Large pretrained vision-language-action models achieve strong robot-manipulation performance, while compact alternatives have largely pursued efficiency by compressing the prevailing observation-to-action paradigm. We investigate whether predictive sensorimotor modeling can make more effective use of a limited parameter budget than direct observation-to-action mapping. We present PredVLA, a language-conditioned predictive-coding policy with only 0.68 million trainable network parameters and no robot-data pretraining. Its hierarchical recurrent dynamics predict visual features and proprioception, while observations influence latent state only through prediction-error-driven online inference. On LIBERO, PredVLA achieves an 86.9% mean success rate across the three short-horizon suites and 75.4% across all four suites. Under a controlled comparison using the same frozen front end, demonstrations, action decoder, and evaluation protocol, PredVLA achieves 3.7x and 7.4x the three-suite mean success rates of parameter-matched Transformer and LSTM behavior-cloning policies, respectively. A mechanism-by-mechanism transition to the recurrent behavior-cloning baseline shows that replacing the predictive pathway with direct observation input produces the largest single performance drop, accounting for approximately $70\%$ of the endpoint gap. Further ablations identify distinct contributions from training-time latent inference, test-time error regression, hierarchical timescales, and sensory prediction-error channels. Together, these results support predictive sensorimotor modeling as a strong inductive bias for compact language-conditioned robot control.

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