We propose an improvement to the information leadership (IL) measure of price discovery of Yan and Zivot (2010), and the information leadership share (ILS) measure of Putniņš (2013). Our improved PIL and PILS measures integrate the price discovery share (PDS) of Shen et al. (2024) with the component share (CS) measure. Our improved PIL measure accurately reflects the ratio of initial responses of competing markets to a permanent shock in the presence of correlated reduced-form vector error correction model residuals, thereby substantially generalizing the IL measure for practical applications. Simulation evidence strongly supports the superiority of our improved PIL measure over a wide spectrum of existing price discovery metrics (Lien and Shrestha, 2009; Putniņš, 2013; Sultan and Zivot, 2015; Patel et al., 2020). We demonstrate the effectiveness of our improved measure by examining price discovery for various Chinese stocks cross-listed in Shanghai and Hong Kong (SH-HK) both before and after the initiation of the Shanghai-Hong Kong Stock Connect.
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