# Are ERDFs Devoted to Boosting ICTs in SMEs Inefficient? A Three-Stage SBM Approach

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

Authors | Main Topics Addressed |
---|---|

Cuadrado-Roura and Garcia-Tabuenca [42] | Analyzed EU programs and policies aimed at the successful use of ICT in SMEs, focusing on Spain |

Santinha and Soares [40] | Analyzed several initiatives undertaken by the European Commission since the Lisbon summit of March 2000, particularly European regional policies related to the effective integration of ICTs into business processes |

Galloway and Mochrie [48] | Aimed to compile the extremely diverse literature on the use of ICTs in rural SMEs to offer an overview of the generic policy concerns |

Skoko et al. [44] | Suggested an ICT adoption model in Australian and Croatian SMEs |

Colombo and Grilli [49] | Evaluated if both horizontally general purpose direct support mechanisms at the national and local levels allowed for the effective deployment of public funds, with a focus on the Italian ICT services industry |

Plomp et al. [45] | Ex post assessment of the Netherlands ICT policy program for SMEs that took place between 2002 and 2007 |

Plomp et al. [46] | Proposed simple, awareness-focused policy programs rather than extensive, government-supported initiatives in the Netherlands |

Calle et al. [43] | Assessment of the first public initiatives to help Spanish SMEs in their digital transformation |

Kalpaka et al. [51] | Proposed digital innovation hubs as a policy instrument to boost the digitalization of SMEs, focusing on the ERDF of 2021–2027 |

Henderson [47] | Investigated the influence of digitization on demand-side policies that encourage SMEs to embrace broadband and digital technologies |

Kergroach [52] | Appraisal of the government challenges in fostering digital transformation in OECD SMEs |

Dionysopoulou and Tsakopoulou [50] | Looked at the ongoing policy initiatives in Greece to support the digital transformation of Greek tourism SMEs on a national level |

Dong and Meng [41] | Observed the lessons learned from the EU’s experience in assisting the digital transformation of SMEs as a benchmark for Chinese SMEs |

## 3. Methodology

#### 3.1. First Stage: Computing Efficiencies for Every DMU with Original Inputs and Outputs through the SBM Model

_{ij}, i = 1, 2, …, m, j = 1, 2, …, n] being the matrix of inputs (m × n), Y = [y

_{rj}, r = 1, 2, …, s, j = 1, 2, …, n] being the vector of outputs (s × n), and the rows of the matrices for DMU

_{k}are ${\mathit{x}}_{k}^{T}$ and ${\mathit{y}}_{k}^{T}$, respectively, with

^{T}representing the transpose of a vector.

*****= $\mathbf{\u0245}$*/t*, ${s}_{}^{-*}$ = ${S}_{}^{-}$/t*, ${s}_{}^{+*}$ = ${S}_{}^{+}$/t*.

**Definition**

**1**.

_{k}is efficient if${\rho}^{*}=1$, meaning that${\mathit{s}}_{}^{-*}$ =

**0**and${\mathit{s}}_{}^{+*}=\mathit{0}$.

**Definition**

**2**.

_{k}is E

_{k}= {j:${\lambda}_{j}^{*}0$, j = 1, …, n}.

**Definition**

**3**.

_{k}is:

_{k}can be 1, even if the DMU is inefficient, to check if a DMU

_{k}is inefficient or not, both Model (1) and Tone’s model must be solved. If DMU

_{k}is efficient in accordance with Model (1), Tone’s model should be applied to compute its Super-SBM non-oriented efficiency score.

