MacroModelling.Beta — MethodBeta(μ, σ, lower_bound, upper_bound; μσ)
+Convenience wrapper for the truncated Beta distribution.
If μσ = true then μ and σ are translated to the parameters of the distribution. Otherwise μ and σ represent the parameters of the distribution.
Arguments
μ[Type:Real]: mean or first parameter of the distribution,σ[Type:Real]: standard deviation or first parameter of the distributionlower_bound[Type:Real]: truncation lower bound of the distributionupper_bound[Type:Real]: truncation upper bound of the distribution
Keyword Arguments
μσ[Type:Bool]: switch whether μ and σ represent the moments of the distribution or their parameters
MacroModelling.Beta — MethodBeta(μ, σ; μσ)
+Convenience wrapper for the Beta distribution.
If μσ = true then μ and σ are translated to the parameters of the distribution. Otherwise μ and σ represent the parameters of the distribution.
Arguments
μ[Type:Real]: mean or first parameter of the distribution,σ[Type:Real]: standard deviation or first parameter of the distribution
Keyword Arguments
μσ[Type:Bool]: switch whether μ and σ represent the moments of the distribution or their parameters
MacroModelling.Gamma — MethodGamma(μ, σ, lower_bound, upper_bound; μσ)
+Convenience wrapper for the truncated Inverse Gamma distribution.
If μσ = true then μ and σ are translated to the parameters of the distribution. Otherwise μ and σ represent the parameters of the distribution.
Arguments
μ[Type:Real]: mean or first parameter of the distribution,σ[Type:Real]: standard deviation or first parameter of the distributionlower_bound[Type:Real]: truncation lower bound of the distributionupper_bound[Type:Real]: truncation upper bound of the distribution
Keyword Arguments
μσ[Type:Bool]: switch whether μ and σ represent the moments of the distribution or their parameters
MacroModelling.Gamma — MethodGamma(μ, σ; μσ)
+Convenience wrapper for the Gamma distribution.
If μσ = true then μ and σ are translated to the parameters of the distribution. Otherwise μ and σ represent the parameters of the distribution.
Arguments
μ[Type:Real]: mean or first parameter of the distribution,σ[Type:Real]: standard deviation or first parameter of the distribution
Keyword Arguments
μσ[Type:Bool]: switch whether μ and σ represent the moments of the distribution or their parameters
MacroModelling.InverseGamma — MethodInverseGamma(μ, σ, lower_bound, upper_bound; μσ)
+Convenience wrapper for the truncated Inverse Gamma distribution.
If μσ = true then μ and σ are translated to the parameters of the distribution. Otherwise μ and σ represent the parameters of the distribution.
Arguments
μ[Type:Real]: mean or first parameter of the distribution,σ[Type:Real]: standard deviation or first parameter of the distributionlower_bound[Type:Real]: truncation lower bound of the distributionupper_bound[Type:Real]: truncation upper bound of the distribution
Keyword Arguments
μσ[Type:Bool]: switch whether μ and σ represent the moments of the distribution or their parameters
MacroModelling.InverseGamma — MethodInverseGamma(μ, σ; μσ)
+Convenience wrapper for the Inverse Gamma distribution.
If μσ = true then μ and σ are translated to the parameters of the distribution. Otherwise μ and σ represent the parameters of the distribution.
Arguments
μ[Type:Real]: mean or first parameter of the distribution,σ[Type:Real]: standard deviation or first parameter of the distribution
Keyword Arguments
μσ[Type:Bool]: switch whether μ and σ represent the moments of the distribution or their parameters
MacroModelling.Normal — MethodNormal(μ, σ, lower_bound, upper_bound)
+Convenience wrapper for the truncated Normal distribution.
Arguments
μ[Type:Real]: mean of the distribution,σ[Type:Real]: standard deviation of the distributionlower_bound[Type:Real]: truncation lower bound of the distributionupper_bound[Type:Real]: truncation upper bound of the distribution
MacroModelling.SS — FunctionSee get_steady_state
MacroModelling.SSS — MethodWrapper for get_steady_state with stochastic = true.
MacroModelling.autocorr — FunctionMacroModelling.corr — FunctionSee get_correlation
MacroModelling.cov — FunctionWrapper for get_moments with covariance = true and non_stochastic_steady_state = false, variance = false, standard_deviation = false.
MacroModelling.export_dynare — FunctionSee write_mod_file
MacroModelling.export_mod_file — FunctionSee write_mod_file
MacroModelling.export_model — FunctionSee write_mod_file
MacroModelling.export_to_dynare — FunctionSee write_mod_file
MacroModelling.fevd — FunctionMacroModelling.get_IRF — FunctionSee get_irf
MacroModelling.get_SS — FunctionSee get_steady_state
MacroModelling.get_SSS — MethodWrapper for get_steady_state with stochastic = true.
MacroModelling.get_autocorr — FunctionMacroModelling.get_autocorrelation — Methodget_autocorrelation(
+ 𝓂;
+ autocorrelation_periods,
+ parameters,
+ algorithm,
+ verbose
+)
+Return the autocorrelations of endogenous variables using the first, pruned second, or pruned third order perturbation solution.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
autocorrelation_periods[Default:1:5]: periods for which to return the autocorrelationparameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.algorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_autocorrelation(RBC)
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ Autocorrelation_orders ∈ 5-element UnitRange{Int64}
+And data, 4×5 Matrix{Float64}:
+ (1) (2) (3) (4) (5)
+ (:c) 0.966974 0.927263 0.887643 0.849409 0.812761
+ (:k) 0.971015 0.931937 0.892277 0.853876 0.817041
+ (:q) 0.32237 0.181562 0.148347 0.136867 0.129944
+ (:z) 0.2 0.04 0.008 0.0016 0.00032MacroModelling.get_calibrated_parameters — Methodget_calibrated_parameters(𝓂; values)
+Returns the parameters (and optionally the values) which are determined by a calibration equation.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
values[Default:false, Type:Bool]: return the values together with the parameter names
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_calibrated_parameters(RBC)
+# output
+1-element Vector{String}:
+ "δ"MacroModelling.get_calibration_equation_parameters — Methodget_calibration_equation_parameters(𝓂)
+Returns the parameters used in calibration equations which are not used in the equations of the model (see capital_to_output in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_calibration_equation_parameters(RBC)
+# output
+1-element Vector{String}:
+ "capital_to_output"MacroModelling.get_calibration_equations — Methodget_calibration_equations(𝓂)
+Return the calibration equations declared in the @parameters block. Calibration equations are additional equations which are part of the non-stochastic steady state problem. The additional equation is matched with a calibated parameter which is part of the equations declared in the @model block and can be retrieved with: get_calibrated_parameters
In case programmatic model writing was used this function returns the parsed equations (see loop over shocks in example).
Note that the ouput assumes the equations are equal to 0. As in, k / (q * 4) - capital_to_output implies k / (q * 4) - capital_to_output = 0 and therefore: k / (q * 4) = capital_to_output.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_calibration_equations(RBC)
+# output
+1-element Vector{String}:
+ "k / (q * 4) - capital_to_output"MacroModelling.get_conditional_forecast — Methodget_conditional_forecast(
+ 𝓂,
+ conditions;
+ shocks,
+ initial_state,
+ periods,
+ parameters,
+ variables,
+ conditions_in_levels,
+ levels,
+ verbose
+)
+Return the conditional forecast given restrictions on endogenous variables and shocks (optional) in a 2-dimensional array. The algorithm finds the combinations of shocks with the smallest magnitude to match the conditions.
Limited to the first order perturbation solution of the model.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.conditions[Type:Union{Matrix{Union{Nothing,Float64}}, SparseMatrixCSC{Float64}, KeyedArray{Union{Nothing,Float64}}, KeyedArray{Float64}}]: conditions for which to find the corresponding shocks. The input can have multiple formats, but for all types of entries the first dimension corresponds to the number of variables and the second dimension to the number of periods. The conditions can be specified using a matrix of typeMatrix{Union{Nothing,Float64}}. In this case the conditions are matrix elements of typeFloat64and all remaining (free) entries arenothing. You can also use aSparseMatrixCSC{Float64}as input. In this case only non-zero elements are taken as conditions. Note that you cannot condition variables to be zero using aSparseMatrixCSC{Float64}as input (use other input formats to do so). Another possibility to input conditions is by using aKeyedArray. You can use aKeyedArray{Union{Nothing,Float64}}where, similar toMatrix{Union{Nothing,Float64}}, all entries of typeFloat64are recognised as conditions and all other entries have to benothing. Furthermore, you can specify in the primary axis a subset of variables (of typeSymbolorString) for which you specify conditions and all other variables are considered free. The same goes for the case when you useKeyedArray{Float64}}as input, whereas in this case the conditions for the specified variables bind for all periods specified in theKeyedArray, because there are nonothingentries permitted with this type.
