It depends. At least that was our conclusion last night at the PSER event I spoke at last night. When asked that question fellow panelist Rod McDermott of McDermott & Bull Executive Search had one viewpoint (His partnership develops business in almost identical ways as law firms so his answer was on point).
He stated that at his firm of 25 it hasn't made any sense yet. They are very focused on using past and existing clients to pump new opportunities into their pipeline, and in making a choice with limited budget, direct mail has been decidedly more effective for their goal.
What he is doing is sending letters to their contact base, every month, that lists the type of searches they are doing and highlights what their successes have been. It does not say, "hey you should call us..." Just what his firm has been up to. And it works. The calls for new work come in from those letters.
For him, advertising is shouting at too large an audience to be effective.
Of course, I had a counterpoint. Unlike his firm, mine is much larger and advertising is not so much about generating sales on "this day", but about controlling our core message. Everyday I have 145 attorneys in the marketplace interacting with clients and prospects, each telling the story of the firm in their own words. In a perfect world each will describe the firm with similar words and consistent message; But it is not a perfect world.
Advertising permits me to state the core message of the firm across a broader audience and bring together all of their "mini-messages" under a single banner.
How an attorney in our public law section describes the firm WILL be a bit different from how an attorney in our corporate practice describes us. They are trying to say the same thing but will use different words based on perspective and practice. Advertising offers me the opportunity to help their words make sense for the whole firm.
So the answer is; It depends. Advertising is just one tactic available in the big mix of all marketing tactics. Picking tactics is a strategic choice and it is up to you to pick the right ones.