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.
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
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.
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.
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.
This activates EasyReg module DATATAB:
Select all the employment variables, and click "Selection OK":
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
Click "Done". Then file c:\Migration\INDICES.TXT is created. This file is in EasyReg space delimited text format.
Run EasyReg, and open "Menu > Miscellaneous modules > POISSONG: Poisson gravity model". The first window is:
Select (by double-clicking) the variables
Double-click the dependent variable Y = OUT_MIG_1984, and click "Continue".
EasyReg automatically selects the other variables as the independent (exogenous) variables. Click "Selection OK".
We need an intercept to estimate the parameter go. Thus, click "Continue".
The general form of the dynamic Poisson gravity model is
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".
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".
Next, select Z = 1983-all empl. Double-click it, and then click "Selection OK".
The employment opportunity index Fraction > %change(1983_all_empl) and the constant 1 are now selected automatically. Click "Continue".
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.
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".
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.
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.