This study examines the effect of a family’s economic background on the chances of a twelfth grade high school student to obtain a first (bachelor) degree. The study analyses the marks obtained in the matriculation certificate by twelfth grade students in 1992-97, together with their parents’ demographic and social data taken from the 1995 census, and information about those among the same individuals who completed a first degree by 2002. It estimates the probability that an individual who finishes twelfth grade will go on to higher education, as a function of his matriculation details and family background. Among those entitled to a matriculation certificate in the academic track, the main difference in the probability of obtaining a degree is between those whose parents are in the lower fifth of the income distribution and those whose parents are in the upper three fifths of the distribution. Among those who were not entitled to a matriculation certificate when they completed twelfth grade, it was found that the higher their parents’ income quintile, the greater the probability that the student would obtain a first degree. The findings regarding students graduating with a matriculation certificate in the academic track support the hypothesis that those whose parents are in the lowest income quintile suffer from a liquidity constraint and are therefore prevented from engaging in tertiary education. On the other hand, regarding those not entitled to a matriculation certificate it is reasonable to assume that part of the difference in the probability of obtaining a first degree that derives from their parents’ income does not reflect a liquidity constraint but other factors, e.g., environmental factors, or efforts to achieve a social status. When we examine the relative importance of the parents’ income in explaining the difference in the percent obtaining a first degree between the stronger and the weaker groups we find that parents’ income explains less than 20 percent of the gap.