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Regional convergence within particular country — An approach based on the regional price deflators
Economic Modelling 57 (2016) 171–179
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Regional convergence within particular country — An approach based on the regional price deflators Bartlomiej Rokicki a,b,⁎, Geoffrey J.D. Hewings b a b
University of Warsaw, Faculty of Economic Sciences, Poland; University of Illinois, Urbana, IL 61801-3671, United States University of Illinois, Regional Economics Applications Laboratory, Urbana, IL 61801-3671, United States
a r t i c l e
i n f o
Article history: 21 May 2015 30 March 2016 Accepted 29 April 2016 Available online xxxx JEL classification: E30 O10 R10
a b s t r a c t This paper applies regional price deflators for Polish NUTS2 regions and US states in order to reassess regional income convergence within particular country. We find that the regional income disparities decrease significantly once we account for regional price differentials. Moreover, we prove that the application of regional price deflators has significant impact on the results of both σ and β-convergence analysis. They also influence the conclusions concerning the magnitude of spatial spillovers. The above results can have important policy implications, in particular concerning the EU Cohesion Policy financial allocations and the assessment of policy effectiveness. © 2016 Elsevier B.V. All rights reserved.
Keywords: Regional convergence Regional price deflators Cohesion policy
1. Introduction The evolution of regional income convergence within different countries, and the European Union (EU) member states in particular, has been thoroughly discussed in many papers. The research on regional income convergence was pioneered by Barro and Sala-i-Martin (1991 and 1992) who revealed a negative relationship between economic growth rate and the initial level of income both across US states and across European regions. They found that there was an absolute βconvergence across both 73 Western European regions and the regions within particular countries between 1950 and 1985. Surprisingly, the speed of convergence was very similar in all cases and reached about 2% yearly. This last result has been a subject of controversy in the literature. As a matter of fact, many other studies show that the speed of convergence appears to depend on the estimation strategy applied by the researchers (e.g. Abreu et al., 2005; Arbia et al., 2008). One of the crucial points at the time of estimating regional income convergence within particular country is the choice of price deflator. As claimed by Tabuchi (2001), the high income regions tend to have
⁎ Corresponding author at: University of Warsaw, Faculty of Economic Sciences. Dluga 44/50, 00-241 Warsaw, Poland. E-mail addresses: [email protected] (B. Rokicki), [email protected] (G.J.D. Hewings).
http://dx.doi.org/10.1016/j.econmod.2016.04.019 0264-9993/© 2016 Elsevier B.V. All rights reserved.
higher level of prices than the low income ones. Hence, the use of average national price deflator will most likely lead to an artificial increase of income in the better developed areas and a decrease in the lagging behind ones. This in turn would result in overestimation of existing regional income differentials. On the contrary, the application of regional price deflators should lower the overall level of income disparities expressed by sigma convergence (as compared to the results obtained once applying average national price deflator). At the same time, the impact of regional price deflators on dynamic indicator of regional income differentials, such as beta convergence, is unclear since it depends on the evolution of regional price indices.1 Also, it is uncertain what would be the impact of the regional price deflators on the spatial income spillovers. While the point made above may be well-known in the convergence literature in Europe there are no studies analyzing the impact of regional price deflators on the results of convergence analysis. This paper adds to the existing convergence literature by showing the impact of the regional price deflators on the analysis of regional income disparities within a given country. In particular it compares the results of convergence analysis, in the case of Poland between 2000 and 2011 at the NUTS2 level, based on the per capita GDP deflated by 1 There should be a significant impact only if the regional inflation rates differ substantially over the analyzed period.
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regional price deflators and per capita GDP deflated by national price deflator.2 Still, in order to verify the robustness of our results we also apply regional price deflators for the US states for the 2008–2013 period.3 We consider both β-convergence and σ-convergence approaches and apply different econometric techniques in order to show that the results of previous studies may overestimate the overall level of regional income disparities. They may also lead to different conclusions concerning regional convergence patterns. The overestimation of regional income disparities can have important policy implications, in particular concerning the EU Cohesion Policy. Here, the financial allocations are closely linked to the relative level of regional income. Hence, the change in relative income, due to the application of regional price deflators, could lead to a significant change in allocation patterns. Moreover, we believe that the inclusion of regional price deflators can influence the conclusions drawn from research focused on the structural policy effectiveness. The remainder of the paper is as follows. In the next section we briefly review the existing literature on income convergence. Thereafter we present the research methodology. Section 4 discusses empirical results and Section 5 concludes.
2. Literature review There can be distinguished to main strands in the literature on income convergence. The first one, triggered by seminal papers by Abramovitz (1986) and Baumol (1986), focuses on the evolution of income disparities across countries. It also tries to explain the factors that influence that process (e.g. Alam, 1992; King and RamloganDobson, 2015; Próchniak and Witkowski, 2013). The second strand concentrates on the evolution of regional income convergence within different countries, and the European Union member states in particular. Here, the interest of many researchers and policy makers is driven by the existence of the EU Cohesion Policy that nowadays accounts for almost a half of the Community budget. Hence, both supporters and skeptics of the policy are constantly searching for arguments in favor or against its continuation. The research on regional income convergence within particular countries was pioneered Barro and Sala-i-Martin (1991 and 1992) who showed a negative relationship between economic growth rate and the initial level of income both across US states and across European regions. They found that there was an absolute βconvergence across both 73 Western European regions and the regions within particular countries between 1950 and 1985. Surprisingly, the speed of convergence was very similar in all cases and reached about 2% yearly. During the last two decades or so, the results reported by Barro and Sala-i-Martin have been a subject of criticism. Indeed, many other studies show that the speed of convergence appears to depend on the estimation strategy applied by the researchers (e.g. Abreu et al., 2005; Arbia et al., 2008). Hence, many authors suggested different methodological improvements that could lead to different conclusions concerning the evolution of regional income convergence. Here, among others, we can mention the inclusion of spatial spillovers (e.g. Arbia and Paelinck, 2003; Arbia et al., 2010), the distribution dynamics approach (e.g. Fischer and Stumpner, 2008; Maza et al., 2012; Quah, 1997) or different estimation approaches (e.g. weighted approach by Petrakos and Artelaris, 2009; pair-wise approach by Le Pen, 2011; semiparametric approach by Azomahou et al., 2011). Somehow surprisingly there are hardly studies that focus on issues related to the 2 The existing studies tend to use nominal data deflated by national PPP deflators in order to express data in constant prices that allows for analysis among different member states. Yet, the application of national PPP deflators has no impact on convergence analysis within particular country, as compared to analysis based on data expressed in current prices (e.g. nominal per capita GDP). 3 Regional price deflators for the US are available for the 2008–2013 period only.
statistical data. Even though the data inaccuracy may have, in fact, a greater impact on the results of convergence analysis than mere differences in econometric approaches. For instance, Cameron and Muellbauer (2000) claim that, because of the downward bias in South East region income levels in the 1980s, the results of studies on regional income convergence within the UK (e.g. Quah, 1996 or Sala-i-Martin, 1996) are seriously biased. Potentially, one of the main sources of data inaccuracy is the lack of regional price deflators. European national statistical offices do not provide such a data (so obviously neither does the Eurostat, that relies on the data received from national statistical authorities) since most of them do not collect the representative data on prices at regional level.4 The same applies to the countries such as US where regional price deflators were not available until few years back and cover very short period of time. As a result, all of the studies rely on the regional per capita GDP that, in order to be internationally comparable, is deflated using national Purchase Power Parities (PPP) or Purchase Power Standards (PPS5) deflators. The problem is that such an approach leads to overvaluation of per capita income in regions with regional price indices higher than the national average and undervaluation of income in areas with price indices below the national average. This is because these are the high income regions with big agglomerations that tend to have higher level of prices than the low income ones (e.g. Tabuchi, 2001). Hence, we might expect that the application of regional price deflators (instead of national average) should lower the overall level of income disparities since it would reduce the real per capita income6 in better developed regions and increase in the worse developed ones. At the same time its impact on dynamic indicator of regional income such as beta convergence is unclear since it depends on the evolution of regional price indices.7 Also, it is uncertain what would be the impact of the regional price deflators on the regional income spillovers. While the analysis of the impact of regional price deflators on the different regional convergence indicators can seem interesting from the purely scientific point of view it may have also important policy implications. First of all, mind that the per capita income criterion is not only the main criterion used to qualify the NUTS2 level regions into different priority groups under the EU Cohesion Policy but also the one used to determine the level of financial allocations for regions within each priority group. Hence, the small change in relative income level caused by the application of regional price deflators could potentially lead to substantial alteration in the amount of structural funding received from the EU.8 Still, the application of regional price deflators could also change the negative conclusions concerning the effectiveness of EU structural policies in terms of their impact on regional economic performance (e.g. Boldrin and Canova, 2001; Dall'erba and Le Gallo, 2008). This might occur once we assume that the least developed areas had been in fact growing faster (in real terms) than previously assumed.
4 Hence, there are very few examples of regional price deflators calculated by researchers. For instance, Aten et al. (2012) estimate regional price parities for the US states and metropolitan areas, Brandt and Holz (2006) provide a set of provincial-level spatial price deflators for China, Čadil et al. (2014) calculate regional PPP deflators for the 14 Czech NUTS3 regions in 2007 and Rokicki (2015) computes regional price deflators for Polish NUTS2 regions. 5 Eurostat provides an artificial currency indicator such as PPS for EU countries that has the same purchasing power in all member states. 6 Please note, that in the remainder of the paper we refer to the real per capita income as income deflated by regional price deflators. On the other hand, when we name nominal per capita income we refer to regional income deflated by average national price deflator. 7 There should be a significant impact only if the regional inflation rates differ substantially over the analyzed period. 8 Imagine the region with per capita income just below or above the 75% EU average. Here, if regional prices differ significantly from national average then the application of regional price indices could lead to reassessment of its relative level of income and qualification to a different priority group. This in turn would mean either a gain or loss in structural funding worth millions of euro.
