Children with Medicaid are far more likely than those with private insurance to be turned away by medical specialists or be made to wait more than a month for an appointment, even for serious medical problems, a new study finds.

Lower payments by Medicaid, delays in paying and red tape are largely to blame, researchers say.

The study, with findings that match anecdotal reports from other parts of the country, is one of only a few efforts to measure access to health care among people with Medicaid. Nationwide, those patients are caught between states’ threats to cut Medicaid payments and the Obama administration’s plans to use the program to cover more and more people as part of its health care law.

“There’s never been a study this comprehensive or this rigorous that actually measured access to specialty care, let alone children’s access,” said Dr. Karin V. Rhodes, an author of the study and director of emergency care policy research in the department of emergency medicine at the University of Pennsylvania.

The study used a “secret shopper” technique in which researchers posed as the parent of a sick or injured child and called 273 specialty practices in Cook County, Ill., to schedule appointments. The callers, working from January to May 2010, described problems that were urgent but not emergencies, like diabetes, seizures, uncontrolled asthma, a broken bone or severe depression. If they were asked, they said that primary care doctors or emergency departments had referred them.