“Sign in as Different User” option is missing in SharePoint 2013.

Note that you may have experienced that the “Sign in as a Different User” menu command is missing in SharePoint 2013.
This option is useful when testing applications, but it can lead to problems especially when opening documents, say in Microsoft Word. So, it may be for these reasons that the option has been removed in SharePoint 2013.
You can add the menu item back in by doing this edit on all servers in your SharePoint farm which is this option has missing.

1. Browse the location “C:\Program Files\Common Files\Microsoft Shared\Web Server
    Extensions\15\TEMPLATE\CONTROLTEMPLATES”. 
2. Open “Welcome.ascx” using Notepad (or any text editor).
3. Paste the below code in the “Welcome.ascx” before the existing element with the id of “ID_RequestAccess”

<SharePoint:MenuItemTemplate runat="server" ID="ID_LoginAsDifferentUser"
 Text="<%$Resources:wss,personalactions_loginasdifferentuser%>"
 Description="<%$Resources:wss,personalactions_loginasdifferentuserdescription%>"
 MenuGroupId="100"
 Sequence="100"

 UseShortId="true"/>

4. Save the File.
    Now the menu option should be displayed as below.