Some desiderata for the measurement of price discovery across markets

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A Structural Analysis of Price Discovery Measures (2010, methodology): “Assuming all elements ofD0 are nonzero and |D0| 6= 0, the restriction cov(e1,t, e2,t) = 0 implies the result in (27) σ(2)T σ(2)P = d0,1d P 0,2 −d0,1d0,2 With uncorrelated reduced form VEC errors, the IS of market 1 is given by”
Island Goes Dark: Transparency, Fragmentation, and Regulation (2005, methodology): “While liquidity externalities are one of the most important issues in market design [Madhavan (2000)] and market regulation [Macey and O'Hara (1999)], it has been difficult to document their importance in practice.”
Realized Variance and Market Microstructure Noise (2006, background): “This relation is discussed in Johansen (1996), see also Hansen & Johansen (1998, pp. 27-28), and similar arguments later appeared in de Jong (2002) and Baillie, Booth, Tse & Zabotina (2002), see also Harris et al. (2002) and Lehmann (2002).”
What Do Price Discovery Metrics Really Measure (2013, background): “Price discovery, a fundamentally important role of secondary markets, is the “efficient and timely incorporation of the information implicit in investor trading into market prices” (Lehmann, 2002, p. 259).”