Negative feedback is a fundamental concept in control systems, where the output of a system is fed back and compared with a reference input to generate an error signal. This error signal is then used to adjust the system's input or parameters to minimize the difference between the output and the reference input. Closed-loop control systems rely on negative feedback to maintain stability and achieve desired performance.

In a closed-loop control system, negative feedback can have various effects on system performance and characteristics. However, it is important to note that negative feedback does not reduce the overall gain or the sensitivity to parameter variation, contrary to options (a) and (d). Additionally, negative feedback does not improve disturbance rejection, as stated in option (c). The correct answer, option (b), states that negative feedback does not reduce bandwidth. Let's explore this in more detail.

1. Negative feedback and overall gain:
- Negative feedback can actually increase the overall gain of a closed-loop control system. By comparing the output with the reference input and generating an error signal, the system can adjust its input or parameters to minimize the error. This leads to a higher overall gain, as the system can actively correct deviations from the desired output.

2. Negative feedback and sensitivity to parameter variation:
- Negative feedback does not reduce the sensitivity of a closed-loop control system to parameter variation. Sensitivity refers to how changes in system parameters affect the system's performance. In a closed-loop control system, the sensitivity to parameter variation depends on the system's structure and design, rather than the presence of negative feedback. Therefore, negative feedback alone cannot reduce sensitivity to parameter variation.

3. Negative feedback and disturbance rejection:
- Negative feedback helps in reducing the effect of disturbances on the system's output. By continuously comparing the output with the reference input, the system can actively counteract disturbances and maintain the desired output. However, it is important to note that negative feedback alone does not improve disturbance rejection. The ability to reject disturbances depends on the design of the control system, including the controller and the plant dynamics.

4. Negative feedback and bandwidth:
- Bandwidth refers to the range of frequencies over which a control system can effectively operate. Negative feedback does not reduce bandwidth. In fact, it can help in stabilizing the system and extending its usable bandwidth. By continuously comparing the output with the reference input, negative feedback allows the system to actively adjust its response to different frequencies, ensuring stability and performance over a wide range of frequencies.

In summary, negative feedback in a closed-loop control system does not reduce the overall gain, improve disturbance rejection, or reduce sensitivity to parameter variation. However, it can help in stabilizing the system and extending its usable bandwidth. Hence, option (b) is the correct answer.