Keyword Arguments
shocks[Default:nothing, Type:Union{Matrix{Union{Nothing,Float64}}, SparseMatrixCSC{Float64}, KeyedArray{Union{Nothing,Float64}}, KeyedArray{Float64}, Nothing} = nothing]: known values of shocks. This entry allows the user to include certain shock values. By entering restrictions on the shock sin this way the problem to match the conditions on endogenous variables is restricted to the remaining free shocks in the repective period. The input can have multiple formats, but for all types of entries the first dimension corresponds to the number of shocks and the second dimension to the number of periods. The shocks can be specified using a matrix of typeMatrix{Union{Nothing,Float64}}. In this case the shocks are matrix elements of typeFloat64and all remaining (free) entries arenothing. You can also use aSparseMatrixCSC{Float64}as input. In this case only non-zero elements are taken as certain shock values. Note that you cannot condition shocks to be zero using aSparseMatrixCSC{Float64}as input (use other input formats to do so). Another possibility to input known shocks is by using aKeyedArray. You can use aKeyedArray{Union{Nothing,Float64}}where, similar toMatrix{Union{Nothing,Float64}}, all entries of typeFloat64are recognised as known shocks and all other entries have to benothing. Furthermore, you can specify in the primary axis a subset of shocks (of typeSymbolorString) for which you specify values and all other shocks are considered free. The same goes for the case when you useKeyedArray{Float64}}as input, whereas in this case the values for the specified shocks bind for all periods specified in theKeyedArray, because there are nonothingentries permitted with this type.initial_state[Default:[0.0], Type:Vector{Float64}]: provide state (in levels, not deviations) from which to start IRFs. Relevant for normal IRFs. The state includes all variables as well as exogenous variables in leads or lags if present.periods[Default:40, Type:Int]: the total number of periods is the sum of the argument provided here and the maximum of periods of the shocks or conditions argument.parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.conditions_in_levels[Default:true, Type:Bool]: indicator whether the conditions are provided in levels. Iftruethe input to the conditions argument will have the non stochastic steady state substracted.levels[Default:false, Type:Bool]: return levels or absolute deviations from steady state.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+using SparseArrays, AxisKeys
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+# c is conditioned to deviate by 0.01 in period 1 and y is conditioned to deviate by 0.02 in period 3
+conditions = KeyedArray(Matrix{Union{Nothing,Float64}}(undef,2,2),Variables = [:c,:y], Periods = 1:2)
+conditions[1,1] = .01
+conditions[2,2] = .02
+
+# in period 2 second shock (eps_z) is conditioned to take a value of 0.05
+shocks = Matrix{Union{Nothing,Float64}}(undef,2,1)
+shocks[1,1] = .05
+
+get_conditional_forecast(RBC_CME, conditions, shocks = shocks, conditions_in_levels = false)
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables_and_shocks ∈ 9-element Vector{Symbol}
+→ Periods ∈ 42-element UnitRange{Int64}
+And data, 9×42 Matrix{Float64}:
+ (1) (2) … (41) (42)
+ (:A) 0.0313639 0.0134792 0.000221372 0.000199235
+ (:Pi) 0.000780257 0.00020929 -0.000146071 -0.000140137
+ (:R) 0.00117156 0.00031425 -0.000219325 -0.000210417
+ (:c) 0.01 0.00600605 0.00213278 0.00203751
+ (:k) 0.034584 0.0477482 … 0.0397631 0.0380482
+ (:y) 0.0446375 0.02 0.00129544 0.001222
+ (:z_delta) 0.00025 0.000225 3.69522e-6 3.3257e-6
+ (:delta_eps) 0.05 0.0 0.0 0.0
+ (:eps_z) 4.61234 -2.16887 0.0 0.0
+
+# The same can be achieved with the other input formats:
+# conditions = Matrix{Union{Nothing,Float64}}(undef,7,2)
+# conditions[4,1] = .01
+# conditions[6,2] = .02
+
+# using SparseArrays
+# conditions = spzeros(7,2)
+# conditions[4,1] = .01
+# conditions[6,2] = .02
+
+# shocks = KeyedArray(Matrix{Union{Nothing,Float64}}(undef,1,1),Variables = [:delta_eps], Periods = [1])
+# shocks[1,1] = .05
+
+# using SparseArrays
+# shocks = spzeros(2,1)
+# shocks[1,1] = .05MacroModelling.get_conditional_variance_decomposition — Methodget_conditional_variance_decomposition(
+ 𝓂;
+ periods,
+ parameters,
+ verbose
+)
+Return the conditional variance decomposition of endogenous variables with regards to the shocks using the linearised solution.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
periods[Default:[1:20...,Inf], Type:Union{Vector{Int},Vector{Float64},UnitRange{Int64}}]: vector of periods for which to calculate the conditional variance decomposition. If the vector conatinsInf, also the unconditional variance decomposition is calculated (same output asget_variance_decomposition).parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+get_conditional_variance_decomposition(RBC_CME)
+# output
+3-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 7-element Vector{Symbol}
+→ Shocks ∈ 2-element Vector{Symbol}
+◪ Periods ∈ 21-element Vector{Float64}
+And data, 7×2×21 Array{Float64, 3}:
+[showing 3 of 21 slices]
+[:, :, 1] ~ (:, :, 1.0):
+ (:delta_eps) (:eps_z)
+ (:A) 0.0 1.0
+ (:Pi) 0.00158668 0.998413
+ (:R) 0.00158668 0.998413
+ (:c) 0.0277348 0.972265
+ (:k) 0.00869568 0.991304
+ (:y) 0.0 1.0
+ (:z_delta) 1.0 0.0
+
+[:, :, 11] ~ (:, :, 11.0):
+ (:delta_eps) (:eps_z)
+ (:A) 1.29651e-31 1.0
+ (:Pi) 0.0245641 0.975436
+ (:R) 0.0245641 0.975436
+ (:c) 0.0175249 0.982475
+ (:k) 0.00869568 0.991304
+ (:y) 7.63511e-5 0.999924
+ (:z_delta) 1.0 0.0
+
+[:, :, 21] ~ (:, :, Inf):
+ (:delta_eps) (:eps_z)
+ (:A) 2.47454e-30 1.0
+ (:Pi) 0.0156771 0.984323
+ (:R) 0.0156771 0.984323
+ (:c) 0.0134672 0.986533
+ (:k) 0.00869568 0.991304
+ (:y) 0.000313462 0.999687
+ (:z_delta) 1.0 0.0MacroModelling.get_corr — FunctionSee get_correlation
MacroModelling.get_correlation — Methodget_correlation(𝓂; parameters, algorithm, verbose)
+Return the correlations of endogenous variables using the first, pruned second, or pruned third order perturbation solution.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.algorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_correlation(RBC)
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ 𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑠 ∈ 4-element Vector{Symbol}
+And data, 4×4 Matrix{Float64}:
+ (:c) (:k) (:q) (:z)
+ (:c) 1.0 0.999812 0.550168 0.314562
+ (:k) 0.999812 1.0 0.533879 0.296104
+ (:q) 0.550168 0.533879 1.0 0.965726
+ (:z) 0.314562 0.296104 0.965726 1.0MacroModelling.get_cov — FunctionWrapper for get_moments with covariance = true and non_stochastic_steady_state = false, variance = false, standard_deviation = false.
MacroModelling.get_covariance — MethodWrapper for get_moments with covariance = true and non_stochastic_steady_state = false, variance = false, standard_deviation = false.
MacroModelling.get_dynamic_auxilliary_variables — Methodget_dynamic_auxilliary_variables(𝓂)
+Returns the auxilliary variables, without timing subscripts, part of the augmented system of equations describing the model dynamics. Augmented means that, in case of variables with leads or lags larger than 1, or exogenous shocks with leads or lags, the system is augemented by auxilliary variables containing variables or shocks in lead or lag. because the original equations included variables with leads or lags certain expression cannot be negative (e.g. given log(c/q) an auxilliary variable is created for c/q).
See get_dynamic_equations for more details on the auxilliary variables and equations.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_dynamic_auxilliary_variables(RBC)
+# output
+3-element Vector{String}:
+ "kᴸ⁽⁻²⁾"
+ "kᴸ⁽⁻³⁾"
+ "kᴸ⁽⁻¹⁾"MacroModelling.get_dynamic_equations — Methodget_dynamic_equations(𝓂)
+Return the augmented system of equations describing the model dynamics. Augmented means that, in case of variables with leads or lags larger than 1, or exogenous shocks with leads or lags, the system is augemented by auxilliary equations containing variables in lead or lag. The augmented system features only variables which are in the present [0], future [1], or past [-1]. For example, Δk_4q[0] = log(k[0]) - log(k[-3]) contains k[-3]. By introducing 2 auxilliary variables (kᴸ⁽⁻¹⁾ and kᴸ⁽⁻²⁾ with ᴸ being the lead/lag operator) and augmenting the system (kᴸ⁽⁻²⁾[0] = kᴸ⁽⁻¹⁾[-1] and kᴸ⁽⁻¹⁾[0] = k[-1]) we can ensure that the timing is smaller than 1 in absolute terms: Δk_4q[0] - (log(k[0]) - log(kᴸ⁽⁻²⁾[-1])).
In case programmatic model writing was used this function returns the parsed equations (see loop over shocks in example).
