











































© 2012 Nicolaus Copernicus University Press. All rights reserved.  
http://www.dem.umk.pl/dem 

DYNAMIC ECONOMETRIC MODELS 
Vol. 12 ( 2012) 111−122 

Submitted October 25, 2012  ISSN 
Accepted December 20, 2012 1234-3862 

Michał Bernard Pietrzak, Natalia Drzewoszewska,  
Justyna Wilk* 

The Analysis of Interregional Migrations in Poland  
in the Period 2004–2010 Using Panel Gravity Model 

A b s t r a c t. The paper discusses the problem of migration in spatial and temporal perspective. 
The objective is to evaluate the intensity and direction of selected economic variables impact on 
the volume of interregional migration flows in Poland in the period 2004–2010. The analysis was 
performed using panel gravity model with fixed effects. The socio-economic situation and espe-
cially the level of salaries determine migration directions in Poland. Significant movements keep 
occurring between economically stronger regions. They indicate tendencies towards obtaining 
positive net migration. 

K e y w o r d s: interregional migration, panel gravity model.  

J E L Classification: C23, C32, J61, R11, R15 

Introduction 
 Migrations represent an integral part underlying the functioning of societies 
and economies. In the times of market economy internal migrations, which oc-
cur within the territory of a given country, are of particular importance. They 
regulate both, the size and structure of human resources as well as job market 
situation and the consumption of goods and services, etc. Therefore they are of 
not just demographic dimension but also of economic one and have significant 
impact on regional development. In spite of the above, Polish population is 
characterized by a relatively low territorial mobility, in particular with reference 

                                                 
* Correspondence to: Michał Bernard Pietrzak, Nicolaus Copernicus University, ul. Gagarina 

13a, 87-100 Toruń, e-mail: pietrzak@umk.pl, Natalia Drzewoszewska, Nicolaus Copernicus 
University, ul. Gagarina 13a, 87-100 Toruń, e-mail: drzewonata@gmail.com, Justyna Wilk, 
Wroclaw University of Economics, ul. Nowowiejska 3, 58-500 Jelenia Góra, e-mail: 
juwil2002@interia.pl. 



Michał Pietrzak, Natalia Drzewoszewska, Justyna Wilk 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 111–122 

112 

to long distance migrations. For this reason it is of crucial importance to re-
search conditions responsible for interregional migration flows. 
 In terms of relatively stable political and cultural terms, the strongest deter-
minants of migration processes in Poland are represented by economic and so-
cial motives, among others, the tendency towards improving the living condi-
tions and standard. Their origin is, to a great extent, influenced by socio-
economic situation in a given region, owing to a significant level of regional 
level diversification in Poland. 
 Migrations represent a specific phenomenon, characterized by flows, since 
they occur in a territorial space. Migration flows occur between two territorial 
units. Therefore their conditions should be analyzed in the context of pushing 
and pulling factors influencing population migrations, as well as consider geo-
graphic distance. Such approach to the discussed phenomenon is possible once 
gravity model is applied. Questions related to gravity model implementation 
were discussed, among others, in the economic studies by: Tinbergen (1962), 
Chojnicki (1966), Anderson (1979), Grabiński et al., (1988), Sen, Smith (1995); 
Frankel, Stein, Wei (1995), Helliwell (1997), Egger (2002), Baltagi, Egger, 
Pfaffermayr (2003), Anderson, van Wincoop (2004), Roy (2004); Serlenga, 
Shin (2007), Faustino, Leitão (2008), LeSage, Pace (2009), Kabir, Salim 
(2010). 
 Migrations are, at the same time, characterized by long-term processes 
which take many years to be carried out. Their analysis in spatial perspective 
exclusively, e.g. covering just one year, does not allow for an overall evaluation 
of the occurred phenomenon. In such a situation one of the solutions is to apply 
an aggregated size of migration flows in relation to a given period. This ap-
proach, however, does not allow for the description of changes taking place in a 
given time. In such circumstances the best solution seems to use a panel model 
which facilitates the analysis of the studied phenomenon regarding its cross-
sectional and temporal aspects. Additionally, it allows for considering individu-
al effects with regard to territorial units covered by the study, as well as time 
effects referring to the years under analysis. Therefore it facilitates data hetero-
geneity presentation which could not be accounted for by explanatory variables 
in the model. 
 The paper discusses the proposal of an approach to be applied in modelling 
phenomena characterized by flows and analyzed in spatial and temporal per-
spective. Such standpoint is based on the construction of a panel gravity model. 
The purpose of the paper is to apply this approach in the estimation of both 
intensity and directions, regarding the impact of economic aspects illustrating 
socio-economic situation in the regions, on the size of interregional migration 
flows in Poland in the period 2004–20101. 

