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trunk manual: rewrote sections for initval and endval 

git-svn-id: https://www.dynare.org/svn/dynare/dynare_v4@2296 ac1d8469-bf42-47a9-8791-bf33cf982152
time-shift
sebastien 2008-12-05 17:41:01 +00:00
parent 2134146033
commit 71e5b5a806
1 changed files with 70 additions and 71 deletions
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@ -302,7 +302,7 @@ Depending on the computing tasks requested in the <filename class="extension">.m
</para> </para>
<para> <para>
The <varname>oo_</varname> structure is also saved in a file called <replaceable>FILENAME</replaceable><filename>_results.mat</filename>. The <varname>M_</varname> and <varname>oo_</varname> structures are also saved in a file called <replaceable>FILENAME</replaceable><filename>_results.mat</filename>.
</para> </para>
</refsect1> </refsect1>
@ -667,7 +667,7 @@ end;
The following program: The following program:
<programlisting> <programlisting>
model; model;
# gamma = 1 - 1/sigma # gamma = 1 - 1/sigma;
u1 = c1^gamma/gamma; u1 = c1^gamma/gamma;
u2 = c2^gamma/gamma; u2 = c2^gamma/gamma;
end; end;
@ -695,27 +695,29 @@ end;
</sect1> </sect1>
<sect1><title>Initial and terminal conditions</title> <sect1><title>Initial and terminal conditions</title>
<para>
In many contexts, it is necessary to compute the steady state of a non-linear model <xref linkend='initval'/> specifies then numerical initial values for the non-linear solver. <para>For most simulation exercises, it is necessary to provide initial (and possibly terminal) conditions. It is also necessary to provide initial guess values for non-linear solvers. The following statements are used for those purposes:</para>
<itemizedlist>
<listitem><para><xref linkend='initval'/></para></listitem>
<listitem><para><xref linkend='initval_file'/></para></listitem>
<listitem><para><xref linkend='endval'/></para></listitem>
<listitem><para><xref linkend='histval'/></para></listitem>
</itemizedlist>
<para>In many contexts (determistic or stochastic), it is necessary to compute the steady state of a non-linear model: <xref linkend='initval'/> then specifies numerical initial values for the non-linear solver.
</para> </para>
<para> <para>
Used in perfect foresight mode, the types of forward-loking models for which Dynare was designed require both initial and terminal conditions. Most often these initial and terminal conditions are static equilibria, but not necessarily. Used in perfect foresight mode, the types of forward-loking models for which Dynare was designed require both initial and terminal conditions. Most often these initial and terminal conditions are static equilibria, but not necessarily.
</para> </para>
<para> <para>
One typical application is to consider an economy at the equilibrium, trigger a shock in first period, and study the trajectory of return at the initial equilbrium. To do that, one needs <xref linkend='initval'/> and <xref linkend='shocks'/>(see next section). One typical application is to consider an economy at the equilibrium, trigger a shock in first period, and study the trajectory of return at the initial equilbrium. To do that, one needs <xref linkend='initval'/> and <xref linkend='shocks'/> (see <xref linkend="sec:shocks"/>.
</para> </para>
<para> <para>
Another one is to study, how an economy, starting from arbitrary initial conditions converges toward equilibrium. To do that, one needs <xref linkend='initval'/> and <xref linkend='endval'/>; Another one is to study, how an economy, starting from arbitrary initial conditions converges toward equilibrium. To do that, one needs <xref linkend='initval'/> and <xref linkend='endval'/>;
</para> </para>
<para> <para>
For models with lags on more than one period, the command <xref linkend='histval'/> permits to specify different historical initial values in different periods. For models with lags on more than one period, the command <xref linkend='histval'/> permits to specify different historical initial values for periods before the beginning of the simulation.
</para> </para>
<itemizedlist>
<listitem><para><xref linkend='initval'/></para></listitem>
<listitem><para><xref linkend='initval_file'/></para></listitem>
<listitem><para><xref linkend='endval'/></para></listitem>
<listitem><para><xref linkend='histval'/></para></listitem>
</itemizedlist>
<refentry id="initval"> <refentry id="initval">
<refmeta> <refmeta>
@ -729,35 +731,44 @@ For models with lags on more than one period, the command <xref linkend='histval
<refsynopsisdiv> <refsynopsisdiv>
<cmdsynopsis> <cmdsynopsis>
<command>initval;</command><sbr/> <command>initval</command>;<sbr/>
<arg choice="plain"> <arg rep="repeat" choice="plain">
<replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable>; <replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable> ;
</arg><sbr/> </arg>
<arg rep="repeat"> <command>end</command>;
<replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable>;
</arg><sbr/>
<arg choice="plain">
end;
</arg>
</cmdsynopsis> </cmdsynopsis>
</refsynopsisdiv> </refsynopsisdiv>
<refsect1><title>Description</title> <refsect1><title>Description</title>
<para> <para>The <command>initval</command> block serves two purposes: declaring the initial (and possibly terminal) conditions in a simulation exercise, and providing guess values for non-linear solvers.</para>
<replaceable>EXPRESSION</replaceable> is any valid expression returning a numerical value and can contain already initialized variable names.
