A key idea in the literature on trade and growth is that trade liberalization may affect plants' innovative activities through increased competition. Theoretical predictions, however, remain ambiguous, and it has been difficult to investigate this relationship empirically because R&D expenditure data is rarely available at the plant level. This paper takes the advantage of a newly constructed combination of Mexican plant-level datasets to examine the extent to which tariff changes lead to changes in R&D through increased competition. The combined dataset has two unique features: it contains (1) the amount of R&D on product innovation and on process innovation, and (2) the trade classification categories of plants' outputs and inputs, which allows me to construct plant-level tariff changes and to control for industry time effects. The degree of tariff reduction is not correlated with initial plant characteristics, suggesting that the tariff reduction is exogenous for plants. The key finding is that the reduction of the tariffs of the goods produced by Mexican firms induced those plants to increase total R&D. This suggests that trade liberalization stimulates plants' innovative activities through increased competition. I also find that the pattern would not be discernable using the measures of plant behavior and trade exposure available in typical plant-level datasets - measured total factor productivity and industry-level average tariffs. Additional results using process R&D and product R&D expenditure information suggest that trade liberalization affects plants' capability through the effects of competition on plants' incentive to increase cost efficiency rather than through the effects on incentive to create new products or to upgrade the quality.