Note that the ouput assumes the equations are equal to 0. As in, kᴸ⁽⁻¹⁾[0] - k[-1] implies kᴸ⁽⁻¹⁾[0] - k[-1] = 0 and therefore: kᴸ⁽⁻¹⁾[0] = k[-1].
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_dynamic_equations(RBC)
+# output
+12-element Vector{String}:
+ "1 / c[0] - (β / c[1]) * (α * ex" ⋯ 25 bytes ⋯ " - 1) + (1 - exp(z{δ}[1]) * δ))"
+ "(c[0] + k[0]) - ((1 - exp(z{δ}[0]) * δ) * k[-1] + q[0])"
+ "q[0] - exp(z{TFP}[0]) * k[-1] ^ α"
+ "eps_news{TFP}[0] - eps_news{TFP}[x]"
+ "z{TFP}[0] - (ρ{TFP} * z{TFP}[-1] + σ{TFP} * (eps{TFP}[x] + eps_news{TFP}[-1]))"
+ "eps_news{δ}[0] - eps_news{δ}[x]"
+ "z{δ}[0] - (ρ{δ} * z{δ}[-1] + σ{δ} * (eps{δ}[x] + eps_news{δ}[-1]))"
+ "Δc_share[0] - (log(c[0] / q[0]) - log(c[-1] / q[-1]))"
+ "kᴸ⁽⁻³⁾[0] - kᴸ⁽⁻²⁾[-1]"
+ "kᴸ⁽⁻²⁾[0] - kᴸ⁽⁻¹⁾[-1]"
+ "kᴸ⁽⁻¹⁾[0] - k[-1]"
+ "Δk_4q[0] - (log(k[0]) - log(kᴸ⁽⁻³⁾[-1]))"MacroModelling.get_equations — Methodget_equations(𝓂)
+Return the equations of the model. In case programmatic model writing was used this function returns the parsed equations (see loop over shocks in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_equations(RBC)
+# output
+7-element Vector{String}:
+ "1 / c[0] = (β / c[1]) * (α * ex" ⋯ 25 bytes ⋯ " - 1) + (1 - exp(z{δ}[1]) * δ))"
+ "c[0] + k[0] = (1 - exp(z{δ}[0]) * δ) * k[-1] + q[0]"
+ "q[0] = exp(z{TFP}[0]) * k[-1] ^ α"
+ "z{TFP}[0] = ρ{TFP} * z{TFP}[-1]" ⋯ 18 bytes ⋯ "TFP}[x] + eps_news{TFP}[x - 1])"
+ "z{δ}[0] = ρ{δ} * z{δ}[-1] + σ{δ} * (eps{δ}[x] + eps_news{δ}[x - 1])"
+ "Δc_share[0] = log(c[0] / q[0]) - log(c[-1] / q[-1])"
+ "Δk_4q[0] = log(k[0]) - log(k[-4])"MacroModelling.get_estimated_shocks — Methodget_estimated_shocks(
+ 𝓂,
+ data;
+ parameters,
+ data_in_levels,
+ smooth,
+ verbose
+)
+Return the estimated shocks based on the Kalman smoother or filter (depending on the smooth keyword argument) using the provided data and first order solution of the model. Data is by default assumed to be in levels unless data_in_levels is set to false.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.data[Type:KeyedArray]: data matrix with variables (StringorSymbol) in rows and time in columns
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.data_in_levels[Default:true, Type:Bool]: indicator whether the data is provided in levels. Iftruethe input to the data argument will have the non stochastic steady state substracted.smooth[Default:true, Type:Bool]: whether to return smoothed (true) or filtered (false) shocks.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+simulation = simulate(RBC);
+
+get_estimated_shocks(RBC,simulation([:c],:,:simulate))
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Shocks ∈ 1-element Vector{Symbol}
+→ Periods ∈ 40-element UnitRange{Int64}
+And data, 1×40 Matrix{Float64}:
+ (1) (2) (3) (4) … (37) (38) (39) (40)
+ (:eps_z₍ₓ₎) 0.0603617 0.614652 -0.519048 0.711454 -0.873774 1.27918 -0.929701 -0.2255MacroModelling.get_estimated_variable_standard_deviations — Methodget_estimated_variable_standard_deviations(
+ 𝓂,
+ data;
+ parameters,
+ data_in_levels,
+ smooth,
+ verbose
+)
+Return the standard deviations of the Kalman smoother or filter (depending on the smooth keyword argument) estimates of the model variables based on the provided data and first order solution of the model. Data is by default assumed to be in levels unless data_in_levels is set to false.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.data[Type:KeyedArray]: data matrix with variables (StringorSymbol) in rows and time in columns
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.data_in_levels[Default:true, Type:Bool]: indicator whether the data is provided in levels. Iftruethe input to the data argument will have the non stochastic steady state substracted.smooth[Default:true, Type:Bool]: whether to return smoothed (true) or filtered (false) shocks.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+simulation = simulate(RBC);
+
+get_estimated_variable_standard_deviations(RBC,simulation([:c],:,:simulate))
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Standard_deviations ∈ 4-element Vector{Symbol}
+→ Periods ∈ 40-element UnitRange{Int64}
+And data, 4×40 Matrix{Float64}:
+ (1) (2) (3) (4) … (38) (39) (40)
+ (:c) 1.23202e-9 1.84069e-10 8.23181e-11 8.23181e-11 8.23181e-11 8.23181e-11 0.0
+ (:k) 0.00509299 0.000382934 2.87922e-5 2.16484e-6 1.6131e-9 9.31323e-10 1.47255e-9
+ (:q) 0.0612887 0.0046082 0.000346483 2.60515e-5 1.31709e-9 1.31709e-9 9.31323e-10
+ (:z) 0.00961766 0.000723136 5.43714e-5 4.0881e-6 3.08006e-10 3.29272e-10 2.32831e-10MacroModelling.get_estimated_variables — Methodget_estimated_variables(
+ 𝓂,
+ data;
+ parameters,
+ data_in_levels,
+ levels,
+ smooth,
+ verbose
+)
+Return the estimated variables based on the Kalman smoother or filter (depending on the smooth keyword argument) using the provided data and first order solution of the model. Data is by default assumed to be in levels unless data_in_levels is set to false.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.data[Type:KeyedArray]: data matrix with variables (StringorSymbol) in rows and time in columns
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.data_in_levels[Default:true, Type:Bool]: indicator whether the data is provided in levels. Iftruethe input to the data argument will have the non stochastic steady state substracted.levels[Default:false, Type:Bool]: return levels or absolute deviations from steady state.smooth[Default:true, Type:Bool]: whether to return smoothed (true) or filtered (false) shocks.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+simulation = simulate(RBC);
+
+get_estimated_variables(RBC,simulation([:c],:,:simulate))
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ Periods ∈ 40-element UnitRange{Int64}
+And data, 4×40 Matrix{Float64}:
+ (1) (2) (3) (4) … (37) (38) (39) (40)
+ (:c) -0.000640535 0.00358475 0.000455785 0.00490466 0.0496719 0.055509 0.0477877 0.0436101
+ (:k) -0.00671639 0.0324867 0.00663736 0.0456383 0.500217 0.548478 0.481045 0.437527
+ (:q) 0.00334817 0.0426535 -0.0247438 0.0440383 -0.0114766 0.113775 -0.00867574 0.00971302
+ (:z) 0.000601617 0.00626684 -0.00393712 0.00632712 -0.00771079 0.0112496 -0.00704709 -0.00366442MacroModelling.get_fevd — FunctionMacroModelling.get_first_order_solution — MethodWrapper for get_solution with algorithm = :first_order.
MacroModelling.get_forecast_error_variance_decomposition — FunctionMacroModelling.get_girf — MethodWrapper for get_irf with shocks = :simulate.
MacroModelling.get_irf — Methodget_irf(
+ 𝓂,
+ parameters;
+ periods,
+ variables,
+ shocks,
+ negative_shock,
+ initial_state,
+ levels,
+ verbose
+)
+Return impulse response functions (IRFs) of the model in a 3-dimensional array. Function to use when differentiating IRFs with repect to parameters.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.parameters[Type:Vector]: Parameter values in alphabetical order (sorted by parameter name).
