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= Testing program for problem A = | <<TableOfContents>> |
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== Status of testing program == | = Status of testing program = |
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1. accuracy on a sphere in the state space 1. accuracy on a stochastic simulation |
1. Accuracy on a sphere in the state space 1. Accuracy on a stochastic simulation |
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For the time being, only the following solutions are implemented: | The following solutions are implemented: |
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* Pichler * Judd, Maliar and Maliar (JMM), clusters+RBF+Monomials (CRM) method * Judd, Maliar and Maliar (JMM), stochastic simulation algorith (SSA) method |
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Others are coming soon. == Installing and running the program == |
= Installation = |
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* GNU Fortran 95 compiler (gfortran); under Cygwin, you have to manually install it: the package is downloadable [http://quatramaran.ens.fr/~coudert/gfortran/gfortran-4.4-Cygwin-i686.tar.bz2 here], and installation instructions are [http://gcc.gnu.org/wiki/GFortranBinariesCygwin there] | * GNU Fortran 95 compiler (gfortran); under Cygwin, you have to manually install it: the package is downloadable [[http://quatramaran.ens.fr/~coudert/gfortran/gfortran-4.4-Cygwin-i686.tar.bz2|here]], and installation instructions are [[http://gcc.gnu.org/wiki/GFortranBinariesCygwin|there]] |
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svn checkout http://www.cepremap.cnrs.fr/svn/JedcTestSuiteTestsA | svn checkout https://www.dynare.org/svn/jedctestsuite |
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Then go into the {{{JedcTestSuiteTestsA}}}, and configure the package. | Then go into the {{{jedctestsuite/JedcTestSuiteTestsA}}} directory, and configure the package. |
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This should have created a program called {{{tester}}}. Run this program with: | This should have created a program called {{{tester}}}. = Running the program = The testing program is run with: |
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(it is important to run it from the directory where it was built) | It is important to run it from the directory where it was built. |
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== Code overview == | <<Anchor(options)>> The program accepts several options: * {{{-a}}}: use an alternative specification for the aggregate ressource constraint error, as suggested by Benjamin Malin (see [[#arcresid|below]]) * {{{-A}}}: use an alternative specification for the aggregate ressource constraint error, as suggested by Paul Pichler (see [[#arcresid|below]]) * {{{-b INTEGER}}}: start computations with a given specification (designated by an integer between 1 and 30); indices 1 to 5 are for A1 by increasing number of countries, indices 6 to 9 are for A2, ... * {{{-B INTEGER}}}: only do computations for a given specification (same numbering scheme than for {{{-b}}} option) * {{{-d}}}: for each model and each participant solution, create a CSV file containing simulated data for accuracy tests 1 and 2 (see [[#csv|below]]) * {{{-g}}}: always use product 4-point Gauss-Hermite for numerical integration (see [[#integration|below]]) * {{{-m}}}: always use monomial degree 5 rule for numerical integration (see [[#integration|below]]) * {{{-q}}}: always use quasi-Monte Carlo for numerical integration (see [[#integration|below]]) * {{{-r INTEGER}}}: seed for the random number generator used in tests 2 and 3 (Default: 0) * {{{-s NAME}}}: compute tests only for solution {{{NAME}}}. Possible values are {{{kkm}}}, {{{kkk}}}, {{{pichler}}}, {{{jmm-crm}}} and {{{jmm-ssa}}} * {{{-t INTEGER}}}: compute only the specified accuracy test. Possible values are 1, 2 or 3 * {{{-u INTEGER}}}: number of points to be used in Test 1 (Default: 100) * {{{-v INTEGER}}}: number of simulations to be used in Test 2 (Default: 1000) * {{{-w INTEGER}}}: number of simulations to be used in Test 3 (Default: 10000) <<Anchor(csv)>> = CSV files = == Test 1 == The first <<latex($$n$$)>> columns (where <<latex($$n$$)>> is the number of countries) contain the state variable for capital stock (stock accumulated at end of previous period). The next <<latex($$5n+1$$)>> columns