I don’t know or understand why, but I pasted this into wp-content/themes/twentysixteen/functions.php and it worked:
function wpse61674_archives_shortcode_cb( $atts ) {
return '<h2 class="widget-title">Archives</h2><ul>'.wp_get_archives(array('format'=>'html','echo'=>false,'type'=>'yearly')).'</ul>';
}
add_shortcode( 'archives', 'wpse61674_archives_shortcode_cb' );
I found this code somewhere on the internet, but it wasn’t part of the wordpress documentation on archives shortcode.