</para> <refsect2><title>In a deterministic (<foreignphrase>i.e.</foreignphrase> perfect foresight) model</title>
<para>
The <command>initval;</command> ... <command>end;</command> block serves two purposes. It set the initial and, possibly, terminal conditions for the simulation and provides numerical initialization for various computation tasks (<xref linkend='steady'/>, <xref linkend='simul'/>, <xref linkend='stoch_simul'/>). <para>First, it provides the initial conditions for all the endogenous and exogenous variables at all the periods preceeding the first simulation period (unless some of these initial values are modified by <xref linkend="histval"/>).</para>
</para>
<para> <para>Second, in the absence of an <xref linkend="endval"/> block, it also sets the terminal conditions for all the periods succeeding the last simulation period.</para>
Theoreticaly, initial conditions are only necessary for lagged variables. However, as <command>initval</command> provides also numerical initialization, it is necessary to provide values for all variables in the model, except if the model is declared as linear.
</para> <para>Third, it provides initial guess values for the non-linear solver implemented in <xref linkend="simul"/>. If there is no <xref linkend="endval"/> block, it provides initial guess values for all the simulation dates; otherwise, it provides initial guess values for all dates before the first simulation period (and <xref linkend="endval"/> provides the rest).</para>
<para>
For stochastic models, it isn't necessary to delcare 0 as initial values for exogneous stochastic variables as it is the only possible value. <para>For this last reason, it necessary to provide values for all the endogenous variables in an <command>initval</command> block (even though, theoretically, initial conditions are only necessary for lagged variables). If some exogenous variables are not mentionned in the <command>initval</command> block, a zero value is assumed.</para>
</para>
<para> <para>Note that if the <command>initval</command> block is immediately followed by a <xref linkend="steady"/> command, its semantics is changed. The <xref linkend="steady"/> command will compute the steady state of the model for all the endogenous variables, assuming that exogenous variables are kept constant to the value declared in the <command>initval</command> block, and using the values declared for the endogenous as initial guess values for the non-linear solver. An <command>initval</command> block followed by <xref linkend="steady"/> is formally equivalent to an <command>initval</command> block with the same values for the exogenous, and with the associated steady state values for the endogenous.</para>
When the <command>initval</command> block is followed by the command <xref linkend='steady'/>, it is not necessary to provide exact initialization values for the endogenous variables. <xref linkend='steady'/> will use the values provided in the <command>initval</command> block as initial guess in the non-linear equation solver and computes exact values for the endogenous variables at the steady state. The steady state is defined by keeping constant the value of the exogenous variables.
</para> </refsect2>
<refsect2><title>In a stochastic model</title>
<para>The main purpose of <command>initval</command> is to provide initial guess values for the non-linear solver in the steady state computation. Note that if the <command>initval</command> block is not followed by <xref linkend="steady"/>, the steady state computation will still be triggered by subsequent commands (<xref linkend="stoch_simul"/>, <xref linkend="estimation"/>...).</para>
<para>It is not necessary to declare <literal>0</literal> as initial value for exogenous stochastic variables, since it is the only possible value.</para>
<para>This steady state will be used as the initial condition at all the periods preceeding the first simulation period for the two possible types of simulations in stochastic mode:</para>
<itemizedlist>
<listitem><para>in <xref linkend="stoch_simul"/>, if the <option>simul</option> or <option>periods</option> options are specified</para></listitem>
<listitem><para>in <xref linkend="forecast"/> (in this case, note that it is still possible to modify some of these initial values with <xref linkend="histval"/>)</para></listitem>
</itemizedlist>
</refsect2>
</refsect1> </refsect1>
<refsect1><title>Example</title> <refsect1><title>Example</title>
@ -796,32 +807,25 @@ steady;
<refsynopsisdiv> <refsynopsisdiv>
<cmdsynopsis> <cmdsynopsis>
<command>endval;</command><sbr/> <command>endval</command>;<sbr/>
<arg choice="plain"> <arg rep="repeat" choice="plain">
<replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable>; <replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable> ;
</arg><sbr/> </arg>
<arg rep="repeat"> <command>end</command>;
<replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable>;
</arg><sbr/>
<arg choice="plain">
end;
</arg>
</cmdsynopsis> </cmdsynopsis>
</refsynopsisdiv> </refsynopsisdiv>
<refsect1><title>Description</title> <refsect1><title>Description</title>
<para>
<replaceable>EXPRESSION</replaceable> is any valid expression returning a numerical value and can contain already initialized variable names. <para>The <command>endval</command> block makes only sense in a determistic model, and serves two purposes.</para>
</para>
<para> <para>First, it sets the terminal conditions for all the periods succeeding the last simulation period.</para>
The optional <command>endval;</command> ... <command>end;</command> block serves two purposes. It set the terminal conditions for the simulation with the LBJ alogrithm, when those differ from the initial conditions. When it is the case, the <command>endval</command> block also provides the numerical initialization for various computation tasks (<xref linkend='steady'/>, <xref linkend='simul'/>), starting in period 1.
