Have 1.6 million undocumented immigrants left the U.S. this year? Researchers say it's too soon to know.

Homeland Security Secretary Kristi Noem said last week that the number of unauthorized immigrants living in the U.S. has declined by 1.6 million since President Trump began his immigration crackdown .

"This is massive," Noem said in a statement, crediting the decline in part to an ad campaign warning undocumented immigrants to leave or face arrest and deportation .

"This new data shows illegal aliens are hearing our message," she added. In the Department of Homeland Security's news release , Noem did not specify how many of those individuals were believed to have departed the U.S. voluntarily, versus those who have been deported.

But the vast majority would have had to have left without making any contact with DHS to reach that total. According to internal government figures