Keyword Arguments
periods[Default:40, Type:Int]: number of periods for which to calculate the IRFs. In case a matrix of shocks was provided, periods defines how many periods after the series of shocks the simulation continues.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.shocks[Default::all]: shocks for which to calculate the IRFs. Inputs can be a shock name passed on as either aSymbolorString(e.g.:y, or "y"), orTuple,MatrixorVectorofStringorSymbol.:simulatetriggers random draws of all shocks. A series of shocks can be passed on using either aMatrix{Float64}, or aKeyedArray{Float64}as input with shocks (SymbolorString) in rows and periods in columns. The period of the simulation will correspond to the length of the input in the period dimension + the number of periods defined inperiods. If the series of shocks is input as aKeyedArray{Float64}make sure to name the rows with valid shock names of typeSymbol. Any shocks not part of the model will trigger a warning.:nonein combination with aninitial_statecan be used for deterministic simulations.negative_shock[Default:false, Type:Bool]: calculate a negative shock. Relevant for generalised IRFs.initial_state[Default:[0.0], Type:Vector{Float64}]: provide state (in levels, not deviations) from which to start IRFs. Relevant for normal IRFs. The state includes all variables as well as exogenous variables in leads or lags if present.levels[Default:false, Type:Bool]: return levels or absolute deviations from steady state.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_irf(RBC, RBC.parameter_values)
+# output
+4×40×1 Array{Float64, 3}:
+[:, :, 1] =
+ 0.00674687 0.00729773 0.00715114 0.00687615 … 0.00146962 0.00140619
+ 0.0620937 0.0718322 0.0712153 0.0686381 0.0146789 0.0140453
+ 0.0688406 0.0182781 0.00797091 0.0057232 0.00111425 0.00106615
+ 0.01 0.002 0.0004 8.0e-5 2.74878e-29 5.49756e-30MacroModelling.get_irf — Methodget_irf(
+ 𝓂;
+ periods,
+ algorithm,
+ parameters,
+ variables,
+ shocks,
+ negative_shock,
+ generalised_irf,
+ initial_state,
+ levels,
+ verbose
+)
+Return impulse response functions (IRFs) of the model in a 3-dimensional KeyedArray. Values are returned in absolute deviations from the (non) stochastic steady state by default.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
periods[Default:40, Type:Int]: number of periods for which to calculate the IRFs. In case a matrix of shocks was provided, periods defines how many periods after the series of shocks the simulation continues.algorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.shocks[Default::all]: shocks for which to calculate the IRFs. Inputs can be a shock name passed on as either aSymbolorString(e.g.:y, or "y"), orTuple,MatrixorVectorofStringorSymbol.:simulatetriggers random draws of all shocks. A series of shocks can be passed on using either aMatrix{Float64}, or aKeyedArray{Float64}as input with shocks (SymbolorString) in rows and periods in columns. The period of the simulation will correspond to the length of the input in the period dimension + the number of periods defined inperiods. If the series of shocks is input as aKeyedArray{Float64}make sure to name the rows with valid shock names of typeSymbol. Any shocks not part of the model will trigger a warning.:nonein combination with aninitial_statecan be used for deterministic simulations.negative_shock[Default:false, Type:Bool]: calculate a negative shock. Relevant for generalised IRFs.generalised_irf[Default:false, Type:Bool]: calculate generalised IRFs. Relevant for nonlinear solutions. Reference steady state for deviations is the stochastic steady state.initial_state[Default:[0.0], Type:Vector{Float64}]: provide state (in levels, not deviations) from which to start IRFs. Relevant for normal IRFs. The state includes all variables as well as exogenous variables in leads or lags if present.levels[Default:false, Type:Bool]: return levels or absolute deviations from steady state.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_irf(RBC)
+# output
+3-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ Periods ∈ 40-element UnitRange{Int64}
+◪ Shocks ∈ 1-element Vector{Symbol}
+And data, 4×40×1 Array{Float64, 3}:
+[:, :, 1] ~ (:, :, :eps_z):
+ (1) (2) … (39) (40)
+ (:c) 0.00674687 0.00729773 0.00146962 0.00140619
+ (:k) 0.0620937 0.0718322 0.0146789 0.0140453
+ (:q) 0.0688406 0.0182781 0.00111425 0.00106615
+ (:z) 0.01 0.002 2.74878e-29 5.49756e-30MacroModelling.get_irfs — FunctionSee get_irf
MacroModelling.get_jump_variables — Methodget_jump_variables(𝓂)
+Returns the jump variables of the model. Jumper variables occur in the future and not in the past or occur in all three: past, present, and future.
In case programmatic model writing was used this function returns the parsed variables (see z in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_jump_variables(RBC)
+# output
+3-element Vector{String}:
+ "c"
+ "z{TFP}"
+ "z{δ}"MacroModelling.get_mean — MethodWrapper for get_moments with mean = true, and non_stochastic_steady_state = false, variance = false, standard_deviation = false, covariance = false
MacroModelling.get_moments — Methodget_moments(
+ 𝓂;
+ parameters,
+ non_stochastic_steady_state,
+ mean,
+ standard_deviation,
+ variance,
+ covariance,
+ variables,
+ derivatives,
+ parameter_derivatives,
+ algorithm,
+ dependencies_tol,
+ verbose,
+ silent
+)
+Return the first and second moments of endogenous variables using the first, pruned second, or pruned third order perturbation solution. By default returns: non stochastic steady state (SS), and standard deviations, but can optionally return variances, and covariance matrix.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.non_stochastic_steady_state[Default:true, Type:Bool]: switch to return SS of endogenous variablesmean[Default:false, Type:Bool]: switch to return mean of endogenous variables (the mean for the linearised solutoin is the NSSS)standard_deviation[Default:true, Type:Bool]: switch to return standard deviation of endogenous variablesvariance[Default:false, Type:Bool]: switch to return variance of endogenous variablescovariance[Default:false, Type:Bool]: switch to return covariance matrix of endogenous variablesvariables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.derivatives[Default:true, Type:Bool]: calculate derivatives with respect to the parameters.parameter_derivatives[Default: :all]: parameters for which to calculate partial derivatives. Inputs can be a parameter name passed on as either aSymbolorString(e.g.:alpha, or "alpha"), orTuple,MatrixorVectorofStringorSymbol.:allwill include all parameters.algorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.dependencies_tol[Default:1e-12, Type:AbstractFloat]: tolerance for the effect of a variable on the variable of interest when isolating part of the system for calculating covariance related statisticsverbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+moments = get_moments(RBC);
+
+moments[1]
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ Steady_state_and_∂steady_state∂parameter ∈ 6-element Vector{Symbol}
+And data, 4×6 Matrix{Float64}:
+ (:Steady_state) (:std_z) (:ρ) (:δ) (:α) (:β)
+ (:c) 5.93625 0.0 0.0 -116.072 55.786 76.1014
+ (:k) 47.3903 0.0 0.0 -1304.95 555.264 1445.93
+ (:q) 6.88406 0.0 0.0 -94.7805 66.8912 105.02
+ (:z) 0.0 0.0 0.0 0.0 0.0 0.0moments[2]
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ Standard_deviation_and_∂standard_deviation∂parameter ∈ 6-element Vector{Symbol}
+And data, 4×6 Matrix{Float64}:
+ (:Standard_deviation) (:std_z) … (:δ) (:α) (:β)
+ (:c) 0.0266642 2.66642 -0.384359 0.2626 0.144789
+ (:k) 0.264677 26.4677 -5.74194 2.99332 6.30323
+ (:q) 0.0739325 7.39325 -0.974722 0.726551 1.08
+ (:z) 0.0102062 1.02062 0.0 0.0 0.0MacroModelling.get_non_stochastic_steady_state — MethodWrapper for get_steady_state with stochastic = false.
MacroModelling.get_nonnegativity_auxilliary_variables — Methodget_nonnegativity_auxilliary_variables(𝓂)
+Returns the auxilliary variables, without timing subscripts, added to the non-stochastic steady state problem because certain expression cannot be negative (e.g. given log(c/q) an auxilliary variable is created for c/q).
See get_steady_state_equations for more details on the auxilliary variables and equations.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_nonnegativity_auxilliary_variables(RBC)
+# output
+2-element Vector{String}:
+ "➕₁"
+ "➕₂"MacroModelling.get_parameters — Methodget_parameters(𝓂; values)
+Returns the parameters (and optionally the values) which have an impact on the model dynamics but do not depend on other parameters and are not determined by calibration equations.
In case programmatic model writing was used this function returns the parsed parameters (see σ in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
values[Default:false, Type:Bool]: return the values together with the parameter names
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_parameters(RBC)
+# output
+7-element Vector{String}:
+ "σ{TFP}"
+ "σ{δ}"
+ "ρ{TFP}"
+ "ρ{δ}"
+ "capital_to_output"
+ "alpha"
+ "β"MacroModelling.get_parameters_defined_by_parameters — Methodget_parameters_defined_by_parameters(𝓂)
+Returns the parameters which are defined by other parameters which are not necessarily used in the equations of the model (see α in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_parameters_defined_by_parameters(RBC)
+# output
+1-element Vector{String}:
+ "α"MacroModelling.get_parameters_defining_parameters — Methodget_parameters_defining_parameters(𝓂)
+Returns the parameters which define other parameters in the @parameters block which are not necessarily used in the equations of the model (see alpha in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_parameters_defining_parameters(RBC)
+# output
+1-element Vector{String}:
+ "alpha"MacroModelling.get_parameters_in_equations — Methodget_parameters_in_equations(𝓂)
+Returns the parameters contained in the model equations. Note that these parameters might be determined by other parameters or calibration equations defined in the @parameters block.
In case programmatic model writing was used this function returns the parsed parameters (see σ in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_parameters_in_equations(RBC)
+# output
+7-element Vector{String}:
+ "α"
+ "β"
+ "δ"
+ "ρ{TFP}"
+ "ρ{δ}"
+ "σ{TFP}"
+ "σ{δ}"MacroModelling.get_perturbation_solution — MethodSee get_solution
MacroModelling.get_second_order_solution — MethodWrapper for get_solution with algorithm = :second_order.
