ARE THE MARGINAL CONVERGENCE OUTCOMES OF THE COHESION POLICY DIMINISHING?

Significant disparities still exist between regions of the European Union, even though substantial Cohesion investments are directed to address this issue. To adjust the Cohesion Policy (CP), researchers assess the returns of the CP, but almost all studies are carried out at NUTS1&2 or a country level, even though significant disparities occur at NUTS3 level. Moreover, just a few studies examine the non-linear effects of the CP, and none of them covers the NUTS3 disaggregation level. Filling the gap of previous contributions, the paper aims to investigate convergence outcomes of the CP at NUTS2&3 level and to identify whether the marginal effect of the CP is diminishing. The estimation strategy is based on the modified specification of the difference-in-differences estimator that has an advantage while examining policy effects, using non-experimental data. Based on research findings, the essential guidelines for the improvement of the CP can be drawn up: i) the distribution policy of Cohesion investments should focus on smaller territorial units to reduce disparities at NUTS3 level; ii) the intensity of the CP’s transfers has to be optimised because excessive intensity does not provide a positive return.


Introduction
One of the issues of the European Union (EU) is the disparities between and within Member States (MS). The European Commission (EC) is addressing this issue by shaping CP and the allocation of the support from European Regional Development (ERDF) and Cohesion Funds (CF). One of the ultimate goals of CP's investments is to strengthen economic and social cohesion by correcting imbalances between EU regions. Given the importance of CP's goals, great attention was paid in previous research to examine how successfully CP implemented these goals. However, the scientific studies most often investigate the impact of the CP on economic growth at countries, NUTS1&2 disaggregation level and leave open the question what are the convergence outcomes of the CP and especially at NUTS3 level.
Some authors identified an "optimal" level of CP investments' intensity but their studies cover NUTS1&2 or country disaggregation, leaving the question what is the "optimal" level of the intensity at NUTS3 disaggregation level in terms of the impact on regional disparities. To address this gap, the paper aims to evaluate non-linear convergence outcomes of the CP at NUTS2&3 disaggregation level and to provide main guidelines for the adjustment of the EU's CP. This research supplements previous contributions by identifying an "optimal" level of CP investments' intensity for positive marginal convergence outcomes at NUTS2&3 disaggregation level.
The methodology is based on a difference-in-differences (DiD) approach to test empirically non-linear convergence effects of the EU's regional support at NUTS 3 level over the 2000-2006 and 2007-2013 programming periods. The rest of the paper is organized as follows: Section 1 presents a literature review focusing on the non-linear relationship between CP and its outcomes. Section 2 describes the model based on difference-in-differences estimator to estimate the conditional marginal convergence outcomes of the CP. Section 3 presents and discusses the results of the estimations and provides possible directions for the improvement of the CP. The last section concludes the paper.

Literature review on the non-linear relationship between the Cohesion Policy and its outcomes
thors confirm the positive and significant impact of regional support on economic growth or convergence. However, it should be noted that research also provides evidence on the heterogeneity of the CP outcomes, which might be related to diminishing return, substitution effect and moral hazard phenomenon (see Table 1). These effects may impose a non-linear (in the form of inverted U-shaped letter) relationship between CP investments' intensity and its outcomes, i.e. that marginal effect of the CP is not constant (conditional).

