# Non-Parametric Analysis of Efficiency: An Application to the Pharmaceutical Industry

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Background

_{i}is (log) output for the ith decision-making unit or DMU, x

_{i}is a vector of inputs for the ith DMU, ε

_{i}the vector of parameters to be estimated, u

_{i}captures the (one sided) inefficiency of the ith DMU and v

_{i}represents stochastic shocks. m(.) is the production function, usually assumed to be Cobb Douglas or Translog. The estimation is ordinarily implemented by maximum likelihood or other appropriate methodologies.

#### Data Envelopment Analysis

_{B}> y

_{A}, while using the same amount of input since x

_{A}= x

_{B}. Alternatively, D and E produce the same output, y

_{D}= y

_{E}, but firm D consumes a smaller amount of input than E, x

_{D}< x

_{E}.

_{i}is a vector of M outputs and x

_{i}a vector of K inputs.

_{i}is the input oriented efficiency score for the ith firm.

_{i}, the input-oriented technical efficiency score for the ith firm, indicates to what extent the inputs can be reduced in percent while keeping the output constant. For example, if DMU i has an efficiency score of 90%, it can reduce all inputs by 10% while offering the same amount of output.

## 3. Material and Method: Data and Empirical Strategy

- (i)
- Manufacture of basic pharmaceutical products and pharmaceutical preparations;
- (ii)
- Research and experimental development on biotechnology.

## 4. Stage 1: Computation of Efficiency Scores

- Huge: if the average real turnover over the period exceeds 2000 million euros.
- Very big: if the average real turnover is less or equal than 2000 million euros and higher than 426.92 million euros.
- Quite big: if the average real turnover is less or equal than 426.92 million euros and higher than 38.86 million euros.
- Medium: if the average real turnover is less or equal than 38.86 million euros and higher than 8.10 million euros.
- Small: if the average real turnover is less or equal than 8.10 million euros and higher than 2.10 million euros.
- Very small: if the average real turnover is less or equal than 2.10 million euros.

## 5. Stage 2: Variables Correlated with Efficiency

#### 5.1. Overview

#### 5.2. Qualitative Implications

#### 5.2.1. Tobit Estimation

_{it}* is the latent or unobservable efficiency, θ

_{it}is the observable efficiency, x

_{it}is a matrix of covariates, β is a vector of coefficients, u

_{i}is the time invariant component of the error term, ε

_{it}is the time-varying component of the error term, i indexes firms and t time.

_{it}in each case.

_{i}component of the error term is rejected at the 99% significance level for the four models, hence supporting the utilization of the random-effects model.

#### 5.2.2. Classical Estimation

_{it}is efficiency, x

_{it}is a matrix of covariates, β is a vector of coefficients, u

_{i}is the time invariant component of the error term, ε

_{it}is the time-varying component of the error term, i indexes firms and t time.

#### 5.2.3. Simar–Wilson Estimation

#### 5.3. Quantitative Implications

_{j}on the dependent variable, defined as:

- -
- As far the particular goal of this subsection is concerned, the Simar–Wilson tool implies marginal effects slightly larger (about 15–35%) but of the same order of magnitude than those obtained from Tobit/pure random-effects model.
- -
- In general terms, more research at the theoretical level and probably Monte Carlo simulations are necessary to know in more detail the properties of the Simar–Wilson estimator. This exceeds the scope of this paper.
- -
- The Simar–Wilson procedure may be useful for applied research, especially in conjunction with other methodologies, although it has a higher cost in computing time if compared with Tobit or classical models.

