"Sign in as Different User" menu option is missing in SharePoint Server 2013
To work around this issue, use one of the following methods
- Start Internet Explorer by using the Run as different user option, and then go to the SharePoint site.
Note: The Run as different user option is visible if you hold the Shift key when you right-click a program icon.
- Access the SharePoint site by using the the URL as http://siteurl/_layouts/closeConnection.aspx?loginasanotheruser=true
This option uses an unsupported browser feature which is unreliable and causes other issues. Currently this option does not work in IE 10 and Safari.