I've read some literature on measuring capital control / financial openness, but I am wondering if there is any data directly collected by international organizations like IMF that measure capital control.
Indeed the IMF reports on this. A recent review-overview paper is
In the introduction, the authors write
"The aim of this article is to help researchers better understand the range of choices they have in measuring financial integration and globalization, the pros and cons associated with each, and some of the reasons behind the divergence in findings in the literature. In particular, it describes de jure, de facto, and “hybrid” indicators, and comparatively analyzes their data properties and how these measures relate to one another"
The main "De jure" (as the authors characterize it) resource (on which many scholars have built various indexes using wildly different methodologies) is the IMF's report Annual Report on Exchange Arrangements and Exchange Restrictions (AREAER)
As the authors write, after presenting the various "De jure" indices,
"De jure indices of financial globalization do not reflect the extent to which actual capital flows evolve in response to legal restrictions, either because of a lack of enforcement, or because controls in one area may induce a response in other asset flows. Also, even the more disaggregated indices may not capture subtle, but possibly important differences between countries’ capital control regimes. De jure measures, therefore, do not necessarily reflect a country’s actual degree of financial integration, highlighted by the fact that even countries with relatively closed capital accounts became substantially more financially integrated over the past decades... Thus, "de facto", or in some cases “blended,” measures present an alternative way to measure a country’s integration into global finance markets. These can be divided into three categories: quantity-based, price-based, and hybrid measures."
They then move on to a detailed study of many of all the above indices, and they conclude (they have also conveniently summarized qualitative assessments of each index in tables):
"A key result is that most of the measures provide information that is linked in a meaningful way to economic outcomes. The exception is IF-Heritage, an indicator that we found not to be correlated with other indices, to have no measurable impact on economic growth, and to be linked in the factor analysis to unique dynamics that are not easily interpretable. Correlation and factor analyses suggest that investigators using de facto indicators of financial globalization will find differing identifying variances from those found in the de jure measures. In part, this is because de facto measures likely reflect the influences of many political and economic factors, of which legal restrictions of the capital accounts, as indicated by the de jure measures, are but one."
"The bottom line of this paper is that researchers in this field have an unusually large choice of indicators, most of which are valid, with unique advantages and disadvantages."