## 6. Concluding Remarks

- -
- The average level of efficiency in the industry is moderate, 0.341. This figure is not far from results obtained by other studies for alternative samples. Efficiency exhibits a decreasing trend over the years 2010–2018.
- -
- Efficiency levels display a large level of heterogeneity when particular dimensions of companies are considered. Efficiency is higher for those companies whose main activity is manufacturing of pharmaceutical products than for firms focused on R&D activities. This result may be traced to the relative youth of R&D firms, which cannot fully exploit the learning curve yet. The specialization of this kind of firms in a few projects, characterized by low rates of success, may also be a relevant factor in this respect.
- -
- We find a complex relationship between size and efficiency. By and large, bigger firms are more efficient, but only beyond the threshold of 426.92 million euros of turnover per year. Medium-size and small firms register the poorest levels of efficiency, whereas very small firms perform slightly better. This suggests that firms may benefit from either scale economies or high levels of specialization, while the middle ground does not yield good results.
- -
- Our findings suggest that sound financial structures, lower employee costs and higher margins are correlated with higher levels of efficiency. Moreover, the idiosyncratic aspects of the country of origin of the firms may foster or jeopardize productivity.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

Variable | Description | Source |
---|---|---|

OPRE—Operating Revenue (Turnover) | Total Operating Revenues (Net Sales + Other Operating Revenues + Stock Variations) | Amadeus |

TOAS—Total Assets | Total Assets (Fixed Assets + Current Assets) | Amadeus |

PRMA—Profit Margin (%) | (Profit Before Tax/Operating Revenue) * 100 | Amadeus |

EMPL—Number of Employees | Total Number of Employees included in the Company’s payroll | Amadeus |

CFOP—Cash Flow/Operating Revenue (%) | (Cash Flow/Operating Revenue) * 100 | Amadeus |

SCT—Cost of Employees/Operating Revenue (%) | (Cost of Employees/Operating Revenue) * 100 | Amadeus |

COLL—Collection Period (days) | (Debtors/Operating Revenue) * 360 | Amadeus |

Yearly deflator | Computed from the Harmonized European Index | Eurostat |

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**Figure 1.**The intuitions behind the ideas of efficiency and frontier. Note: The figure portrays the ideas of efficiency and frontier. x is input and y is output. The concave solid line represents the technology or frontier of possibilities of production, the maximum attainable amount of output for each value of the input endowment. The dots A, B, C, D and E represent decision-making units or DMUs, i.e., firms, organizations, institutions, etc., whose efficiency is considered. Intuitively, B is more efficient than A because it produces more output than A (y

_{B}> Y

_{A}) with the same amount of input (x

_{B}= x

_{A}). Similarly, D is more efficient than E since D uses a smaller amount of input (x

_{D}< X

_{E}) to produce the same amount of output (Y

_{D}= Y

_{E}). The closer a DMU is to the frontier, the larger its level of efficiency. Source: own elaboration.

**Figure 2.**Average real turnover (in constant euros of 2015) and average number of employees over time by main activity. Notes: The figure displays the time pattern for average real turnover and average number of employees over 2010–2018, disaggregated by main activity of firms. Averages have been computed from the data year by year. Two main categories are considered: firms whose main activity is the manufacture of basic pharmaceutical products (manufacturers), and companies focused on research and experimental development on biotechnology (research and development (R&D) firms). Average turnover exhibits a decreasing trend over the period, with a big drop in 2012 for manufacturers, and an increasing trend for R&D firms since 2013. Average number of employees decreases over the period for the first category of firms and increases since 2016 for the second. Source: own elaboration with data from the Amadeus data basis).

**Figure 3.**Efficiency in the pharma and biotechnological European industry by main activity, 2010–2018. Note: the figure summarizes the yearly trend of average efficiency, for the whole sample and disaggregated by categories corresponding to the main activity of firms. Efficiency decreases over the period, with a partial recovery in 2015–2016. Source: own elaboration.

**Figure 4.**Average efficiency, pharma and biotechnological industry by size, 2010–2018. Note: the figure summarizes the yearly trend of average efficiency of the firms in our sample, disaggregated by size of firms. Size is proxied by real turnover. Efficiency decreases over the period for all categories except for the huge and very big firms. The thresholds are detailed in the main text. Source: own elaboration.

