Dynare预处理器：宏观经济模型求解利器

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"Dynare Reference Manual" Dynare是一款强大的宏观经济和金融模型分析工具，它作为Matlab的预处理器，能够将模型文件转换为Matlab可读的.m文件，便于进行动态随机一般均衡（DSGE）模型的求解与分析。这款软件在经济学研究领域广泛应用，尤其适合处理复杂的经济模型。在安装和配置方面，Dynare有如下要求和步骤： 1. 软件要求：Dynare依赖于MATLAB或GNU Octave环境运行，因此在安装前需要确保系统中已经安装了这些基础软件。同时，不同操作系统（如Windows、Debian GNU/Linux、Ubuntu或MacOSX）的安装方法也会有所不同。 2. Windows上的安装：用户可以通过下载 Dynare 的安装包，按照向导提示完成安装过程，确保安装路径无误，并将Dynare添加到系统的PATH环境变量中。 3. Debian GNU/Linux和Ubuntu上的安装：通常可以通过包管理器（如apt）来安装，使用命令行输入相应的安装指令，安装完成后需设置环境变量以指向Dynare的安装位置。 4. MacOSX的安装：用户可以利用Homebrew等包管理工具进行安装，或者手动下载源码编译安装。同样需要设置环境变量以便MATLAB或Octave能找到Dynare。 5. 其他系统的安装：对于未列出的操作系统，用户需要从源码编译安装，这通常涉及到下载源代码，配置编译环境，然后编译和安装。 6. 配置 Dynare：无论是MATLAB还是GNU Octave，都需要配置Dynare的路径，使其能正确识别和调用。这通常通过修改启动脚本或者设置环境变量来实现。 7. 运行 Dynare： Dynare 可以通过命令行调用，执行模型文件。在模型文件中，用户可以定义模型方程、设定参数、指定求解方法等。 Dynare 还提供了一些钩子（hooks）功能，允许用户在模型处理的不同阶段插入自定义代码，以满足特定的需求。 8. 理解预处理器：Dynare 的预处理器会解析模型文件中的命令，生成用于求解的内部表示。这包括处理模型的结构（如方程的定义），指定模型的识别条件，以及处理内生和外生变量的定义。此外，Dynare支持多种模型类型，如RBC（Real Business Cycle）、DSGE、VAR（Vector Autoregression）等，并提供了丰富的命令集用于建模和估计。用户可以通过文档了解每个命令的详细用法和示例，以便更好地运用Dynare进行模型分析。为了保证正确引用 Dynare 在研究成果中的贡献，手册还提供了引用指南。同时，Dynare遵循GNU Free Documentation License，允许用户自由复制、分发和修改文档，进一步促进了知识的共享和传播。 Dynare 是一个强大且灵活的工具，它简化了宏观经济模型的构建和分析流程，使得研究者能够更专注于模型设计和经济问题的研究，而非底层的计算细节。通过深入理解和熟练使用 Dynare，用户可以高效地进行经济模型的建模、求解和仿真，为学术研究和政策制定提供有力的支持。

Chapter 4: The Model ﬁle 12

It is possible to mix deterministic and stochastic shocks to build models where agents know

from the start of the simulation about future exogenous changes. In that case stoch_simul will

compute the rational expectation solution adding future information to the state space (nothing

is shown in the output of stoch_simul) and forecast will compute a simulation conditional

on initial conditions and future information.

varexo_det commands can appear several times in the ﬁle and Dynare will concatenate them.

Options

long_name = QUOTED_STRING

Like [long name], page 11 but value stored in M_.exo_det_names_long.

Example

varexo m gov;

varexo_det tau;

[Command]parameters PARAMETER_NAME [$LATEX_NAME$]

[(long name=QUOTED_STRING)]. . . ;

Description

This command declares parameters used in the model, in variable initialization or in shocks

declarations. See Section 4.1 [Conventions], page 10, for the syntax of PARAMETER NAME.

Optionally it is possible to give a L

X name to the parameter.

The parameters must subsequently be assigned values (see Section 4.4 [Parameter initialization],

page 18).

parameters commands can appear several times in the ﬁle and Dynare will concatenate them.

Options

long_name = QUOTED_STRING

Like [long name], page 11 but value stored in M_.param_names_long.

Example

parameters alpha, bet;

[Command]change_type (var | varexo | varexo det | parameters) VARIABLE_NAME |

PARAMETER_NAME. . .;

Description

Changes the types of the speciﬁed variables/parameters to another type: endogenous, exogenous,

exogenous deterministic or parameter.

It is important to understand that this command has a global eﬀect on the ‘.mod’ ﬁle: the type

change is eﬀective after, but also before, the change_type command. This command is typically

used when ﬂipping some variables for steady state calibration: typically a separate model ﬁle is

used for calibration, which includes the list of variable declarations with the macro-processor,

and ﬂips some variable.

