  We study the price impact of order book events - limit orders, market orders
and cancelations - using the NYSE TAQ data for 50 U.S. stocks. We show that,
over short time intervals, price changes are mainly driven by the order flow
imbalance, defined as the imbalance between supply and demand at the best bid
and ask prices. Our study reveals a linear relation between order flow
imbalance and price changes, with a slope inversely proportional to the market
depth. These results are shown to be robust to seasonality effects, and stable
across time scales and across stocks. We argue that this linear price impact
model, together with a scaling argument, implies the empirically observed
"square-root" relation between price changes and trading volume. However, the
relation between price changes and trade volume is found to be noisy and less
robust than the one based on order flow imbalance.