Moral hazard phenomenon
This phenomenon is related to the considered parties' aspirations to obtain additional benefits taking higher risks and often violating established rules. As regions receive ERDF and CF support only below a certain level of development, to achieve or preserve beneficiary status, the regional or national government may manipulate statistics. It can lead to funding cut-off from productive projects and result in lower or even negative outcomes of the CP. The rate of convergence between regions may decrease or even increase regional divergence if ERDF and/or CF transfers are directed to regions that have already reached a high level of development. Corruption in support allocation schemes is also related to a moral hazard phenomenon and can lead to the same results. Beugelsdijk and Eijffinger (2005) Diminishing returns, substitution effects and moral hazard phenomenon justify the importance to determine the "optimal" intensity level of ERDF and CF transfers. Determining the "optimal" intensity level would allow a more rational redistribution of CP funds and make CP more effective. However, just a few previous studies (Mohl & Hagen, 2008;Wostner & Šlander, 2009;Becker et al., 2012;Kyriacou & Roca-Sagales, 2012;Pinho et al., 2015a;Pellegrini & Ceruqua, 2016;Pontarollo, 2017;Cerqua & Pellegrini, 2018;Di Cataldo & Monastiriotis, 2020) investigated potentially diminishing marginal outcomes of the CP. They all (except Mohl & Hagen, 2008) have revealed that after a certain level of ERDF and/ or CF commitments' intensity, additional payments do not generate significant positive outcomes. Mohl and Hagen (2008) revealed that CP's transfers do not affect economic growth rate significantly and, considering this, conclude that it does not matter which "dose" of CP's transfers regions have received. Becker et al. (2012) identified that beyond approximately 1.3 per cent of regional GDP, additional ERDF and CF transfers do not promote economic growth and the optimal desirable level of ERDF and CF transfer's intensity is 0.4 per cent of regional GDP. Pontarollo (2017) investigated non-linear relation between CP's transfers decomposed by intervention area (productive environment, human capital and infrastructure) and productivity as well as economic growth. The assessment results revealed that when the intensity of transfers exceeds 0.15-0.70 per cent of regional GDP (depending on the intervention area), the marginal effect of transfers becomes negative. According to Pinho's et al. (2015a) findings, this boundary line is 3 per cent of countries GDP. According to Cerqua and Pellegrini's (2018) estimations, the outcomes of CP's transfers become statistically negligible and negative when intensity exceeds 305-350 Euro per capita. Di Cataldo and Monastiriotis (2020) have confirmed the hypothesis of diminishing returns of EU Funds in the UK case. Authors conclude that none of the regions in the UK exceeds the maximum desirable intensity threshold estimated by Cerqua and Pellegrini (2018).
It should be noted that Becker et al. (2012) expected to find a minimum diserble level of ERDF and CP transfer intensity below which transfers would not generate positive growth effect but above witch they would. However, the evaluation results rejected this assumption and the authors conclude that there is no evidence for exsistence of a minimum diserable level of regional transfers. Bandonio and Pellegrini (2016), European Commission (2016), Pellegrini and Cergua (2016) agree that ERDF and CF transfers' intensity matters for returns, but do not highlight a desirable level. Also, it should be noted that previous studies do not determine the desirable level of ERDF and CF transfer's intensity at NUTS3 level and for positive impact on convergence.

