To what extent do SMEs contribute to Europe’s patent stock? A methodological outline for creating a Europe-wide SME technology indicator

Abstract

In this paper, we outline a methodology to assess the contribution of SMEs in corporate patenting for an extended set of European countries. The methodology consists of harmonizing, matching and disambiguating corporate applicant names from patent databases on the one hand and company names obtained from financial directories on the other hand. In order to address remaining gaps, additional sampling and extrapolation efforts are required to obtain reliable indicators. We propose a method to devise such additional efforts by means of stratified random sampling. Combining both approaches yields accurate indicators about the contribution of SMEs to the patent stock of the countries under study. The resulting indicators can be instrumental in guiding and assessing IPR and innovation policy initiatives at European and/or member state level.

Appendices

Appendix 1: Sampling methodology

The sample size is calculated by means of stratified random sampling. The sample size n_D in the full target population D is calculated as:

$${n}_{D}=\frac{{\left(\sum_{h=1}^{H}{W}_{h}.{S}_{h}\right)}^{2}}{\mathrm{V}\left({\widehat{\theta }}_{D}\right)+\frac{1}{{N}_{D}}\sum_{h=1}^{H}{W}_{h}.{S}_{h}^{2}}$$

where $\mathrm{V}\left(\widehat{\theta }D\right)$ is the variance of the estimated overall share of SMEs, H is the number of strata in the target population D, W_h = N_h / N_D, where N_h is the number of enterprises in stratum h; N_D is the total number of enterprises in target population D; and ${S}_{h}^{2}$ is the stratum variance for the SME dummy variable y_a. The numerator reflects the variance within each stratum multiplied by the size of the strata. In other words, for strata with more firms, more n will be included. A similar observation can be made with respect to the variance (S_h); this will be highest when the proportion of large and small firms is equal (50 × 50 = 2 500 whereas 90 × 10 = 900).

The stratum variance, ${S}_{h}^{2}$ can be expressed as follows:

$${S}_{h}^{2}=\frac{1}{{N}_{h}-1}{\sum_{k\epsilon {a}_{h}}\left({y}_{a}\left(k\right)-\frac{1}{{N}_{h}}\sum_{k\epsilon {a}_{h}}{y}_{a\left(k\right)}\right)}^{2}$$

In practice, the stratum variance S_h² is not known. The variance per country per quantile for the matched applicants with sufficient information to determine company size is used as a proxy. To calculate the stratum variance for the SME dummy variable for strata reporting fewer than 10% SMEs among the matched applicants with sufficient information, the SME percentage was set to 10% to ensure that at least some firms were sampled.

The confidence interval for the estimated overall proportion of SMEs, with approximate confidence level of 95%, is given by:

$${\widehat{\theta }}_{D}\pm \mathrm{1,96}.\sqrt{V\left({\widehat{\theta }}_{D}\right)}$$

The precision, α (set at 0.025 for a two-sided alternative) in terms of the length of the confidence interval:

$${\propto }_{D}=\mathrm{1,96}. \sqrt{V\left({\widehat{\theta }}_{D}\right)}$$

From which one can deduce that the variance $V\left({\widehat{\theta }}_{D}\right)$ can be expressed as:

$$V\left({\widehat{\theta }}_{D}\right)={\left(\frac{{\propto }_{D}}{\mathrm{1,96}}\right)}^{2}$$

In the formula for overall sample size we then substitute the variance $V\left({\widehat{\theta }}_{D}\right)$, by the precision level we require. Aiming for greater precision will result in higher values for ${n}_{D}.$

It is assumed that all strata are equally important and, hence, the Neyman allocation (Cochran, 1977) can be used. The total sample size in the target population is distributed among strata, so the sample size in stratum h, n_h is given by:

$${n}_{h}={n}_{D}.\frac{{N}_{h}.{S}_{h}}{\sum_{h=1}^{H}{N}_{h}.{S}_{h}}$$

Decimals resulting from strata sample size computation are rounded up to the next integer. In addition, due to the skewed patent volume distribution—a minority of companies tend to account for more than half of the patent volume in most countries—the minimum sample size for the on average smaller top quantiles with populations of 200 applicants or fewer is set at 5.¹¹ The resulting sample sizes per stratum, and the population values on which their computation is based, are reported in Table 8. Strata with 200 applicants or fewer account for 2952 of the total population of applicants. The calculated sample sizes for strata containing more than 200 applicants represent 72,804 applicants or the rest of the population. In total, 1,849 applicants have to be verified: 433 applicants represent strata containing no more than 200 applicants, 1416 applicants account for the remaining strata with more than 200 applicants.