#### 3.2. Second Stage: Obtaining the Adjusted Input and Output Factors for Inefficient DMUs Using the SFA Model

#### 3.3. Third Stage: Computing the Efficiencies of Every DMU with the Adjusted Inputs and Outputs through the SBM Model

_{j}(j = 1, …, n) is found to be efficient in the first stage and ${x}_{ij}^{A}={x}_{ij}+\left[\underset{i}{\mathrm{max}}\left\{f\left({Z}_{j},{\beta}^{i}\right)\right\}-f\left({Z}_{j},{\beta}^{i}\right)\right]+\left[\underset{j}{\mathrm{max}}\left\{{v}_{ij}\right\}-{v}_{ij}\right]$ if otherwise. Similarly, ${y}_{rj}^{A}={y}_{rj}$ if DMU

_{j}(j = 1, …, n) is found to be efficient in the first stage and ${y}_{rj}^{A}={y}_{rj}+\left[f\left({Z}_{j},{\beta}^{r}\right)-\underset{r}{\mathrm{min}}\left\{f\left({Z}_{j},{\beta}^{r}\right)\right\}\right]+\left[{v}_{rj}-\underset{r}{\mathrm{min}}\left\{{v}_{rj}\right\}\right]$ if otherwise.

## 4. Data

#### 4.1. Input and Output Factors

#### 4.1.1. “Total Eligible Costs Decided” and “Total Eligible Spending”

#### 4.1.2. “Number of Operations Supported”

#### 4.2. Contextual Variables

## 5. Discussion of Results

#### 5.1. First Stage: Computing the Efficiencies for Every DMU with the Original Inputs and Outputs through the SBM Model

#### 5.2. Second Stage: Obtaining the Adjusted Input and Output Factors for Inefficient DMUs Using the SFA Model

_{PC}and greater number of SMEs more susceptible to process innovation do not always have to apply for more ERDF-supported initiatives, since they show a higher efficiency in seeking funds.

#### 5.3. Third Stage: Computing the Efficiencies of Every DMU with the Adjusted Inputs and Outputs through the SBM Model

#### 5.4. Robustness Study and Sensitivity Analysis

#### 5.4.1. Robustness Study

#### 5.4.2. Sensitivity Analysis

## 6. Conclusions and Further Research

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**OPs that increased their technical efficiency with adjusted factors. Source: Authors’ own computation.

**Figure 2.**Results of the robustness analysis per OP (non-adjusted factors). Source: Authors’ own computation.

**Figure 3.**Results of the robustness analysis per OP (adjusted factors). Source: Authors’ own computation.

**Figure 4.**The sensitivity analysis for the Total Eligible Spending (

**a**) and Number of Operations (

**b**) without adjustments and the sensitivity analysis for the for the Total Eligible Spending (

**c**) and Number of Operations (

**d**) with adjustments. The x-axis of each graph represents the original efficiency score, and the y-axis represents the recalculated efficiency by omitting one output factor at a time. The solid blue lines represent the lines of the best fit. Source: Authors’ own computation.

Statistics | Total Eligible Spending | Number of Operations | Total Eligible Costs Decided |
---|---|---|---|

Mean | 15,861,300 | 409 | 28,169,468 |

Median | 3,238,795 | 27 | 5,000,000 |

Standard Deviation | 38,520,025 | 1068 | 63,497,428 |

Minimum | 68,486 | 1 | 251,294 |

Maximum | 237,904,467 | 5457 | 311,154,920 |

Count | 51 | 51 | 51 |

Environmental Factors | Mean | Standard Deviation | Min | Max |
---|---|---|---|---|

Population with Tertiary Education | 0.5767 | 0.1916 | 0.1156 | 1 |

Digital Skills | 0.5359 | 0.1949 | 0.2814 | 0.9318 |

R&D Expenditures in the Business Sector | 0.3105 | 0.2101 | 0.0215 | 0.8024 |

ICT Specialists | 0.4018 | 0.2527 | 0.0470 | 1 |

Product Process Innovators | 0.5529 | 0.2511 | 0.1767 | 1 |

GDPPPPpc | 87.72 | 23.9315 | 49.09 | 178.30 |

Statistics | Efficiency | Total Eligible Spending | Number of Operations | Total Eligible Costs Decided | |
---|---|---|---|---|---|

