**RF_Finder Help Page**

*
RF_Finder.exe*

** **

**The model: It
is assumed that a model of some aspect of the economy is specified by a system
of simultaneous equations, **

**f
**
^{i }**(Y, Z) = 0, ** **i**** = 1 to
** **n,**** (1) **

**where Y is an
n-vector of endogenous variables and Z is an m-vector of exogenous variables.
The system is studied by, and the potential for its acceptance or rejection
resides in, the method of comparative statics. Such analysis assesses the
effects of changes in the entries of Z on the entries of Y with respect to a
referent solution as specified by a linear system of differentials:**

**For econometric
purposes, this system is rewritten as a linear system (with error terms omitted
here) as given by,**

** **

**βY = γZ, (3)**

** **

**where
**
**β and γ ** **are appropriately dimensioned matrices. (3) is
usually called the ** **structural form**** of the model. The system (3) is then
manipulated for estimation purposes, again with the error terms omitted, to
give, **

**
(4)**** **

**where π = β**^{-1}**γ.**

** **

**Testing the Model:**** In using RF_Finder.exe, the sign patterns of β, γ, and the estimated π
are specified by the user and placed in ascii-text files, using (say) MS
Notepad. The application assumes that the files are placed in the same directory
as the executable. The application searches for, loads, and uses as appropriate,
three files: Beta.txt, Gamma.txt and Pi_Hat.txt.
**

**The file formats are,**

**Beta.txt**

4

1,-1,0,0

0,1,1,0

1,0,1,1

-1,0,1,1

** The first
entry in beta.txt is n, the number of endogenous
variables. The next entries are each of the (for n = 4) the four rows of β.
These entries are set to 0 if the corresponding entry of β is zero, 1 or
-1 for positive or negative nonzeros, or 2 for a nonzero with an unspecified
sign. For this case, the simulation assigns a positive or negative nonzero to
the entry approximately half the time each. As seen, the entries are in the
CSV-format with carriage return delimited lines.**

**Gamma.txt**

4

1,-1,0,0

-1,1,0,0

0,-1,1,0

0,0,0,1

**The first entry
in Gamma.txt is m, the number of exogenous variables. The other entries are otherwise specified as in Beta.txt.
**

**Pi_Hat.txt**

**-1,-1,1,-1
-1,-1,1,-1
1,1,-1,1
-1,-1,1,-1**

**The simulation
is written under the assumption that β is irreducible, that β**^{-1}** has
no zero entries otherwise, and that γ is configured such that π has no (logical)
zero entries. Accordingly, the entries of P_Hat.txt must be all nonzero with
specified signs, i.e., each entry must be specified as either 1 or -1. All
three of these files must be specified with consistent dimensions and resident
in the same directory in which RF_Finder is running. All of the examples
linked below of RF_Finder report screens use the above sign patterns with the
simulation run for 10,000 trials; however, each report is for a different run,
so there may be small differences in commonly reported magnitudes. The point of
the displays is to explain content and format.**

**The screen
image of RF_Finder.exe is given below. The report shown on the application’s
screen was generated by first clicking on the button
**
**Gamma is On**** which is an
on/off toggle and reads Gamma is Off prior to the click. If the application is
set for Gamma is Off then it is assumed that γ = I. Then the button Get Beta
and Gamma was clicked, resulting in the image shown.**

**
**

**In the above,
the beta and gamma arrays are those specified above. The array displayed between
them:**

**Boolean Inverse ('NZ' = Non-Zero)
NZ NZ NZ NZ
NZ NZ NZ NZ
NZ NZ NZ NZ
NZ NZ NZ NZ **

**This array is computed to ensure that (as
assumed) the beta.txt array is irreducible. This is confirmed if all entries are
designated by "NZ.," as here. The simulation is set up limiting n and m to each
be no larger than 20.**

**The sampling algorithm assigns the nozeros
in beta and gamma from the open interval, ]0,MatScale[, selecting the values
subject to a uniform distribution. The value of MatScale is given in the
adjacent yellow text box and can be edited by the user.**

**The integer in the yellow text box
adjacent to "# of Trials" (equal to 10,000 by default, as shown above)
also can be
set by the user, with an upper bound of 2,000,000. This number sets the number
of quantitative samples that will be constructed for the structural arrays, from
which the corresponding reduced form will be computed as given in (4) above. The
white text box below, adjacent to "# of Interations" will report the the number
of iterations as performed. The simulation will run the specified number of
trials. The itemization of "# Systems" and "# Count" can be ignored, as they
relate to error control for the simulation only when the "Simulate" option is
selected as described below. Nevertheless, they must fully tabulate before the
simulation is finished.**

**As given above, the most direct use of
RF_Finder is to sample the structure and count the number of times that the user
specified reduced form sign pattern shows up for the samples taken. This option
is selected by clicking on the command button labeled [Reduced form Search].****
**
**Click here**** to see the report generated for the example being used here.**

**RF_Finder can also be used to compile the
results of the Monte Carlo in terms of tabulating the reduced form sign patterns
that were found in the sampling. This is done for the rows and columns of the
reduced form for n, m each no larger than twenty and for the entire reduced form
sign patterns that contain no more than twenty-five entries. The reports below
were derived from 1,000,000 samples with the tabulations reported on initiated
by clicking on the button
.**

**
Click here
**

**This report can also be seen clicking
on on
RF_Finder.exe's display.**

**Click here****
**
**to see the "Column Report."
**

**This report
can be seen by clicking on
on RF_Finder.exe's
display.**

**Click here****
**
**
to see the "System Report" (for nm
≤ 25). **

**This report can be seen by clicking on
****
on RF_Finder.exe's display.**

**Click here****
** **to check the estimated reduced
form (i.e., the user specified Pi_Hat.txt).**

** This report can be seen by clicking
on ****
on RF_Finder.exe's display.**

**In the above reports, entropy is computed
by the formula,**

**where F**_{i}** is the frequency of the
ith row, column, or system sign pattern. The amount of information provided by
the structural sign pattern is derived from the entropy measure as,**

**The upper bound for entropy and the lower
bound for INFO% are computed assuming that the distrinbutions of the sign
patterns found were uniform.**