                                                 
1 “A region” in the investigation is interpreted as “a voivodship” which is a unit of territorial 

division in Poland (NUTS 2). Interregional migrations means migration flows between voivod-
ships. 



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DYNAMIC ECONOMETRIC MODELS 12 (2012) 109–120 

113 

 The size of migrations, based on the previous and current permanent resi-
dence, was accepted as a dependant variable. The set of explanatory variables 
included indicators responsible for the size of GDP, value of investment out-
lays, level of earnings and unemployment rate. The role of geographical dis-
tance was also considered. Due to the fact that the intensity of internal migra-
tions in Poland is, to a great extent, influenced by economic prosperity, the 
study distinguishes two time spans, i.e. 2004–2007 and 2008–2010. Such solu-
tion allowed for determining economic prosperity impact on potential reasons 
underlying interregional migrations. 
 Panel gravity model with fixed effects was constructed in order to measure 
the researched interdependencies. Both, individual and temporal, effects were 
analyzed. Haussman-Taylor estimator was used to estimate of the structural 
parameters of the model. 
 Three research hypotheses were put forward within the framework of the 
carried out objective. The first assumes that economic factors, defining regional 
socio-economic situation, represent the determinants of interregional migration 
directions in Poland. Following the second hypothesis, during economic down-
turn in Poland (in the period 2008–2010) the influence of analyzed factors on 
the level of interregional migration movements was smaller against the previous 
period of prosperity (2004–2007). In line with the third hypothesis it was as-
sumed that regions featuring a relatively favourable socio-economic situation 
present a positive net migration. 
 The first part of the paper discusses the construction of panel gravity model 
with fixed effects. The second focuses on the analysis scope and the considered 
model specifications. The final part presents the results of conducted research. 

1. The Construction of Panel Gravity Model 
Gravity models describe relations occurring between the size of flows in rela-
tion to a given category (e.g. economic) in territorial space – from the origin 
region to a destination one – and explanatory variables characteristic for both 
regions. The influence of explanatory variables on a dependent variable is con-
sidered in the context of push factors influencing flows from origin regions and 
pull factors attracting migrations to destination regions. Additionally, gravity 
models allow for considering the role of a distance (e.g. geographical, temporal) 
between regional units (see Chojnicki, 1966; Grabiński et al., 1988; Sen, Smith, 
1995). The dissemination of gravity models in economic studies resulted from 
research results published by Tinbergen, who applied gravity model in interna-
tional trade studies (see Tinbergen, 1962).  
The typical gravity model formula (following logarithmic linearization2) takes 
the below form (see Sen, Smith, 1996; LeSage, Pace, 2009) 

                                                 
2 All variables are expressed in natural logarithms. 
 



Michał Pietrzak, Natalia Drzewoszewska, Justyna Wilk 

DYNAMIC ECONOMETRIC MODELS 12 (2012) 111–122 

114 

,0 εdXXY +−++= γβββ ddoo  (1) 

where: 
Y – vector of flow values between regions, 
Xo, Xd – vectors of explanatory variable values respectively for origin and 

destination regions,  
d – vector representing distance between each pair of regions,  

0β  – constant, 
γββ ,, do  –structural parameters of the model, 

ε – vector of random component.  
 Cross-sectional (spatial) and temporal data analysis applies panel models 
among which fixed effects models, the so called FE models, are responsible for 
macroeconomic phenomena. Panel models present a major advantage over 
standard cross-sectional ones owing to their possibility of taking temporal 
changes into consideration. Additionally, distinguishing individual and time 
effects from the fixed ones allows for data heterogeneity description, which is 
not accounted for by explanatory variables (see Baltagi, 2005). 
In case when the research object is represented by a migration phenomenon 
analyzed not only in spatial, but also temporal perspective, the authors suggest 
to construct a panel gravity model with fixed effects which may take the form 
of the formula below: 

,][][][][][ εZγβXβXααY +++++= ditdoitotiit  (2) 

where: 
][itY  – vector of flow values between regions (i=1,2,...,N, i – object’s num-

ber3, t=1,2,...,T – number of time period), 
][][ , itdito XX  – matrixes of explanatory variables values respectively for 

origin and destination regions,  
Z – matrix covering variables fixed in time, including distance between re-

gions, 
][iα  – vector of individual effects,  

][tα  – vector of time effects, 
γββ ,, do – vectors of structural parameters of the model, 

ε  – vector of the random component. 