MacroModelling.get_shock_decomposition — Methodget_shock_decomposition(
+ 𝓂,
+ data;
+ parameters,
+ data_in_levels,
+ smooth,
+ verbose
+)
+Return the shock decomposition in absolute deviations from the non stochastic steady state based on the Kalman smoother or filter (depending on the smooth keyword argument) using the provided data and first order solution of the model. Data is by default assumed to be in levels unless data_in_levels is set to false.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.data[Type:KeyedArray]: data matrix with variables (StringorSymbol) in rows and time in columns
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.data_in_levels[Default:true, Type:Bool]: indicator whether the data is provided in levels. Iftruethe input to the data argument will have the non stochastic steady state substracted.smooth[Default:true, Type:Bool]: whether to return smoothed (true) or filtered (false) shocks.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+simulation = simulate(RBC);
+
+get_shock_decomposition(RBC,simulation([:c],:,:simulate))
+# output
+3-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 4-element Vector{Symbol}
+→ Shocks ∈ 2-element Vector{Symbol}
+◪ Periods ∈ 40-element UnitRange{Int64}
+And data, 4×2×40 Array{Float64, 3}:
+[showing 3 of 40 slices]
+[:, :, 1] ~ (:, :, 1):
+ (:eps_z₍ₓ₎) (:Initial_values)
+ (:c) 0.000407252 -0.00104779
+ (:k) 0.00374808 -0.0104645
+ (:q) 0.00415533 -0.000807161
+ (:z) 0.000603617 -1.99957e-6
+
+[:, :, 21] ~ (:, :, 21):
+ (:eps_z₍ₓ₎) (:Initial_values)
+ (:c) 0.026511 -0.000433619
+ (:k) 0.25684 -0.00433108
+ (:q) 0.115858 -0.000328764
+ (:z) 0.0150266 0.0
+
+[:, :, 40] ~ (:, :, 40):
+ (:eps_z₍ₓ₎) (:Initial_values)
+ (:c) 0.0437976 -0.000187505
+ (:k) 0.4394 -0.00187284
+ (:q) 0.00985518 -0.000142164
+ (:z) -0.00366442 8.67362e-19MacroModelling.get_shocks — Methodget_shocks(𝓂)
+Returns the exogenous shocks.
In case programmatic model writing was used this function returns the parsed variables (see eps in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_shocks(RBC)
+# output
+4-element Vector{String}:
+ "eps_news{TFP}"
+ "eps_news{δ}"
+ "eps{TFP}"
+ "eps{δ}"MacroModelling.get_simulation — MethodWrapper for get_irf with shocks = :simulate. Function returns values in levels by default.
MacroModelling.get_solution — Methodget_solution(𝓂; parameters, algorithm, verbose)
+Return the solution of the model. In the linear case it returns the linearised solution and the non stochastic steady state (SS) of the model. In the nonlinear case (higher order perturbation) the function returns a multidimensional array with the endogenous variables as the second dimension and the state variables and shocks as the other dimensions.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.algorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model. Only linear algorithms allowed.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
The returned KeyedArray shows as columns the endogenous variables inlcuding the auxilliary endogenous and exogenous variables (due to leads and lags > 1). The rows and other dimensions (depending on the chosen perturbation order) include the SS for the linear case only, followed by the states, and exogenous shocks. Subscripts following variable names indicate the timing (e.g. variable₍₋₁₎ indicates the variable being in the past). Superscripts indicate leads or lags (e.g. variableᴸ⁽²⁾ indicates the variable being in lead by two periods). If no super- or subscripts follow the variable name, the variable is in the present.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_solution(RBC)
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Steady_state__States__Shocks ∈ 4-element Vector{Symbol}
+→ Variables ∈ 4-element Vector{Symbol}
+And data, 4×4 adjoint(::Matrix{Float64}) with eltype Float64:
+ (:c) (:k) (:q) (:z)
+ (:Steady_state) 5.93625 47.3903 6.88406 0.0
+ (:k₍₋₁₎) 0.0957964 0.956835 0.0726316 -0.0
+ (:z₍₋₁₎) 0.134937 1.24187 1.37681 0.2
+ (:eps_z₍ₓ₎) 0.00674687 0.0620937 0.0688406 0.01MacroModelling.get_ss — FunctionSee get_steady_state
MacroModelling.get_standard_deviation — MethodWrapper for get_moments with standard_deviation = true and non_stochastic_steady_state = false, variance = false, covariance = false.
MacroModelling.get_state_variables — Methodget_state_variables(𝓂)
+Returns the state variables of the model. State variables occur in the past and not in the future or occur in all three: past, present, and future.
In case programmatic model writing was used this function returns the parsed variables (see z in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_state_variables(RBC)
+# output
+10-element Vector{String}:
+ "c"
+ "eps_news{TFP}"
+ "eps_news{δ}"
+ "k"
+ "kᴸ⁽⁻²⁾"
+ "kᴸ⁽⁻³⁾"
+ "kᴸ⁽⁻¹⁾"
+ "q"
+ "z{TFP}"
+ "z{δ}"MacroModelling.get_statistics — Methodget_statistics(
+ 𝓂,
+ parameter_values;
+ parameters,
+ non_stochastic_steady_state,
+ mean,
+ standard_deviation,
+ variance,
+ covariance,
+ autocorrelation,
+ autocorrelation_periods,
+ algorithm,
+ verbose
+)
+Return the first and second moments of endogenous variables using either the linearised solution or the pruned second or third order perturbation solution. By default returns: non stochastic steady state (SS), and standard deviations, but can also return variances, and covariance matrix. Function to use when differentiating model moments with repect to parameters.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.parameter_values[Type:Vector]: Parameter values.
Keyword Arguments
parameters[Type:Vector{Symbol}]: Corresponding names of parameters values.non_stochastic_steady_state[Default:Symbol[], Type:Vector{Symbol}]: if values are provided the function returns the SS of endogenous variablesmean[Default:Symbol[], Type:Vector{Symbol}]: if values are provided the function returns the mean of endogenous variables (the mean for the linearised solutoin is the NSSS)standard_deviation[Default:Symbol[], Type:Vector{Symbol}]: if values are provided the function returns the standard deviation of the mentioned variablesvariance[Default:Symbol[], Type:Vector{Symbol}]: if values are provided the function returns the variance of the mentioned variablescovariance[Default:Symbol[], Type:Vector{Symbol}]: if values are provided the function returns the covariance of the mentioned variablesautocorrelation[Default:Symbol[], Type:Vector{Symbol}]: if values are provided the function returns the autocorrelation of the mentioned variablesautocorrelation_periods[Default:1:5]: periods for which to return the autocorrelation of the mentioned variablesalgorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_statistics(RBC, RBC.parameter_values, parameters = RBC.parameters, standard_deviation = RBC.var)
+# output
+1-element Vector{Any}:
+ [0.02666420378525503, 0.26467737291221793, 0.07393254045396483, 0.010206207261596574]MacroModelling.get_std — FunctionWrapper for get_moments with standard_deviation = true and non_stochastic_steady_state = false, variance = false, covariance = false.
MacroModelling.get_steady_state — Methodget_steady_state(
+ 𝓂;
+ parameters,
+ derivatives,
+ stochastic,
+ algorithm,
+ parameter_derivatives,
+ verbose,
+ silent
+)
+Return the (non stochastic) steady state and derivatives with respect to model parameters.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.derivatives[Default:true, Type:Bool]: calculate derivatives with respect to the parameters.stochastic[Default:false, Type:Bool]: return stochastic steady state using second order perturbation. No derivatives are calculated.algorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.parameter_derivatives[Default: :all]: parameters for which to calculate partial derivatives. Inputs can be a parameter name passed on as either aSymbolorString(e.g.:alpha, or "alpha"), orTuple,MatrixorVectorofStringorSymbol.:allwill include all parameters.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
The columns show the SS and parameters for which derivatives are taken. The rows show the variables.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+get_steady_state(RBC)
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables_and_calibrated_parameters ∈ 4-element Vector{Symbol}
+→ Steady_state_and_∂steady_state∂parameter ∈ 6-element Vector{Symbol}
+And data, 4×6 Matrix{Float64}:
+ (:Steady_state) (:std_z) (:ρ) (:δ) (:α) (:β)
+ (:c) 5.93625 0.0 0.0 -116.072 55.786 76.1014
+ (:k) 47.3903 0.0 0.0 -1304.95 555.264 1445.93
+ (:q) 6.88406 0.0 0.0 -94.7805 66.8912 105.02
+ (:z) 0.0 0.0 0.0 0.0 0.0 0.0MacroModelling.get_steady_state_equations — Methodget_steady_state_equations(𝓂)
+Return the non-stochastic steady state (NSSS) equations of the model. The difference to the equations as they were written in the @model block is that exogenous shocks are set to 0, time subscripts are eliminated (e.g. c[-1] becomes c), trivial simplifications are carried out (e.g. log(k) - log(k) = 0), and auxilliary variables are added for expressions that cannot become negative.
Auxilliary variables facilitate the solution of the NSSS problem. The package substitutes expressions which cannot become negative with auxilliary variables and adds another equation to the system of equations determining the NSSS. For example, log(c/q) cannot be negative and c/q is substituted by an auxilliary varaible ➕₁ and an additional equation is added: ➕₁ = c / q.