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3. Research methodology and data
ln ðy
yi;t
i;t−T
The lack of studies concerning the evolution of regional income inequalities, which rely on regional price deflators, cannot be really surprising. The main problem here is the absence of necessary statistical data on regional prices. That is why we focus on Poland, where such data is available for 16 regions at the NUTS2 level for the period 2000– 2011. Hence, it is possible to compute a time series of regional price deflators. This constitutes the first stage of our research. These deflators are thereafter applied in the analysis of the evolution of regional income disparities. Still, in order to verify the robustness of our results we also use the data on price deflators published by Bureau of Economic Analysis and analyze the evolution of regional income differentials between 51 US states during the 2008–2013 period. As far as we are concerned this is the only country other than Poland where the time series of reliable regional price deflators are available.9 In our analysis we consider both β-convergence and σ-convergence approaches in order to show the impact of regional PPP deflators on different measures of regional income disparities. We analyze several different specifications so as to verify to what extent the results are sensible to the application of regional PPP deflators. In the case of βconvergence we run unconditional, conditional and spatial lag and spatial error specifications.10 In the case of σ-convergence we test traditional and weighted approaches.11 The baseline β-convergence regressions are based on panel estimation of the classical unconditional convergence equation: ln
yi;t
!
yi;t−T
¼ α þ β ln yi;t−T þ εi;t
173
ÞÞ show the impact of economic growth in surrounding areas
on growth rate in the given region. Also, the spatial error term (λWεi,t) measures the impact of the error in neighborhood regions on the error term in the given region. The baseline coefficient of variation (σ-convergence) is expressed by the formula: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X ln ðyi;t − ln ðyt ÞÞ2 σt ¼ t n i¼1
ð4Þ
where y is the average per capita income for the whole country. Its weighted version is given by: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX ln ðyi;t − ln ðyt ÞÞ2 P i;t σt ¼ t
ð5Þ
i¼1
ð1Þ
where yi,t is per capita GDP in region i at time t. The estimation controls for seasonality problems. Here, following the Solow–Swan model, we should expect to find the regions with initial higher level of per capita income to grow slower than the lagging behind ones. However, this requires to assume that all of them share the same technology, savings rate, depreciation rate and population growth rate.12 Our simple conditional convergence specification is given by Eq. (2) below: ln
yi;t
!
yi;t−T
¼ α þ β ln yi;t−T þ γDi þ εi;t
ð2Þ
where Di is a dummy variable for region i. In this case we allow the regions to differ in terms of the model parameters. As a result we may find the conditional convergence even though there is no absolute (unconditional) one. Finally, we analyze spatial extension of the Eq. (1) in the form of the fixed-effects spatial autoregressive model: ln
yi;t yi;t−T
!
n X ¼ α þ β ln yi;t−T þ ρ wi; j ln i−1
yi;t yi;t−T
! þ εi;t
ð3Þ
where wi,j is an element of a spatial weights matrix W, with n representing the number of regions and εi , t = λWεi , t + ui , t where n
ui , t ~ Nid(0, σ2). Here, spatial spillovers expressed by spatial lag (∑wi; j i−1
9
As mentioned before, Brandt and Holz (2006) provide a set of provincial-level spatial price deflators for China. Still, the data on prices covers very few products (at most 60) which casts serious doubts on the reliability of regional price deflators they provide. 10 Obviously, these are only some of the many possible specifications. See Abreu et al. (2005) and Arbia et al. (2008) for more detailed surveys on different convergence analysis specifications. 11 See Petrakos and Artelaris (2009) for details on the weighted approach. 12 For details about the theoretical propositions behind the classical convergence approach see for example Barro and Sala-i-Martin (1991 and 1992).
Fig. 1. Regional differentials in prices between Polish regions in 2000 and 2011 (national average = 1). Source: Authors' elaboration.
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Fig. 2. Regional differentials in prices between US states in 2008 and 2013 (national average = 1). Source: Authors' elaboration.
Table 1 Regional per capita GDP in 2011 at the NUTS2 level in Poland — the impact of the PPP deflators. Source: Authors' elaboration. Region
Dolnośląskie Kujawsko-pomorskie Lubelskie Lubuskie Łódzkie Małopolskie Mazowieckie Opolskie Podkarpackie Podlaskie Pomorskie Śląskie Świętokrzyskie Warmińsko-mazurskie Wielkopolskie Zachodniopomorskie Poland
Nominal per capita GDP (PLN)
Nominal per capita GDP Poland = 100
Real per capita GDP (PLN)
Real per capita GDP Poland = 100
44,961 32,596 26,919 32,795 36,750 34,107 64,790 31,771 26,801 28,485 37,822 42,830 29,552 28,635 41,285 33,485 39,665
1.134 0.822 0.679 0.827 0.927 0.860 1.633 0.801 0.676 0.718 0.954 1.080 0.745 0.722 1.041 0.844 1.000
43,386 33,784 27,778 31,851 36,387 34,098 61,189 31,797 27,902 29,311 35,945 42,450 30,539 28,906 42,608 32,868 39,665
1.094 0.852 0.700 0.803 0.917 0.860 1.543 0.802 0.703 0.739 0.906 1.070 0.770 0.729 1.074 0.829 1.000
where Pi stays for the share of region's i population in total country population. Hence, in the weighted approach the regions with a larger share of national population have a greater impact on the overall value of sigma convergence. In the Polish case we should expect the weighted sigma convergence to be higher than the traditional one since the best developed region Mazowieckie is also by far the region with the highest number of inhabitants.13 More complex situation can be observed in the case of the US states. First because of the much higher number of territorial units, and second because the states with the highest per capita income are not necessarily the biggest in terms of population (e.g. District of Columbia). Please note, that this paper is focused on the issues related to the choice of regional income variable and its impact on the results of convergence analysis. Hence, we provide the results of β-convergence regressions as an illustration only. This is particularly important taking into account the fact that our observations (particularly in the case of the US states) cover very short period of time while the convergence process is a long term phenomenon. Therefore, here we do not discuss in detail questions concerning different econometric strategies and their consequences. Nor we analyze estimated convergence speeds. Regional price deflators for Poland are estimated in accordance to the common Eurostat/OECD methodology. Although this methodology 13 So the significant difference between the regional income and national average in its case counts more in the weighted approach.
Table 2 Regional per capita GDP in 2013 at the state level in the US — the impact of the PPP deflators. Source: Authors' elaboration. State
Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming United States
Real per capita GDP US =
100
Real per capita GDP (USD)
37,189 66,817 38,762 36,539 53,505 50,457 62,989 59,767 159,506
0.768 1.381 0.801 0.755 1.106 1.043 1.302 1.235 3.296
42,405 63,035 39,920 41,759 47,645 49,371 58,054 58,942 135,519
0.876 1.302 0.825 0.863 0.984 1.020 1.200 1.218 2.800
38,197 42,262 49,087 34,608 51,434 43,347 48,554 44,462 38,371 45,588 37,405 53,176 61,191 41,169 52,372 31,642 41,963 38,021 51,664 42,883 48,099 55,959 38,971 62,130 43,200 63,911 44,579 40,957 49,897 46,560 46,679 35,608 46,875 41,295 52,623 42,474 42,814 51,351 53,735 34,742 45,676 61,297 48,397
0.789 0.873 1.014 0.715 1.063 0.896 1.003 0.919 0.793 0.942 0.773 1.099 1.264 0.851 1.082 0.654 0.867 0.786 1.068 0.886 0.994 1.156 0.805 1.284 0.893 1.321 0.921 0.846 1.031 0.962 0.965 0.736 0.969 0.853 1.087 0.878 0.885 1.061 1.110 0.718 0.944 1.267 1.000
38,661 45,987 42,244 37,293 50,925 47,426 53,770 48,967 43,065 49,987 38,286 47,950 57,028 43,704 53,660 36,454 47,044 40,277 57,087 43,669 45,419 48,873 41,022 53,886 47,110 69,925 49,753 45,558 50,554 47,221 47,583 39,346 53,510 45,580 54,419 43,698 42,729 49,855 52,069 39,301 49,167 63,984 48,397
0.799 0.950 0.873 0.771 1.052 0.980 1.111 1.012 0.890 1.033 0.791 0.991 1.178 0.903 1.109 0.753 0.972 0.832 1.180 0.902 0.938 1.010 0.848 1.113 0.973 1.445 1.028 0.941 1.045 0.976 0.983 0.813 1.106 0.942 1.124 0.903 0.883 1.030 1.076 0.812 1.016 1.322 1.000
Nominal per capita GDP (USD)
Nominal per capita GDP US =
100
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175
Fig. 3. Unweighted and weighted sigma convergence among Polish NUTS2 regions between 2000 and 2011. Source: Authors' elaboration.
is usually used to allow income comparisons between different countries it may also be applied in order to analyze the evolution of real income level between different regions within the some state. It is based on the expenditure side of the Gross Domestic Product and employs the EKS (Éltetö–Köves–Szulc) method that requires data concerning both the prices of representative goods and services and the structure of spending (that is necessary to weight price indices calculated for particular base categories).14 In the first step, we apply data concerning prices at the base category level to calculate unweighted PPP indices for each pair of regions. These are so called Fisher type PPP that rely on Laspayers index for products representative for the first region and Paasche index for products representative for the second one. The above indices are defined as follows:
LAB
Standardized PPP deflators at the base categories must be then aggregated using weights for particular base categories in the overall expenditure. This is done in a similar way as described for particular base categories. Hence, first we compute the Laspayers index defined as:
LAB
Xn EKSiA EiB i¼1 EKS ¼ Xn iB E i¼1 iB
where E stays for expenditure in base category i in region B. Then we calculate Paasche and Fisher indices, following the formulas: P AB ¼
n1 P iA A ¼ ∏ i∈RA P iB
ð11Þ
ð6Þ F AB ¼
1 : LBA qffiffiffiffiffiffiffiffiffiffiffiffiffiffi LAB P AB :
ð12Þ
ð13Þ
where RA stays for products representative for region A. P AB ¼ ∏ i∈RB
P iB P iA
n1
B
ð7Þ
where RB stays for products representative for region B. F AB ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi LAB P AB :
ð8Þ
Still, the Fisher type PPP does not accomplish the transitivity condition which is achieved by applying the EKS method. The EKS PPP between regions j and k can be computed using the following formula: 1 F jl n EKSjk ¼ F 2jk ∏ l≠ j;k F kl
ð9Þ
where j ,k ,l ϵ N. Finally, we need to standardize the EKS indices in order to get PPP deflators that have a group of regions as a basis. We achieve this by calculating. EKSA ¼ ¼
14
EKSAA
EKSAB
∏i¼A EKSiA EKSAn
∏i¼A EKSiB
n
¼ 1 X i
n ∏i¼A EKSin
1 X
n
¼… 1 X i ð10Þ
i
See European Communities/OECD (2006) for more details.