                                                 
3 In case of panel gravity models, which analyze interregional migration flows, a pair of re-

gions represents an object (unit). For n analyzed regions n2 objects are included in the study, i.e. 
pairs of regions between which migrations are observed. 



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115 

2. Modelling of Interregional Migrations in Poland 
 The purpose of the study is to identify both the intensity and direction of the 
selected economic categories’ influence, which to some extent serve as an illus-
tration of socio-economic situation, on interregional migration movements in 
Poland in the years 2004–2010. 
 Within the analyzed period of time two sub-periods were distinguished. The 
first refers to the years 2004–2007, right after Polish accession to the European 
Union structures, representing the period of Polish economy prosperity. These 
years were characterized by the significant intensity of domestic migrations. 
The second time span covers the years 2008–2010 and is analyzed in the con-
text of global financial and economic crisis also experienced by Polish econo-
my. This period featured economic downturn and lower intensity, as well as 
stability, in migration flows within the country borders. 
 Panel gravity model with fixed effects, represented by the formula (2), was 
applied for the description of spatial-temporal migration aspects. The size of 
migration flows between regions was adopted as the dependant variable4. On 
the other hand, the selected economic indicators were accepted as explanatory 
variables, i.e. GDP per capita, the size of investment per resident, average 
monthly salary before tax and the registered unemployment rate. 
 Separate models were constructed for both time periods. Due to the strong 
statistical correlation of explanatory variables5 the panel gravity models were 
performed separately for every analyzed economic variable6. Additionally, in 
case of each model the impact of geographical distance on the size of migration 
movements was examined7. Table 1 presents variables included in the study. 
 The model assumes the possibility of individual effects occurrence for each 
analyzed pair of regions, as well as time effects for particular years8. Three 
model specifications were considered and represented by formulas (3–5), i.e. 
panel gravity model FE: 

− with both individual and time effects (formula 3), 
− with individual effects only (formula 4), 
− with time effects only (formula 5). 

 

                                                 
4 The analyzed migration flows require their origin region i and their destination region j to be 

specified. Each pair of regions is included in the panel twice to model the size of migration flows 
in both directions. The study does not cover internal regional migration flows. 

5 Distinguishing two periods of time did not influence, to a large extent, the decrease of statis-
tical correlation level between explanatory variables. 

6 It has to be considered that the regressions obtained represent gross regressions and apart 
from the effect of explanatory variables adopted in the model they also reflect impacts of varia-
bles correlated with them. 

7 Geographical distance between regional (voivodship) centroids was analyzed. 
8 In case of the analyzed panel data a pair of regions represents a unit (240 pairs of regions), 

between which migration flows occur, while the time span is one year (2004, 2005,...,2010). 



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Table 1. Variables included in the analysis of interregional migrations 
Variable Definition Accepted 

measure unit 

Migrations Size of interregional migration flows (permanent residence) accord-
ing to previous and current residence address person 

GDP Gross Domestic Product per capita 1000 PLN per 
person 

Investments Investment outlays in enterprises per resident 1000 PLN per 
person 

Salaries Average gross monthly salary in national economy 100 PLN 

Unemployment Registered unemployment rate % 
Distance Geographical distance (distance between regional centroids) km 

 The estimation stage, during panel gravity models application, is a problem-
atic one. While analyzing the effect of distance on the size of migrations it has 
to be considered that this variable is fixed in time. The presence of such varia-
ble, or a set of variables fixed in time, excludes the ordinary estimation of FE 
model parameters with individual effects due to the occurring collinearity. The 
solution to the problem is the application of Hausman-Taylor estimator since it 
allows for estimations of all model parameters (see Hausman, Taylor, 1981). 
 Four separate models, referring to a selected explanatory variable9, were 
defined for each model specification and two analyzed time periods. In case of 
one explanatory variable and fixed in time distance between regions, panel 
gravity model represented by formula (2), depending on selected effects, is re-
duced to the following form: 