Example

Chapter 4: The Model ﬁle 13

var y, w;

parameters alpha, bet;

...

change_type(var) alpha, bet;

change_type(parameters) y, w;

Here, in the whole model ﬁle, alpha and beta will be endogenous and y and w will be parameters.

[Command]predetermined_variables VARIABLE_NAME. . .;

Description

In Dynare, the default convention is that the timing of a variable reﬂects when this variable

is decided. The typical example is for capital stock: since the capital stock used at current

period is actually decided at the previous period, then the capital stock entering the production

function is k(-1), and the law of motion of capital must be written:

k = i + (1-delta)*k(-1)

Put another way, for stock variables, the default in Dynare is to use a “stock at the end of the

period” concept, instead of a “stock at the beginning of the period” convention.

The predetermined_variables is used to change that convention. The endogenous variables

declared as predetermined variables are supposed to be decided one period ahead of all other

endogenous variables. For stock variables, they are supposed to follow a “stock at the beginning

of the period” convention.

Note that Dynare internally always uses the “stock at the end of the period” concept, even

when the model has been entered using the predetermined_variables-command. Thus, when

plotting, computing or simulating variables, Dynare will follow the convention to use variables

that are decided in the current period. For example, when generating impulse response functions

for capital, Dynare will plot k, which is the capital stock decided upon by investment today (and

which will be used in tomorrow’s production function). This is the reason that capital is shown

to be moving on impact, because it is k and not the predetermined k(-1) that is displayed. It

is important to remember that this also aﬀects simulated time series and output from smoother

routines for predetermined variables. Compared to non-predetermined variables they might

otherwise appear to be falsely shifted to the future by one period.

Example

The following two program snippets are strictly equivalent.

Using default Dynare timing convention:

var y, k, i;

...

model;

y = k(-1)^alpha;

k = i + (1-delta)*k(-1);

...

end;

Using the alternative timing convention:

var y, k, i;

predetermined_variables k;

...

model;

y = k^alpha;

k(+1) = i + (1-delta)*k;

...

end;

Chapter 4: The Model ﬁle 14

[Command]trend_var (growth factor = MODEL_EXPRESSION) VARIABLE_NAME

[$LATEX_NAME$]. . .;

Description

This optional command declares the trend variables in the model. See Section 4.1 [Conventions],

page 10, for the syntax of MODEL EXPRESSION and VARIABLE NAME. Optionally it is

possible to give a L

X name to the variable.

The variable is assumed to have a multiplicative growth trend. For an additive growth trend,

use log_trend_var instead.

Trend variables are required if the user wants to be able to write a nonstationary model in the

model block. The trend_var command must appear before the var command that references

the trend variable.

trend_var commands can appear several times in the ﬁle and Dynare will concatenate them.

If the model is nonstationary and is to be written as such in the model block, Dynare will

need the growth factor of every trend variable in order to stationarize the model. The growth

factor must be provided within the declaration of the trend variable, using the growth_factor

keyword. All endogenous variables and parameters referenced in MODEL EXPRESSION must

already have been declared by the var and parameters commands.

Example

trend_var (growth_factor=gA) A;

[Command]log_trend_var (log growth factor = MODEL_EXPRESSION) VARIABLE_NAME

[$LATEX_NAME$]. . .;

Description

Same as trend_var, except that the variable is supposed to have an additive trend (or, to put

it otherwise, to be equal to the log of a variable with a multiplicative trend).

4.3 Expressions

Dynare distinguishes between two types of mathematical expressions: those that are used to de-

scribe the model, and those that are used outside the model block (e.g. for initializing parameters or

variables, or as command options). In this manual, those two types of expressions are respectively

denoted by MODEL EXPRESSION and EXPRESSION.

Unlike MATLAB or Octave expressions, Dynare expressions are necessarily scalar ones: they

cannot contain matrices or evaluate to matrices

Expressions can be constructed using integers (INTEGER), ﬂoating point numbers (DOUBLE),

parameter names (PARAMETER NAME), variable names (VARIABLE NAME), operators and

functions.

The following special constants are also accepted in some contexts:

[Constant]inf

Represents inﬁnity.

[Constant]nan

“Not a number”: represents an undeﬁned or unrepresentable value.

Note that arbitrary MATLAB or Octave expressions can be put in a ‘.mod’ ﬁle, but those expressions have to

be on separate lines, generally at the end of the ﬁle for post-processing purposes. They are not interpreted by

Dynare, and are simply passed on unmodiﬁed to MATLAB or Octave. Those constructions are not addresses in

this section.

Chapter 4: The Model ﬁle 15

4.3.1 Parameters and variables

Parameters and variables can be introduced in expressions by simply typing their names. The

semantics of parameters and variables is quite diﬀerent whether they are used inside or outside the

model block.