contain current endogenous variables as simulated by participant's solution (note that those include the state variable for TFP level). The last <<latex($$5n+1$$)>> columns are the residual of all equations. == Test 2 == The first <<latex($$5n+1$$)>> columns contain current endogenous variables (note that capital has end-of-period stock timing convention). The next <<latex($$n+1$$)>> columns contains simulated shocks (the last one is the global shock). The last <<latex($$5n+1$$)>> columns are the residual of all equations. Note that the first line contains initial values, obtained after dropping 500 first simulated periods. <<Anchor(integration)>> = Numerical integration = Three methods of numerical integration are implemented in the testing program: * product 4-point Gauss-Hermite * monomial degree 5 rule, as described in Judd (1998) "Numerical Methods in Economics", p. 275, eq. 7.5.11 * quasi-Monte Carlo using 1000 points; the sequence of points is drawn from a Niederreiter generator Note that for <<latex($$N$$)>> countries, the dimension of the integration problem of Euler errors is <<latex($$N+1$$)>>. The default behaviour of the program is to use Gauss-Hermite up to dimension 6 (i.e. when <<latex($$N\leq 5$$)>>), and monomial degree 5 rule above. It is possible to alter this behaviour by forcing the program to use a given integration method (see [[#options|options]]). <<Anchor(arcresid)>> = Aggregate resource constraint residual = There are three possible ways of computing the aggregate ressource constraint residual. The default, suggested by Michel Juillard's May 2007 note, is: <<latex($$\frac{Y-C-I+\delta K -CAC}{Y-CAC}$$)>> (where <<latex($$CAC$$)>> stands for capital adjustment cost). An alternative, triggered by {{{-a}}} option, and suggested by Benjamin Malin, is: <<latex($$\frac{Y-C-I+\delta K -CAC}{Y+K}$$)>> Another alternative, triggered by {{{-A}}} option, and suggested by Paul Pichler, is: <<latex($$\frac{Y-C-I+\delta K -CAC}{Y}$$)>> Benjamin Malin's version obviously gives lower error approximations in absolute value, since it has the greatest denominator. = Code overview = |
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Note that in class {{{ModelSpec}}}, the convention is to work with a vector of variables [[latex($$y_t$$)]] of length [[latex($$5n+1$$)]] (where [[latex($$n$$)]] is the number of countries). The vector [[latex($$y_t$$)]] contains consumption level [[latex($$c_t^j$$)]], labor [[latex($$l_t^j$$)]], investment [[latex($$i_t^j$$)]], capital (end of period stock)[[latex($$k_{t+1}^j$$)]], technology level [[latex($$a_t^j$$)]] and [[latex($$\lambda_t$$)]] (Lagrange multiplier of aggregate budget constraint) (see {{{ModelSpec.hh}}} for more details). Shocks are in a vector [[latex($$e_t$$)]] of size [[latex($$n+1$$)]] (idiosyncratic shocks + global shock). | Note that in class {{{ModelSpec}}}, the convention is to work with a vector of variables <<latex($$y_t$$)>> of length <<latex($$5n+1$$)>> (where <<latex($$n$$)>> is the number of countries). The vector <<latex($$y_t$$)>> contains consumption level <<latex($$c_t^j$$)>>, labor <<latex($$l_t^j$$)>>, investment <<latex($$i_t^j$$)>>, capital (end of period stock)<<latex($$k_{t+1}^j$$)>>, technology level <<latex($$a_t^j$$)>> and <<latex($$\lambda_t$$)>> (Lagrange multiplier of aggregate budget constraint) (see {{{ModelSpec.hh}}} for more details). Shocks are in a vector <<latex($$e_t$$)>> of size <<latex($$n+1$$)>> (idiosyncratic shocks + global shock). |
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Relative errors are computed using [[latex($$y_{t-1}$$)]], [[latex($$y_t$$)]], [[latex($$y_{t+1}$$)]] and [[latex($$e_t$$)]], following section 1.5 of Michel's May 2007 notes. The forward looking part of the Euler equation is separately computed by {{{ModelSpec::forward_part()}}}, so that it can be integrated over, and then fed back to {{{ModelSpec::errors()}}} (which computes the [[latex($$5n+1$$)]] errors). | Relative errors are computed using <<latex($$y_{t-1}$$)>>, <<latex($$y_t$$)>>, <<latex($$y_{t+1}$$)>> and <<latex($$e_t$$)>>, following section 1.5 of Michel's May 2007 notes. The forward looking part of the Euler equation is separately computed by {{{ModelSpec::forward_part()}}}, so that it can be integrated over, and then fed back to {{{ModelSpec::errors()}}} (which computes the <<latex($$5n+1$$)>> errors). |