Efficient DMUs | Mean | 1.20 | 46,026,233.00 | 1310.40 | 75,514,839.90 |

Median | 1.16 | 9,217,730.00 | 339.50 | 9,633,113.00 | |

Standard Deviation | 0.23 | 74,818,282.11 | 2108.72 | 118,719,405.31 | |

Minimum | 1.00 | 329,249.00 | 1.00 | 251,294.00 | |

Maximum | 1.71 | 237,904,467.00 | 5457.00 | 311,154,920.00 | |

Count | 10 | 10 | 10 | 10 | |

Inefficient DMUs | Mean | 0.20 | 8,503,999.66 | 189.54 | 16,621,815.98 |

Median | 0.06 | 1,963,414.00 | 14.00 | 4,901,930.00 | |

Standard Deviation | 0.25 | 17,671,362.04 | 415.58 | 34,228,777.84 | |

Minimum | 0.00 | 68,486.00 | 1.00 | 373,794.00 | |

Maximum | 0.96 | 102,175,668.00 | 2184.00 | 202,847,237.00 | |

Count | 41 | 41 | 41 | 41 |

MS (2 Digit ISO) | OP | Nº of Times as Benchmark | Rank | Total Eligible Spending | Number of Operations | Total Eligible Costs Decided |
---|---|---|---|---|---|---|

FR | Provence-Alpes-Côte d’Azur—ERDF/ESF/YEI | 20 | 1 | 329,249 | 1 | 251,294 |

CZ | Enterprise and Innovation for Competitiveness—CZ—ERDF | 1 | 2 | 237,904,467 | 451 | 311,154,920 |

ES | Multi-regional Spain—ERDF | 14 | 3 | 58,864,158 | 5108 | 95,971,219 |

ES | País Vasco—ERDF | 26 | 4 | 3,964,897 | 575 | 4,618,616 |

ES | Extremadura—ERDF | 27 | 5 | 1,560,112 | 810 | 4,823,735 |

GR | Competitiveness Entrepreneurship and Innovation—GR—ERDF/ESF | 0 | 6 | 100,667,978 | 5457 | 275,856,182 |

BG | Innovations and Competitiveness—BG—ERDF | 4 | 7 | 33,942,154 | 228 | 38,612,352 |

LT | EU Structural Funds Investments—LT—ERDF/ESF/CF/YEI | 0 | 8 | 7,607,793 | 210 | 7,786,656 |

GR | Epirus—ERDF/ESF | 3 | 9 | 4,593,855 | 144 | 4,593,855 |

PL | Podkarpackie Voivodeship—ERDF/ESF | 0 | 10 | 10,827,667 | 120 | 11,479,570 |

Factor | Average Original | Average Projection | Variation |
---|---|---|---|

Total Eligible Spending | 8,504,000 | 8,716,600 | 3% |

Number of Operations | 189.54 | 783.72 | 313% |

Total Eligible Costs Decided | 16,621,816 | 13,041,314.01 | −22% |

Variables | Slacks | |
---|---|---|

Total Eligible Spending | Number of Operations | |

Constant | −242,050 *** | 237.20 *** |

Population with Tertiary Education | −890,650 *** | - |

Digital Skills | −890,970 *** | 195.99 *** |

ICT Specialists | 1,417,700 *** | 135.17 *** |

Product Process Innovators | - | −73.17 *** |

GDPPPP_{pc} | 1286 *** | −3.39 *** |

Sigma-squared | 8.91 × 10^{11} *** | 8.11 × 10^{5} *** |

Gamma | 0.98 ** | 0.99 ** |

Log-likelihood Function | −593.83 | −308.67 |

Statistics | Efficiency | Total Eligible Spending | Number of Operations | Total Eligible Costs Decided | |
---|---|---|---|---|---|