Note that the ouput assumes the equations are equal to 0. As in, -z{δ} * ρ{δ} + z{δ} implies -z{δ} * ρ{δ} + z{δ} = 0 and therefore: z{δ} * ρ{δ} = z{δ}.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_steady_state_equations(RBC)
+# output
+9-element Vector{String}:
+ "(-β * ((k ^ (α - 1) * α * exp(z{TFP}) - δ * exp(z{δ})) + 1)) / c + 1 / c"
+ "((c - k * (-δ * exp(z{δ}) + 1)) + k) - q"
+ "-(k ^ α) * exp(z{TFP}) + q"
+ "-z{TFP} * ρ{TFP} + z{TFP}"
+ "-z{δ} * ρ{δ} + z{δ}"
+ "➕₁ - c / q"
+ "➕₂ - c / q"
+ "(Δc_share - log(➕₁)) + log(➕₂)"
+ "Δk_4q - 0"MacroModelling.get_stochastic_steady_state — MethodWrapper for get_steady_state with stochastic = true.
MacroModelling.get_third_order_solution — MethodWrapper for get_solution with algorithm = :third_order.
MacroModelling.get_var — FunctionWrapper for get_moments with variance = true and non_stochastic_steady_state = false, standard_deviation = false, covariance = false.
MacroModelling.get_var_decomp — FunctionMacroModelling.get_variables — Methodget_variables(𝓂)
+Returns the variables of the model without timing subscripts and not including auxilliary variables.
In case programmatic model writing was used this function returns the parsed variables (see z in example).
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z{TFP}[1]) * k[0]^(α - 1) + (1 - exp(z{δ}[1]) * δ))
+ c[0] + k[0] = (1 - exp(z{δ}[0])δ) * k[-1] + q[0]
+ q[0] = exp(z{TFP}[0]) * k[-1]^α
+ for shock in [TFP, δ]
+ z{shock}[0] = ρ{shock} * z{shock}[-1] + σ{shock} * (eps{shock}[x] + eps_news{shock}[x-1])
+ end
+ Δc_share[0] = log(c[0]/q[0]) - log(c[-1]/q[-1])
+ Δk_4q[0] = log(k[0]) - log(k[-4])
+end
+
+@parameters RBC begin
+ σ = 0.01
+ ρ = 0.2
+ capital_to_output = 1.5
+ k[ss] / (4 * q[ss]) = capital_to_output | δ
+ alpha = .5
+ α = alpha
+ β = 0.95
+end
+
+get_variables(RBC)
+# output
+7-element Vector{String}:
+ "c"
+ "k"
+ "q"
+ "z{TFP}"
+ "z{δ}"
+ "Δc_share"
+ "Δk_4q"MacroModelling.get_variance — MethodWrapper for get_moments with variance = true and non_stochastic_steady_state = false, standard_deviation = false, covariance = false.
MacroModelling.get_variance_decomposition — Methodget_variance_decomposition(𝓂; parameters, verbose)
+Return the variance decomposition of endogenous variables with regards to the shocks using the linearised solution.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+get_variance_decomposition(RBC_CME)
+# output
+2-dimensional KeyedArray(NamedDimsArray(...)) with keys:
+↓ Variables ∈ 7-element Vector{Symbol}
+→ Shocks ∈ 2-element Vector{Symbol}
+And data, 7×2 Matrix{Float64}:
+ (:delta_eps) (:eps_z)
+ (:A) 1.69478e-29 1.0
+ (:Pi) 0.0156771 0.984323
+ (:R) 0.0156771 0.984323
+ (:c) 0.0134672 0.986533
+ (:k) 0.00869568 0.991304
+ (:y) 0.000313462 0.999687
+ (:z_delta) 1.0 0.0MacroModelling.gr_backend — Functiongr_backend()Renaming and reexport of Plot.jl function gr() to define GR.jl as backend
MacroModelling.import_dynare — FunctionMacroModelling.import_model — FunctionMacroModelling.plot_IRF — FunctionSee plot_irf
MacroModelling.plot_conditional_forecast — Methodplot_conditional_forecast(
+ 𝓂,
+ conditions;
+ shocks,
+ initial_state,
+ periods,
+ parameters,
+ variables,
+ conditions_in_levels,
+ levels,
+ show_plots,
+ save_plots,
+ save_plots_format,
+ save_plots_path,
+ plots_per_page,
+ verbose
+)
+Plot conditional forecast given restrictions on endogenous variables and shocks (optional) of the model. The algorithm finds the combinations of shocks with the smallest magnitude to match the conditions and plots both the endogenous variables and shocks.
The left axis shows the level, and the right axis the deviation from the non stochastic steady state. Variable names are above the subplots, conditioned values are marked, and the title provides information about the model, and number of pages.
Limited to the first order perturbation solution of the model.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.conditions[Type:Union{Matrix{Union{Nothing,Float64}}, SparseMatrixCSC{Float64}, KeyedArray{Union{Nothing,Float64}}, KeyedArray{Float64}}]: conditions for which to find the corresponding shocks. The input can have multiple formats, but for all types of entries the first dimension corresponds to the number of variables and the second dimension to the number of periods. The conditions can be specified using a matrix of typeMatrix{Union{Nothing,Float64}}. In this case the conditions are matrix elements of typeFloat64and all remaining (free) entries arenothing. You can also use aSparseMatrixCSC{Float64}as input. In this case only non-zero elements are taken as conditions. Note that you cannot condition variables to be zero using aSparseMatrixCSC{Float64}as input (use other input formats to do so). Another possibility to input conditions is by using aKeyedArray. You can use aKeyedArray{Union{Nothing,Float64}}where, similar toMatrix{Union{Nothing,Float64}}, all entries of typeFloat64are recognised as conditions and all other entries have to benothing. Furthermore, you can specify in the primary axis a subset of variables (of typeSymbolorString) for which you specify conditions and all other variables are considered free. The same goes for the case when you useKeyedArray{Float64}}as input, whereas in this case the conditions for the specified variables bind for all periods specified in theKeyedArray, because there are nonothingentries permitted with this type.
Keyword Arguments
shocks[Default:nothing, Type:Union{Matrix{Union{Nothing,Float64}}, SparseMatrixCSC{Float64}, KeyedArray{Union{Nothing,Float64}}, KeyedArray{Float64}, Nothing} = nothing]: known values of shocks. This entry allows the user to include certain shock values. By entering restrictions on the shock sin this way the problem to match the conditions on endogenous variables is restricted to the remaining free shocks in the repective period. The input can have multiple formats, but for all types of entries the first dimension corresponds to the number of shocks and the second dimension to the number of periods. The shocks can be specified using a matrix of typeMatrix{Union{Nothing,Float64}}. In this case the shocks are matrix elements of typeFloat64and all remaining (free) entries arenothing. You can also use aSparseMatrixCSC{Float64}as input. In this case only non-zero elements are taken as certain shock values. Note that you cannot condition shocks to be zero using aSparseMatrixCSC{Float64}as input (use other input formats to do so). Another possibility to input known shocks is by using aKeyedArray. You can use aKeyedArray{Union{Nothing,Float64}}where, similar toMatrix{Union{Nothing,Float64}}, all entries of typeFloat64are recognised as known shocks and all other entries have to benothing. Furthermore, you can specify in the primary axis a subset of shocks (of typeSymbolorString) for which you specify values and all other shocks are considered free. The same goes for the case when you useKeyedArray{Float64}}as input, whereas in this case the values for the specified shocks bind for all periods specified in theKeyedArray, because there are nonothingentries permitted with this type.initial_state[Default:[0.0], Type:Vector{Float64}]: provide state (in levels, not deviations) from which to start IRFs. Relevant for normal IRFs. The state includes all variables as well as exogenous variables in leads or lags if present.periods[Default:40, Type:Int]: the total number of periods is the sum of the argument provided here and the maximum of periods of the shocks or conditions argument.parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.
conditions_in_levels [Default: true, Type: Bool]: indicator whether the conditions are provided in levels. If true the input to the conditions argument will have the non stochastic steady state substracted.
levels[Default:false, Type:Bool]: return levels or absolute deviations from steady state.show_plots[Default:true, Type:Bool]: show plots. Separate plots per shocks and varibles depending on number of variables andplots_per_page.save_plots[Default:false, Type:Bool]: switch to save plots using path and extension fromsave_plots_pathandsave_plots_format. Separate files per shocks and variables depending on number of variables andplots_per_pagesave_plots_format[Default::pdf, Type:Symbol]: output format of saved plots. See input formats compatible with GR for valid formats.save_plots_path[Default:pwd(), Type:String]: path where to save plotsplots_per_page[Default:9, Type:Int]: how many plots to show per pageverbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling, StatsPlots
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+# c is conditioned to deviate by 0.01 in period 1 and y is conditioned to deviate by 0.02 in period 3
+conditions = KeyedArray(Matrix{Union{Nothing,Float64}}(undef,2,2),Variables = [:c,:y], Periods = 1:2)
+conditions[1,1] = .01
+conditions[2,2] = .02
+
+# in period 2 second shock (eps_z) is conditioned to take a value of 0.05
+shocks = Matrix{Union{Nothing,Float64}}(undef,2,1)
+shocks[1,1] = .05
+
+plot_conditional_forecast(RBC_CME, conditions, shocks = shocks, conditions_in_levels = false)
+
+# The same can be achieved with the other input formats:
+# conditions = Matrix{Union{Nothing,Float64}}(undef,7,2)
+# conditions[4,1] = .01
+# conditions[6,2] = .02
+
+# using SparseArrays
+# conditions = spzeros(7,2)
+# conditions[4,1] = .01
+# conditions[6,2] = .02
+
+# shocks = KeyedArray(Matrix{Union{Nothing,Float64}}(undef,1,1),Variables = [:delta_eps], Periods = [1])
+# shocks[1,1] = .05
+
+# using SparseArrays
+# shocks = spzeros(2,1)
+# shocks[1,1] = .05MacroModelling.plot_conditional_variance_decomposition — Methodplot_conditional_variance_decomposition(
+ 𝓂;
+ periods,
+ variables,
+ parameters,
+ show_plots,
+ save_plots,
+ save_plots_format,
+ save_plots_path,
+ plots_per_page,
+ verbose
+)
+Plot conditional variance decomposition of the model.