To illustrate the sampling methodology, the computation of sample size for the third quantile of non-matched Belgian corporate applicants, containing 669 patentees (see Table 7), is explained. The computation of the parts constituting the formula for the stratum sample size n_h is illustrated sequentially.

The proportion of the stratum population in the full target population is calculated as follows:

$${W}_{str.3\backslash NM\backslash BE}=\frac{{N}_{str.3\backslash NM\backslash BE}}{{N}_{D}}=\frac{669}{75 567}=0.0089$$

As a proxy for ${S}_{h}^{2}$—the stratum variance for the SME dummy variable y_a—the variance per country per quantile for the matched applicants with sufficient information to determine company size is used. In the case of the third quantile for Belgium (669 corporate applicants), matching Amadeus with PATSTAT resulted in the identification of 213 SMEs and 359 large companies.

$${S}_{str.3\backslash NM\backslash BE}^{2} =\frac{1}{\left(213+359\right)-1}*\left[\begin{array}{c}{210*\left(1-\frac{1}{\left(213+359\right)}\left(213*1+359*0\right)\right)}^{2}+\\ {359*\left(0-\frac{1}{\left(213+359\right)}\left(213*1+359*0\right)\right)}^{2}\end{array}\right]=0.2341$$

Departing from a required 5% significance level for the proportion of SMEs, the ${\alpha }_{D}$ is set at 0.025 against a two-sided alternative:

$$V\left({\widehat{\theta }}_{D}\right)={\left(\frac{0.025}{1.96}\right)}^{2}=0.000163$$

The full sample size ${n}_{D}$ for all strata with populations of 200 or more (see above) is then computed as¹²:

$${n}_{D}=\frac{{\left[\begin{array}{c}\left({W}_{str.i\backslash MBU\backslash AT}*{S}_{str.i\backslash MBU\backslash AT}\right)+\dots +\left({W}_{str.i\backslash MBU\backslash SE}*{S}_{str.i\backslash MBU\backslash SE}\right)+\\ \left({W}_{str.i\backslash NM\backslash AT}*{S}_{str.i\backslash NM\backslash AT}\right)+\dots +\left({W}_{str.i\backslash NM\backslash SE}*{S}_{str.i\backslash NM\backslash SE}\right)\end{array}\right]}^{2}}{\begin{array}{c}0.000163+\frac{1}{75 567}*\\ \left[\begin{array}{c}\left({W}_{str.i\backslash MBU\backslash AT}*{{S}_{str.i\backslash MBU\backslash AT}}^{2}\right)+\dots +\left({W}_{str.i\backslash MBU\backslash SK}*{{S}_{str.i\backslash MBU\backslash SE}}^{2}\right)+\\ \left({W}_{str.i\backslash NM\backslash AT}*{{S}_{str.i\backslash NM\backslash AT}}^{2}\right)+\dots +\left({W}_{str.i\backslash MBU\backslash SK}*{{S}_{str.i\backslash NM\backslash SE}}^{2}\right)\end{array}\right]\end{array}}=\mathrm{1,399}$$

with i representing the quantile number of the strata with populations of more than 200 applicants.

Finally, the following formula computes the sample size that is representative for the third quantile of unmatched Belgian corporate applicants:

$${n}_{h}={n}_{D}.\frac{\frac{669}{75 567}*0.2341}{\left[\begin{array}{c}\left({W}_{str.i\backslash MBU\backslash AT}*{S}_{str.i\backslash MBU\backslash AT}\right)+\dots +\left({W}_{str.i\backslash MBU\backslash SK}*{S}_{str.3\backslash MBU\backslash SE}\right)+\\ \left({W}_{str.i\backslash NM\backslash AT}*{S}_{str.i\backslash NM\backslash AT}\right)+\dots +\left({W}_{str.i\backslash NM\backslash SK}*{S}_{str.3\backslash NM\backslash SE}\right)\end{array}\right]}=13$$

Appendix 2

See Tables 10, 11, and 12.

Table 10 Distribution of corporate applicants after the 1st stage of classification based on entity-level size indicators only

Table 11 Shares of applicants classifiable as actual SMEs and large firms after the classification stage (in %)

Table 12 Shares of applicants classifiable as actual SMEs and large firms after the extrapolation stage (in %)