,][][0][][][ εdXXααY +++++= γββ itdditotiit  (3) 

,][][0][][ εdXXαY ++++= γββ itdditoiit  (4) 
,][][0][][ εdXXαY ++++= γββ itdditotit  (5) 

where: 
][itY  – vector of flow values between regions (i=1,2,...,N, i – object’s num-

ber, t=1,2,...,T – number of time period), 
][][ , itdito XX  – vectors of explanatory variable values respectively for origin 

and destination regions,  
][iα , ][tα  – vectors of individual and time effects,  

d – vector representing distance between each pair of regions,  
, ,o dβ β γ  –structural parameters of the model, 

                                                 
9 Finally 24 models were estimated, 12 for each analyzed period of time. Adequate tests con-

firmed statistical significance of individual effects or periodical effects in case of each specifica-
tion. 



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117 

ε  – vector of the random component. 
 Prior to the estimation of subsequent FE panel gravity model the specifica-
tions’ significance, both jointly and separately, was analyzed for individual and 
time effects. The obtained test statistics indicated statistical significance of ef-
fects for all three specifications. Having performed the estimation of the model 
specifications the statistical significance of the models' parameters were per-
formed. The economic verification of the models with regard to interpretability 
of the obtained estimates was done as well. 
 Statistical insignificance of parameter estimations for the majority of ac-
cepted explanatory variables, or no possibility for correct interpretation of the 
analyzed economic phenomena impact, were characteristic for model specifica-
tion with joint individual and time effects, as well as the specification with indi-
vidual effects. Therefore, considering individual effects provided an opportunity 
for capturing spatial heterogeneity but, at the same time, did not allow for im-
pact measurement of the analyzed potential determinants on migration phenom-
enon10. It was only the choice of the final model specification, including time 
effects, which allowed for obtaining substantively interpretable parameter esti-
mates for the selected explanatory variables. Therefore the following part of the 
paper presents 8 models, out of 24 analyzed specifications, four in each sub-
period. 

3. Determinants for Interregional Migrations in Poland  
in the Period 2004–2010 

 Table 2 shows the results of estimation of panel gravity models with time 
effects for four explanatory variables. 
 Negative estimates of the distance parameter and its statistical significance 
for all models indicate the decreasing trends in migration intensity, proportion-
ally to geographical distance increase between regions. This confirms unceasing 
timeliness of gravity model concept which assumes that geographical distance11 
represents one of the basic factors determining the size of migration flows. In 
case of the remaining explanatory variables, i.e. GDP, Investments, Salaries and 
Unemployment, for origin regions and destination ones parameters β1 and β2 
proved to be statistically significant at 5% level of significance. Therefore it 
may be agreed that all accepted variables describe, to some extent, the determi-
nants of interregional migration flows in Poland. 

 

                                                 
10 It presents an interesting situation and may result from strong correlation of individual ef-

fects with the analyzed explanatory variables. Such correlation probably resulted in the occur-
rence of parameters insignificance for selected variables and changes in values or the sign of the 
obtained estimates of the parameters. 

11 Distance measure between regions in the gravity model of migration flows reflects costs of 
moving the place of residence. 



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Table 2. The results of estimation of panel gravity models in the period 2004–2007 

GDP Investments 
Parameters Estimates p-value Parameters Estimates p-value 

α2004 1.385 0.02 α2004 12.646 0.0 
α2005 1.165 0.04 α2005 12.388 0.0 
α2006 0.948 0.1 α2006 12.140 0.0 