Finally, we apply the EKS method in order to meet the transitivity condition and standardization in accordance with the Eqs. (9) and (10). This way we get the average PPP deflators for each region. These deflators are afterwards used to adjust the data on regional per capita income. Our data on regional prices covers the 2000–2011 and accounts for over 300 representatives of consumer goods and services. In this sense it is much more detailed than the data used in the recent paper by Rokicki (2015). Most of the data on prices is unpublished and has been obtained courtesy of Polish Central Statistical Office. Almost all of the remaining data comes from the different publications of the Polish Central Statistical Office and covers the 2000–2011 period. In particular, the data on regional per capita income comes from the Local Data Bank and is compiled in accordance with the Polish Classification of Activities 2007 (PKD 2007)15 and the European System of National and Regional Accounts (the ESA 1995),16 while data on expenditure comes from the Household Budget Survey. We use yearly data expressed in Polish zloty. The only exception applies to the regional per capita income data from Eurostat that is expressed in PPS. The data used to compute spatial weights matrix and maps comes from the ESRI shapefile data for Polish NUTS2 regions. The data on US states per capita income and regional price deflators comes from the Bureau of Economic Analysis. The data on regional population used to compute the weighted sigma convergence comes from US Census Bureau.17 All the above data covers 2008–2013 period. The 15
Here, the latest available data comes from 2011. At the time of preparing the paper the Polish Central Statistical Office did not provide the data covering the whole 2000–2011 period in accordance with the ESA 2010 standard. 17 See Intercensal Estimates of the Resident Population for the United States, Regions, States, and Puerto Rico. 16
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Fig. 4. Unweighted and weighted sigma convergence among US states between 2008 and 2013. Source: Authors' elaboration.
data used to compute spatial weights matrix and maps comes from the ESRI shapefile data for US states. 4. Empirical results Regional price deflators calculated in accordance with the Eurostat/ OECD methodology confirm the existence of substantial price differentials between Polish regions. Moreover, Fig. 1 shows that although there have been some changes in terms of spatial distribution of regional price deflators between 2000 and 2011,18 on average the highest level of prices can be found in the best developed areas with big agglomerations (e.g. Warsaw, Katowice, Wrocław or Gdańsk). On the other hand these are the rural areas that tend to experience the lowest level of prices (e.g. eastern Poland). In 2000 the highest levels of price indices are observed in the capital region (Mazowieckie) and the region placed at the western border of the country (Lubuskie). On the other hand, the lowest levels of prices are found in the central and eastern part of Poland. In 2011 the Mazowieckie (Warsaw) maintains the highest level of price index. However, the Pomorskie (Gdańsk) voivodship replaces Lubuskie as a second region with the highest prices. Other regions with big cities, such as Dolnośląskie (Wrocław) or Śląskie (Katowice) also have higher than average price indices. At the same time the group of regions with the lowest values of regional price deflators expands into all eastern border regions and Wielkopolskie region. The Polish case is not particularly exceptional since substantial differences in prices exist also between US states. Again, on average these are regions with big agglomerations that have the highest level of prices (e.g. New York, Los Angeles, Washington and Chicago), while the lowest price indices can be found in rural areas. It can be easily verified on Fig. 2 that the highest price indices can be found in New York (New York), District of Columbia (Washington) and California (Los Angeles). On the other hand the states with the lowest prices are located mostly within the rural Midwest region (e.g. Iowa or Missouri). Here, Illinois (Chicago) can be considered as an exception, surrounded by experiencing lower price indices Midwest states. There is no big change in the spatial pattern of regional price indices between 2008 and 2013. The most notable exception is an increase of relative price indices in certain Midwest states such as North Dakota, Nebraska and Kansas. So as to more accurate evaluation of the impact of regional price deflators, on per capita GDP in particular Polish regions, we calculate the indices showing the regional/national average ratio in 2011 before and after using the deflators (see Table 1). Here, columns 1 and 3 show absolute values of regional per capita GDP while columns 2 and 4 report relative per capita GDP level (as compared to national average), 18
Most likely due to the EU accession.
Table 3 The results of the β-convergence analysis for Polish NUTS2 regions. Source: Authors' elaboration. Variables
Nominal per capita GDP
(1)
(2)
(3)
(4)
(5)
(6)
Model
Model
Model
Model
Model
Model
0.011⁎ (0.006)
Real per capita GDP Lambda Rho Constant Time dummies Region dummies Observations Log likelihood
−0.228⁎⁎⁎
0.010 (0.006) 0.006
0.005⁎⁎
(0.008)
(0.008) −0.237 (0.317) −0.214 (0.316) 0.003 (0.074) Yes No 176 454.35
−0.268 (0.329) −0.214 (0.324) −0.062 −0.019 −0.040 (0.060) (0.078) (0.062) Yes Yes Yes No No No 176 176 176 469.88 453.13 471.29
(0.067)
−0.307⁎⁎⁎ (0.064)
2.306⁎⁎⁎ (0.665) Yes Yes 176 488.01
3.101⁎⁎⁎ (0.633) Yes Yes 176 473.93
OLS estimation (Models 1–2 and 5–6), LM estimation (Models 3–4). Robust standard errors in parentheses Spatial specifications based on the inverse distance matrix. ⁎⁎⁎ p b 0.01. ⁎⁎ p b 0.05. ⁎ p b 0.1.
before and after using price deflators respectively. As expected, nominal per capita GDP (column 1) is lower than real per capita GDP (column 3) in the three best developed regions (Dolnośląskie, Mazowieckie, Śląskie).19 This in turn leads to a decrease of their relative real per capita income (column 4) as compared to the relative nominal per capita income (column 2). In the case of the richest Mazowieckie voivodship its per capita income decreases, as compared to the national average, by more than 9 percentage points. The difference between the nominal and real per capita GDP relative to national average is smaller for Dolnośląskie and Śląskie. Here it does not exceed 4 percentage points and 1 percentage point respectively. Exactly opposite results can be found for the low income areas such as Lubelskie, Podkarpackie, Podlaskie, Świętokrzyskie and Warmińskomazurskie, where the overall level of prices is lower than national average. Here we find that the relative level of per capita income increases between 0.7 percentage point (Warmińsko-Mazurskie) and 2.7 percentage points (Podkarpackie). In this sense the impact of regional price deflators seems to be smaller than for the best developed regions.
19
Here, the overall level of prices is above the national average.
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Table 4 The results of the β-convergence analysis for US states. Source: Authors' elaboration. Variables
Nominal per capita GDP
(1)
(2)
(3)
(4)
(5)
(6)
Model
Model
Model
Model
Model
Model
−0.007 (0.005)
−0.001 (0.005) −0.008 (0.007)
Real per capita GDP Lambda Rho Constant Time dummies Region dummies Observations Log likelihood
0.043 (0.054) Yes No 255 605.37
0.059 (0.071) Yes No 255 612.72
0.757⁎⁎⁎ (0.082) −0.999⁎⁎⁎ (0.284) −0.023 (0.049) Yes No 255 614.04
−0.004⁎ (0.006) 0.728⁎⁎⁎ (0.091) −0.841⁎⁎ (0.295) 0.008 (0.061) Yes No 255 620.83
−0.371⁎⁎⁎ (0.084)
3.871⁎⁎⁎ (0.884) Yes Yes 255 679.77
−0.405⁎⁎⁎ (0.086)
4.282⁎⁎⁎ (0.916) Yes Yes 255 683.39
OLS estimation (Models 1–2 and 5–6), LM estimation (Models 3–4). Robust standard errors in parentheses. Spatial specifications based on the inverse distance matrix. ⁎⁎⁎ p b 0.01. ⁎⁎ p b 0.05. ⁎ p b 0.1.
Similar results can be found for the US states in 2013 (see Table 2). Here, per capita GDP decreases significantly after applying regional price deflators, in regions with the highest income level and increases in regions with the lowest income level.20 In particular, relative per capital income decreases by almost 50 percentage points in District of Columbia, more than 17 percentage points in New York, more than 10 percentage points in Connecticut and almost 8 percentage points in Alaska. On the other hand we find that relative real per capita GDP is higher than the nominal one by more than 10 percentage points in Alabama, almost 10 percentage points in Mississippi and West Virginia, almost 8 percentage points in South Carolina and more than 5 percentage points in Idaho. The above suggests that we might observe a reduction in dispersion of regional per capita GDP (σ-convergence) once we refer to the real instead of nominal values. Indeed, unweighted σ-convergence in Poland in 2011 falls from 0.265, calculated for nominal per capita income, to 0.248 computed using the data adjusted for regional prices. The impact is slightly bigger once we apply the weighted approach. Here, the value of coefficient of variation decreases from 0.268 for nominal per capita GDP to 0.246 for the real one. It appears, however, that the application of regional price deflators hardly affects the evolution of σ-convergence between 2000 and 2011 (see Fig. 3). The evolution of variation coefficient for nominal and real per capita GDP looks pretty similar. In this sense, there is no difference between un-weighted and weighted approach. Although, it is clear that regional price deflators have greater impact on weighted σconvergence during the whole analyzed period. The US data seems to confirm that our findings concerning the impact of regional price indices on regional income disparities are rather universal. Unweighted σ-convergence for US states in 2013 reaches 0.249 once we use nominal per capita GDP and falls to 0.204 when we use real per capita GDP. Similar impact can be observed in the case of weighted approach — here the value of σ-convergence falls from 0.170 to 0.121 once we apply real income instead of the nominal one. Again, there is no visible impact on the evolution of σ-convergence (see Fig. 4). However, regional price deflators have slightly bigger
20 Few exceptions exist (e.g. North Dakota or Wyoming). Here, per capita GDP increases as a result of applying regional price deflators even though their nominal income is much higher than national average. This may be explained, however, by the fact that the above regions are mostly rural with a lack of important agglomerations. Hence, their overall price levels are below the national average even though the relative per capita income is high.
