On the bi-dimensionality of liquidity

Variations in overall liquidity can be measured by simultaneous changes in both immediacy costs and depth. Liquidity changes, however, are ambiguous whenever both liquidity dimensions do not reinforce each other. In this paper, ambiguity is characterized using an instantaneous time-varying elasticity concept. Several bi-dimensional liquidity measures that cope with the ambiguity problem are constructed. First, it is shown that bi-dimensional measures are superior since commonalities in overall liquidity cannot be fully explained by the common factors in one-dimensional proxies of liquidity. Second, it is shown that an infinitesimal variation in either market volatility or trading activity augments the probability of observing an unambiguous liquidity adjustment. Ambiguity strongly depends on the expected (deterministic) component of volatility.