Efficient DMUs | Mean | 1.15 | 34,224,227.54 | 1190.82 | 56,264,030.64 |

Median | 1.10 | 2,016,502.16 | 323.85 | 3,015,425.50 | |

Standard Deviation | 0.15 | 65,761,340.90 | 1832.82 | 104,511,357.35 | |

Minimum | 1.00 | 329,249.00 | 1.00 | 251,294.00 | |

Maximum | 1.49 | 237,904,467.00 | 5457.00 | 311,154,920.00 | |

Count | 14 | 14 | 14 | 14 | |

Inefficient DMUs | Mean | 0.43 | 9,490,069.87 | 374.48 | 17,539,092.57 |

Median | 0.41 | 3,591,017.20 | 260.17 | 5,637,368.00 | |

Standard Deviation | 0.21 | 17,915,300.53 | 291.66 | 35,107,221.84 | |

Minimum | 0.01 | 657,276.80 | 2.00 | 671,429.00 | |

Maximum | 0.88 | 103,201,263.85 | 1550.54 | 202,847,237.00 | |

Count | 37 | 37 | 37 | 37 |

OP | Nº of Times as Benchmark with Adjustment | Nº of Times as Benchmark without Adjustment | Rank with Adjustments | Rank without Adjustments |
---|---|---|---|---|

Provence-Alpes-Côte d’Azur—ERDF/ESF/YEI | 0 | 20 | 1 | 1 |

Enterprise and Innovation for Competitiveness—CZ—ERDF | 1 | 1 | 2 | 2 |

Multi-regional Spain—ERDF | 9 | 14 | 3 | 3 |

Berlin—ERDF | 18 | 0 | 4 | 22 |

Competitiveness Entrepreneurship and Innovation—GR—ERDF/ESF | 0 | 0 | 5 | 6 |

Haute-Normandie—ERDF/ESF/YEI | 4 | 0 | 6 | 27 |

Central Macedonia—ERDF/ESF | 25 | 0 | 7 | 12 |

Extremadura—ERDF | 2 | 27 | 8 | 5 |

Puglia—ERDF/ESF | 10 | 0 | 9 | 17 |

Innovations and Competitiveness—BG—ERDF | 7 | 4 | 10 | 7 |

Melilla—ERDF | 0 | 0 | 11 | 43 |

Umbria—ERDF | 4 | 0 | 12 | 13 |

Sachsen—ERDF | 6 | 0 | 13 | 11 |

Upper Norrland—ERDF | 0 | 0 | 14 | 28 |

Factor | Average Original | Average Projection | Variation |
---|---|---|---|

Total Eligible Spending | 9,490,070 | 9,699,250 | 2% |

Number of Operations | 374 | 789 | 111% |

Total Eligible Costs Decided | 17,539,093 | 12,998,433 | −26% |

Variables | Slope | |1-slope| | R^{2} | Classification |
---|---|---|---|---|

Total Eligible Spending (non-adjusted) | 0.6432 | 0.3568 | 0.556 | Output |

Number of Operations (non-adjusted) | 0.5627 | 0.4373 | 0.421 | Output |

Total Eligible Spending (adjusted) | 0.8105 | 0.1895 | 0.529 | Output |

Number of Operations (adjusted) | 0.6524 | 0.3476 | 0.377 | Output |

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## Share and Cite

**MDPI and ACS Style**

Henriques, C.; Viseu, C.
Are ERDFs Devoted to Boosting ICTs in SMEs Inefficient? A Three-Stage SBM Approach. *Sustainability* **2022**, *14*, 10552.
https://doi.org/10.3390/su141710552

**AMA Style**

Henriques C, Viseu C.
Are ERDFs Devoted to Boosting ICTs in SMEs Inefficient? A Three-Stage SBM Approach. *Sustainability*. 2022; 14(17):10552.
https://doi.org/10.3390/su141710552

**Chicago/Turabian Style**

Henriques, Carla, and Clara Viseu.
2022. "Are ERDFs Devoted to Boosting ICTs in SMEs Inefficient? A Three-Stage SBM Approach" *Sustainability* 14, no. 17: 10552.
https://doi.org/10.3390/su141710552