impact on weighted σ-convergence between 2008 and 2013. Note, that the overall impact of regional price indices is in fact greater in the US case as compared to the Polish one. This is not surprising though taking into account that the number of US states more than triplicates the number of Polish NUTS2 regions. Hence, comparing Poland with other European countries we may expect that the impact of regional price deflators would be bigger in the ones with greater number of NUTS2 regions (e.g. Germany) and smaller in the ones with less regions (e.g. Hungary). The introduction of the regional price deflators has also a significant impact on the results of the absolute β-convergence analysis during the 2000–2011 period (see Table 3). The OLS panel regression based on Eq. 1 and nominal per capita GDP shows statistically significant divergence process with the income coefficient 0.011 (Model 1). This result was reported also in other studies (e.g. Czyż and Hauke, 2011). Yet, this is not the case of the regression based on real per capita GDP, where the coefficient on income is lower (0.006) and not statistically significant (Model 2). Similar results in terms of the income coefficients are obtained for the LM spatial regressions based on the Eq. (3) (Models 3 and 4). Here, spatial error is larger though (lambda − 0.268 versus −0.237) while using nominal income. At the same time spatial lag is almost identical in both specifications (rho −0.214). Both spatial parameters are not statistically significant in this case. Finally, both nominal and real data regressions confirm the existence of conditional beta convergence based on Eq. (2) (Models 5 and 6). Still, the coefficient for real per capita GDP is much higher than its nominal counterpart (− 0.307 versus −0.228). The results of convergence regressions based on the data for US states show in general similar pattern, although the differences between nominal and real variables are smaller. This is not surprising though taking into account very short period of available data. The coefficients for absolute beta convergence reported in Table 4 (Models 1 and 2) are negative (−0.007 versus −0.008) but not statistically significant. The differences are more visible in the case of Models 3 and 4 where both spatial coefficients are larger and statistically significant in regressions based on nominal per capita GDP (lambda 0.757 versus 0.728, rho −0.999 versus −0.841). Finally, the coefficient for conditional convergence (Models 5 and 6) is also higher in the specification based on nominal income (−0.371) as compared to the specification based on income deflated by regional price deflators (−0.405). If we assume that the above results are universal they may have important policy implications. Once we prove that the application of
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Table 5 Regional per capita income in 2011 at the NUTS2 level in Poland (in PPS) — the impact of the PPP deflators. Source: Authors' elaboration. Region
Nominal per capita PPS
Nominal per capita PPS EU = 100
Real per capita PPS
Real per capita PPS EU = 100
Dolnośląskie Kujawsko-Pomorskie Lubelskie Lubuskie Łódzkie Małopolskie Mazowieckie Opolskie Podkarpackie Podlaskie Pomorskie Śląskie Świętokrzyskie Warmińsko-Mazurskie Wielkopolskie Zachodniopomorskie Poland
18,500 13,400 11,100 13,500 15,200 14,100 26,700 13,100 11,100 11,800 15,600 17,700 12,200 11,800 17,000 13,800 16,400
0.734 0.532 0.440 0.536 0.603 0.560 1.060 0.520 0.440 0.468 0.619 0.702 0.484 0.468 0.675 0.548 0.651
17,852 13,888 11,454 13,112 15,050 14,096 25,216 13,111 11,556 12,142 14,826 17,543 12,607 11,912 17,545 13,546 16,400
0.708 0.551 0.455 0.520 0.597 0.559 1.001 0.520 0.459 0.482 0.588 0.696 0.500 0.473 0.696 0.538 0.651
Note that by nominal per capita PPS we understand the PPS obtained with the average national level of prices.
regional price deflators has a significant impact on the results of convergence analysis we may speculate whether they could influence the conclusions drawn from research focused on the effectiveness of EU structural policies. Moreover, we may also wonder to what extent the inclusion of the PPP deflators would change the allocation of financial resources under the EU Cohesion Policy. In particular, the possibility of applying the real per capita GDP could significantly affect the situation of NUTS2 regions above and beyond the 75% EU average income threshold.21 In accordance to the Eurostat data, there were almost 30 NUTS2 regions with per capita income between 70% and 80% of EU27 average at the time of setting up financial allocations for the current financial perspective.22 That means that a significant number of regions could potentially see their allocations for the 2014–2020 period either improved or worsened substantially. To see the point we compare the relative per capita income of Polish NUTS2 regions, expressed as a percentage of EU average in PPS, computed without and with regional price deflators in 2011. The results are shown in Table 5 that is prepared in a similar way to that of the Tables 1 and 2. Hence columns 1 and 3 show absolute values of regional per capita income (in PPS) while columns 2 and 4 relative per capita income, before and after applying regional price deflators respectively. It can be clearly seen that in the case of the poorest Polish regions the application of regional price deflators can improve their relative per capita income by around 2 percentage points (e.g. Podkarpackie). On the other hand the relative income of the best developed areas can decrease as much as 5 percentage points (e.g. Mazowieckie). These results mean that very likely the application of regional price indices would cause several poor regions of better developed countries (e.g. France, Italy or Spain) to go beyond the 75% threshold and lose their “less developed region” status. At the same time some high income regions from poorer countries (e.g. Bulgaria, Poland or Slovakia) could fall below the 75% threshold and be considered as “less developed” ones. This could be the case of Dolnośląskie in the next financial perspective.
21 Applied to qualify the regions either to “less developed” or “transition” category which determine the level of financial allocations. 22 The European Commission uses 3-year average of regional per capita income compiled using the latest available data at the time of deciding financial allocations.
5. Conclusion This paper reconsiders the regional income convergence within the particular countries taking as an example the evolution of income disparities among 16 NUTS2 Polish regions and 51 US states. We find that the application of regional price deflators has a significant impact on statistical data, in terms of relative regional per capita income level. We also show that the average level of regional income dispersion is lower, as compared to the nominal data. Finally, we confirm that the regional price deflators may influence the β-convergence analysis. In our case, the estimated parameters either change the statistical significance (absolute convergence in the case of Polish data) or the value of coefficient (conditional convergence in both cases). Regional price deflators also influence statistical significance of spatial spillovers. It is difficult to assess to what extent the results obtained for Poland can be considered as a representative for other European countries. The results obtained for US states suggest however, that our findings can be consider as universal. This implies that regional price indices should be taken into account at the time of analyzing regional income disparities. This is particularly important in the European Union where the regional per capita income is the main criterion taking into account at the time of determining financial allocations under the EU Cohesion Policy programs. Therefore it would be highly recommended to start gathering the data necessary for the compilation of regional price indices in all EU member states. Acknowledgments We would like to thank the three anonymous referees for useful comments and suggestions. B. Rokicki gratefully acknowledge the financial support from the Polish National Science Center under the grant DEC-2011/03/D/HS4/00868. References Abramovitz, M., 1986. Catching-up, forging ahead, and falling behind. J. Econ. Hist. 46, 385–406. Abreu, M., de Groot, H.L.F., Florax, R.J.G.M., 2005. A meta-analysis of b-convergence: the legendary 2%. J. Econ. Surv. 19, 389–420. Alam, M.S., 1992. Convergence in developed countries: an empirical investigation. Rev. World Econ. 128 (2), 189–201. Arbia, G., Paelinck, J.H.P., 2003. Economic convergence or divergence? Modeling the interregional dynamics of EU regions, 1985–1999. J. Geogr. Syst. 5 (3), 291–314. Arbia, G., Le Gallo, J., Piras, G., 2008. Does evidence on regional economic convergence depend on the estimation strategy? Outcomes from analysis of a set of NUTS2 EU regions. Spat. Econ. Anal. 3 (2), 209–224. Arbia, G., Battisti, M., Di Vaio, G., 2010. Institutions and geography: empirical test of spatial growth models for European regions. Econ. Model. 27, 12–21. Aten, B.H., Figueroa, E.B., Martin, T.M., 2012. Regional price parities for states and metropolitan areas, 2006–2010. Surv. Curr. Bus. 92 (8), 229–242. Azomahou, T.T., El ouardighi, J., Nguyen-Van, P., Cuong Pham, T., 2011. Testing convergence of European regions: a semiparametric approach. Econ. Model. 28, 1202–1210. Barro, R., Sala-i-Martin, X., 1991. Convergence across states and regions. Brook. Pap. Econ. Act. 1, 107–182. Barro, R.J., Sala-i-Martin, X., 1992. Convergence. J. Polit. Econ. 100 (2), 223–251. Baumol, W.J., 1986. Productivity growth, convergence, and welfare: what the long-run data show. Am. Econ. Rev. 76, 1072–1085. Boldrin, M., Canova, F., 2001. Inequality and convergence: reconsidering European regional policies. Econ. Policy 32, 207–253. Brandt, L., Holz, C.A., 2006. Spatial price differences in China: estimates and implications. Econ. Dev. Cult. Chang. 55 (1), 43–86. Čadil, J., Mazouch, P., Musil, M., Kramulová, J., 2014. True regional purchasing power: evidence from the Czech Republic. Post-Communist Econ. 26 (2), 241–256. Cameron, G., Muellbauer, J., 2000. Earning biases in the United Kingdom regional accounts: some economic policy and research implications. Econ. J. 110 (464), 412–429. Czyż, T., Hauke, J., 2011. Evolution of regional disparities in Poland. Quaestiones Geographicae 30 (2), 35–48. Dall'erba, S., Le Gallo, J., 2008. Regional convergence and the impact of European structural funds over 1989–1999: a spatial econometric analysis. Pap. Reg. Sci. 87 (2), 219–244. European Communities/OECD (2006). EUROSTAT-OECD Methodological Manual on Purchasing Power Parities. Office for Official Publications of the European Communities. Fischer, M.M., Stumpner, P., 2008. Income distribution dynamics and cross-region convergence in Europe. Spatial filtering and novel stochastic kernel representations. J. Geogr. Syst. 10 (2), 109–140.
B. Rokicki, G.J.D. Hewings / Economic Modelling 57 (2016) 171–179 King, A., Ramlogan-Dobson, C., 2015. International income convergence: is Latin America actually different? Econ. Model. 49, 212–222. Le Pen, Y., 2011. A pair-wise approach to output convergence between European regions. Econ. Model. 28, 955–964. Maza, A., Hierro, M., Villaverde, J., 2012. Income distribution dynamics across European regions: re-examining the role of space. Econ. Model. 29, 2632–2640. Petrakos, G., Artelaris, P., 2009. European regional convergence revisited: a weighted least squares approach. Growth Chang. 40 (2), 314–331. Próchniak, M., Witkowski, B., 2013. Time stability of the beta convergence among EU countries: Bayesian model averaging perspective. Econ. Model. 30, 322–333.
