This is one of the most influential papers on the size of the placebo effect, its a metanalysis.
https://math.dartmouth.edu/~doyle/docs/40/PlaceboArticle.pdf
Although they don't call it that, the measure they call pooled standardised mean difference is effectively an effect size measure (similar to Cohen's d). The study combines a number of different conditions and treatments, most of which have a psychological component (obesity, depression, smoking cessation, anxiety, etc), so if we'd expect to see placebo effects anywhere it would be here.
Here are the overall effect sizes, depending on whether outcomes was measured on a subjective scale (e.g., self report) or an objective scale:
Subjective -0.36 (confidence interval -0.47 to -0.25)
Objective -0.12 (confidence interval -0.27 to 0.03) This is a null effect.
So no effect on objective measures, even in these illnesses that might b expected to be highly responsive.
From the discussion:
"It is difficult to distinguish between reporting bias and a true effect of placebo on subjective outcomes, since a patient may tend to try to please the investigator and report improvement when none has occurred. The fact that placebos had no significant effect on objective continuous outcomes suggests that reporting bias may have been a factor in the trials with subjective outcomes."