Price dynamics and trading volume: A semiparametric approach

In this paper we investigate the relation between price impact and trading volume for a sample of stocks listed on the New York Stock Exchange. The parametric VAR-models that have been used in the literature impose strong proportionality and symmetry restrictions on the price impact of trades, although market microstructure theory provides many reasons why these restrictions would not hold. We analyze a more flexible semiparametric partially linear specification and establish significant evidence for a nonlinear, asymmetric, increasing, and concave relation between trading volume and both immediate and persistent price impact. Moreover, we compare the price-impact functions obtained in the partially linear model to the ones generated by the parametric models and show that there are considerable differences. We test the parametric specifications against the partially linear model and show that the parametric models are rejected in favor of the semiparametric model. We also test the partially linear model against a more flexible fully nonparametric specification and show that this test does not reject the partially linear model.