switchMap is not a function

You also need to add the switchMap operator:

import 'rxjs/add/operator/switchMap';

Here is the culprit searchQuery = new Subject<string>();

A Subject is not an observable, but your function is asking for one, so modify it like this

ngOnInit() {
    this.employeeSearchService.searchEmployees(this.searchQuery.asObservable())...
}