This paper presents a parametric video prediction scheme with backprop-based motion estimation, in response to the CLIC challenge on P-frame compression. Recognizing that most learning-based video codecs rely on optical flow-based temporal prediction and suffer from having to signal a large amount of motion information, we propose to perform parametric overlapped block motion compensation on a sparse motion field. In forming this sparse motion field, we conduct the steepest descent algorithm on a loss function for identifying critical pixels, of which the motion vectors are communicated to the decoder. Moreover, we introduce a critical pixel dropout mechanism to strike a good balance between motion overhead and prediction quality. Compression results with HEVC-based residual coding on CLIC validation sequences show that our parametric video prediction achieves higher PSNR and MS-SSIM than optical flow-based warping. Moreover, our critical pixel dropout mechanism is found beneficial in terms of rate-distortion performance. Our scheme offers the potential for working with learned residual coding.