Efficiency Mean | Standard Deviation | Coefficient of Variation | |
---|---|---|---|

Whole sample | 0.341 | 0.265 | 0.777 |

Manufacturers | 0.381 | 0.266 | 0.698 |

R&D firms | 0.281 | 0.251 | 0.893 |

**Table 2.**Relative efficiency in the pharma and biotechnological European industry by size, 2010–2018.

Mean | Standard Deviation | Coefficient of Variation | |
---|---|---|---|

Huge | 0.98 | 0.039 | 0.039 |

Very big | 0.765 | 0.205 | 0.267 |

Quite big | 0.425 | 0.266 | 0.625 |

Medium | 0.312 | 0.218 | 0.698 |

Small | 0.267 | 0.19 | 0.71 |

Very Small | 0.318 | 0.288 | 0.9 |

**Table 3.**Efficiency in the pharma and biotechnological European industry by activity, yearly results, 2010–2018.

2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | |
---|---|---|---|---|---|---|---|---|---|

Whole sample | 0.428 | 0.392 | 0.348 | 0.308 | 0.304 | 0.292 | 0.383 | 0.311 | 0.334 |

Manufacturers | 0.481 | 0.449 | 0.391 | 0.351 | 0.334 | 0.335 | 0.409 | 0.34 | 0.367 |

R&D firms | 0.338 | 0.277 | 0.263 | 0.243 | 0.267 | 0.231 | 0.345 | 0.272 | 0.294 |

Model 1 | Model 2 | Model 3 | Model 4 | |
---|---|---|---|---|

profit_margin | 0.1539 *** | |||

(7.00) | ||||

Germany | 0.0799 | 0.1178 ** | 0.0818 | 0.1045 * |

(1.38) | (2.02) | (1.49) | (1.89) | |

Spain | −0.0232 | −0.0614 | 0.0305 | 0.0435 |

(0.44) | (1.10) | (0.54) | (0.87) | |

France | 0.0100 | 0.0544 | −0.0117 | 0.0167 |

(0.17) | (0.94) | (0.21) | (0.31) | |

Sweden | 0.2977 *** | 0.2615 *** | 0.2389 *** | 0.3008 *** |

(3.93) | (3.44) | (3.45) | (4.13) | |

Italy | 0.1421 *** | 0.1549 *** | 0.1587 *** | 0.1374 *** |

(2.62) | (2.85) | (2.85) | (2.79) | |

UK | 0.1389 *** | 0.1637 *** | 0.1128 *** | 0.1356 *** |

(3.62) | (4.16) | (2.88) | (3.64) | |

Manufacturers | 0.0660 ** | 0.1599 *** | ||

(2.00) | (4.96) | |||

Huge | 0.2054 ** | 0.2393 *** | ||

(2.49) | (3.02) | |||

Verybig | 0.1276 *** | 0.1163 *** | ||

(3.61) | (3.24) | |||

Quitebig | 0.0215 | 0.0179 | ||

(1.39) | (1.09) | |||

year2014 | −0.0795 *** | −0.0744 *** | −0.0633 *** | −0.0738 *** |

(6.90) | (6.37) | (5.88) | (6.16) | |

year2015 | −0.1733 *** | −0.0758 *** | −0.0556 *** | −0.1537 *** |

(4.97) | (4.69) | (5.31) | (4.35) | |

year2016 | 0.0373 *** | 0.0465 *** | 0.0439 *** | 0.0441 *** |

(3.32) | (4.12) | (4.34) | (3.79) | |

cash_flow | 0.1650 *** | |||

(6.86) | ||||

Biotech | −0.1384 *** | −0.0494 | ||

(4.21) | (1.59) | |||

Medium | −0.0300 * | |||

(1.81) | ||||

Small | −0.0614 *** | |||

(3.22) | ||||

Verysmall | −0.0069 | |||

(0.29) | ||||

collection_period | −0.0226 *** | |||

(4.44) | ||||

employee_cost | −0.3739 *** | |||

(10.22) | ||||

_cons | 0.2808 *** | 0.3788 *** | 0.2245 *** | 0.4390 *** |

(7.95) | (12.50) | (6.37) | (15.49) | |

Likelihood Ratio test of σ^{2}_{u} = 0: X^{2}(1) | 928.17 *** | 980.9 *** | 1505.81 *** | 771.79 *** |

Likelihood Ratio test of σ^{2}_{u} = 0: p value | 0 | 0 | 0 | 0 |

Number observations | 1547 | 1344 | 1850 | 1353 |

^{2}

_{u}= 0 distributed as X

^{2}(1). * p < 0.1; ** p < 0.05; *** p < 0.01.

