Economies of scale and scope, merger effects, and ownership difference: an empirical analysis of universities in Japan

ABSTRACTThis paper evaluates economies of scale and scope, and the merger effect among national universities in Japan. We apply SUR for the total translog cost function in FY2014 and FY2018. The main results are: (i) there exist economies of scale as a whole university; (ii) but there exist no clear economies of scope except for in research; (iii) there are cost saving effects with mergers among single colleges, but not in the case of mergers of general universities and medical colleges, (iv) both the costs of a public and a private university are higher than those of a national university.KEYWORDS: Higher educationEconomies of scaleEconomies of scopeMerger of universities Disclosure statementNo potential conflict of interest was reported by the author(s).Notes1 In Table A1 (Appendix), studies of the stochastic cost frontier approach, which estimates economies of scale and scope, are listed. Other studies using this approach to estimate the efficiency level of universities are Stevens (Citation2005), McMillan and Chan (Citation2006), Agasisti and Salerno (Citation2007), Lenton (Citation2008), Kempkes and Pohl (Citation2008, Citation2010), Yamasaki and Itaba (Citation2009, Citation2010), Johnes and Johnes (Citation2009), Johnes and Schwarzenberger (Citation2011), Mamun (Citation2012), Suhara (Citation2014), Johnes and Johnes (Citation2016), Gralka (Citation2018), Agasisti and Gralka (Citation2019), Fu et al. (Citation2019), Maeda (Citation2020).2 As we note in the literature review, it is reasonable and common that three university output measures be used—undergraduate education, graduate education, and research. In fact, as for types of education, education for undergraduate and graduate students differs because graduate education is more related to research, an activity distinct from education. The main goal of research is the production of papers, patents, etc. Therefore, we use these three output measures.3 According to Christensen and Greene (Citation1976), estimating cost function alone leads to multicollinearity problems because the information of the input share equations cannot be used. As a result, the explanatory variables in a translog cost function are inaccurate parameter estimates. As the simultaneous method of the cost function and the input share equations as a system increases the degree of freedom, the accuracy of the estimates increases, compared to a case of a single estimation method using the cost function only.4 As for output measure, universities of more than 95% in undergraduate education, of more than 93% in graduate education and of more than 96% in research satisfy the monotonicity condition. As for input factor price, universities of 100% in both labor and material and other prices, and of more than 98% in capital price satisfy the monotonicity condition.5 The partial derivatives of input prices are stable with little variation across models. As for university type, the partial derivatives of labor prices are higher in single-major colleges with a high labor cost ratio and colleges of education. The partial derivatives of material and other prices are higher in medical schools.6 According to Chung (Citation1994), theory shows that σkk<0. And if σkl > 0, then the relationship between input factors is substitutive, but if σkl<0, then the relationship is complementary. σkk=C⋅CkkCkCkσkl=C⋅CklCkClCkk=∂2C∂wk2,Ckl=∂2C∂wk∂wl,Ck=∂C∂wk,Cl=∂C∂wl, for k,l=L,K,M(k≠l).7 We apply a statistical test of the structural changes between FY2014 and FY2018. The Wald test result shows that the constant terms in FY2014 and FY2018 change. Therefore, we include the FY2018 dummy.8 As for taking very small numbers without zero output for the calculation of economies of scope, there are several studies. For example, Kim and Clark (Citation1988) take 10% of sample average in the water supply industry. Goldberg et al. (Citation1991) use $1million for the very small numbers in the security stock industry. Rezvanian and Mehdian (Citation2002) take minimum values among samples in the commercial bank industry. Therefore, this study thinks that 0.001 is small enough compared with the sample mean.