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Let's say a trader is trading in a LOB and he places an order deep in the book. How close can he be to the touch until he has temporary or even permanent price impact? This assumes he cancels after T amount of time and does not get executed.

Most models show price impact of a trade. What is the impact of an order? An order at the touch must have some impact since many participants use the microprice/imbalance as a signal of future price movements.

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    $\begingroup$ Interesting question. My intuition is that the deep order is not worth much, because it can be withdrawn at any time. Any value derives from the chance that a very large order in the opposite direction sweeps the whole book. $\endgroup$ – dm63 Dec 19 '18 at 3:09
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Presumably a large enough order will trigger some algo's to take action. It likely depends on the typical volume seen in that market. If the market is very liquid and an order is placed 5% away from the most recent trade then it will likely have less impact than an order placed closer to the spread.

I haven't seen any research on this subject myself.

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