Another solution that works with non transparent backgrounds: Set the shadow on a pseudo element
CSS
#outer {
border: 1px solid black;
height: 200px;
position: relative;
width: 200px;
background-color: white;
}
#outer:after {
content: "";
box-shadow: 0 0 10px rgba(0, 0, 0, 0.5) inset;
height: 100%;
position: absolute;
width: 100%;
left: 0px;
top: 0px;
}
#inner {
background-color: #55A8FF;
bottom: 0;
height: 50px;
left: 0;
position: absolute;
width: 100%;
}