There have been many attempts at answer this question, all of which have been plagued by serious measurement issues. The recent release of new data both on sanctions and protests allows for a more convincing analysis, which Julia Grauvogel, Amanda Licht, and Christian von Soest provide in this paper.
One big problem any study of the impact of sanctions must deal with is that of strategic interaction. When an episode ends at the threat state, we don't get to observe what would have happened if sanctions had been imposed. So if we don't look at what effect threats themselves have, we're not getting the full story.
GLvS thus look separately at the impact of new threats and new impositions on protest activity. They also allow for the possibility that certain types of threats (impositions) might have a bigger effect. Under the assumption that the primary channel through which sanctions increase protests is through signaling that the international community shares (some of) the goals of the protesters, they check to see if it matters whether the sanctioners specifically targeted the human rights practices of the target regime, whether the sanctions are narrowly targeted at the regime and its supporters, and whether they are multilateral in nature.
Somewhat surprisingly, the authors find that none of that seems to matter. We of course need to be careful, because the absence of evidence is not the same as evidence of absence, but it appears that context isn't too important. However, they do find, as expected, that threats are associated with an increase in protests, whereas the actual imposition of sanctions is not.
Details of the Argument
One of the strengths of the paper is the careful measurement of the key variables. The data are from the Mass Mobilization Project, collected by Pat Regan (Notre Dame) and Dave Clark (Binghamton University), and sponsored by the Political Instability Task Force. Data will be publicly available at Binghamton in the summer of 2014. Regan and Clark relied upon careful coding procedures to ensure that events are distinct and that start and end dates are available for every case. The data are also less tainted by media bias, since the collection procedures sought balance in events across states. Moreover, to ensure that the authors are identifying the impact of sanction threats and impositions, rather than picking up differences across cases driven by other factors, GLvS normalize the dependent variable by the baseline rate of protests in each country. That is, their dependent variable takes on a value of one if and only if that country-month saw an increase in protests greater than or equal to the standard deviation in protests for that country for that year. Otherwise it is equal to zero. (Decreases are treated as missing, ensuring that all comparisons are between increases and the status quo.) This is important, because some countries have frequent protests, with little variation from month to month in the level of protest activity. Others have few protests and equally little variation. Still others tend to have few protests most of the time, but are more variable in their experiences.
As I said above, the interpretation of the interactive effects is tricky. The authors largely do not find clear, unambiguous evidence that different types of sanctions have different effects. But if we look at the coefficient estimates, we see that this is generally because the standard errors are large, not because our best estimate of the additional impact of the contextual variables is particularly close to zero. In other words, the analysis no more provides clear, unambiguous evidence that context does not matter than it does the opposite. We just don't have a very good sense, one way or the other, of whether it matters that sanctioners draw attention to the human rights practices of the target regime, or narrowly target members of the regime through asset freezes and travel bans, or whether the sanctions originate in a single country.