Spurious correlations are often induced both in regression analyses using ratio data and in logarithms of these ratio data (Kusakabe 2002a, b, 2011). Path analysis in the present study proves the process for the induction of spurious correlations in regression analysis. Population size always affects social variables, and therefore a correlation in a regression always consists of both direct effects and indirect effects via the population size between the relevant variables. In this sense, neither a per capita value nor a logarithm of per capita can be used in OLS regressions. From these analyses, the following results were elucidated. ① In regression analyses using ratio data or logarithms of these, incorrect results came about in 20% of cases (Table 3). These results show that OLS regressions using ratio data artifi cially induce the incorrect spurious correlation due to indirect effects via the population size. ② Second-order partial correlation is equivalent to the direct effect of the 4-variable recursive model in the structural equation modeling and is highly useful for the test of causality of the variables in question.
As an example, the current research critically analyzes the paper by Per Pettersson-Lidbom (2012 in Journal of Public Economics) and the negative correlation found in that paper is shown to be induced by the spurious negative effect due to population size.
Finally, I present the Law of Power Function in a broad sence for preventing the fallacious causal relationships between the social variables in the cross-section analyses.