Past studies propose many possible explanations to the lead-lag relationship. However, it is not easy to clarify the contributions of contract differences, which simultaneously exist among those highly related financial securities, to the lead-lag phenomenon. The TAIEX and the Mini-TAIEX stock index futures are identical except for their contract sizes and the trading volume of the TAIEX index futures is much higher than that of the Mini-TAIEX. By employing the vector error correction model (VECM), Gonzalo-Granger information share, and generalized impulse response functions and variance decompositions, this paper finds that there exists a strong information transmission from the TAIEX index futures to the Mini-TAIEX index futures. This result suggests that, due to higher liquidity, the TAIEX index futures play a significantly important role in price discovery.