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Solution methods are implemented via a subclass of {{{ModelSolution}}} (see {{{kkm/KKMSolution.cc}}} and {{{kkk/KKKSolution.cc}}}). The purpose of these classes is to provide a uniformized wrapper around the participant's solutions. The main method of those classes is the policy function, which provides [[latex($$y_t$$)]] given [[latex($$y_{t-1}$$)]] and [[latex($$e_t$$)]]. | Solution methods are implemented via a subclass of {{{ModelSolution}}} (see {{{kkm/KKMSolution.cc}}} and {{{kkk/KKKSolution.cc}}}). The purpose of these classes is to provide a uniformized wrapper around the participant's solutions. The main method of those classes is the policy function, which provides <<latex($$y_t$$)>> given <<latex($$y_{t-1}$$)>> and <<latex($$e_t$$)>>. |
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=== KKM solution === | == KKM solution == |
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Source for KKM solution is in {{{kkm/}}} subdirectory. It consists of a non-linear solver (all the Fortran files in {{{kkk/}}}), which are combined in {{{libhybrid.a}}} by the Makefile. | Source for KKM solution is in {{{kkm/}}} subdirectory. It consists of a non-linear solver (all the Fortran files in {{{kkm/}}}), which are combined in {{{libhybrid.a}}} by the Makefile. |
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The following should also be noted: 1. KKM don't provide a value for [[latex($$\lambda_t$$)]]. The testing program uses the value of [[latex($$\tau_1 u'(c_1)$$)]] (marginal utility of first country) as a replacement. 1. tests for specification A2 with KKM solution give abnormally large errors on marginal labor equation, because KKM did not implement the right specification in that case (they use [[latex($$\gamma=1$$)]] and [[latex($$\eta=1$$)]] instead of [[latex($$\gamma=0.25$$)]] and [[latex($$\eta=0.1$$)]]) 1. KKM don't provide a solution for specification A7 with 4 and 6 countries, because their solution method doesn't converge with those particular specifications 1. in some tests, the technological shock falls outside of the truncated interval. The program prints messages like: {{{error: tech shock above zmax in function ChebPoly}}}. This issue yet needs to be solved. |
Note that since KKM don't provide a value for <<latex($$\lambda_t$$)>>, the testing program uses the value of <<latex($$\tau^1 u'_c(c^1_t, l^1_t)$$)>> (marginal utility of consumption of first country) as a replacement. |
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=== KKK solution === | == KKK solution == |
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Note that the simulated time paths computed by the testing program do not use the technique of "pruning" the 3rd and higher order terms (as described in Kim, Kim, Schaumburg and Sims (2007)), while "pruning" was used in KKK's 2007 paper. This is simply due to the fact that the testing program uses a generic simulation routine, only based on the one-period ahead policy function provided by the participants; it does not exploit the pecularities of a given solution. == Pichler solution == Data for Pichler solution is in {{{pichler/}}} subdirectory. There is one MAT-file for each specification. Class {{{PichlerSolution}}} reads the MAT files, and computes the policy function, according to the Matlab files provided by Pichler. == JMM solutions == Data for the two solution provided by JMM are {{{jmm/}}} subdirectory. The simulation code is the same for the two methods: only the data, provided in MAT files, differ. Classes {{{JMMCRMSolution}}} and {{{JMMSSASolution}}} read the MAT files, and compute the policy function, according to the MATLAB files. As KKM, this solution doesn't provide a value for <<latex($$\lambda_t$$)>>: the value used here is the mean of weighted marginal utilities of consumption. = Test results = Here are preliminary test results for Test 1 for 2 countries [[attachment:test1.pdf]] |
Contents
Status of testing program
The program performs the following tests:
- Accuracy on a sphere in the state space
- Accuracy on a stochastic simulation
- Den Haan Marcet statistics
The following solutions are implemented:
- Krueger, Kubler and Malin (KKM)
- Kim, Kim and Kollman (KKK)
- Pichler
- Judd, Maliar and Maliar (JMM), clusters+RBF+Monomials (CRM) method
- Judd, Maliar and Maliar (JMM), stochastic simulation algorith (SSA) method
Installation
The testing program is designed to run on the two following platforms: GNU/Linux and Windows/Cygwin.
