How to create a floating action button (FAB) in android, using AppCompat v21?

I would like to create a floating action button (to add items to a listview), like google calendar, maintaining compatibility with pre-lollipop Android versions (before 5.0).

I created this layout:

Activity main_activity.xml:

<LinearLayout ... >

     <include
         layout="@layout/toolbar"/>

     <RelativeLayout ... >

     <!-- My rest of the layout -->

          <!-- Floating action button -->
          <ImageButton style="@style/AppTheme"
                     android:layout_width="60dp"
                     android:layout_height="60dp"
                     android:text="New Button"
                     android:id="@+id/button"
                     android:src="@drawable/ic_fab"
                     android:background="@drawable/fab"
                     android:layout_alignParentBottom="true"
                     android:layout_alignParentRight="true"
                     android:layout_marginBottom="24dp"
                     android:layout_marginRight="24dp"/>

     </RelativeLayout>

 </LinearLayout>

Drawable fab.xml:

<?xml version="1.0" encoding="utf-8"?>
<shape xmlns:android="http://ift.tt/nIICcg"
       android:shape="oval">
    <solid android:color="#ffa48bc0"/>
</shape>

Style styles.xml

<resources>
    <style name="AppTheme" parent="Theme.AppCompat.Light.NoActionBar">
        <item name="colorPrimary">#ff1d79b1</item>
        <item name="colorPrimaryDark">#ff084d95</item>
    </style>
</resources>

The result is similar, but there isn't the shading, a characteristic of material design:

Calendar's floating action button:

My app's floating action button:

How can I add the shading to my button?

I have already used the attribute elevation, but does not work