An analysis of test results from all state school pupils in England by the Institute of Fiscal Studies revealed that the difference in performance between September and August-born children is still significant at the age of 18.
Researchers recommended national tests should be reformed so children are expected to achieve academic levels by a certain age rather than the end of a school year.
The idea could form part of a new Children's Plan being published in December which will set out policy for the next decade.
The institute found that summer-born children get some boost from starting school in September alongside older classmates, but the effect is not enough to counteract the disadvantage of being young.
August-born girls were 5.5 percentage points less likely to get five good GCSEs, than September-born girls, with August-born boys 6.1 percentage points behind September-born boys.
The report, funded by the Esmee Fairbairn foundation and the Department for Children, Schools and Families, concludes: "August-born children are, on average, being penalised simply because of an unlucky birth draw.
"This is not acceptable on either equity or efficiency grounds, and steps should be taken to eliminate this penalty." The researchers say that pass marks for tests up to the age of 14 could be varied according to the month of birth.
They also suggest that the "progress" tests currently being piloted could be adapted so that performance is judged according to the exact age that children pass a particular level, rather than the score they achieve.
The study recommends that children are entitled to free nursery education from the beginning of the year in which they turn three rather than the beginning of the term after they turn three and that all children start formal schooling in September of the year in which they turn five.
The study's conclusion on starting ages was based on comparing children's results in authorities which admitted all children to reception in September of the year in which they are five, with those that allow later start dates.
But it only looked at test results and did not consider social or behavioural impacts.
The first report of the Primary Review, published earlier this month, highlighted concerns among immigrant parents from Europe that the English starting age was too young.
English parents did not object to children starting reception at four, but were concerned that children were suddenly pitched into formal schooling at five.
Caroline Sharp, principal research officer at the National Foundation for Educational Research, suggested that a school starting age of six would diminish the problems at the outset.
She also backed tests which take age into account.
Lord Adonis, schools minister, said the progress test pilots may address the "birth date issue".
"Understanding why some children fall behind their peers is important to building a better education system," he said.
'When You Are Born Matters: The Impact of Date of Birth on Child Cognitive Outcomes in England,' by Claire Crawford, Lorraine Dearden and Costas Meghir from the Institute for Fiscal Studies.