My experience says that there is no corelation between the education level of the family business owners and the productivity of family managed businesses. However, some research is trying to establish positive corelation.
Theoretically it is possible to argue that the higher the owner's education the higher the organization's productivity will be. The main reason is that education is a critical driver of right decision making. However, this hypothesized positive relationship between education and productivity of the business may get cancelled or reduced owing to moderators. For example, the owner improved his education (specially business management or relevant technical aspects of the business) but could not get improved productivity because his employees were not sufficiently motivated to increase productivity. Some examples of moderators include employees' competence, increased competition of highly established business organizations in the same industry, reduced purchasing capacity of customers, and unethical behaviour of some employees.
Before you make any proposition, Sonia, I would recommend you to drill deep into literature. It is a social phenomenon. Results would be different in different context (country). It may be different at different time in the same context. Do not get into the trap of generalization.
Normaly there is sound correlation between level of education and business performance, however the existing relationship is contracarsal time to time.
If there was corelation, all university professors should be great business person with high productivity rather than drop outs like Bill gate and Steve Jobs.
the education level of family business is an elemental variable even if we include all the owners. The productivity, however, is conceptual and arriving at a operational definition would entail many elemental variables. This should also include risk-taking ability as many academicians have very low or no appetite for risk-taking in business parlance. Professors have good knowledge but family businesses have entrepreneurial ability which needs to be measured. Does it really pass down from first generation to the other? Many research questions need to be formulated.
One cannot say that there is no relevance of education level for productivity in family business. There are two types of education, formal and informal. The former provides degree/diploma/certificate but the later does not have any document though the incumbent might have had deep informal education. Bill Gates, Steeve Jobs, Ghanshyam Das Birla belonged to this categoty. G D Birla's sons and daughtes had formal education, Basnt Kumar Birla havig been educated in M.I.T, USA. His off springs Aditya and Kumar, too, had quality higher education abroad. The scenario about the corelation, thus, changes over time. It is dynamic.
This is controversial, though a person started a business without any formal education definitely he might try to gain formal education later to manage the business in better way. So, i think we can't clearly distinguish the concept (Education from business performance) clearly. At many stages of a business it requires a formal level of education that is why many people follow masters or equivalent or higher degree later though hey had not formally graduated form a university.
I found a positive corelation between the owner's education and his acceptance of technology for supply chain efficiency. You may find my research paper here.
You are lucky to find a positive corelation between the owner's education and his acceptance of technology for supply chain efficiency. It very much depends on the sample that you had. The outcome of your study cannot be generalized.