They are white by convention,
and they heat by convection.
I am sorry this answer is mostly theoretical, however I was unable to find any practical material in this area so far.
The question contains a significant misconception, and that is that a heating radiator transfers energy mostly by radiation. As Wikipedia articles describe, in a typical case it does not work this way:
In practice, the term "radiator" refers to any of a number of devices in which a liquid circulates through exposed pipes (often with fins or other means of increasing surface area), notwithstanding that such devices tend to transfer heat mainly by convection and might logically be called convectors
Given the radiator temperature, most of the radiation happens out of the visible spectrum, therefore visible characteristics of the radiator have almost no effect. See Black-body radiation Wikipedia article:
A black-body at room temperature appears black, as most of the energy it radiates is infra-red and cannot be perceived by the human eye.
As one can see in the Black-body spectrum for temperatures between 300 K and 1000 K, even if the radiator was 227 °C (500 K) hot, its radiation would be well beyond visible spectrum. This can be easily verified by observing radiators in the dark. If there was any emission in the visible spectrum, the radiators would glow.
Moreover, the question does not define radiator efficiency at all. While the term may seem clear and intuitive, in fact it is not. One could say in principle each radiator is 100 % effective, as there is no thermal loss possible (thermal "loss" is the desired property here). It would be possible to define radiator efficiency to be related to the output power, or by the difference between input and output water temperature. In practice it is necessary to consider efficiency of the whole heating system, including the control devices. See also
quite old Painting Radiators article (dated July 19, 1935, I did not attempt to verify it the dating is genuine):
The heat that is developed by burning fuel is transferred to the rooms by means of the radiators. A radiator
neither creates nor destroys heat and a large radiator, while it can put more heat into a room than a small one, must be
supplied with all of the heat it puts in. In the sense that they ultimately transfer all the heat supplied into the room, all
radiators are 100% efficient. The word "efficiency" is, however, used in other ways, and it is now customary to use it on
all possible occasions, but it is hardly correct to say that putting metallic paint on a radiator reduces its efficiency when
the effect is merely to reduce its capacity. The size of the radiators in a house can only affect the fuel required for heating
by increasing or decreasing the heat wasted in transmission from boiler to radiator and that lost up the chimney. Only
when the radiators are so small as to render the whole heating plant ineffective is an appreciable saving of fuel to be
expected by installing larger radiators.