Methodology and data
Most of the papers that deal with the outcomes of the CP adopt the model of conditional beta-convergence. This model allows to estimate the linear and non-linear effect of the CP on growth directly since the average growth rate is used as a dependent variable. Aiming to estimate the relation between transfers' intensity and disparities among EU regions, we can not rely on the same approach. Our model is grounded on a difference-in-differences (DiD) approach. The initial specification of the linear regression equation, which allows to estimate unconditional DiD parameter, is: Y is the variable in the i-th region whose disparities between CP's beneficiaries and developed regions are under examination. 0 b is the estimated average , i t Y in the group of developed regions over the reference period. 2 t t is a dummy variable equal to 1 for the CP intervention period and equal to 0 for the reference period. 1 b shows how the average Y i,t in the group of developed regions changed over the CP intervention period, compared with the reference period, i.e. how variable under consideration has changed without CP intervention.
, i t CP is a dummy variable equal to 1 if the region received CP's transfers and 0 otherwise. 2 b shows how the average it Y differed between CP's beneficiaries and developed regions already before the CP took place, i.e. shows the initial (over the reference period) difference between CP's beneficiaries and developed areas. The parameter on 2 b is expected to be negative since CP focuses on less developed areas. DiD b is the DiD parameter which shows the effect of the CP, i.e. whether the initial negative differences between CP beneficiaries and developed regions became smaller due to the CP. Positive parameter on DiD b would give evidence that initial differences over the reference period became smaller over CP's intervention period, i.e. CP's transfers contributed to diminishing regional disparities. ε , i t is the error term. Research assumes that regions will not respond to CP's transfers in the same way simply because the amount of transfers is not constant across regions. To put in other words, the effect of the CP hinges on the amount of transfers. Thus, some heterogeneity in the impact across regions is expected as well. It is possible to estimate DiD, assuming heterogeneity of the CP's effect by interacting where DiD b now measures the effect of CP transfers' intensity change by one unit on regional disparities.
To relax an assumption that the marginal effect of , i t ICP on the disparities is constant, i.e. the relationship is linear, and aiming to estimate the maximum desirable intensity level of CP's transfers, which still has a positive effect, and a minimal level of intensity that starts to have a significant impact, quadratic specification is introduced. To account for other factors affecting , that corresponds to a vector of time-varying factors, and θ i that corresponds to a vector of time-constant factors are added: would give evidence of a quadratic form of relationship in the form of an inverted U. In the case of interactive Eqs (1) and (2), after the first differencing or time-demeaned transformations 1 , they collapse to simple additive models for the second (CP intervention) period, and estimated standard errors on coefficients associated with DiD parameter are unconditional. However, in the case of the Eq. (3) the multiplicative term is retained after the first differencing or time-demeaned transformations for the second period (t2 = 1): ( ) where .. stands for the time-demeaned variable 2 . Therefore, not only the marginal effect of ICP is conditioned on the value of i ICP itself, but following Rodriguez-Pose and Garcilazo (2015) and Pinho et al. (2015b), it can be argued that the standard error of the estimated slope coefficient is also conditioned on i ICP value and standard error of the sum ( ) Examination hodifferent intensity levels of CP transfers' intensity over the two last programming periods is related to diminishing regional disparities at NUTS2&3 disaggregation 1 These two alternative transformations are used to control all region-specific time-constant effects, i.e. θ i . For example, geographical position of the region, which determines its access to infrastructure, such as seaports, highways, etc. or economic linkages between regions, which can be an important growth factor for peripheral regions situated near the core regions. Having little possibility to control these effects by including all necessary variables at NUTS2&3 disaggregation level, an unexplained variation which now would account for a part of the error term could lead to a correlation between ε , i t and , i t Y as well as between ε , i t and , i t ICP . This correlation is very likely to occur since CP's transfers are not randomly distributed among regions, but depends on region's characteristics, which are also related to its growth and thus impose endogeneity problem. 2 Using the first differencing, would yield quite the same equation, just 0 b would not be retained.
is based on two databases. Compared to the study carried out concerning 2000-2006 programming period (SWECO, 2008), the report for 2007-2013 programming period (Ciffolilli et al., 2015) collects data on expenditure and not only allocations to selected projects. Having just allocations data for 2000-2006 period, but aiming to compare effects of two last fully expired programming periods, and considering that expenditure but not allocations could make an effect, few assumptions are put forward regarding policy intervention periods and calculation of CP transfers' intensity:  For 2000-2006SWECO (2008 database contains data at NUTS2&3 levels for the Cohesion Fund, ERDF Objective 1, ERDF Objective 2, URBAN and INTERREG IIIA allocations. The total amount mapped in the database for NUTS3 is 149.819 bill. EUR which is 93.5% and for NUTS2 is 156.174 bill. EUR which is 97.5% of the total CF and ERDF budget for the 2000-2006 programming period. All current EU MS except Bulgaria, Romania and Croatia could receive funding for the 2000-2006 programming period. Thus there were 1251 NUTS3 and 260 NUTS2 level regions (according to NUTS classification that existed) under CP consideration. 188 NUTS 2 regions received funding and 72 did not. According to descriptive statistics, a minimum of transfers' intensity was 0.03%, maximum -2.92% with the average and median of 0.39% and 0.20%, respectively. Over the same period, 871 NUTS 3 regions received funding a 380 did not. According to descriptive statistics, a minimum of transfers' intensity was 0.01%, maximum -8.44% with the average and median of 0.37% and 0.13%, respectively.
For the 2007-2013 programming period, Ciffolilli's et al. (2015) database contains cumulative expenditures of both ERDF and CF programmes at the NUTS2 (276) and 3 (1342) levels of EU reg f all 28 EU countries and covers the Convergence, Regional Competitiveness a Employment as well as the European Territorial Cooperation Objectives for the 2007-2013 programming period. The total amount mapped in the database for NUTS3 is 200.193 bill. EUR which is 97.3% and for NUTS2 is 202.854 bill. EUR which is 98.6% of the total expenditures by the end of 2014. 191 NUTS2 regions received funding, and 85 did not. According to descriptive statistics, a minimum of transfers' intensity was 0.03%, maximum -4.66% with the average and median of 0.72% and 0.34%, respectively. Over the same period, 958 NUTS3 regions received funding, and 384 did not. According to descriptive statistics, a minimum of transfers' intensity was 0.02%, maximum -8.81% with the average and median of 0.63% and 0.15%, respectively. Table A1 (see Appendix) reports information on two variables considered in the research as the dependent since the aim is to estimate to what extent CP contributed to diminishing disparities among regions in terms of development level and productivity. Data on productivity over 1995-1999 is missing for Greece, except for Attiki, the Netherlands, and four UK regions. Data on Mayotte (France) is missing for all years. For Poland, the average was calculated including just two years, 1998 and 1999. Table A2 (see Appendix) reports information about control variables included in the model.

