(4)–(6); and, second, the use of the residuals as relative variables to estimate the system of Eqs.
As no evident correlation was found, all the relative variables can be used for the successive data treatment.
The other important point is that relative variables, like night/day ratio, are more stable than absolute values of the occurrence rate.
Lower case letters denote relative variables (^{mathrm{a}}) The data here runs from 2008q1 to 2012q3 due to data limitations in (tc_{it}).
These relative variables are constructed as difference in the numerical values of the respective variables for i and j multiplied by indicator variables for i being more educated/older.
Since our relative variables are created by orthogonalizing the regional variables with respect to the national average, there is no reason for fixed effects to be introduced in the estimated equations.
It is important to note that, by creating relative variables through beta-differenciation, we isolate the part of the variation in the regional variable that is not due to national changes.
In computing the values of the relative variables (n), (u), and (pr) as beta-differences, we follow the same methodology than Decressin and Fatás (1995) and Broersma and van Dijk (2002), who also use the residuals from Eqs. (4)–(6).
In MLQPR, a quadratic polynomial regression function is established to describe the relationship between SVI and the relative variables, and the important terms of the quadratic polynomial regression function are determined by the significant test of the corresponding coefficients.
We owe this point to an anonymous referee who made us note that fixed effects were already introduced when defining the relative variables and, thus, were no longer required when estimating.