α2007 0.596 0.3 α2007 11.686 0.0 

β1 1.286 0.0 β1 0.695 0.0 

β2 2.598 0.0 β2 1.444 0.0 

γ -1.413 0.0 γ -1.445 0.0 
R2 Coefficient   68%  R2 Coefficient   66% 

Salaries Unemployment 
Parameters Estimates p-value Parameters Estimates p-value 

α2004 -47.015 0.0 α2004 18.695 0.0 
α2005 -47.306 0.0 α2005 18.584 0.0 

α2006 -47.633 0.0 α2006 18.393 0.0 

α2007 -48.239 0.0 α2007 18.043 0.0 

β1 2.845 0.0 β1 -0.375 0.0 

β2 5.058 0.0 β2 -1.106 0.0 

γ -1.500 0.0 γ -1.564 0.0 
 R2 Coefficient   72% R2 Coefficient   48% 

 Regarding the first three explanatory variables (GDP, Investments and Sala-
ries) positive estimates of β1 and β2 parameters were obtained, however in case 
of Unemployment the respective values were negative. This means that higher 
GDP, Investments and Salaries level and lower Unemployment level act as a 
pull factors to the destination region, but also a push ones from the origin re-
gion. This observation provides grounds for concluding that the population from 
regions characterized by better socio-economic situation presents higher territo-
rial mobility than residents of poorer regions. Therefore it is highly likely that 
the most intensive migration flows occur between more developed regions. On 
the other hand, an unfavourable level of these determinants functions as the 
factor which slows migrations down. Weak position of a given region is trans-
lated, to a great extent, into lowering local community living standards (includ-
ing worse financial stability) and plays the crucial role in their migration poten-
tial reduction. 



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 The results of parameter estimations, referring to panel gravity models with 
time effects for the period 2008–2010 for four explanatory variables, are illus-
trated in Table 3. 

Table 3. The results of estimation for panel gravity models in the period 2008–2010 

GDP Investments 
Parameters Estimates p-value Parameters Estimates p-value 

α2008 0.395 0.6 α2008 11.377 0.0 
α2009 0.217 0.8 α2009 11.569 0.0 
α2010 0.251 0.7 α2010 11.604 0.0 

β1 1.250 0.0 β1 0.565 0.0 

β2 2.512 0.0 β2 1.204 0.0 

γ -1.387 0.0 γ -1.404 0.0 

R2 Coefficient   69% R2 Coefficient   59% 
 

Salaries Unemployment 
Parameters Estimates p-value Parameters Estimates p-value 

α2008 -49.789 0.0 α2008 18.412 0.0 
α2009 -50.160 0.0 α2009 18.897 0.0 
α2010 -50.455 0.0 α2010 18.984 0.0 

β1 2.875 0.0 β1 -0.596 0.0 

β2 5.098 0.0 β2 -1.429 0.0 

γ -1.494 0.0 γ  -1.482 0.0 

R2 Coefficient   71% R2 Coefficient   55% 

 Models referring to the period 2008–2010 include all explanatory variables 
which are statistically significant, while the same signs of parameter estimates 
allow for identical interpretation of their influence directions as in the period 
2004–2007. In this period it was also confirmed that migration intensity keeps 
decreasing along with increasing distance between regions, proved by γ parame-
ter with negative sign. Additionally, the statistical significance of parameters for 
the accepted economic variables allows for the first hypothesis verification that 
socio-economic situation in Poland, which to some extent is represented by the 
adopted economic indicators, presents an important determinant of domestic 
interregional migration directions. 
 It should also be observed that the impact intensity of adopted explanatory 
variables on migration phenomenon is diversified. Variables can be arranged 
according to their impact on interregional movements. The size of explanatory 



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DYNAMIC ECONOMETRIC MODELS 12 (2012) 111–122 

120 

variable impact intensity results from the total (in absolute terms) value of esti-
mates of the parameters (see tab. 4). The higher the total value the more intense 
migratory movements should be expected as the result of changes in the level of 
explanatory variables. The highest values of the parameter estimates regarding 
structural models, in case of both analyzed periods of time, referred to Salaries 
and then subsequently to GDP. The sequence of variables by the significance 
level did not present radical changes in relation to economic prosperity trans-
formations. However, in times of crisis the impact intensity of all variables (ex-
cept Distance) was reduced. Most probably also other factors, not covered by 
the study, did play major role in the discussed period of time. 

