sashgera,
<select onChange="var x = document.getElementById('zzz');x.focus(); x.value = this.value; ">
<option value="выбор">выбор</option>
<option value="тест">тест</option>
</select>
<input id="zzz" class="filter" name="livefilter" type="text" value="" />
http://learn.javascript.ru/focus-blur#метод-elem-focus