SharePoint 2010 had an option “Log in as another user.” In 2013, this option (default) is not present. With a little modification you can retrieve this option.
Navigate to the “Login as a different user page”
A quick way to go to the page is to adjust the URL. Go to the following URL.
http://<siteURL>/_layouts/closeConnection.aspx?loginasanotheruser=true
! Please note the capital C in Connection
After the pags is loaded the familiar pop up appears to you to fill in your username and password. After submitting you wil be returned to the previous page.
Change Welcome.ascx
A more permanent solution is to cutomize the welcome page. I found this i a post of Gokan Ozcifci. This post explains how to add the an element in Welcome.ascx.
<SharePoint:MenuItemTemplate runat="server" ID="ID_LoginAsDifferentUser" Text="<%$Resources:wss,personalactions_loginasdifferentuser%>" Description="<%$Resources:wss,personalactions_loginasdifferentuserdescription%>" MenuGroupId="100" Sequence="100" UseShortId="true" />
Wictor Wilén has made a WSP project to change welcome control.
Bookmarklet to Sign in as a Different User
Another option is to use a JavaScript bookmarklet using your URL plus some client object model which can be checked here: http://corypeters.net/2012/10/sharepoint-2013-sign-in-as-another-user/
Caution