You need the following software to run the program:
- GNU C++ compiler (g++)
GNU Fortran 95 compiler (gfortran); under Cygwin, you have to manually install it: the package is downloadable here, and installation instructions are there
development files for the GNU Scientific Library (GSL), which should be in a package called libgsl0-dev
- GNU make
- subversion
- MATLAB
Download the source of the testing program with:
svn checkout https://www.dynare.org/svn/jedctestsuite
Then go into the jedctestsuite/JedcTestSuiteTestsA directory, and configure the package.
Under GNU/Linux, type:
./configure --with-matlab=/usr/local/matlab76
(where you should give the right MATLAB installation directory)
Under Windows/Cygwin, type:
export FC=/usr/local/gfortran/bin/gfortran export FCLIBS=/usr/local/gfortran/lib/gcc/i686-pc-cygwin/4.4.0/libgfortran.a ./configure --with-matlab=/cygdrive/c/Progra~1/MATLAB
(note that you shoud use "Progra~1" instead of "Program Files" when giving the path to MATLAB directory, since spaces in pathnames are not supported)
Finally, compile the testing program by typing:
make
This should have created a program called tester.
Running the program
The testing program is run with:
./tester
It is important to run it from the directory where it was built.
The program will perform the tests for each of the 30 specifications, and for each specification for each solution method. For accuracy tests 1 and 2, it displays relative error for every equation. For accuracy test 3, and for all Euler equations (first separately, then together), it computes the DHM statistics several times, and displays the fraction of times that the statistics was out of the bilateral 5% confidence interval.
The program accepts several options:
-a: use an alternative specification for the aggregate ressource constraint error, as suggested by Benjamin Malin (see below)
-A: use an alternative specification for the aggregate ressource constraint error, as suggested by Paul Pichler (see below)
-b INTEGER: start computations with a given specification (designated by an integer between 1 and 30); indices 1 to 5 are for A1 by increasing number of countries, indices 6 to 9 are for A2, ...
-B INTEGER: only do computations for a given specification (same numbering scheme than for -b option)
-d: for each model and each participant solution, create a CSV file containing simulated data for accuracy tests 1 and 2 (see below)
-g: always use product 4-point Gauss-Hermite for numerical integration (see below)
-m: always use monomial degree 5 rule for numerical integration (see below)
-q: always use quasi-Monte Carlo for numerical integration (see below)
-r INTEGER: seed for the random number generator used in tests 2 and 3 (Default: 0)
-s NAME: compute tests only for solution NAME. Possible values are kkm, kkk, pichler, jmm-crm and jmm-ssa
-t INTEGER: compute only the specified accuracy test. Possible values are 1, 2 or 3
-u INTEGER: number of points to be used in Test 1 (Default: 100)
-v INTEGER: number of simulations to be used in Test 2 (Default: 1000)
-w INTEGER: number of simulations to be used in Test 3 (Default: 10000)
CSV files
Test 1
The first columns (where
is the number of countries) contain the state variable for capital stock (stock accumulated at end of previous period). The next
columns contain current endogenous variables as simulated by participant's solution (note that those include the state variable for TFP level). The last
columns are the residual of all equations.
Test 2
The first columns contain current endogenous variables (note that capital has end-of-period stock timing convention). The next
columns contains simulated shocks (the last one is the global shock). The last
columns are the residual of all equations. Note that the first line contains initial values, obtained after dropping 500 first simulated periods.
