Create drop down menu with the child categories of a category

Question

I'm trying to create a drop down that has the child categories of a specific category as options.

This is my PHP:

$args = array('child_of' => 88);
$categories = get_categories( $args );
foreach($categories as $category) { 
    echo $category->name;
    echo "<option value='$category->name'>
                            $category->name</option>";
}

For some reason it's not working. I'm not even getting an error on the front-end.