`steady` (Model)

Compute steady state or balance-growth path of the model

Syntax

[model, success, info] = steady(model, ...)

Input arguments

model [ Model ]

Model for which the steady state values of its variables will be calculated.

Output arguments

model [ Model ]

Model with its newly calculated steady state values assigned.

success [ logical ]

A 1-by-n array of true or false where n is the number of parameter variants in the model; each true indicates a successeful completion (convergence) of steady state calculations.

info [ struct ]

Output info structure with the following fields:

.ExitFlags - a 1-by-n cell array of arrays of solver.ExitFlag objects; the {i}(j) element indicates the exit flag for the i-th parameter variant and j-th block of steady equations.

.Blazer - contains a solver.blazer.Steady object used when calculating the steady state values for each parameter variant.

Options

Warning=true [ true | false ]

Display Iris warning messages produced by this function.

Options for nonlinear models

Blocks=true [ true | false ] - Rearrange steady-state equations in sequential blocks before computing steady state.
Endogenize=[ ] [ @auto | cellstr | char | empty ] - List of parameters that will be endogenized when computing the steady state; the number of endogenized parameters must match the number of transtion variables exogenized in the Exogenize= option; the use of the keyword @auto is explained in Description.
Exogenize= [ @auto | cellstr | char | empty ] - List of transition variables that will be exogenized when computing the steady state; the number of exogenized variables must match the number of parameters exogenized in the 'Exogenize=' option; the use of the keyword @auto is explained in Description.
Fix=[ ] [ cellstr | Except | empty ] - List of variables whose steady state (both level and change) will not be computed and kept fixed to the currently assigned values; alternatively an Except wrapper object can be used to specify that all variables are to be fixed except those listed.
FixGrowth=[ ] [ cellstr | empty ] - Same as Fix= except that this option fixes only the steady-state first difference (variables not declared as log) or the steady-state rates of change (variables declared as log) of each variables listed.

FixLevel=[ ] [ cellstr | empty ] - Same as Fix= except that this option fixes only the steady-state level of each variable listed.

Growth=[] [ true | false | empty ]

If true, both the steady-state levels and steady-state changes (differences or growth rates, depending on the log status of the respective variable) will be computed; if false, only the levels will be computed assuming that either all model variables are stationary, have stochastic trend without deterministic drift, or that the correct steady-state changes are already assigned in the model object.

LogMinus=empty [ cell | char | empty ] - List of log variables whose steady state will be restricted to negative values in this run of sstate(~).
Reuse=false [ true | false ] - Reuse the steady-state values calculated for one parameter variant to initialize the steady-state calculation for the next parameter variant.
Solver="qnsd" [ "qnsd" | "newton" | "fsolve" | "lsqnonlin" | cell ]

Numerical nonlinear solver (optionally also specified including non-default settings) used in steady state calculations; see Description; the default solver, "qnsd", is an Iris quasi-Newton steepest-descent based algorithm.
Unlog=[ ] [ cell | char | empty ] - List of log variables that will be temporarily treated as non-log variables in this run of steady(~), i.e. their steady-state levels will not be restricted to either positive or negative values.

Options for linear models

Solve=false [ true | false ]

Calculate first-order solution before steady state.

Description

Option Growth=

The option Growth= is false by default which is consistent with one of the following situations:

all model variables are either stationary or have stochastic trend but no deterministic trend (no deterministic trend: the simplest example is a plain vanilla random walk with no drift);
the steady-state first differences (for variables not declared as log) and steady-state rates of growth (for variables declared as log) have been assigned (as imaginary parts) in the model object for all variables before running sstate(~)(~).

If some variables have an unknown deterministic trend (drift) in steady state (for instance, a balanced growth path model), sstate(~)(~) needs to be run with Growth=true.

Lower and Upper Bounds

Use options 'LevelWithin=' and 'ChangeWithin=' to impose lower and/or upper bounds on steady-state levels and/or growth rates of selected variables. Create a struct with a 1-by-2 vector [lower, upper] for each variable that is supposed to be bounded when the steady state is being calculated, and pass the struct into the respective option. User -Inf or Inf if only one of the bounds is specified. For instance, the following piece of code

bnd = struct( );
bnd.X = [0, 10];
bnd.Y = [-Inf, 20];
bnd.Z = [5, Inf];

specifies lower bounds for variables X and Z, and upper bounds for variables X and Y. The variables that are not bounded do not need to be included in the struct.

Using @auto in Options Exogenize= and Endogenize=

The keyword @auto refers to !steady-autoswaps definitions and can be used in the options Exogenize= and Exogenize= in the following three possible combinations:

Setting both Exogenize= and Endogenize= to @auto will exogenize all variables from !steady-autoswaps definitions and endogenize all corresponding parameters.
Assigning the option Exogenize= an explicit list of variables while setting Endogenize= to @auto will exogenize only the listed variables while endogenizing the same number of the corresponding parameters from !steady-autoswaps definitions. The listed variables must each be found on the left-hand sides of a !steady-autoswaps definition.
Setting Exogenize= to @auto while assigning the option Endogenize= an explicit list of parameters will exogenize only the variables that occur on the left-hand sides of those !steady-autoswaps definitions that have the listed parameters on their right-hand sides. The listed parameters must each be found on the right-hand side of a !steady-autoswaps definition.

Options Fix=, FixLevel= and FixGrowth=

Options Fix=, FixLevel= and FixGrowth= can be used for fixing the steady state of a subset of variables (their steady-state levels, changes, or both) to values supplied by the user before running sstate(~). The fixed values need to be assigned to the respective variables directly in the model object, and obviously need to be the correct steady-state values. The variables are excluded from the list of unknowns when the steady-state equations are being solved.

The list of variables assigned to the three options can be also defined inversely using a Except wrapper object, constructed by passing the list of variables that are not to be fixed. For instance, in

sstate(m, 'FixGrowth=', Except('x', 'y'))

the steady-state growth of all variables except x and y will be fixed (and needs to be supplied before calling this sstate(~)).

Example

This example illustrates the use of the keyword @auto in exogenizing/endogenizing variabes/parameters. Assume that the underlying model file included the following sections:

!variables
    W, X, Y, Z

!parameters
    alpha, beta, gamma, delta

!steady-autoswaps
    W := alpha;
    Y := beta;
    Z := delta;

Running the following command

m = sstate(m, 'Exogenize=', @auto, 'Endogenize=', @auto)

will calculate the steady state with all three variables from the !steady-autoswaps defintions, W, Y, and Z, exogenized to their currently assigned values while endogenizing the three corresponding parameters, alpha, beta, and delta.