Contrary to popular belief, schools have improved over the past 20 years, says the report, which analysed standardised test scores gleaned by the National Assessment of Educational Progress.

Scores in the mathematics and verbal tests of black and Hispanic teenagers improved significantly over this 20-year period, which means that the gap between them and white pupils narrowed. The scores went up by an average of 3 percentage points for white students, 11 points for Hispanic students and 19 for black students.

The Rand Corporation researchers looked at how family considerations might be affecting performance. They wanted to see what effects divorce, illegitimacy and being the children of working mothers might have on how well the pupils did at school.

They found that family structure had little effect. The most important family factors contributing to higher scores in the tests were a drop in family size, freeing more resources for each child, and a rise in parents’ educational levels. The most important factor of all was better-educated parents.

In 1970, for example, 38 per cent of the mothers had not completed high school. In 1990, the figure had dropped to 17 per cent.

The positive influences of better-educated parents and smaller families were offset to some extent by an increase in births to younger mothers, and an increase in the number of poor, single-parent families.

But the Rand Corporation analysis found that two trends which had worried policy-makers - an increase in the number of working mothers and an increase in single mothers - had no significant effect when considered alone.

The improvements in test scores suggest, say the researchers, that desegregation and increased spending in schools, especially on ethnic minorities, have paid off. The researchers’ next project is to look at which programmes work and why.

“The country should be cautious about dismantling programmes until we know which deserve to go and which to continue,” said David Grissmer, the leader of the Rand study.