4.3.1.1 Inside the model

Parameters used inside the model refer to the value given through parameter initialization (see

Section 4.4 [Parameter initialization], page 18) or homotopy_setup when doing a simulation, or are

the estimated variables when doing an estimation.

Variables used in a MODEL EXPRESSION denote current period values when neither a lead

or a lag is given. A lead or a lag can be given by enclosing an integer between parenthesis just after

the variable name: a positive integer means a lead, a negative one means a lag. Leads or lags of

more than one period are allowed. For example, if c is an endogenous variable, then c(+1) is the

variable one period ahead, and c(-2) is the variable two periods before.

When specifying the leads and lags of endogenous variables, it is important to respect the

following convention: in Dynare, the timing of a variable reﬂects when that variable is decided. A

control variable — which by deﬁnition is decided in the current period — must have no lead. A

predetermined variable — which by deﬁnition has been decided in a previous period — must have

a lag. A consequence of this is that all stock variables must use the “stock at the end of the period”

convention. Please refer to Mancini-Griﬀoli (2007) for more details and concrete examples.

Leads and lags are primarily used for endogenous variables, but can be used for exogenous

variables. They have no eﬀect on parameters and are forbidden for local model variables (see

Section 4.5 [Model declaration], page 18).

4.3.1.2 Outside the model

When used in an expression outside the model block, a parameter or a variable simply refers to

the last value given to that variable. More precisely, for a parameter it refers to the value given

in the corresponding parameter initialization (see Section 4.4 [Parameter initialization], page 18);

for an endogenous or exogenous variable, it refers to the value given in the most recent initval or

endval block.

4.3.2 Operators

The following operators are allowed in both MODEL EXPRESSION and EXPRESSION:

• binary arithmetic operators: +, -, *, /, ^

• unary arithmetic operators: +, -

• binary comparison operators (which evaluate to either 0 or 1): <, >, <=, >=, ==, !=

Note that these operators are diﬀerentiable everywhere except on a line of the 2-dimensional

real plane. However for facilitating convergence of Newton-type methods, Dynare assumes that,

at the points of non-diﬀerentiability, the partial derivatives of these operators with respect to

both arguments is equal to 0 (since this is the value of the partial derivatives everywhere else).

The following special operators are accepted in MODEL EXPRESSION (but not in EXPRES-

SION):

[Operator]STEADY_STATE (MODEL_EXPRESSION)

This operator is used to take the value of the enclosed expression at the steady state. A typical

usage is in the Taylor rule, where you may want to use the value of GDP at steady state to

compute the output gap.

[Operator]EXPECTATION (INTEGER) (MODEL_EXPRESSION)

This operator is used to take the expectation of some expression using a diﬀerent information

set than the information available at current period. For example, EXPECTATION(-1)(x(+1))

Chapter 4: The Model ﬁle 16

is equal to the expected value of variable x at next period, using the information set available

at the previous period. See Section 4.6 [Auxiliary variables], page 21, for an explanation of how

this operator is handled internally and how this aﬀects the output.

4.3.3 Functions

4.3.3.1 Built-in Functions

The following standard functions are supported internally for both MODEL EXPRESSION and

EXPRESSION:

[Function]exp (x)

Natural exponential.

[Function]log (x)

[Function]ln (x)

Natural logarithm.

[Function]log10 (x)

Base 10 logarithm.

[Function]sqrt (x)

Square root.

[Function]abs (x)

Absolute value.

Note that this function is not diﬀerentiable at x = 0. However, for facilitating convergence of

Newton-type methods, Dynare assumes that the derivative at x = 0 is equal to 0 (this assumption

comes from the observation that the derivative of abs(x) is equal to sign(x) for x 6= 0 and from

the convention for the derivative of sign(x) at x = 0).

[Function]sign (x)

Signum function.

Note that this function is not diﬀerentiable at x = 0. However, for facilitating convergence

of Newton-type methods, Dynare assumes that the derivative at x = 0 is equal to 0 (this

assumption comes from the observation that both the right- and left-derivatives at this point

exist and are equal to 0).

[Function]sin (x)

[Function]cos (x)

[Function]tan (x)

[Function]asin (x)

[Function]acos (x)

[Function]atan (x)

Trigonometric functions.

[Function]max (a, b)

[Function]min (a, b)

Maximum and minimum of two reals.

Note that these functions are diﬀerentiable everywhere except on a line of the 2-dimensional real

plane deﬁned by a = b. However for facilitating convergence of Newton-type methods, Dynare

assumes that, at the points of non-diﬀerentiability, the partial derivative of these functions with

respect to the ﬁrst (resp. the second) argument is equal to 1 (resp. to 0) (i.e. the derivatives at

the kink are equal to the derivatives observed on the half-plane where the function is equal to

its ﬁrst argument).

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