Hagerty, Edward H., Head, aged 60, married, at age 25, born Michigan, parents born Irish Free State, millwright, lumber company Hagerty, Bridget, Wife, aged 57, married, at age 22, born Irish Free State, parents born same, immigrated 1888 Hagerty, Edward H. Jr., son, aged 35, single, born Minnesota Hagerty, James, son, aged 22, single, born Minnesota
Irish Free State = Republic of Ireland (ie, not Northern Ireland)
You can order Edward Sr.'s death certificate from the state of Minnesota:
Name: Edward H Hagerty Gender: Male Marriage Date: 1 May 1894 Marriage Place: St Paul, Ramsey, Minnesota Spouse's Name: Bridget McMannamon Spouse Gender: Female Event Type: Marriage FHL Film Number: 1313193
The Edward that the other poster found was born 25 August 1869 (according to the Michigan birth records at familysearch.org).
In the 1905 Minnesota State Census, Edward was enumerated twice -- once he indicates he was born in Michigan; the second time, he says he was born in Ireland. If he was indeed born in Ireland, that would explain why we can't find him in the US prior to his marriage.