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Quah, D., 1996. Regional convergence clusters across Europe. Eur. Econ. Rev. 40, 951–958. Quah, D., 1997. Empirics for growth and distribution: stratification, polarization, and convergence clubs. J. Econ. Growth 2 (1), 27–59. Rokicki, B., 2015. Regional PPP deflators for Poland and their use. Ekonomista 1, 67–80. Sala-i-Martin, X., 1996. The classical approach to convergence analysis. Econ. J. 106, 1019–1036. Tabuchi, T., 2001. On interregional price differentials. Japan. Econ. Rev. 52, 104–115.
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Economic Modelling journal homepage: www.elsevier.com/locate/ecmod
Regional convergence within particular country — An approach based on the regional price deflators Bartlomiej Rokicki a,b,⁎, Geoffrey J.D. Hewings b a b
University of Warsaw, Faculty of Economic Sciences, Poland; University of Illinois, Urbana, IL 61801-3671, United States University of Illinois, Regional Economics Applications Laboratory, Urbana, IL 61801-3671, United States
a r t i c l e
i n f o
Article history: 21 May 2015 30 March 2016 Accepted 29 April 2016 Available online xxxx JEL classification: E30 O10 R10
a b s t r a c t This paper applies regional price deflators for Polish NUTS2 regions and US states in order to reassess regional income convergence within particular country. We find that the regional income disparities decrease significantly once we account for regional price differentials. Moreover, we prove that the application of regional price deflators has significant impact on the results of both σ and β-convergence analysis. They also influence the conclusions concerning the magnitude of spatial spillovers. The above results can have important policy implications, in particular concerning the EU Cohesion Policy financial allocations and the assessment of policy effectiveness. © 2016 Elsevier B.V. All rights reserved.
Keywords: Regional convergence Regional price deflators Cohesion policy
1. Introduction The evolution of regional income convergence within different countries, and the European Union (EU) member states in particular, has been thoroughly discussed in many papers. The research on regional income convergence was pioneered by Barro and Sala-i-Martin (1991 and 1992) who revealed a negative relationship between economic growth rate and the initial level of income both across US states and across European regions. They found that there was an absolute βconvergence across both 73 Western European regions and the regions within particular countries between 1950 and 1985. Surprisingly, the speed of convergence was very similar in all cases and reached about 2% yearly. This last result has been a subject of controversy in the literature. As a matter of fact, many other studies show that the speed of convergence appears to depend on the estimation strategy applied by the researchers (e.g. Abreu et al., 2005; Arbia et al., 2008). One of the crucial points at the time of estimating regional income convergence within particular country is the choice of price deflator. As claimed by Tabuchi (2001), the high income regions tend to have
⁎ Corresponding author at: University of Warsaw, Faculty of Economic Sciences. Dluga 44/50, 00-241 Warsaw, Poland. E-mail addresses: [email protected] (B. Rokicki), [email protected] (G.J.D. Hewings).
http://dx.doi.org/10.1016/j.econmod.2016.04.019 0264-9993/© 2016 Elsevier B.V. All rights reserved.
higher level of prices than the low income ones. Hence, the use of average national price deflator will most likely lead to an artificial increase of income in the better developed areas and a decrease in the lagging behind ones. This in turn would result in overestimation of existing regional income differentials. On the contrary, the application of regional price deflators should lower the overall level of income disparities expressed by sigma convergence (as compared to the results obtained once applying average national price deflator). At the same time, the impact of regional price deflators on dynamic indicator of regional income differentials, such as beta convergence, is unclear since it depends on the evolution of regional price indices.1 Also, it is uncertain what would be the impact of the regional price deflators on the spatial income spillovers. While the point made above may be well-known in the convergence literature in Europe there are no studies analyzing the impact of regional price deflators on the results of convergence analysis. This paper adds to the existing convergence literature by showing the impact of the regional price deflators on the analysis of regional income disparities within a given country. In particular it compares the results of convergence analysis, in the case of Poland between 2000 and 2011 at the NUTS2 level, based on the per capita GDP deflated by 1 There should be a significant impact only if the regional inflation rates differ substantially over the analyzed period.
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regional price deflators and per capita GDP deflated by national price deflator.2 Still, in order to verify the robustness of our results we also apply regional price deflators for the US states for the 2008–2013 period.3 We consider both β-convergence and σ-convergence approaches and apply different econometric techniques in order to show that the results of previous studies may overestimate the overall level of regional income disparities. They may also lead to different conclusions concerning regional convergence patterns. The overestimation of regional income disparities can have important policy implications, in particular concerning the EU Cohesion Policy. Here, the financial allocations are closely linked to the relative level of regional income. Hence, the change in relative income, due to the application of regional price deflators, could lead to a significant change in allocation patterns. Moreover, we believe that the inclusion of regional price deflators can influence the conclusions drawn from research focused on the structural policy effectiveness. The remainder of the paper is as follows. In the next section we briefly review the existing literature on income convergence. Thereafter we present the research methodology. Section 4 discusses empirical results and Section 5 concludes.
2. Literature review There can be distinguished to main strands in the literature on income convergence. The first one, triggered by seminal papers by Abramovitz (1986) and Baumol (1986), focuses on the evolution of income disparities across countries. It also tries to explain the factors that influence that process (e.g. Alam, 1992; King and RamloganDobson, 2015; Próchniak and Witkowski, 2013). The second strand concentrates on the evolution of regional income convergence within different countries, and the European Union member states in particular. Here, the interest of many researchers and policy makers is driven by the existence of the EU Cohesion Policy that nowadays accounts for almost a half of the Community budget. Hence, both supporters and skeptics of the policy are constantly searching for arguments in favor or against its continuation. The research on regional income convergence within particular countries was pioneered Barro and Sala-i-Martin (1991 and 1992) who showed a negative relationship between economic growth rate and the initial level of income both across US states and across European regions. They found that there was an absolute βconvergence across both 73 Western European regions and the regions within particular countries between 1950 and 1985. Surprisingly, the speed of convergence was very similar in all cases and reached about 2% yearly. During the last two decades or so, the results reported by Barro and Sala-i-Martin have been a subject of criticism. Indeed, many other studies show that the speed of convergence appears to depend on the estimation strategy applied by the researchers (e.g. Abreu et al., 2005; Arbia et al., 2008). Hence, many authors suggested different methodological improvements that could lead to different conclusions concerning the evolution of regional income convergence. Here, among others, we can mention the inclusion of spatial spillovers (e.g. Arbia and Paelinck, 2003; Arbia et al., 2010), the distribution dynamics approach (e.g. Fischer and Stumpner, 2008; Maza et al., 2012; Quah, 1997) or different estimation approaches (e.g. weighted approach by Petrakos and Artelaris, 2009; pair-wise approach by Le Pen, 2011; semiparametric approach by Azomahou et al., 2011). Somehow surprisingly there are hardly studies that focus on issues related to the 2 The existing studies tend to use nominal data deflated by national PPP deflators in order to express data in constant prices that allows for analysis among different member states. Yet, the application of national PPP deflators has no impact on convergence analysis within particular country, as compared to analysis based on data expressed in current prices (e.g. nominal per capita GDP). 3 Regional price deflators for the US are available for the 2008–2013 period only.
statistical data. Even though the data inaccuracy may have, in fact, a greater impact on the results of convergence analysis than mere differences in econometric approaches. For instance, Cameron and Muellbauer (2000) claim that, because of the downward bias in South East region income levels in the 1980s, the results of studies on regional income convergence within the UK (e.g. Quah, 1996 or Sala-i-Martin, 1996) are seriously biased. Potentially, one of the main sources of data inaccuracy is the lack of regional price deflators. European national statistical offices do not provide such a data (so obviously neither does the Eurostat, that relies on the data received from national statistical authorities) since most of them do not collect the representative data on prices at regional level.4 The same applies to the countries such as US where regional price deflators were not available until few years back and cover very short period of time. As a result, all of the studies rely on the regional per capita GDP that, in order to be internationally comparable, is deflated using national Purchase Power Parities (PPP) or Purchase Power Standards (PPS5) deflators. The problem is that such an approach leads to overvaluation of per capita income in regions with regional price indices higher than the national average and undervaluation of income in areas with price indices below the national average. This is because these are the high income regions with big agglomerations that tend to have higher level of prices than the low income ones (e.g. Tabuchi, 2001). Hence, we might expect that the application of regional price deflators (instead of national average) should lower the overall level of income disparities since it would reduce the real per capita income6 in better developed regions and increase in the worse developed ones. At the same time its impact on dynamic indicator of regional income such as beta convergence is unclear since it depends on the evolution of regional price indices.7 Also, it is uncertain what would be the impact of the regional price deflators on the regional income spillovers. While the analysis of the impact of regional price deflators on the different regional convergence indicators can seem interesting from the purely scientific point of view it may have also important policy implications. First of all, mind that the per capita income criterion is not only the main criterion used to qualify the NUTS2 level regions into different priority groups under the EU Cohesion Policy but also the one used to determine the level of financial allocations for regions within each priority group. Hence, the small change in relative income level caused by the application of regional price deflators could potentially lead to substantial alteration in the amount of structural funding received from the EU.8 Still, the application of regional price deflators could also change the negative conclusions concerning the effectiveness of EU structural policies in terms of their impact on regional economic performance (e.g. Boldrin and Canova, 2001; Dall'erba and Le Gallo, 2008). This might occur once we assume that the least developed areas had been in fact growing faster (in real terms) than previously assumed.
4 Hence, there are very few examples of regional price deflators calculated by researchers. For instance, Aten et al. (2012) estimate regional price parities for the US states and metropolitan areas, Brandt and Holz (2006) provide a set of provincial-level spatial price deflators for China, Čadil et al. (2014) calculate regional PPP deflators for the 14 Czech NUTS3 regions in 2007 and Rokicki (2015) computes regional price deflators for Polish NUTS2 regions. 5 Eurostat provides an artificial currency indicator such as PPS for EU countries that has the same purchasing power in all member states. 6 Please note, that in the remainder of the paper we refer to the real per capita income as income deflated by regional price deflators. On the other hand, when we name nominal per capita income we refer to regional income deflated by average national price deflator. 7 There should be a significant impact only if the regional inflation rates differ substantially over the analyzed period. 8 Imagine the region with per capita income just below or above the 75% EU average. Here, if regional prices differ significantly from national average then the application of regional price indices could lead to reassessment of its relative level of income and qualification to a different priority group. This in turn would mean either a gain or loss in structural funding worth millions of euro.
