RF_Finder Help Page

RF_Finder.exe is a Monte Carlo simulation, compiled to run under recent versions of Windows, that samples the quantitative realizations of structural arrays defined only in terms of their sign patterns, and constructs the corresponding reduced forms. In its most straight-forward application, the user specifies (in files to be read by the program) the sign patterns of the structural arrays, as well as the sign pattern of a proposed, estimated reduced form. The simulation then draws samples of the structural arrays as dictated by the given sign patterns, computes the corresponding reduced form, and compares the sign pattern of this result with that given by the user. The sampling can be conducted thousands, even millions of times, as specified by the user. When done, the number of times the user-specified reduced form sign pattern was found is reported. As described below, the simulation can also be used to find other information about the proposed structural sign patterns.

 

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-1γ.

 

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 to see the initial report of the simulation which is also the "Row Report."

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 Fi 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.