All variables are first differences of the logarithmic transformation, The transition variable is assumed to be the difference of (the logarithm of) the gross enrolment ratio up to two lags, We use tests robust to outliers because our sample could be affected by the “baby boom” in Spain in the 60 s, which might potentially be reflected in the education variables (i.e. our regressor of interest). Standard linearity tests (Teräsvirta, 1994, 1998) can be misleading in the presence of outliers. van Dijk et al. (1999) advocate linearity tests that display a better level and power performance than the standard ones if outliers are present