Numerical integration
Three methods of numerical integration are implemented in the testing program:
- product 4-point Gauss-Hermite
- monomial degree 5 rule, as described in Judd (1998) "Numerical Methods in Economics", p. 275, eq. 7.5.11
- quasi-Monte Carlo using 1000 points; the sequence of points is drawn from a Niederreiter generator
Note that for countries, the dimension of the integration problem of Euler errors is
.
The default behaviour of the program is to use Gauss-Hermite up to dimension 6 (i.e. when ), and monomial degree 5 rule above.
It is possible to alter this behaviour by forcing the program to use a given integration method (see options).
Aggregate resource constraint residual
There are three possible ways of computing the aggregate ressource constraint residual.
The default, suggested by Michel Juillard's May 2007 note, is:
(where stands for capital adjustment cost).
An alternative, triggered by -a option, and suggested by Benjamin Malin, is:
Another alternative, triggered by -A option, and suggested by Paul Pichler, is:
Benjamin Malin's version obviously gives lower error approximations in absolute value, since it has the greatest denominator.
Code overview
The class ModelSpec implements the abstract representation of a given specification, and has 8 subclasses ModelSpecA1, ModelSpecA2, ... corresponding to the 8 models. An instance of such a class contains all the parameters of the model and the logic for computing the relative errors of all equations, given the values of the variables and the shocks.
Note that in class ModelSpec, the convention is to work with a vector of variables of length
(where
is the number of countries). The vector
contains consumption level
, labor
, investment
, capital (end of period stock)
, technology level
and
(Lagrange multiplier of aggregate budget constraint) (see ModelSpec.hh for more details). Shocks are in a vector
of size
(idiosyncratic shocks + global shock).
Relative errors are computed using ,
,
and
, following section 1.5 of Michel's May 2007 notes. The forward looking part of the Euler equation is separately computed by ModelSpec::forward_part(), so that it can be integrated over, and then fed back to ModelSpec::errors() (which computes the
errors).
Solution methods are implemented via a subclass of ModelSolution (see kkm/KKMSolution.cc and kkk/KKKSolution.cc). The purpose of these classes is to provide a uniformized wrapper around the participant's solutions. The main method of those classes is the policy function, which provides given
and
.
The three tests are implemented in class SolutionTester.
The main function is in tester.cc: it constructs the abstract representations of the 30 model specifications, and then performs the tests for all solution methods.
KKM solution
Source for KKM solution is in kkm/ subdirectory. It consists of a non-linear solver (all the Fortran files in kkm/), which are combined in libhybrid.a by the Makefile.
Each of the TestA* subdirectory contains three Fortran 90 files, and a CSV file with Chebychev polynomial coefficients for each number of countries.
Since KKM's code makes uses of global variables, it was necessary to create a dynamically loadable object for each specification, and to load objects on the fly (see class KKMSolution).
Note that since KKM don't provide a value for , the testing program uses the value of
(marginal utility of consumption of first country) as a replacement.
KKK solution
Data for KKK solution is in kkk/ subdirectory. There is one MAT-file for each specification.
Class KKKSolution reads the files, and computes the second-order approximation.
Note that the simulated time paths computed by the testing program do not use the technique of "pruning" the 3rd and higher order terms (as described in Kim, Kim, Schaumburg and Sims (2007)), while "pruning" was used in KKK's 2007 paper. This is simply due to the fact that the testing program uses a generic simulation routine, only based on the one-period ahead policy function provided by the participants; it does not exploit the pecularities of a given solution.
Pichler solution
Data for Pichler solution is in pichler/ subdirectory. There is one MAT-file for each specification.
Class PichlerSolution reads the MAT files, and computes the policy function, according to the Matlab files provided by Pichler.
JMM solutions
Data for the two solution provided by JMM are jmm/ subdirectory. The simulation code is the same for the two methods: only the data, provided in MAT files, differ.
Classes JMMCRMSolution and JMMSSASolution read the MAT files, and compute the policy function, according to the MATLAB files.
As KKM, this solution doesn't provide a value for : the value used here is the mean of weighted marginal utilities of consumption.
Test results
Here are preliminary test results for Test 1 for 2 countries test1.pdf