</para> <para>Second, it provides initial guess values for the non-linear solver implemented in <xref linkend="simul"/>, for all dates after the first simulation period (<xref linkend="initval"/> provides the initial guess values for the dates before the first simulation period).</para>
<para>
Theoreticaly, terminal conditions are required in the LBJ algorithm only for forward variables. However, as <command>endval</command> provides also numerical initialization, it is necessary to provide values for all variables in the model. <para>For this last reason, it necessary to provide values for all the endogenous variables in an <command>endval</command> block (even though, theoretically, initial conditions are only necessary for forward variables). If some exogenous variables are not mentionned in the <command>endval</command> block, a zero value is assumed.</para>
</para>
<para> <para>Note that if the <command>endval</command> block is immediately followed by a <xref linkend="steady"/> command, its semantics is changed. The <xref linkend="steady"/> command will compute the steady state of the model for all the endogenous variables, assuming that exogenous variables are kept constant to the value declared in the <command>endval</command> block, and using the values declared for the endogenous as initial guess values for the non-linear solver. An <command>endval</command> block followed by <xref linkend="steady"/> is formally equivalent to an <command>endval</command> block with the same values for the exogenous, and with the associated steady state values for the endogenous.</para>
When the <command>endval</command> block is followed by the command <xref linkend='steady'/>, it is not necessary to provide exact values for the endogenous variables. <xref linkend='steady'/> will use the values provided in the <command>endval</command> block as initial guess in the non-linear equation solver and computes exact values for the endogenous variables at the steady state. The steady state is defined by keeping constant the value of the exogenous variables.
</para>
</refsect1> </refsect1>
<refsect1><title>Example</title> <refsect1><title>Example</title>
@ -846,7 +850,7 @@ end;
steady; steady;
</programlisting> </programlisting>
<para> <para>
The initial equilibrium is comptuted by <xref linkend='steady'/> for x=1, and the terminal one, for x=2. The initial equilibrium is computed by <xref linkend='steady'/> for <literal>x=1</literal>, and the terminal one, for <literal>x=2</literal>.
</para> </para>
</refsect1> </refsect1>
</refentry> </refentry>
@ -863,16 +867,11 @@ The initial equilibrium is comptuted by <xref linkend='steady'/> for x=1, and th
<refsynopsisdiv> <refsynopsisdiv>
<cmdsynopsis> <cmdsynopsis>
<command>histval;</command><sbr/> <command>histval</command>;<sbr/>
<arg choice="plain"> <arg rep="repeat" choice="plain">
<replaceable>VARIABLE_NAME</replaceable> (<replaceable>INTEGER</replaceable>) = <replaceable>EXPRESSION</replaceable>; <replaceable>VARIABLE_NAME</replaceable> = <replaceable>EXPRESSION</replaceable> ;
</arg><sbr/> </arg>
<arg rep="repeat"> <command>end</command>;
<replaceable>VARIABLE_NAME</replaceable> (<replaceable>INTEGER</replaceable>) = <replaceable>EXPRESSION</replaceable>;
</arg><sbr/>
<arg choice="plain">
end;
</arg>
</cmdsynopsis> </cmdsynopsis>
</refsynopsisdiv> </refsynopsisdiv>
@ -919,7 +918,7 @@ end;
</refentry> </refentry>
</sect1> </sect1>
<sect1><title>Shocks on exogenous variables</title> <sect1 id="sec:shocks"><title>Shocks on exogenous variables</title>
<para> <para>
In a deterministic context, when one wants to study the transition of one equilibrium position to another, it is equivalent to analyze the consequences of a permanent shock and this in done in Dynare through the proper use of <xref linkend='initval'/> and <xref linkend='endval'/>. In a deterministic context, when one wants to study the transition of one equilibrium position to another, it is equivalent to analyze the consequences of a permanent shock and this in done in Dynare through the proper use of <xref linkend='initval'/> and <xref linkend='endval'/>.
</para> </para>