Guided tour on the Poisson gravity model of Bierens & Kontuly


In this guided tour I will explain how to estimate the dynamic Poisson gravity model in:

This model takes the form



The estimation is conducted via a separate plug-in module (POISSONG) of the econometric freeware package EasyReg International (shortly EasyReg), version April 1, 2007, or later.

To install EasyReg, and prepare it for estimation of the dynamic Poisson gravity model, follow the steps below.

  1. Download and install EasyReg.

    Of course, if you have already installed a previous version of EasyReg, this step can be skipped. However, in that case I recommend a preliminary upgrade step.

    In the sequel I will assume that EasyReg is installed in default folder

    c:\Program Files\EasyReg International

  2. Run EasyReg, and open "WWW > Upgrade EasyReg to the latest version":

    EasyReg window

    If there is a newer module DATATAB available, you have to upgrade EasyReg, either by completing the upgrade via "WWW > Upgrade EasyReg to the latest version", or via the EasyReg download web page. The latest version of module DATATAB is needed to construct the employment opportunity indices.

  3. Download at least the guided tour on how to import data files in EasyReg space delimited text format, but I recommend to download all guided tours on importing data.

  4. The plug-in module POISSONG is not part of the standard version of EasyReg. It is one of the miscellaneous modules that have to be downloaded separately. To add these modules to EasyReg, open and run the self-extracting WinZip file: Then the miscellaneous modules involved are extracted in default EasyReg folder c:\Program Files\EasyReg International. Once you have done that, module POISSONG is available via "Menu > Miscellaneous modules > POISSONG: Poisson gravity model":

    EasyReg window

Importing the data

The data used in Bierens and Kontuly (2007) is available as file MIGRATION_DATA.TXT. This file is in EasyReg space delimited text format. It contains the out-migration and employment data, but not the employment opportunity indices. These indices have to be computed via a separate program. See the next section.

To import this data in EasyReg, follow the two steps below.

  1. Copy-Paste the contents of MIGRATION_DATA.TXT into Wordpad, create a new folder, say c:\Migration, and save the Wordpad file as c:\Migration\MIGRATION_DATA.TXT

  2. Read first the guided tour on how to import data files in EasyReg space delimited text format, and then follow the instructions in this guided tour to import c:\Migration\MIGRATION_DATA.TXT. Declare the data as cross-section data. At the end of this procedure you have to decide where to start-up EasyReg. Choose the folder c:\Migration. Then the data will be stored in subfolder c:\Migration\EASYREG.DAT

Create and import the employment opportunity indices

As said before, the employment opportunity indices are not included in file MIGRATION_DATA.TXT. To make them, and merge them with the already imported data, follow the steps below.

  1. Open "Menu > Data analysis > Make data table":

    EasyReg Window

    This activates EasyReg module DATATAB:

    EasyReg Window

    Select all the employment variables, and click "Selection OK":

    EasyReg Window

    Uncheck the box "Include the observation numbers in the file", and then click the button (2). Then EasyReg will be minimized to an icon on the Taskbar, and the selected data are imported in Notepad, in EasyReg space delimited text format:


    Save this file in folder c:\Migration as EMPLOYMENT.TXT

  2. Restore and close EasyReg.

  3. Save program EmploymentOpportunityIndices.exe under the same name in folder c:\Migration. This works best with Internet Explorer or Netscape. Mozella Firefox automatically saves the file to your a download folder, from where you then have to move it to folder c:\Migration (The Visual Basic 5 code of this program can be viewed here).

  4. Run c:\Migration\EmploymentOpportunityIndices.exe

    Click "Start":

    Click "Continue":

    Click "Done". Then file c:\Migration\INDICES.TXT is created. This file is in EasyReg space delimited text format.

  5. Run EasyReg, open "File > Get data > Choose an EasyReg data file in space delimited text format", navigate to c:\Migration\INDICES.TXT, import it as cross-section data, start EasyReg in c:\Migration, and merge the data. See the guided tour on importing data files in EasyReg space delimited text format.

Estimating the Poisson gravity model

Run EasyReg, and open "Menu > Miscellaneous modules > POISSONG: Poisson gravity model". The first window is:

EasyReg window

Select (by double-clicking) the variables

  1. OUT_MIG_1984
  2. OUT_MIG_1983
  3. 1983-all empl.
  4. 1982-all empl.
  5. Fraction > %change(1983_all_empl)
The latter is the employment opportunity index. Then click "Selection OK".

EasyReg window

Click "Continue".

EasyReg window

Double-click the dependent variable Y = OUT_MIG_1984, and click "Continue".

EasyReg window

Click "Continue".

EasyReg window

EasyReg automatically selects the other variables as the independent (exogenous) variables. Click "Selection OK".

EasyReg window

We need an intercept to estimate the parameter go. Thus, click "Continue".

EasyReg window

Click "Continue".

EasyReg window

The general form of the dynamic Poisson gravity model is

Y ~ Poisson(Z.[b(1)Y(-1)/Z(-1)+b(2)X(1)+b(3)X(2)+...])

where Y is the dependent variable, Y(-1) is the lagged dependent variable, Z is an exogenous variable, Z(-1) is the lagged value of Z, and X(1), X(2),... are other exogenous variables (one of the X variables may be the constant 1). In Bierens and Kontuly (2007) Y is the out-migration from a region, Z is the employment in that region in the previous year, X(1) is an employment opportunity index, and X(2) = 1. In the case under review

We need to select the lagged dependent variable Y(-1) = OUT_MIG_1983. Double-click it, and then click "Selection OK".

EasyReg window

The variable Z is the employment variable: Z = 1983-all empl. However, we need to select first the lagged employment variable: Z(-1) = 1982-all empl. Double-click it, and then click "Selection OK".

EasyReg window

Next, select Z = 1983-all empl. Double-click it, and then click "Selection OK".

EasyReg window

The employment opportunity index Fraction > %change(1983_all_empl) and the constant 1 are now selected automatically. Click "Continue".

EasyReg window

The log-likelihood will be maximized via the Newton iteration method. There is no need to adjust the stopping rules. Thus click "Start Newton iteration". Then in less than a second the maximum likelihood (ML) estimation results appear.

EasyReg window

The parameter b(1) is the ML estimate of ao, b(2) is the ML estimate of bo, and b(3) is the ML estimate of go.

Since the sample size 75 is small, the asymptotic t-values may not be reliable for testing the significance of the parameters involved. Therefore, it is recommended to compute bootstrap quantiles of the maximum likelihood estimates. The bootstrap procedure involved is explained in the appendix of Bierens and Kontuly (2007). Thus, click "Bootstrap".

EasyReg window

What is displayed here are the bootstrap quantiles of b(1). The 5% and 95% quantiles form the lower and upper bound, respectively, of the 90% confidence interval of ao.

Click "Continue".

EasyReg window

Leave the box "Write the results to file EASYREG.DAT\OUTPUT.TXT when done" checked.

Click "Done" and "Cancel". Then you will jump back to the EasyReg front window.


The output is stored in, or appended to, file OUTPUT.TXT in folder c:\Migration\EASYREG.DAT. To view the output, open "Menu > Output > View output text file" in the EasyReg front window.

The estimation results are, of course, exactly the same as the corresponding results for year 1984 in Bierens and Kontuly (2007). However, the bootstrap results differ slightly, because the random number generator is seeded randomly each time.

This is the end of the guided tour on the Poisson gravity model of Bierens & Kontuly.