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3. Research methodology and data
ln ðy
yi;t
i;t−T
The lack of studies concerning the evolution of regional income inequalities, which rely on regional price deflators, cannot be really surprising. The main problem here is the absence of necessary statistical data on regional prices. That is why we focus on Poland, where such data is available for 16 regions at the NUTS2 level for the period 2000– 2011. Hence, it is possible to compute a time series of regional price deflators. This constitutes the first stage of our research. These deflators are thereafter applied in the analysis of the evolution of regional income disparities. Still, in order to verify the robustness of our results we also use the data on price deflators published by Bureau of Economic Analysis and analyze the evolution of regional income differentials between 51 US states during the 2008–2013 period. As far as we are concerned this is the only country other than Poland where the time series of reliable regional price deflators are available.9 In our analysis we consider both β-convergence and σ-convergence approaches in order to show the impact of regional PPP deflators on different measures of regional income disparities. We analyze several different specifications so as to verify to what extent the results are sensible to the application of regional PPP deflators. In the case of βconvergence we run unconditional, conditional and spatial lag and spatial error specifications.10 In the case of σ-convergence we test traditional and weighted approaches.11 The baseline β-convergence regressions are based on panel estimation of the classical unconditional convergence equation: ln
yi;t
!
yi;t−T
¼ α þ β ln yi;t−T þ εi;t
173
ÞÞ show the impact of economic growth in surrounding areas
on growth rate in the given region. Also, the spatial error term (λWεi,t) measures the impact of the error in neighborhood regions on the error term in the given region. The baseline coefficient of variation (σ-convergence) is expressed by the formula: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n u1 X ln ðyi;t − ln ðyt ÞÞ2 σt ¼ t n i¼1
ð4Þ
where y is the average per capita income for the whole country. Its weighted version is given by: vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n uX ln ðyi;t − ln ðyt ÞÞ2 P i;t σt ¼ t
ð5Þ
i¼1
ð1Þ
where yi,t is per capita GDP in region i at time t. The estimation controls for seasonality problems. Here, following the Solow–Swan model, we should expect to find the regions with initial higher level of per capita income to grow slower than the lagging behind ones. However, this requires to assume that all of them share the same technology, savings rate, depreciation rate and population growth rate.12 Our simple conditional convergence specification is given by Eq. (2) below: ln
yi;t
!
yi;t−T
¼ α þ β ln yi;t−T þ γDi þ εi;t
ð2Þ
where Di is a dummy variable for region i. In this case we allow the regions to differ in terms of the model parameters. As a result we may find the conditional convergence even though there is no absolute (unconditional) one. Finally, we analyze spatial extension of the Eq. (1) in the form of the fixed-effects spatial autoregressive model: ln
yi;t yi;t−T
!
n X ¼ α þ β ln yi;t−T þ ρ wi; j ln i−1
yi;t yi;t−T
! þ εi;t
ð3Þ
where wi,j is an element of a spatial weights matrix W, with n representing the number of regions and εi , t = λWεi , t + ui , t where n
ui , t ~ Nid(0, σ2). Here, spatial spillovers expressed by spatial lag (∑wi; j i−1
9
As mentioned before, Brandt and Holz (2006) provide a set of provincial-level spatial price deflators for China. Still, the data on prices covers very few products (at most 60) which casts serious doubts on the reliability of regional price deflators they provide. 10 Obviously, these are only some of the many possible specifications. See Abreu et al. (2005) and Arbia et al. (2008) for more detailed surveys on different convergence analysis specifications. 11 See Petrakos and Artelaris (2009) for details on the weighted approach. 12 For details about the theoretical propositions behind the classical convergence approach see for example Barro and Sala-i-Martin (1991 and 1992).
Fig. 1. Regional differentials in prices between Polish regions in 2000 and 2011 (national average = 1). Source: Authors' elaboration.
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Fig. 2. Regional differentials in prices between US states in 2008 and 2013 (national average = 1). Source: Authors' elaboration.
Table 1 Regional per capita GDP in 2011 at the NUTS2 level in Poland — the impact of the PPP deflators. Source: Authors' elaboration. Region
Dolnośląskie Kujawsko-pomorskie Lubelskie Lubuskie Łódzkie Małopolskie Mazowieckie Opolskie Podkarpackie Podlaskie Pomorskie Śląskie Świętokrzyskie Warmińsko-mazurskie Wielkopolskie Zachodniopomorskie Poland
Nominal per capita GDP (PLN)
Nominal per capita GDP Poland = 100
Real per capita GDP (PLN)
Real per capita GDP Poland = 100
44,961 32,596 26,919 32,795 36,750 34,107 64,790 31,771 26,801 28,485 37,822 42,830 29,552 28,635 41,285 33,485 39,665
1.134 0.822 0.679 0.827 0.927 0.860 1.633 0.801 0.676 0.718 0.954 1.080 0.745 0.722 1.041 0.844 1.000
43,386 33,784 27,778 31,851 36,387 34,098 61,189 31,797 27,902 29,311 35,945 42,450 30,539 28,906 42,608 32,868 39,665
1.094 0.852 0.700 0.803 0.917 0.860 1.543 0.802 0.703 0.739 0.906 1.070 0.770 0.729 1.074 0.829 1.000
where Pi stays for the share of region's i population in total country population. Hence, in the weighted approach the regions with a larger share of national population have a greater impact on the overall value of sigma convergence. In the Polish case we should expect the weighted sigma convergence to be higher than the traditional one since the best developed region Mazowieckie is also by far the region with the highest number of inhabitants.13 More complex situation can be observed in the case of the US states. First because of the much higher number of territorial units, and second because the states with the highest per capita income are not necessarily the biggest in terms of population (e.g. District of Columbia). Please note, that this paper is focused on the issues related to the choice of regional income variable and its impact on the results of convergence analysis. Hence, we provide the results of β-convergence regressions as an illustration only. This is particularly important taking into account the fact that our observations (particularly in the case of the US states) cover very short period of time while the convergence process is a long term phenomenon. Therefore, here we do not discuss in detail questions concerning different econometric strategies and their consequences. Nor we analyze estimated convergence speeds. Regional price deflators for Poland are estimated in accordance to the common Eurostat/OECD methodology. Although this methodology 13 So the significant difference between the regional income and national average in its case counts more in the weighted approach.
Table 2 Regional per capita GDP in 2013 at the state level in the US — the impact of the PPP deflators. Source: Authors' elaboration. State
Alabama Alaska Arizona Arkansas California Colorado Connecticut Delaware District of Columbia Florida Georgia Hawaii Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming United States
Real per capita GDP US =
100
Real per capita GDP (USD)
37,189 66,817 38,762 36,539 53,505 50,457 62,989 59,767 159,506
0.768 1.381 0.801 0.755 1.106 1.043 1.302 1.235 3.296
42,405 63,035 39,920 41,759 47,645 49,371 58,054 58,942 135,519
0.876 1.302 0.825 0.863 0.984 1.020 1.200 1.218 2.800
38,197 42,262 49,087 34,608 51,434 43,347 48,554 44,462 38,371 45,588 37,405 53,176 61,191 41,169 52,372 31,642 41,963 38,021 51,664 42,883 48,099 55,959 38,971 62,130 43,200 63,911 44,579 40,957 49,897 46,560 46,679 35,608 46,875 41,295 52,623 42,474 42,814 51,351 53,735 34,742 45,676 61,297 48,397
0.789 0.873 1.014 0.715 1.063 0.896 1.003 0.919 0.793 0.942 0.773 1.099 1.264 0.851 1.082 0.654 0.867 0.786 1.068 0.886 0.994 1.156 0.805 1.284 0.893 1.321 0.921 0.846 1.031 0.962 0.965 0.736 0.969 0.853 1.087 0.878 0.885 1.061 1.110 0.718 0.944 1.267 1.000
38,661 45,987 42,244 37,293 50,925 47,426 53,770 48,967 43,065 49,987 38,286 47,950 57,028 43,704 53,660 36,454 47,044 40,277 57,087 43,669 45,419 48,873 41,022 53,886 47,110 69,925 49,753 45,558 50,554 47,221 47,583 39,346 53,510 45,580 54,419 43,698 42,729 49,855 52,069 39,301 49,167 63,984 48,397
0.799 0.950 0.873 0.771 1.052 0.980 1.111 1.012 0.890 1.033 0.791 0.991 1.178 0.903 1.109 0.753 0.972 0.832 1.180 0.902 0.938 1.010 0.848 1.113 0.973 1.445 1.028 0.941 1.045 0.976 0.983 0.813 1.106 0.942 1.124 0.903 0.883 1.030 1.076 0.812 1.016 1.322 1.000
Nominal per capita GDP (USD)
Nominal per capita GDP US =
100
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175
Fig. 3. Unweighted and weighted sigma convergence among Polish NUTS2 regions between 2000 and 2011. Source: Authors' elaboration.
is usually used to allow income comparisons between different countries it may also be applied in order to analyze the evolution of real income level between different regions within the some state. It is based on the expenditure side of the Gross Domestic Product and employs the EKS (Éltetö–Köves–Szulc) method that requires data concerning both the prices of representative goods and services and the structure of spending (that is necessary to weight price indices calculated for particular base categories).14 In the first step, we apply data concerning prices at the base category level to calculate unweighted PPP indices for each pair of regions. These are so called Fisher type PPP that rely on Laspayers index for products representative for the first region and Paasche index for products representative for the second one. The above indices are defined as follows:
LAB
Standardized PPP deflators at the base categories must be then aggregated using weights for particular base categories in the overall expenditure. This is done in a similar way as described for particular base categories. Hence, first we compute the Laspayers index defined as:
LAB
Xn EKSiA EiB i¼1 EKS ¼ Xn iB E i¼1 iB
where E stays for expenditure in base category i in region B. Then we calculate Paasche and Fisher indices, following the formulas: P AB ¼
n1 P iA A ¼ ∏ i∈RA P iB
ð11Þ
ð6Þ F AB ¼
1 : LBA qffiffiffiffiffiffiffiffiffiffiffiffiffiffi LAB P AB :
ð12Þ
ð13Þ
where RA stays for products representative for region A. P AB ¼ ∏ i∈RB
P iB P iA
n1
B
ð7Þ
where RB stays for products representative for region B. F AB ¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi LAB P AB :
ð8Þ
Still, the Fisher type PPP does not accomplish the transitivity condition which is achieved by applying the EKS method. The EKS PPP between regions j and k can be computed using the following formula: 1 F jl n EKSjk ¼ F 2jk ∏ l≠ j;k F kl
ð9Þ
where j ,k ,l ϵ N. Finally, we need to standardize the EKS indices in order to get PPP deflators that have a group of regions as a basis. We achieve this by calculating. EKSA ¼ ¼
14
EKSAA
EKSAB
∏i¼A EKSiA EKSAn
∏i¼A EKSiB
n
¼ 1 X i
n ∏i¼A EKSin
1 X
n
¼… 1 X i ð10Þ
i
See European Communities/OECD (2006) for more details.