The vertical axis shows the share of the shocks variance contribution, and horizontal axis the period of the variance decomposition. The stacked bars represent each shocks variance contribution at a specific time horizon.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
periods[Default:40, Type:Int]: number of periods for which to calculate the IRFs. In case a matrix of shocks was provided, periods defines how many periods after the series of shocks the simulation continues.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.show_plots[Default:true, Type:Bool]: show plots. Separate plots per shocks and varibles depending on number of variables andplots_per_page.save_plots[Default:false, Type:Bool]: switch to save plots using path and extension fromsave_plots_pathandsave_plots_format. Separate files per shocks and variables depending on number of variables andplots_per_pagesave_plots_format[Default::pdf, Type:Symbol]: output format of saved plots. See input formats compatible with GR for valid formats.save_plots_path[Default:pwd(), Type:String]: path where to save plotsplots_per_page[Default:9, Type:Int]: how many plots to show per pageverbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling, StatsPlots
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+plot_conditional_variance_decomposition(RBC_CME)MacroModelling.plot_fevd — FunctionMacroModelling.plot_forecast_error_variance_decomposition — FunctionMacroModelling.plot_girf — MethodWrapper for plot_irf with generalised_irf = true.
MacroModelling.plot_irf — Methodplot_irf(
+ 𝓂;
+ periods,
+ shocks,
+ variables,
+ parameters,
+ show_plots,
+ save_plots,
+ save_plots_format,
+ save_plots_path,
+ plots_per_page,
+ algorithm,
+ negative_shock,
+ generalised_irf,
+ initial_state,
+ verbose
+)
+Plot impulse response functions (IRFs) of the model.
The left axis shows the level, and the right the deviation from the reference steady state. Linear solutions have the non stochastic steady state as reference other solution the stochastic steady state. The horizontal black line indicates the reference steady state. Variable names are above the subplots and the title provides information about the model, shocks and number of pages per shock.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
Keyword Arguments
periods[Default:40, Type:Int]: number of periods for which to calculate the IRFs. In case a matrix of shocks was provided, periods defines how many periods after the series of shocks the simulation continues.shocks[Default::all]: shocks for which to calculate the IRFs. Inputs can be a shock name passed on as either aSymbolorString(e.g.:y, or "y"), orTuple,MatrixorVectorofStringorSymbol.:simulatetriggers random draws of all shocks. A series of shocks can be passed on using either aMatrix{Float64}, or aKeyedArray{Float64}as input with shocks (SymbolorString) in rows and periods in columns. The period of the simulation will correspond to the length of the input in the period dimension + the number of periods defined inperiods. If the series of shocks is input as aKeyedArray{Float64}make sure to name the rows with valid shock names of typeSymbol. Any shocks not part of the model will trigger a warning.:nonein combination with aninitial_statecan be used for deterministic simulations.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.show_plots[Default:true, Type:Bool]: show plots. Separate plots per shocks and varibles depending on number of variables andplots_per_page.save_plots[Default:false, Type:Bool]: switch to save plots using path and extension fromsave_plots_pathandsave_plots_format. Separate files per shocks and variables depending on number of variables andplots_per_pagesave_plots_format[Default::pdf, Type:Symbol]: output format of saved plots. See input formats compatible with GR for valid formats.save_plots_path[Default:pwd(), Type:String]: path where to save plotsplots_per_page[Default:9, Type:Int]: how many plots to show per pagealgorithm[Default::first_order, Type:Symbol]: algorithm to solve for the dynamics of the model.negative_shock[Default:false, Type:Bool]: calculate a negative shock. Relevant for generalised IRFs.generalised_irf[Default:false, Type:Bool]: calculate generalised IRFs. Relevant for nonlinear solutions. Reference steady state for deviations is the stochastic steady state.initial_state[Default:[0.0], Type:Vector{Float64}]: provide state (in levels, not deviations) from which to start IRFs. Relevant for normal IRFs. The state includes all variables as well as exogenous variables in leads or lags if present.verbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling, StatsPlots
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end;
+
+@parameters RBC begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+end;
+
+plot_irf(RBC)MacroModelling.plot_irfs — FunctionSee plot_irf
MacroModelling.plot_model_estimates — Methodplot_model_estimates(
+ 𝓂,
+ data;
+ parameters,
+ variables,
+ shocks,
+ data_in_levels,
+ shock_decomposition,
+ smooth,
+ show_plots,
+ save_plots,
+ save_plots_format,
+ save_plots_path,
+ plots_per_page,
+ transparency,
+ verbose
+)
+Plot model estimates of the variables given the data. The default plot shows the estimated variables, shocks, and the data to estimate the former. The left axis shows the level, and the right the deviation from the reference steady state. The horizontal black line indicates the non stochastic steady state. Variable names are above the subplots and the title provides information about the model, shocks and number of pages per shock.
In case shock_decomposition = true, then the plot shows the variables, shocks, and data in absolute deviations from the non stochastic steady state plus the contribution of the shocks as a stacked bar chart per period.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.data[Type:KeyedArray]: data matrix with variables (StringorSymbol) in rows and time in columns
Keyword Arguments
parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.shocks[Default::all]: shocks for which to plot the estimates. Inputs can be either aSymbol(e.g.:y, or:all),Tuple{Symbol, Vararg{Symbol}},Matrix{Symbol}, orVector{Symbol}.data_in_levels[Default:true, Type:Bool]: indicator whether the data is provided in levels. Iftruethe input to the data argument will have the non stochastic steady state substracted.shock_decomposition[Default:false, Type:Bool]: whether to show the contribution of the shocks to the deviations from NSSS for each variable. Iffalse, the plot shows the values of the selected variables, data, and shockssmooth[Default:true, Type:Bool]: whether to return smoothed (true) or filtered (false) values for the variables, shocks, and decomposition.show_plots[Default:true, Type:Bool]: show plots. Separate plots per shocks and varibles depending on number of variables andplots_per_page.save_plots[Default:false, Type:Bool]: switch to save plots using path and extension fromsave_plots_pathandsave_plots_format. Separate files per shocks and variables depending on number of variables andplots_per_pagesave_plots_format[Default::pdf, Type:Symbol]: output format of saved plots. See input formats compatible with GR for valid formats.save_plots_path[Default:pwd(), Type:String]: path where to save plotsplots_per_page[Default:9, Type:Int]: how many plots to show per pagetransparency[Default:0.6, Type:Float64]: transparency of barsverbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling, StatsPlots
+
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+simulation = simulate(RBC_CME)
+
+plot_model_estimates(RBC_CME, simulation([:k],:,:simulate))MacroModelling.plot_shock_decomposition — MethodWrapper for plot_model_estimates with shock_decomposition = true.
MacroModelling.plot_simulations — MethodWrapper for plot_irf with shocks = :simulate and periods = 100.
MacroModelling.plot_solution — Methodplot_solution(
+ 𝓂,
+ state;
+ variables,
+ algorithm,
+ σ,
+ parameters,
+ show_plots,
+ save_plots,
+ save_plots_format,
+ save_plots_path,
+ plots_per_page,
+ verbose
+)
+Plot the solution of the model (mapping of past states to present variables) around the (non) stochastic steady state (depending on chosen solution algorithm). Each plot shows the relationship between the chosen state (defined in state) and one of the chosen variables (defined in variables).
The (non) stochastic steady state is plotted along with the mapping from the chosen past state to one present variable per plot. All other (non-chosen) states remain in the (non) stochastic steady state.
In the case of pruned solutions there as many (latent) state vectors as the perturbation order. The first and third order baseline state vectors are the non stochastic steady state and the second order baseline state vector is the stochastic steady state. Deviations for the chosen state are only added to the first order baseline state. The plot shows the mapping from σ standard deviations (first order) added to the first order non stochastic steady state and the present variables. Note that there is no unique mapping from the "pruned" states and the "actual" reported state. Hence, the plots shown are just one realisation of inifite possible mappings.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.state[Type:Symbol]: state variable to be shown on x-axis.
