Constructors are closer to static methods rather than "regular" methods. Like static methods, they can be overloaded, but not overriden. That is, they are not inherited but can be redefined.
public BaseClass
{
public BaseClass( String s ) { ... }
public static void doIt ( String s ) { ... }
}
public SubClass extends BaseClass
{
public SubClass( String s ) { ... }
public static void doIt ( String s ) { ... }
}
public SubClass2 extends BaseClass
{
}
new SubClass( "hello" );
SubClass.doIt( "hello" );
new SubClass2( "hello" ); // NOK
SubClass2.doIt( "hello" ); // NOK
Constructors and static methods are never dispatched dynamically (virtually) -- You always know the concrete type you instantiate or the concrete class of the static method. That's why it makes no sense to have abstract constructor and abstract static method. That's why you can also not specify constructor and static method in interfaces.
You can even think of constructor as static factory method (and see the corresponding pattern):
MyClass obj = new MyClass(); // the way it is
MyClass obj = MyClass.new(); // think of it like this
The only case I see where it would make sense to define abstract constructor or abstract static method would be if reflection is used. In this case, you could ensure that all subclass would redefine the corresponding static method or constructor. But reflection is another topic...
Note: in languages such as Smalltalk where classes are regular objects, you can override static method and have abstract constructor. But it doesn't apply to Java because classes are not "regular" objects even if you can get them with reflection.