Table 4. The difference and the total value of parameter estimates regarding the origin 
and destination regions 

Economic variable 
Difference in values of parameter 

estimates (β2-β1) 
Total value of parameter estimates 

|(β2+β1)| 

Period 1 Period 2 Period 1 Period 2 

GDP  1.311723 1.262386 3.885185 3.762408 

Investments  0.749878 0.639443 2.140044 1.768789 
Salaries 2.213778 2.2235 7.902992 7.97324 

Unemployment -0.73106 -0.833313 1.48135 2.024317 

 Therefore, the obtained results allow for concluding that in recent years 
higher salaries represented the strongest factor stimulating Polish population to 
change their place of residence. This observation is of high probability since 
higher salary frequently constitutes not only the most important objective for a 
potential migrant, but just in itself allows for saving financial means indispen-
sable for covering costs of moving to another place. The collected results sug-
gest that the level of salaries is the most important determinant of interregional 
migration flows, which proves the crucial role of job market in exerting impact 
on migrations in Poland. 
 Further analysis of the total value parameter estimates indicates that the 
second in line variable, influencing migration level most intensely, is GDP per 
capita. The impact of investment outlays against unemployment rate is stronger 
in the first period, while in the second it is changed and a reverse situation oc-
curs. 
 In accordance with the second research hypothesis economic factors, in the 
period of prosperity, have a stronger influence on migratory movements than in 
times of economic downturn. The power of these factors’ impact on migrations 
went up regarding values related to job market, i.e. the level of gross average 
monthly salary and the registered unemployment rate. However, in the period 
2008–2010 the intensity of regional GDP per capita and the impact of invest-
ment outlays were reduced. This fact does not allow for an unequivocal verifi-
cation of the second hypothesis. The results obtained suggest the need for more 



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research covering other factors impact to be carried out, especially these refer-
ring to economic development and job market. 
 Interesting conclusions can also be drawn from the interpretation of the 
value of the parameters regarding push and pull factors, i.e. the difference in 
value of β2 and β1 (see tab. 4). Owing to the fact that population migrations be-
tween regions are two-directional, positive parameter estimates for both origin 
and destination regions point to the migratory movements occurring simultane-
ously in both directions. The final balance of population flows is determined by 
the sign of the designated difference. Positive difference indicates higher popu-
lation movement towards regions featuring favourable values of explanatory 
variables. In case of interregional migration flows the positive difference illus-
trates the tendency towards obtaining positive net migration by regions enjoying 
favourable socio-economic situation. On the other hand, negative difference 
underlies tendencies towards more intense population outflow from regions 
showing less attractive values of explanatory variables. This allows for the third 
hypothesis verification following which the regions featuring the highest socio-
economic development present the tendency for positive internal net migration. 

Conclusions 
 The purpose of the paper was to analyze the selected economic variables’ 
impact on interregional migratory movements in Poland in the period 2004–
2010. Panel gravity model with time effects for the assessment of potential de-
terminants’ impact intensity and direction was applied. The conducted research 
indicates the usefulness of such approach in interregional migration phenome-
non modelling in Poland. 
 The results obtained in the investigation allowed for the first research hy-
pothesis adoption according to which socio-economic situation illustrated, to 
some extent, by values of economic indicators represents an important determi-
nant defining interregional migration directions in Poland. The analysis of the 
underlying variables impact intensity in two analyzed periods of time did not 
allow for unequivocal verification of the second hypothesis which suggests a 
relatively higher influence of the discussed economic factors in the period of 
prosperity. It was only in case of GDP and Unemployment that slightly higher 
values of parameter estimates were observed in the period of prosperity. 
 However, it was noticed that the level of salaries represent the most im-
portant determinant of interregional population migration flows, which confirms 
the significant role of job market in relation to migrations. The obtained results 
also emphasized different, in time, nature of impact exerted by factors responsi-
ble for economic development, as well as these related to job market. 
 The conducted analysis also provided grounds for the third research hypoth-
esis verification stating that in regions characterized by the highest level of so-
cio-economic development there is a tendency towards positive migration flow 



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balance. This is definitely one of the factors responsible for the divergence in 
the development of Polish regions. 
 The presented approach does not cover all options possible in relation to the 
phenomenon of migrations. Among the problems still left open for considera-
tion the following should be mentioned: an in-depth analysis of internal migra-
tion determinants in times of crises, analysis of factors influencing interregional 
migrations and also spatial relations which may occur in case of migrations, all 
of them to be studied using panel gravity model with spatial effects. 

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	Introduction
	1. The Construction of Panel Gravity Model
	2. Modelling of Interregional Migrations in Poland
	3. Determinants for Interregional Migrations in Poland  in the Period 2004–2010
	Conclusions
	References

