The classic Chicago School result was that advertising for eyeglasses lowered prices, due to increased competition. It doesn't seem the same is true for pharmaceuticals, as we see from Dhaval Dave and Henry Saffer:
Expenditures on prescription drugs are one of the fastest growing components of national health care spending, rising by almost three-fold between 1995 and 2007. Coinciding with this growth in prescription drug expenditures has been a rapid rise in direct-to-consumer advertising (DTCA), made feasible by the Food and Drug Administration’s (FDA) clarification and relaxation of the rules governing broadcast advertising in 1997 and 1999. This study investigates the separate effects of broadcast and non-broadcast DTCA on price and demand, utilizing an extended time series of monthly records for all advertised and non-advertised drugs in four major therapeutic classes spanning 1994-2005, a period which enveloped the shifts in FDA guidelines and the large expansions in DTCA. Controlling for promotion aimed at physicians, results from fixed effects models suggest that broadcast DTCA positively impacts own-sales and price, with an estimated elasticity of 0.10 and 0.04 respectively. Relative to broadcast DTCA, non-broadcast DTCA has a smaller impact on sales (elasticity of 0.05) and price (elasticity of 0.02). Simulations suggest that the expansion in broadcast DTCA may be responsible for about 19 percent of the overall growth in prescription drug expenditures over the sample period, with over two-thirds of this impact being driven by an increase in demand as a result of the DTCA expansion and the remainder due to higher prices.
The paper is here (NBER gate). Here is a simpler paper on advertising and prescription drug expenditures. Here is a related paper on the advertising topic. Here is another paper which generates higher prices from advertising. Pharmaceuticals could be different from eyeglasses for a few reasons, one being weaker contestability in the market, due to patent protection, another being that consumers process information about health care differently. This paper suggests that co-payments don't much help reduce inappropriate demands for pharmaceuticals.
I thank Eric John Barker for the initial pointer.