Dropdown select em ReactJS

Bem eu fiz um dropdown criando valores como Maior preço, menor preço etc... porém quando eu seleciono um dos dois ele não volta o valor e não trás o objeto que faz referencia.

import React, { PureComponent } from 'react'

class Dropdown extends PureComponent {
constructor(props) {

 super(props);
 this.state = {value: '4'};
 this.handleChange = this.handleChange.bind(this);
 }

 handleChange(event) {
 this.setState({value: event.target.value});
 }

 render() {
 const { itens, className} = this.props
 console.log(itens)
 //let x = event.target.value;
 return (
 <div className='select'>
 <select onChange={this.handleChange} value={this.state.value} className={className} >
 {itens.map((item, i) =>
 <option key={i} value={item.id}>{item.value} </option>

 )}
 </select>
 </div>
 )
 }
}

Dropdown.defaultProps = {
className: 'select__filter'
};
export default Dropdown

import React, { PureComponent } from 'react'
import { Tab } from '../../../../components/Tabs/Tab'
import { Tabs } from '../../../../components/Tabs/Tabs'
import RestaurantCard from '../../../../components/RestaurantCard/index'
import Dropdown from '../Dropdown'

const SECTION = [

 {
 name: "Ver Restaurantes"
 },
 {
 name: "Ver Pratos"
 }
];

const dropdownItens = [{id: 'DISCOUNT', value: 'Melhores descontos'}, { id: 'BIGGER_PRICE', value: 'Maior Preço'}, {id: 'LOWER_PRICE', value: 'Menor Preço'}, {id: 'EVALUATION', value: 'Melhor Avaliado', selected: 'selected'}, {id: 'LOCATION', value: 'Mais Próximos'}]

class FilterTabs extends PureComponent {
state = {
value: '',
id: ''
}

handleChange = (event) => {
 this.setState({ value: event.target.value });
 //this.setState({value: event.target.id});
 }

 render() {

 const { restaurants, size} = this.props;

 return (
 <section className="filter__tabs">
 <section className="container">
 <Tabs>
 {
 SECTION.map(section => (
 <Tab text={`${section.name} (${size})`} key={section.name}>
 <section className="filter__tabs--info">
 <span className="filter__tabs--info-text">
 {`${size} restaurantes encontrados`}
 </span>
 <Dropdown onChange={this.handleChange} itens={dropdownItens}/>
 </section>

 <div className="row">
 {
 restaurants.map(
 restaurant => <RestaurantCard
 key={restaurant.id}
 extra={true}
 data={restaurant} />
 )
 }
 </div>
 </Tab>
 ))
 }
 </Tabs>
 </section>
 </section>
 )
 }
}

export default FilterTabs;