**Table 5.**Variables correlated with efficiency, random effects estimations. Dependent variable is efficiency.

Model 5 | Model 6 | Model 7 | Model 8 | |
---|---|---|---|---|

profit_margin | 0.1531 *** | |||

(5.33) | ||||

Germany | 0.0702 | 0.1064 * | 0.0740 | 0.0908 * |

(1.23) | (1.85) | (1.41) | (1.70) | |

Spain | −0.0210 | −0.0598 ** | 0.0304 | 0.0427 |

(0.55) | (2.04) | (0.66) | (0.87) | |

France | 0.0093 | 0.0504 | −0.0150 | 0.0128 |

(0.19) | (1.08) | (0.32) | (0.28) | |

Sweden | 0.2779 *** | 0.2420 *** | 0.2280 *** | 0.2922 *** |

(3.07) | (3.23) | (3.32) | (3.78) | |

Italy | 0.1375 ** | 0.1488 *** | 0.1529 *** | 0.1336 *** |

(2.52) | (2.74) | (2.86) | (2.78) | |

UK | 0.1340 *** | 0.1538 *** | 0.1041 ** | 0.1295 *** |

(3.44) | (3.91) | (2.51) | (3.70) | |

Manufacturers | 0.0619 * | 0.1534 *** | ||

(1.93) | (4.81) | |||

Huge | 0.1189 *** | 0.1649 *** | ||

(2.63) | (3.72) | |||

Verybig | 0.1277 *** | 0.1247 *** | ||

(4.28) | (4.06) | |||

Quitebig | 0.0233 * | 0.0218 | ||

(1.71) | (1.56) | |||

year2014 | −0.0778 *** | −0.0736 *** | −0.0625 *** | −0.0728 *** |

(8.64) | (7.67) | (7.14) | (7.90) | |

year2015 | −0.1712 *** | −0.0792 *** | −0.0558 *** | −0.1596 *** |

(6.11) | (6.84) | (7.03) | (5.51) | |

year2016 | 0.0366 *** | 0.0450 *** | 0.0430 *** | 0.0430 *** |

(4.09) | (4.52) | (4.78) | (4.46) | |

cash_flow | 0.1661 *** | |||

(5.83) | ||||

Biotech | −0.1298 *** | −0.0421 | ||

(4.42) | (1.44) | |||

Medium | −0.0349 ** | |||

(2.48) | ||||

Small | −0.0648 *** | |||

(3.62) | ||||

Verysmall | −0.0092 | |||

(0.33) | ||||

collection_period | −0.0226 *** | |||

(3.97) | ||||

employee_cost | −0.3701 *** | |||

(7.83) | ||||

_cons | 0.2786 *** | 0.3767 *** | 0.2257 *** | 0.4312 *** |

(7.92) | (15.55) | (6.51) | (19.16) | |

LR test of σ^{2}_{u} = 0: X^{2}(1) | 1306.01 *** | 1656.88 *** | 2561.80 *** | 1156.37 *** |

LR test of σ^{2}_{u} = 0: p value | 0 | 0 | 0 | 0 |

Number of observations | 1547 | 1344 | 1850 | 1353 |

^{2}

_{u}= 0 distributed as X

^{2}(1). * p < 0.1; ** p < 0.05; *** p < 0.01.