Research results and discussion
Tables 2 and 3 report fixed-effects estimates of Eq. (3) for two last programming periods. Estimations are made separately for a sample of NUTS2&3 regions and two dependent variables -per capita GDP and productivity.  Notes: Robust (using HCCME) standard errors are presented in parentheses. *, **, *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. (1) ln GDP refers to estimates where logged regional per capita GDP is used as a dependent variable.
(2) ln GVA refers to estimates where logged regional GVA per worker is used as a dependent variable.  Notes: Robust (using HCCME) standard errors are presented in parentheses. *, **, *** indicate statistical significance at the 10%, 5%, and 1% levels, respectively. (1) ln GDP refers to estimates where logged regional per capita GDP is used as a dependent variable.
(2) ln GVA refers to estimates where logged regional GVA per worker is used as a dependent variable.
The estimated direction of the effect on control variables seems to be reasonable. Higher investment ratio, a more significant share of employed in high-technology sectors, higher population density and thus agglomeration effect, bigger industry sector according to a share of created GVA have a positive and statistically significant effect on regional per capita GDP. A bigger proportion of the working-age population and share of it with tertiary education End of Table 3 seems to have a positive but insignificant effect on per capita GDP in a region. On the contrary, a more significant proportion of the working-age population with primary education and size of the agriculture sector in a region is negatively and significantly related to its per capita GDP. Amount of investment per worker, workers' tertiary education, innovations, and a higher share of empd in industry sector have a significant positive correlation, whereas primary education and employment in agriculture have a significant negative correlation with productivity. Infrastructure measured as the density of motorways has an insignificant positive effect.
All estimations show that CP contributed to diminishing disparities among regions in terms of their development level and productivity. Nevertheless, the relationship between funding intensity and the effect on disparities is non-linear, suggesting that not in all regions and not all support had a positive effect. The last row in Tables 2 and 3 reports the estimated turning point of CP transfer's intensity. The marginal effect of transfer's intensity above this point on diminishing disparities is estimated to be negative. Table A3 (see Appendix) reports which regions were overfunded according to estimated turning points in Tables 2 and 3. Calculations are made separately for both programming periods, taking into account disaggregation level and dependent variable under consideration.
Some differences are comparing two programming periods and two disaggregation levels. The overfunding was more typical for 2007-2013 programming period and NUTS 2 level (over both periods under investigation). Among mostly overfunded dominate regions from Portugal and Greece (over 2000-2006 programming period) and regions from Poland, Hungary, Bulgaria, Portugal and Greece (over 2007-2013 programming period). It seems that a vast amount of ERDF and CF funding for the least developed regions did not help to increase their productivity and development level significantly enough for convergence to occur.
Figures 1-4 present the following relationships: (i) between level of CP's transfers intensity and estimated effect on disparities; (ii) between level of CP's transfers intensity and estimated conditional effect on disparities; (iii) between level of CP's transfers intensity and  2000-2006, GDP 2000-2006, GVA 2007-2013, GDP 2007-2013 standard error of estimated conditional effect on disparities, and (iv) between level of CP's transfers intensity and t-ratio of estimated conditional effect on disparities, respectively. They allow to analyse not only the size but also the significance of the estimated effect. According to estimation results, distribution of ERDF and CF transfers across regions over the last two programng periods was far from being an optimal, considering maximising the effect of ERDF anCF expenditures on diminishing disparities. The same is true for both disaggregation levels and both dependent variables under consideration. Although in a wide range of relatively high transfers' intensity levels its marginal positive (or negative) effect on disparities is estimated as statistically insignificant, in some extreme cases of transfers' intensity not only marginal but also total effect on convergence was significant and negative.  2000-2006, GDP 2000-2006, GVA 2007-2013, GDP 2007-2013 These results are in line with previous research analysing earlier programming periods and effect on other than convergence outcomes. Despite the fact that estimated turning points (the maximum desirable funding intensity) are higher compared to existing empirical evidence (probably due to different outcome variable, analysed period, and method), general conclusion is quite the same -there are too many too much funded regions, which are not spending ERDF and CF allocations efficiently to boost their productivity and growth to ensure regional convergence.
herefore, the re-allocation of ES funds, avoiding overfunding, is crucial over the following programming period to ensure more efficient use. This conclusion also brings us to one more question -what causes the inefficient use of SF and CF funding in highly supported regions? Is it a matter of a simple diminishing returns to investment or more complicated issue related to corruption, misallocation of funds due to shortage of managerial knowledge or week institutional environment? Having a robust answer to this question would allow to firstly direct funding to solve problems in the areas which interfere efficient use of regional support.

