European higher education policies and the problem of estimating a complex model with a small cross-section

This paper discusses the components on components regression, a statistical technique suitable for explorative analyses of small datasets containing multiple independent, mediating and dependent variables. This method is compared to ordinary least squares and principal component regression by means of discussion of their properties and the assumptions underlying these estimators, a simulation and an empirical application to European higher education policy, and economic innovativeness in 32 countries. In the datasets used in this paper, the components on components regression yields more precise estimates of the coefficients of association between independent, mediating and dependent variables, compared to ordinary least squares. Compared to the principal components regression, it leads to a more parsimonious empirical model. The simulation also shows that the standard errors of the coefficients estimated with the components on components regression can be obtained by bootstrapping.