  We study the multi-level order-flow imbalance (MLOFI), which is a vector
quantity that measures the net flow of buy and sell orders at different price
levels in a limit order book (LOB). Using a recent, high-quality data set for 6
liquid stocks on Nasdaq, we fit a simple, linear relationship between MLOFI and
the contemporaneous change in mid-price. For all 6 stocks that we study, we
find that the out-of-sample goodness-of-fit of the relationship improves with
each additional price level that we include in the MLOFI vector. Our results
underline how order-flow activity deep into the LOB can influence the
price-formation process.
