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Asymmetries in bid and ask responses to innovations in the trading process 59
j
fi (MCt,Dt)=1 for all i and j. In this case, the matrix of autoregressive polynomials is
time invariant, At(L)=A(L), and the impact of trades on quotes is perfectly linear.
We will show that this model suffices to illustrate the essentials of the dynamic
relationship between trades and quotes. However, some other aspects of this
relationship can only be captured by considering the more general case.
Following Hasbrouck (1991), we characterize the trading processes using
indicator variables. Namely, xt B S
equals one for buys and zero otherwise, and xt equals one for sells and zero otherwise. The discreteness of these variables,
however, may introduce some problems in the estimation process. 10 To control for
these potential problems, we also estimate Eq. (3.7) using the trade size ex i t to
characterize each transaction. In particular, we define ex i t ¼ xit log ðVtÞ , where Vt is
the size of the t-th trade in shares.
4 Data
The database comprises high frequency data on trades and quotes from two
markets with remarkably different microstructures: the NYSE and the SSE. The
NYSE is a peculiar mixture of microstructure types. It combines an electronic limit
order book, only partially transparent, with monopolist market makers, and an
intensive trading activity at the floor market. The SSE, on the contrary, is a
representative example of an electronic order-driven venue. Liquidity provision
depends exclusively on a fully transparent open limit order book. Twenty levels of
the book are nowadays visible in real time for all market participants. There are no
market makers, no floor trading, price improvements are not possible, and all the
orders are submitted through vendor feeds, and stored or matched electronically.
We use data on two different markets to show that asymmetric dynamics
between ask and bid quotes in response to trades are not exclusive of the NYSE. In
addition, trades in the SSE always involve a market order (or equivalent), the
initiating side, and one or more limit orders stored on the book. Therefore, trades
are straightforwardly classified as either buyer or seller-initiated by simply
identifying the side of the book the market order hits. Thus, with the SSE data we
do not bear the ambiguity and misclassification problems that appear when traditional
trade-direction algorithms, such as Lee and Ready (1991), are applied to
NYSE data (see Ellis et al. 2000, and Odders-White 2000). Finally, using Spanish
data we do not have reporting delays neither in trades nor in quotes since the book
and trade files are updated simultaneously and in real time. Therefore, we avoid the
use ad hoc rules to match trades and quotes, like the classical “five-second rule”
applied to NYSE data. 11
NYSE data is obtained from the TAQ database. We consider two different
sample periods, January to March 1996 and 2000. Several details in the mi-
10 Our model is nonlinear and well behaved around the mean (nonlinear). Like standard linear
probability models (LPM), only in the extremes it can give predictions out of the zero and one
interval. The corresponding estimation theory for dynamic models with weakly dependent
variables is covered in White (1994) and Wooldridge (1994). Park and Phillips (2000) extend it to
cover nonlinear cointegration cases with limited dependent variables.
11 Blume and Goldstein (1997) shows that the “five-second rule” could not be generalized to all
sample periods and markets. However, Odders-White (2000) shows that this rule does not seem to
explain much of the bias induced by the Lee and Ready’s (1991) algorithm.