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A gender gap has been found in mathematics (boys outperform girls) that has prevailed across countries for many decades. Whether this gap results from nature or nurture has been hotly debated. Using the evidence of PISA 2003 and the gender equality index of 2003, some researchers have argued that an improvement in gender equality reduces the gender gap in mathematics. This study used five waves of country-level PISA data and, controlling for country fixed effects, found no evidence to support this argument. Furthermore, individual data for PISA 2012 and the multilevel data model were used. The conclusion drawn also does not support the argument. In fact, the relationship between gender equality and the gender gap in mathematics vanished after PISA 2003.

We study, via quantile regression, time series models whose conditional distribution may change over different quantile range of a threshold variable. We derive the limiting distribution of the estimated threshold parameter under the frameworks of asymptotically shrinking and fixed regime change magnitude. We construct confidence intervals for the estimated threshold parameter via a likelihood-ratio-type statistic and tabulate critical values, and by extensive simulation, we investigate their coverage probabilities. We also derive the Bahadur representation allowing for serially correlated errors and discuss related inference problems on threshold effects. Our asymptotic and simulation results complement the existing literature of Caner (2002), Galvao et al (2011Galvao et al ( , 2014 on threshold regression models.

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