Using a sample of 200,000 pupils in England, an institute at the London School of Economics (LSE) has published a study of school choice, the BBC reports.
Faith schools - outside local authority control - were compared with community schools to measure the impact of parental choice.
Researchers say when a faith school has no competition, its results are lower.
The research from the LSE's Centre for Economic Performance, carried out by Stephen Gibbons, Stephen Machin and Olmo Silva, examines the impact of parental choice on schools, using a sample of 2,400 schools in south-east England.
It found that schools that were in "competition" could have a positive impact on standards.
In addition, the research says that where schools run their admissions process, "there is evidence that competition is positively related to performance".
The research is published as the ATL teachers' union attacks faith schools for a lack of accountability - and calls for them not to "discriminate" in their admissions process.
Conservative leader David Cameron and Prime Minister Tony Blair have recently said they intend to send their children to faith schools, Cameron stating that he is a 'fan' of faith schools.