**Table 6.**Variables correlated with efficiency, Simar–Wilson estimations. Dependent variable is efficiency.

Model 9 | Model 10 | Model 11 | Model 12 | |
---|---|---|---|---|

profit_margin | 0.3089 *** | |||

(9.31) | ||||

Germany | 0.1287 *** | 0.1562 *** | 0.1405 *** | 0.1204 *** |

(4.43) | (4.93) | (3.64) | (4.09) | |

Spain | −0.0356 | −0.0971 *** | −0.0098 | 0.0053 |

(1.36) | (3.25) | (0.24) | (0.20) | |

France | 0.0342 | 0.0684 * | −0.1606 *** | −0.0364 |

(0.92) | (1.72) | (3.06) | (0.97) | |

Sweden | 0.2958 *** | 0.2602 *** | 0.3352 *** | 0.3539 *** |

(8.04) | (6.04) | (7.06) | (8.41) | |

Italy | 0.1548 *** | 0.1539 *** | 0.2307 *** | 0.1506 *** |

(6.13) | (5.67) | (6.41) | (5.99) | |

UK | 0.1439 *** | 0.1596 *** | 0.1370 *** | 0.1396 *** |

(6.89) | (7.33) | (4.97) | (6.81) | |

Manufacturers | 0.0859 *** | 0.3157 *** | ||

(4.54) | (10.51) | |||

Huge | 0.7812 ** | 0.8741 ** | ||

(2.06) | (2.45) | |||

Verybig | 0.4284 *** | 0.3849 *** | ||

(9.48) | (8.47) | |||

Quitebig | 0.0552 *** | 0.0678 *** | ||

(2.98) | (3.63) | |||

year2014 | −0.0994 *** | −0.1072 *** | −0.0982 *** | −0.0977 *** |

(4.20) | (4.16) | (2.80) | (3.77) | |

year2015 | −0.4586 *** | −0.1540 *** | −0.1161 *** | −0.4179 *** |

(9.43) | (5.15) | (3.40) | (8.48) | |

year2016 | 0.0652 *** | 0.0651 *** | 0.0902 *** | 0.0785 *** |

(3.04) | (2.76) | (3.07) | (3.66) | |

cash_flow | 0.3351 *** | |||

(8.31) | ||||

Biotech | −0.1790 *** | −0.0229 | ||

(8.07) | (1.15) | |||

Medium | −0.1294 *** | |||

(6.36) | ||||

Small | −0.1091 *** | |||

(4.63) | ||||

Verysmall | 0.0192 | |||

(0.60) | ||||

collection_period | −0.0568 *** | |||

(4.11) | ||||

employee_cost | −0.6340 *** | |||

(10.95) | ||||

_cons | 0.1328 *** | 0.3237 *** | −0.0524 | 0.3822 *** |

(6.01) | (15.50) | (1.24) | (20.23) | |

Number of observations | 1446 | 1257 | 1741 | 1264 |

Variable | Tobit | Simar–Wilson | Random Effects |
---|---|---|---|

Profit margin | 0.1511 | 0.2053 | 0.1531 |

Cash flow/income | 0.1628 | 0.2189 | 0.1661 |

Collection period | −0.0223 | −0.026 | −0.0226 |

Employee cost | −0.3683 | −0.4215 | −0.3701 |

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**MDPI and ACS Style**

Díaz, R.F.; Sanchez-Robles, B. Non-Parametric Analysis of Efficiency: An Application to the Pharmaceutical Industry. *Mathematics* **2020**, *8*, 1522.
https://doi.org/10.3390/math8091522

**AMA Style**

Díaz RF, Sanchez-Robles B. Non-Parametric Analysis of Efficiency: An Application to the Pharmaceutical Industry. *Mathematics*. 2020; 8(9):1522.
https://doi.org/10.3390/math8091522

**Chicago/Turabian Style**

Díaz, Ricardo F., and Blanca Sanchez-Robles. 2020. "Non-Parametric Analysis of Efficiency: An Application to the Pharmaceutical Industry" *Mathematics* 8, no. 9: 1522.
https://doi.org/10.3390/math8091522