This paper uses seven standard market power indicators (price-cost margin, and six drawn upon the production approach) to estimate the effect market power on the rate of change of total factor productivity for a sample of formal manufacturing firms of Peru for the period 2002-2019. After applying exogeneity tests and implementing panel data with fixed effects instrumental variable method, the results are not clear about the causal relationship between market power and firms‘ TFP. However, when the Double-Debiased machine learning (DML) causal method is applied for fixed effects panel data with and without instruments, firms market power robustly seems not to affect their respective total factor productivity regardless of the market power indicators and instruments used. The paper also presents four examples which are consistent with this causal result suggesting that the relationship between market power and productivity needs to be analyzed on a case-by-case basis considering the product development of sectors, the influence and activities of firms and economic groups in the domestic economy and foreign markets, and the level of development of the country‘s productive structure.