Will Rinehart has a great essay summarizing the literature on advertising effectiveness. The tl;dr version is that you can can persuade the average consumer to try your product in some contexts, but is it is very very hard. In other words, the idea ad men can easily mesmerize customers into buying their products (as argued in the Hidden Persuaders) is total bunk.
Why is persuading consumers so hard?
One reason it is hard to persuade consumers is most of them choose not to be persuaded. Many models of advertising treat consumers like passive receptors for ads. You show them words on a screen and somehow it "changes" their minds (kinda like if Coca-Cola created the Snow Crash virus). But that isn't really how consumers make decisions. Instead, consumers actively decide whether to engage with your ad or not. This insight is formally captured in Becker & Murphy's model of advertising. In their 1993 paper, they argue that consumers approach advertisements in much the same way they approach other goods--they consume them up until the marginal benefit equals the marginal cost. If consumers hate watching ads (i.e. the marginal benefit of watching the first ad is negative), then you have to give them something in return for watching your ad. For example, giving consumers free web content like YouTube videos with your ad stuck in the middle is one way to "pay" them to watch your ad. Of course, even if you "pay" consumers to watch your ad with free web content, that is no guarantee they will actually watch it. The costs may still exceed the benefit if the ad itself is not also mildly entertaining. Maybe that's one reason why ad clickthrough rates are so low?
I don't know about anyone else, but this theory describes how I watch ads. I won't go out of my way to watch your mildly entertaining 30-second commercial. But, if you stick it in the middle of a video on the Philosophy of Mob Psycho 100? Maybe I'll watch....or maybe I won't. Honestly, even when I am getting free content, the benefit from engaging with most ads is too low to bother (I saw this ad 5 times on mute before I realized it was about a car and not a new antidepressant).
So, if ads are so ineffective, why do companies advertise?
Many econometric analyses look at the consequences of advertising on the average consumer's purchases. However, the actual target of ads is not the "average" consumer. It is the marginal consumer. That person that is just on the fence between buying another unit of your product or not. If you can convince those consumers, you might not only sell more units to them, but the increase in demand might put upward pressure on prices that allows you to sell your goods to other customers at a higher price (this is also discussed more formally in Becker and Murphy). So that is the real question companies have to answer. Does that marginal revenue generated by another dollar of advertising exceeds the marginal cost? Answering that question is very difficult as discussed in Lewis and Rao's paper on the Unfavorable Economics of Measuring Returns to Advertising.