Finally, we apply the EKS method in order to meet the transitivity condition and standardization in accordance with the Eqs. (9) and (10). This way we get the average PPP deflators for each region. These deflators are afterwards used to adjust the data on regional per capita income. Our data on regional prices covers the 2000–2011 and accounts for over 300 representatives of consumer goods and services. In this sense it is much more detailed than the data used in the recent paper by Rokicki (2015). Most of the data on prices is unpublished and has been obtained courtesy of Polish Central Statistical Office. Almost all of the remaining data comes from the different publications of the Polish Central Statistical Office and covers the 2000–2011 period. In particular, the data on regional per capita income comes from the Local Data Bank and is compiled in accordance with the Polish Classification of Activities 2007 (PKD 2007)15 and the European System of National and Regional Accounts (the ESA 1995),16 while data on expenditure comes from the Household Budget Survey. We use yearly data expressed in Polish zloty. The only exception applies to the regional per capita income data from Eurostat that is expressed in PPS. The data used to compute spatial weights matrix and maps comes from the ESRI shapefile data for Polish NUTS2 regions. The data on US states per capita income and regional price deflators comes from the Bureau of Economic Analysis. The data on regional population used to compute the weighted sigma convergence comes from US Census Bureau.17 All the above data covers 2008–2013 period. The 15
Here, the latest available data comes from 2011. At the time of preparing the paper the Polish Central Statistical Office did not provide the data covering the whole 2000–2011 period in accordance with the ESA 2010 standard. 17 See Intercensal Estimates of the Resident Population for the United States, Regions, States, and Puerto Rico. 16
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Fig. 4. Unweighted and weighted sigma convergence among US states between 2008 and 2013. Source: Authors' elaboration.
data used to compute spatial weights matrix and maps comes from the ESRI shapefile data for US states. 4. Empirical results Regional price deflators calculated in accordance with the Eurostat/ OECD methodology confirm the existence of substantial price differentials between Polish regions. Moreover, Fig. 1 shows that although there have been some changes in terms of spatial distribution of regional price deflators between 2000 and 2011,18 on average the highest level of prices can be found in the best developed areas with big agglomerations (e.g. Warsaw, Katowice, Wrocław or Gdańsk). On the other hand these are the rural areas that tend to experience the lowest level of prices (e.g. eastern Poland). In 2000 the highest levels of price indices are observed in the capital region (Mazowieckie) and the region placed at the western border of the country (Lubuskie). On the other hand, the lowest levels of prices are found in the central and eastern part of Poland. In 2011 the Mazowieckie (Warsaw) maintains the highest level of price index. However, the Pomorskie (Gdańsk) voivodship replaces Lubuskie as a second region with the highest prices. Other regions with big cities, such as Dolnośląskie (Wrocław) or Śląskie (Katowice) also have higher than average price indices. At the same time the group of regions with the lowest values of regional price deflators expands into all eastern border regions and Wielkopolskie region. The Polish case is not particularly exceptional since substantial differences in prices exist also between US states. Again, on average these are regions with big agglomerations that have the highest level of prices (e.g. New York, Los Angeles, Washington and Chicago), while the lowest price indices can be found in rural areas. It can be easily verified on Fig. 2 that the highest price indices can be found in New York (New York), District of Columbia (Washington) and California (Los Angeles). On the other hand the states with the lowest prices are located mostly within the rural Midwest region (e.g. Iowa or Missouri). Here, Illinois (Chicago) can be considered as an exception, surrounded by experiencing lower price indices Midwest states. There is no big change in the spatial pattern of regional price indices between 2008 and 2013. The most notable exception is an increase of relative price indices in certain Midwest states such as North Dakota, Nebraska and Kansas. So as to more accurate evaluation of the impact of regional price deflators, on per capita GDP in particular Polish regions, we calculate the indices showing the regional/national average ratio in 2011 before and after using the deflators (see Table 1). Here, columns 1 and 3 show absolute values of regional per capita GDP while columns 2 and 4 report relative per capita GDP level (as compared to national average), 18
Most likely due to the EU accession.
Table 3 The results of the β-convergence analysis for Polish NUTS2 regions. Source: Authors' elaboration. Variables
Nominal per capita GDP
(1)
(2)
(3)
(4)
(5)
(6)
Model
Model
Model
Model
Model
Model
0.011⁎ (0.006)
Real per capita GDP Lambda Rho Constant Time dummies Region dummies Observations Log likelihood
−0.228⁎⁎⁎
0.010 (0.006) 0.006
0.005⁎⁎
(0.008)
(0.008) −0.237 (0.317) −0.214 (0.316) 0.003 (0.074) Yes No 176 454.35
−0.268 (0.329) −0.214 (0.324) −0.062 −0.019 −0.040 (0.060) (0.078) (0.062) Yes Yes Yes No No No 176 176 176 469.88 453.13 471.29
(0.067)
−0.307⁎⁎⁎ (0.064)
2.306⁎⁎⁎ (0.665) Yes Yes 176 488.01
3.101⁎⁎⁎ (0.633) Yes Yes 176 473.93
OLS estimation (Models 1–2 and 5–6), LM estimation (Models 3–4). Robust standard errors in parentheses Spatial specifications based on the inverse distance matrix. ⁎⁎⁎ p b 0.01. ⁎⁎ p b 0.05. ⁎ p b 0.1.
before and after using price deflators respectively. As expected, nominal per capita GDP (column 1) is lower than real per capita GDP (column 3) in the three best developed regions (Dolnośląskie, Mazowieckie, Śląskie).19 This in turn leads to a decrease of their relative real per capita income (column 4) as compared to the relative nominal per capita income (column 2). In the case of the richest Mazowieckie voivodship its per capita income decreases, as compared to the national average, by more than 9 percentage points. The difference between the nominal and real per capita GDP relative to national average is smaller for Dolnośląskie and Śląskie. Here it does not exceed 4 percentage points and 1 percentage point respectively. Exactly opposite results can be found for the low income areas such as Lubelskie, Podkarpackie, Podlaskie, Świętokrzyskie and Warmińskomazurskie, where the overall level of prices is lower than national average. Here we find that the relative level of per capita income increases between 0.7 percentage point (Warmińsko-Mazurskie) and 2.7 percentage points (Podkarpackie). In this sense the impact of regional price deflators seems to be smaller than for the best developed regions.
19
Here, the overall level of prices is above the national average.
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Table 4 The results of the β-convergence analysis for US states. Source: Authors' elaboration. Variables
Nominal per capita GDP
(1)
(2)
(3)
(4)
(5)
(6)
Model
Model
Model
Model
Model
Model
−0.007 (0.005)
−0.001 (0.005) −0.008 (0.007)
Real per capita GDP Lambda Rho Constant Time dummies Region dummies Observations Log likelihood
0.043 (0.054) Yes No 255 605.37
0.059 (0.071) Yes No 255 612.72
0.757⁎⁎⁎ (0.082) −0.999⁎⁎⁎ (0.284) −0.023 (0.049) Yes No 255 614.04
−0.004⁎ (0.006) 0.728⁎⁎⁎ (0.091) −0.841⁎⁎ (0.295) 0.008 (0.061) Yes No 255 620.83
−0.371⁎⁎⁎ (0.084)
3.871⁎⁎⁎ (0.884) Yes Yes 255 679.77
−0.405⁎⁎⁎ (0.086)
4.282⁎⁎⁎ (0.916) Yes Yes 255 683.39
OLS estimation (Models 1–2 and 5–6), LM estimation (Models 3–4). Robust standard errors in parentheses. Spatial specifications based on the inverse distance matrix. ⁎⁎⁎ p b 0.01. ⁎⁎ p b 0.05. ⁎ p b 0.1.
Similar results can be found for the US states in 2013 (see Table 2). Here, per capita GDP decreases significantly after applying regional price deflators, in regions with the highest income level and increases in regions with the lowest income level.20 In particular, relative per capital income decreases by almost 50 percentage points in District of Columbia, more than 17 percentage points in New York, more than 10 percentage points in Connecticut and almost 8 percentage points in Alaska. On the other hand we find that relative real per capita GDP is higher than the nominal one by more than 10 percentage points in Alabama, almost 10 percentage points in Mississippi and West Virginia, almost 8 percentage points in South Carolina and more than 5 percentage points in Idaho. The above suggests that we might observe a reduction in dispersion of regional per capita GDP (σ-convergence) once we refer to the real instead of nominal values. Indeed, unweighted σ-convergence in Poland in 2011 falls from 0.265, calculated for nominal per capita income, to 0.248 computed using the data adjusted for regional prices. The impact is slightly bigger once we apply the weighted approach. Here, the value of coefficient of variation decreases from 0.268 for nominal per capita GDP to 0.246 for the real one. It appears, however, that the application of regional price deflators hardly affects the evolution of σ-convergence between 2000 and 2011 (see Fig. 3). The evolution of variation coefficient for nominal and real per capita GDP looks pretty similar. In this sense, there is no difference between un-weighted and weighted approach. Although, it is clear that regional price deflators have greater impact on weighted σconvergence during the whole analyzed period. The US data seems to confirm that our findings concerning the impact of regional price indices on regional income disparities are rather universal. Unweighted σ-convergence for US states in 2013 reaches 0.249 once we use nominal per capita GDP and falls to 0.204 when we use real per capita GDP. Similar impact can be observed in the case of weighted approach — here the value of σ-convergence falls from 0.170 to 0.121 once we apply real income instead of the nominal one. Again, there is no visible impact on the evolution of σ-convergence (see Fig. 4). However, regional price deflators have slightly bigger
20 Few exceptions exist (e.g. North Dakota or Wyoming). Here, per capita GDP increases as a result of applying regional price deflators even though their nominal income is much higher than national average. This may be explained, however, by the fact that the above regions are mostly rural with a lack of important agglomerations. Hence, their overall price levels are below the national average even though the relative per capita income is high.