Conclusions
The previous contributions have left the question what is the "optimal" intensity level of the CP in terms of the impact on regional disparities and especially at NUTS3 disaggregation by covering exclusively NUTS1&2 or country levels and analysing just growth. Our research which includes two last fully expired programming periods, i.e. 2000-2006 and 2007-2013, allowed to evaluate the "optimal" intensity level of CP investments that ensures positive marginal convergence outcomes at NUTS2&3 disaggregation level.  Results considering diminishing marginal outcomes of the CP are in line with previous research which focuses on earlier programming periods and the effect on other than convergence outcomes. Research shows higher turning points (the maximum desirable funding intensity) compared to previous contributions, and this could be due to different applied methodology, alternative CP outcome under consideration, and disaggregation level as well as more recent programming period that is covered in presented research.
Estimation results shed some light on the sources of the heterogeneous outcomes of the CP, i.e. why the effects of CP's investments vary across regions. This analysis also gives some insights on the inter-regional allocation of ERDF and CF: (i) there is a need to focus on smaller territorial units setting the aims and negotiating regarding allocation commitments in order to reduce disparities at NUTS3 disaggregation; ii) the intensity of the CP's investments has to be optimised since excessive intensity does not provide positive returns, thus setting the maximum allocations to GDP ratio and avoiding concentration of the investment in a few heavily underdeveloped regions would increase the overall effectiveness of the CP.
Our study has some limitations that could be addressed in future research. First, estimated turning points based on two last fully expired programming periods could change at some point when the data on ongoing 2014-2020 programming period will become available and will be included in the research. Nevertheless, planning allocations for the next, i.e. programming period of 2021-2027 it is essential to take into account which regions were previously overfunded avoiding same inefficiencies in the future. Second, our research assumes that the marginal effect of the CP on convergence is homogenous across regions. A growing body of literature on moderators of CP outcomes suggests that this could be not the case, and future research could concentrate on finding which factors may shift this turning point.

Funding
This work was supported by the Research Council of Lithuania under agreement No. S-MIP-17-114.

Disclosure statement
We declare that we do not have any competing financial, professional, or personal interests from other parties. Pinho, C., Varum, C., & Antunes, M. (2015b). Under what conditions do structural funds play a significant role in European regional economic growth? Some evidence from recent panel data.