms
 # Auxiliary variables
 Kserv = K * u                                         # Effective capital
-MPKserv = mc .* Z .* m_par.α .* (Kserv ./ N) .^ (m_par.α - 1.0)      # marginal product of Capital
+MPKserv = interest(Kserv, mc.*Z, N, m_par) .+ m_par.δ_0 # mc .* Z .* m_par.α .* (Kserv ./ N) .^ (m_par.α - 1.0)      # marginal product of Capital
 depr = m_par.δ_0 + δ_1 * (u - 1.0) + δ_2 / 2.0 * (u - 1.0)^2.0   # depreciation
 
 Wagesum = N * w                                         # Total wages in economy t
@@ -84,7 +84,7 @@ YREACTION = Ygrowth                                  # Policy reaction function
 distr_y = sum(distrSS, dims = (1, 2))
 
 # tax progressivity variabels used to calculate e.g. total taxes
-tax_prog_scale = (m_par.γ + m_par.τ_prog) / ((m_par.γ + τprog))                        # scaling of labor disutility including tax progressivity
+tax_prog_scale = (m_par.γ + m_par.τprog ) / ((m_par.γ + τprog))                        # scaling of labor disutility including tax progressivity
 incgross = ((n_par.grid_y ./ n_par.H) .^ tax_prog_scale .* mcw .* w .* N ./ Ht)  # capital liquidation Income (q=1 in steady state)
 incgross[end] = (n_par.grid_y[end] .* profits)                         # gross profit income
 inc = τlev .* (incgross .^ (1.0 .- τprog))                                 # capital liquidation Income (q=1 in steady state)
@@ -95,7 +95,7 @@ IncAux = dot(distr_y, incgross)
 
 Htact = dot(
     distr_y[1:end-1],
-    (n_par.grid_y[1:end-1] / n_par.H) .^ ((m_par.γ + m_par.τ_prog) / (m_par.γ + τprog)),
+    (n_par.grid_y[1:end-1] / n_par.H) .^ ((m_par.γ + m_par.τprog ) / (m_par.γ + τprog)),
 )
 ############################################################################
 #           Error term calculations (i.e. model starts here)          #
@@ -232,13 +232,13 @@ F[indexes.LPXA] = log.(LPXA) - (log((qPrime + rPrime - 1.0) / q) - log(RBPrime /
 F[indexes.I] =
     KPrime .- K .* (1.0 .- depr) .-
     ZI .* I .* (1.0 .- m_par.ϕ ./ 2.0 .* (Igrowth - 1.0) .^ 2.0)           # Capital accumulation equation
-F[indexes.N] =
-    log.(N) -
-    log.(
-        ((1.0 - τprog) * τlev * (mcw .* w) .^ (1.0 - τprog)) .^ (1.0 / (m_par.γ + τprog)) .*
-        Ht
-    )   # labor supply
-F[indexes.Y] = log.(Y) - log.(Z .* N .^ (1.0 .- m_par.α) .* Kserv .^ m_par.α)                                          # production function
+
+F[indexes.N] = log.(N) - log.(labor_supply(w.*mcw, τlev, τprog, Ht, m_par))
+    # log.(
+    #     ((1.0 - τprog) * τlev * (mcw .* w) .^ (1.0 - τprog)) .^ (1.0 / (m_par.γ + τprog)) .*
+    #     Ht
+    # )   # labor supply
+F[indexes.Y] = log.(Y) - log.(output(Kserv, Z, N, m_par))    #log.(Z .* N .^ (1.0 .- m_par.α) .* Kserv .^ m_par.α) # Z .* N .^ (1.0 .- m_par.α) .* Kserv .^ m_par.α                                      # production function
 F[indexes.C] = log.(Y .- G .- I .- BD * m_par.Rbar .+ (A .- 1.0) .* RL .* B ./ π) .- log(C)                            # Resource constraint
 
 # Error Term on prices/aggregate summary vars (logarithmic, controls), here difference to SS value averages