impact on weighted σ-convergence between 2008 and 2013. Note, that the overall impact of regional price indices is in fact greater in the US case as compared to the Polish one. This is not surprising though taking into account that the number of US states more than triplicates the number of Polish NUTS2 regions. Hence, comparing Poland with other European countries we may expect that the impact of regional price deflators would be bigger in the ones with greater number of NUTS2 regions (e.g. Germany) and smaller in the ones with less regions (e.g. Hungary). The introduction of the regional price deflators has also a significant impact on the results of the absolute β-convergence analysis during the 2000–2011 period (see Table 3). The OLS panel regression based on Eq. 1 and nominal per capita GDP shows statistically significant divergence process with the income coefficient 0.011 (Model 1). This result was reported also in other studies (e.g. Czyż and Hauke, 2011). Yet, this is not the case of the regression based on real per capita GDP, where the coefficient on income is lower (0.006) and not statistically significant (Model 2). Similar results in terms of the income coefficients are obtained for the LM spatial regressions based on the Eq. (3) (Models 3 and 4). Here, spatial error is larger though (lambda − 0.268 versus −0.237) while using nominal income. At the same time spatial lag is almost identical in both specifications (rho −0.214). Both spatial parameters are not statistically significant in this case. Finally, both nominal and real data regressions confirm the existence of conditional beta convergence based on Eq. (2) (Models 5 and 6). Still, the coefficient for real per capita GDP is much higher than its nominal counterpart (− 0.307 versus −0.228). The results of convergence regressions based on the data for US states show in general similar pattern, although the differences between nominal and real variables are smaller. This is not surprising though taking into account very short period of available data. The coefficients for absolute beta convergence reported in Table 4 (Models 1 and 2) are negative (−0.007 versus −0.008) but not statistically significant. The differences are more visible in the case of Models 3 and 4 where both spatial coefficients are larger and statistically significant in regressions based on nominal per capita GDP (lambda 0.757 versus 0.728, rho −0.999 versus −0.841). Finally, the coefficient for conditional convergence (Models 5 and 6) is also higher in the specification based on nominal income (−0.371) as compared to the specification based on income deflated by regional price deflators (−0.405). If we assume that the above results are universal they may have important policy implications. Once we prove that the application of
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Table 5 Regional per capita income in 2011 at the NUTS2 level in Poland (in PPS) — the impact of the PPP deflators. Source: Authors' elaboration. Region
Nominal per capita PPS
Nominal per capita PPS EU = 100
Real per capita PPS
Real per capita PPS EU = 100
Dolnośląskie Kujawsko-Pomorskie Lubelskie Lubuskie Łódzkie Małopolskie Mazowieckie Opolskie Podkarpackie Podlaskie Pomorskie Śląskie Świętokrzyskie Warmińsko-Mazurskie Wielkopolskie Zachodniopomorskie Poland
18,500 13,400 11,100 13,500 15,200 14,100 26,700 13,100 11,100 11,800 15,600 17,700 12,200 11,800 17,000 13,800 16,400
0.734 0.532 0.440 0.536 0.603 0.560 1.060 0.520 0.440 0.468 0.619 0.702 0.484 0.468 0.675 0.548 0.651
17,852 13,888 11,454 13,112 15,050 14,096 25,216 13,111 11,556 12,142 14,826 17,543 12,607 11,912 17,545 13,546 16,400
0.708 0.551 0.455 0.520 0.597 0.559 1.001 0.520 0.459 0.482 0.588 0.696 0.500 0.473 0.696 0.538 0.651
Note that by nominal per capita PPS we understand the PPS obtained with the average national level of prices.
regional price deflators has a significant impact on the results of convergence analysis we may speculate whether they could influence the conclusions drawn from research focused on the effectiveness of EU structural policies. Moreover, we may also wonder to what extent the inclusion of the PPP deflators would change the allocation of financial resources under the EU Cohesion Policy. In particular, the possibility of applying the real per capita GDP could significantly affect the situation of NUTS2 regions above and beyond the 75% EU average income threshold.21 In accordance to the Eurostat data, there were almost 30 NUTS2 regions with per capita income between 70% and 80% of EU27 average at the time of setting up financial allocations for the current financial perspective.22 That means that a significant number of regions could potentially see their allocations for the 2014–2020 period either improved or worsened substantially. To see the point we compare the relative per capita income of Polish NUTS2 regions, expressed as a percentage of EU average in PPS, computed without and with regional price deflators in 2011. The results are shown in Table 5 that is prepared in a similar way to that of the Tables 1 and 2. Hence columns 1 and 3 show absolute values of regional per capita income (in PPS) while columns 2 and 4 relative per capita income, before and after applying regional price deflators respectively. It can be clearly seen that in the case of the poorest Polish regions the application of regional price deflators can improve their relative per capita income by around 2 percentage points (e.g. Podkarpackie). On the other hand the relative income of the best developed areas can decrease as much as 5 percentage points (e.g. Mazowieckie). These results mean that very likely the application of regional price indices would cause several poor regions of better developed countries (e.g. France, Italy or Spain) to go beyond the 75% threshold and lose their “less developed region” status. At the same time some high income regions from poorer countries (e.g. Bulgaria, Poland or Slovakia) could fall below the 75% threshold and be considered as “less developed” ones. This could be the case of Dolnośląskie in the next financial perspective.
21 Applied to qualify the regions either to “less developed” or “transition” category which determine the level of financial allocations. 22 The European Commission uses 3-year average of regional per capita income compiled using the latest available data at the time of deciding financial allocations.
5. Conclusion This paper reconsiders the regional income convergence within the particular countries taking as an example the evolution of income disparities among 16 NUTS2 Polish regions and 51 US states. We find that the application of regional price deflators has a significant impact on statistical data, in terms of relative regional per capita income level. We also show that the average level of regional income dispersion is lower, as compared to the nominal data. Finally, we confirm that the regional price deflators may influence the β-convergence analysis. In our case, the estimated parameters either change the statistical significance (absolute convergence in the case of Polish data) or the value of coefficient (conditional convergence in both cases). Regional price deflators also influence statistical significance of spatial spillovers. It is difficult to assess to what extent the results obtained for Poland can be considered as a representative for other European countries. The results obtained for US states suggest however, that our findings can be consider as universal. This implies that regional price indices should be taken into account at the time of analyzing regional income disparities. This is particularly important in the European Union where the regional per capita income is the main criterion taking into account at the time of determining financial allocations under the EU Cohesion Policy programs. Therefore it would be highly recommended to start gathering the data necessary for the compilation of regional price indices in all EU member states. Acknowledgments We would like to thank the three anonymous referees for useful comments and suggestions. B. Rokicki gratefully acknowledge the financial support from the Polish National Science Center under the grant DEC-2011/03/D/HS4/00868. References Abramovitz, M., 1986. Catching-up, forging ahead, and falling behind. J. Econ. Hist. 46, 385–406. Abreu, M., de Groot, H.L.F., Florax, R.J.G.M., 2005. A meta-analysis of b-convergence: the legendary 2%. J. Econ. Surv. 19, 389–420. Alam, M.S., 1992. Convergence in developed countries: an empirical investigation. Rev. World Econ. 128 (2), 189–201. Arbia, G., Paelinck, J.H.P., 2003. Economic convergence or divergence? Modeling the interregional dynamics of EU regions, 1985–1999. J. Geogr. Syst. 5 (3), 291–314. Arbia, G., Le Gallo, J., Piras, G., 2008. Does evidence on regional economic convergence depend on the estimation strategy? Outcomes from analysis of a set of NUTS2 EU regions. Spat. Econ. Anal. 3 (2), 209–224. Arbia, G., Battisti, M., Di Vaio, G., 2010. Institutions and geography: empirical test of spatial growth models for European regions. Econ. Model. 27, 12–21. Aten, B.H., Figueroa, E.B., Martin, T.M., 2012. Regional price parities for states and metropolitan areas, 2006–2010. Surv. Curr. Bus. 92 (8), 229–242. Azomahou, T.T., El ouardighi, J., Nguyen-Van, P., Cuong Pham, T., 2011. Testing convergence of European regions: a semiparametric approach. Econ. Model. 28, 1202–1210. Barro, R., Sala-i-Martin, X., 1991. Convergence across states and regions. Brook. Pap. Econ. Act. 1, 107–182. Barro, R.J., Sala-i-Martin, X., 1992. Convergence. J. Polit. Econ. 100 (2), 223–251. Baumol, W.J., 1986. Productivity growth, convergence, and welfare: what the long-run data show. Am. Econ. Rev. 76, 1072–1085. Boldrin, M., Canova, F., 2001. Inequality and convergence: reconsidering European regional policies. Econ. Policy 32, 207–253. Brandt, L., Holz, C.A., 2006. Spatial price differences in China: estimates and implications. Econ. Dev. Cult. Chang. 55 (1), 43–86. Čadil, J., Mazouch, P., Musil, M., Kramulová, J., 2014. True regional purchasing power: evidence from the Czech Republic. Post-Communist Econ. 26 (2), 241–256. Cameron, G., Muellbauer, J., 2000. Earning biases in the United Kingdom regional accounts: some economic policy and research implications. Econ. J. 110 (464), 412–429. Czyż, T., Hauke, J., 2011. Evolution of regional disparities in Poland. Quaestiones Geographicae 30 (2), 35–48. Dall'erba, S., Le Gallo, J., 2008. Regional convergence and the impact of European structural funds over 1989–1999: a spatial econometric analysis. Pap. Reg. Sci. 87 (2), 219–244. European Communities/OECD (2006). EUROSTAT-OECD Methodological Manual on Purchasing Power Parities. Office for Official Publications of the European Communities. Fischer, M.M., Stumpner, P., 2008. Income distribution dynamics and cross-region convergence in Europe. Spatial filtering and novel stochastic kernel representations. J. Geogr. Syst. 10 (2), 109–140.
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