Heterogeneity of educations

H1 states that each person of a founding team has attained a different education.

In order to determine the degree of heterogeneity in this dimension, the Herfindahl-Index of the highest education attained is calculated for each team foundation. The Herfindahl-Index is a measure of concentration. For the present case it is computed as the sum of the squared shares of the different educations in each firm

H =

n

X

i=1

s²_i, (3.11)

where s_i denotes the share of educationi.

The underlying education variable can take on more than 1,000 values, i.e. provides highly detailed information on the educational background of the individuals. Since the discipline of the highest educational attainment is only a crude measure for the task actually fulfilled in the firm – it is both possible that one education enables for several tasks and that one and the same task can be conducted by persons with different educational background – no obvious level of aggregation for this variable exists. Therefore, the variable is not aggregated in any respect for calculating the Herfindahl-Index.¹⁴ Besides, if it turns out that even with such a high number of possible values, the Herfindahl-Index does not take the lowest possible value for all firms, the results are of highly informative value.

14Thus, “education” refers to a combination of years of education and field. These two com-ponents are not separated since it is reasonable to assume that, e.g. someone with a vocational training in a technical field is assigned a different task than an engineer.

There are two important points to note. First, the range of the values of the Herfindahl-Index depends on the number of individuals in the team. For exam-ple: If there are two persons, the Herfindahl-Index can take on the values 1 and ¹₂, in the case of three persons 1, ⁵₉ and ¹₃ etc. This entails the question of how to com-pare Herfindahl-Indices of teams of different size. One possibility is to only consider the number of different educations within a firm. In this case, a team consisting of two persons who have different educations is regarded as diverse as a team consisting of four persons in which two at a time have the same education. Comparing teams of different size this way is just to take the Herfindahl-Index as defined in equation (3.11). A second possibility is to treat teams as equally diverse if all individuals have different educations regardless of team size. This can be achieved by transforming the Herfindahl-Index in the following way

H^tr =

As a result, the Herfindahl-Index takes the value one if all individuals have the same education and becomes zero if each individual attained a different education. For the following analysis, I opted for the transformed index. However, the transformation is not necessary for the following analyses. It is just a matter of defining what is meant by “equally diverse”. Referring to H1, the value of the Herfindahl-Index in equation (3.12) is expected to be zero for all firms, i.e. the individuals within a firm differ from each other with regard to their educations.

The second point to note is that the values of the Herfindahl-Index per se do not provide a means to test H1. The reason is that there is no natural reference level providing a basis to decide whether the heterogeneity in educations is low, high or on an average level. To make such a judgement possible, a statistical test is constructed with the help of which the values of the Herfindahl-Index actually observed are compared with the values of the Herfindahl-Index received in a situation where individuals match randomly. The null hypothesis of this test is

H1₀ :The composition of the actual observed teams with respect to educations equals a random selection of individuals.

To perform the test, mean and variance of the Herfindahl-Index under random assignment (H_random^tr ) have to be determined. However, both values can only be derived analytically for a given team size. Therefore, the distribution of H_random^tr is

simulated. The procedure is as follows: All individuals of a given sector are selected and randomly assigned to firms, maintaining the actually observed size distribution of firms. After that, the Herfindahl-Index per firm is calculated and averaged on the industry level. The resulting value is then stored. The procedure is carried out 1,000 times in total. From the resulting distribution, the lower and upper 0.5, 2.5 and 5 percentiles are determined and then chosen as critical values for the decision whether H_actual^tr and H_random^tr differ significantly at the 1%, 5% and 10% level.¹⁵ Table 3.1 shows the actual average Herfindahl-Index by industry for all firms (column (1)) as well as for firms with university graduates (column (3)) and firms without university graduates (column (5)), respectively. The mean value of the distribution of the average Herfindahl-Index with random assignment of individuals to firms is given in columns (2), (4), and (6). In most cases, the actual Herfindahl-Index is rather close to zero but not exactly zero. And, in almost all industries, the value of the average Herfindahl-Index with random assignment of individuals to firms is even smaller than the actual average Herfindahl-Index. Additionally, the difference between the two values is significant in many cases.¹⁶ Thus, it can be concluded that individuals apparently look systematically for their teammates, but tend to choose partners with similar educations. H1 is therefore rejected.

A possible explanation for the results is that individuals simply do not know persons from other fields. An engineer is much more likely to know other engineers than, say, a person with a business education because they usually have a closer contact especially during their studies. Personal contacts are probably the most common way how individuals come together for a firm foundation. Formal job advertisements (“Wanted: Partner for establishing a firm”) are usually not observed.

15Procedures of random reference points are also used by Ellison and Glaeser (1997) and Armenter and Koren (2008).

16Table 3.9 in the appendix shows the 95%- confidence intervals for the average Herfindahl-Indices. The distributions are not symmetric. Therefore, the mean values in Table 3.1 do not lie in the middle of the interval.

Table 3.1: Heterogeneity of educations in start-up year

industry all firms firms with firms w/o

univ. graduates univ.graduates

total (firms withn >1) 0.131*** 0.049 0.084*** 0.023 0.145*** 0.057

manufacturing

low-technology 0.143*** 0.077 0.103** 0.054 0.164*** 0.082

medium-low technology 0.088* 0.047 0.065* 0.033 0.092 0.051

medium-high technology 0.086 0.039 0.033 0.025 0.098 0.046

high technology 0.099 0.055 0.063 0.040 0.148 0.064

construction work 0.223*** 0.061 0.199*** 0.031 0.228*** 0.064

services

wholesale trade 0.125*** 0.033 0.027 0.015 0.150*** 0.038

retail trade, repair 0.107*** 0.049 0.045** 0.024 0.116*** 0.052

hotels, restaurants 0.103*** 0.060 0.039 0.034 0.110*** 0.064

freight transport 0.082** 0.046 0.044 0.026 0.090** 0.050

knowl.-intens. high-tech serv. 0.112*** 0.032 0.068*** 0.018 0.169** 0.063

knowl.-intens. market serv. 0.128*** 0.028 0.120*** 0.018 0.137*** 0.047

other knowl.-intens. serv. 0.033 0.021 0.000 0.013 0.050 0.026

Notes: The diversity of educations is measured by the Herfindahl-Index of highest educational attainment.

Columns (1), (3) and (5) show the average Herfindahl-Index by industry based on the actual sorting of individuals to firms. Columns (2), (4) and (6) depict the mean value of the distribution of the average Herfindahl-Index by industry generated with random assignment of individuals to firms.

**, **, * indicate whether the values in column (1), (3) and (5) are significantly different from the values in column (2), (4) and (6) at the 1%, 5% and 10% level respectively.

Source:Statistics Denmark, author’s calculations.