Keyword Arguments
variables[Default::all]: variables for which to show the results. Inputs can be a variable name passed on as either aSymbolorString(e.g.:yor "y"), orTuple,MatrixorVectorofStringorSymbol. Any variables not part of the model will trigger a warning.:allwill contain all variables but not the auxilliary ones.:all_including_auxilliaryalso includes the auxilliary variables in the output.algorithm[Default::first_order, Type: Union{Symbol,Vector{Symbol}}]: solution algorithm for which to show the IRFs. Can be more than one, e.g.:[:second_order,:pruned_third_order]"σ[Default:2, Type:Union{Int64,Float64}]: defines the range of the state variable around the (non) stochastic steady state in standard deviations. E.g. a value of 2 means that the state variable is plotted for values of the (non) stochastic steady state in standard deviations +/- 2 standard deviations.parameters[Default:nothing]: If nothing is provided, the solution is calculated for the parameters defined previously. Acceptable inputs are a vector of parameter values, a vector or tuple of pairs of the parameterSymbolorStringand value. If the new parameter values differ from the previously defined the solution will be recalculated.show_plots[Default:true, Type:Bool]: show plots. Separate plots per shocks and varibles depending on number of variables andplots_per_page.save_plots[Default:false, Type:Bool]: switch to save plots using path and extension fromsave_plots_pathandsave_plots_format. Separate files per shocks and variables depending on number of variables andplots_per_pagesave_plots_format[Default::pdf, Type:Symbol]: output format of saved plots. See input formats compatible with GR for valid formats.save_plots_path[Default:pwd(), Type:String]: path where to save plotsplots_per_page[Default:6, Type:Int]: how many plots to show per pageverbose[Default:false, Type:Bool]: print information about how the NSSS is solved (symbolic or numeric), which solver is used (Levenberg-Marquardt...), and the maximum absolute error.
Examples
using MacroModelling, StatsPlots
+
+@model RBC_CME begin
+ y[0]=A[0]*k[-1]^alpha
+ 1/c[0]=beta*1/c[1]*(alpha*A[1]*k[0]^(alpha-1)+(1-delta))
+ 1/c[0]=beta*1/c[1]*(R[0]/Pi[+1])
+ R[0] * beta =(Pi[0]/Pibar)^phi_pi
+ A[0]*k[-1]^alpha=c[0]+k[0]-(1-delta*z_delta[0])*k[-1]
+ z_delta[0] = 1 - rho_z_delta + rho_z_delta * z_delta[-1] + std_z_delta * delta_eps[x]
+ A[0] = 1 - rhoz + rhoz * A[-1] + std_eps * eps_z[x]
+end
+
+@parameters RBC_CME begin
+ alpha = .157
+ beta = .999
+ delta = .0226
+ Pibar = 1.0008
+ phi_pi = 1.5
+ rhoz = .9
+ std_eps = .0068
+ rho_z_delta = .9
+ std_z_delta = .005
+end
+
+plot_solution(RBC_CME, :k)MacroModelling.plotlyjs_backend — Functionplotlyjs_backend()Renaming and reexport of Plot.jl function plotlyjs() to define PlotlyJS.jl as backend
MacroModelling.simulate — MethodWrapper for get_irf with shocks = :simulate. Function returns values in levels by default.
MacroModelling.ss — MethodSee get_steady_state
MacroModelling.sss — MethodWrapper for get_steady_state with stochastic = true.
MacroModelling.std — FunctionWrapper for get_moments with standard_deviation = true and non_stochastic_steady_state = false, variance = false, covariance = false.
MacroModelling.steady_state — FunctionSee get_steady_state
MacroModelling.translate_dynare_file — FunctionMacroModelling.translate_mod_file — Methodtranslate_mod_file(path_to_mod_file)
+Reads in a dynare .mod-file, adapts the syntax, tries to capture parameter definitions, and writes a julia file in the same folder containing the model equations and parameters in MacroModelling.jl syntax. This function is not guaranteed to produce working code. It's purpose is to make it easier to port a model from dynare to MacroModelling.jl.
The recommended workflow is to use this function to translate a .mod-file, and then adapt the output so that it runs and corresponds to the input.
Arguments
path_to_mod_file[Type:AbstractString]: path including filename of the .mod-file to be translated
MacroModelling.var — FunctionWrapper for get_moments with variance = true and non_stochastic_steady_state = false, standard_deviation = false, covariance = false.
MacroModelling.write_dynare_file — FunctionSee write_mod_file
MacroModelling.write_mod_file — Methodwrite_mod_file(m)
+Writes a dynare .mod-file in the current working directory. This function is not guaranteed to produce working code. It's purpose is to make it easier to port a model from MacroModelling.jl to dynare.
The recommended workflow is to use this function to write a .mod-file, and then adapt the output so that it runs and corresponds to the input.
Arguments
𝓂: the object created by@modeland@parametersfor which to get the solution.
MacroModelling.write_to_dynare — FunctionSee write_mod_file
MacroModelling.write_to_dynare_file — FunctionSee write_mod_file
MacroModelling.@model — MacroParses the model equations and assigns them to an object.
Arguments
𝓂: name of the object to be created containing the model information.ex: equations
Variables must be defined with their time subscript in squared brackets. Endogenous variables can have the following:
- present:
c[0] - non-stcohastic steady state:
c[ss]instead ofssany of the following is also a valid flag for the non-stochastic steady state:ss,stst,steady,steadystate,steady_state, and the parser is case-insensitive (SSorsTstwill work as well). - past:
c[-1]or any negative Integer: e.g.c[-12] - future:
c[1]or any positive Integer: e.g.c[16]orc[+16]
Signed integers are recognised and parsed as such.
Exogenous variables (shocks) can have the following:
- present:
eps_z[x]instead ofxany of the following is also a valid flag for exogenous variables:ex,exo,exogenous, and the parser is case-insensitive (ExorexoGenouswill work as well). - past:
eps_z[x-1] - future:
eps_z[x+1]
Parameters enter the equations without squared brackets.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+endProgrammatic model writing
Parameters and variables can be indexed using curly braces: e.g. c{H}[0], eps_z{F}[x], or α{H}.
for loops can be used to write models programmatically. They can either be used to generate expressions where you iterate over the time index or the index in curly braces:
- generate equation with different indices in curly braces:
for co in [H,F] C{co}[0] + X{co}[0] + Z{co}[0] - Z{co}[-1] end = for co in [H,F] Y{co}[0] end - generate multiple equations with different indices in curly braces:
for co in [H, F] K{co}[0] = (1-delta{co}) * K{co}[-1] + S{co}[0] end - generate equation with different time indices:
Y_annual[0] = for lag in -3:0 Y[lag] endorR_annual[0] = for operator = :*, lag in -3:0 R[lag] end
MacroModelling.@parameters — MacroAdds parameter values and calibration equations to the previously defined model.
Arguments
𝓂: name of the object previously created containing the model information.ex: parameter, parameters values, and calibration equations
Parameters can be defined in either of the following ways:
- plain number:
δ = 0.02 - expression containing numbers:
δ = 1/50 - expression containing other parameters:
δ = 2 * std_zin this case it is irrelevant ifstd_zis defined before or after. The definitons including other parameters are treated as a system of equaitons and solved accordingly. - expressions containing a target parameter and an equations with endogenous variables in the non-stochastic steady state, and other parameters, or numbers:
k[ss] / (4 * q[ss]) = 1.5 | δorα | 4 * q[ss] = δ * k[ss]in this case the target parameter will be solved simultaneaously with the non-stochastic steady state using the equation defined with it.
Optional arguments to be placed between 𝓂 and ex
verbose[Default:false, Type:Bool]: print more information about how the non stochastic steady state is solvedsilent[Default:false, Type:Bool]: do not print any informationsymbolic[Default:false, Type:Bool]: try to solve the non stochastic steady state symbolically and fall back to a numerical solution if not possibleperturbation_order[Default:1, Type:Int]: take derivatives only up to the specified order at this stage. In case you want to work with higher order perturbation later on, respective derivatives will be taken at that stage.
Examples
using MacroModelling
+
+@model RBC begin
+ 1 / c[0] = (β / c[1]) * (α * exp(z[1]) * k[0]^(α - 1) + (1 - δ))
+ c[0] + k[0] = (1 - δ) * k[-1] + q[0]
+ q[0] = exp(z[0]) * k[-1]^α
+ z[0] = ρ * z[-1] + std_z * eps_z[x]
+end
+
+@parameters RBC verbose = true begin
+ std_z = 0.01
+ ρ = 0.2
+ δ = 0.02
+ α = 0.5
+ β = 0.95
+endProgrammatic model writing
Variables and parameters indexed with curly braces can be either referenced specifically (e.g. c{H}[ss]) or generally (e.g. alpha). If they are referenced generaly the parse assumes all instances (indices) are meant. For example, in a model where alpha has two indices H and F, the expression alpha = 0.3 is interpreted as two expressions: alpha{H} = 0.3 and alpha{F} = 0.3. The same goes for calibration equations.
