In a number of Southeast Asian countries black markets are known to exist in border regions. Examples include Mongla between Myanmar and China (on the Myanmar side, but running on Chinese currency), Bokeo in Lao (http://wildlife1.org/laoss-special-economic-zone-a-black-hole-for-illegal-wildlife-trade/; http://www.theguardian.com/environment/radical-conservation/2015/mar/19/high-end-laos-resort-serves-up-illegal-wildlife-for-chinese-tourists) and various Vietnamese markets where "wildlife" restaurants are able to provide virtually any species upon request.
These markets are well known, and appear to cater for a largely Chinese and Vietnamese clientele (Bokeo and Mongla are both outside China but both use Chinese currency and timing), yet there seems to have been no successful efforts to regulate these markets and restaurants despite their illegality-any examples (successful or unsuccessful) would be useful
A general model for the question you ask involves three components. 1. The Victims, 2. The Crime, and 3. Policing. But this model has not been put into practice sufficiently because of a lack of the data.
In the US, illegal activities or underground economy have long been recognized but not quantified. One tends to back into an estimate. For instance, if there is a sudden rise in illegal activity, then it will show up in a measure of GDP. So, an estimate of potential GDP vs. Actual will contain the influence, which might require some disaggregation. In some cases, say if the Federal Reserve Bank in Miami is running out of $100 bills, then it may be a measure of illegal activities. A rise in gang related killings at the border may also be a sort of indicator.
In general, if the illegal activities do not fluctuate much, then economic indicators will not vary much, and will still be good for economic analyses and forecasts. If the problem is about obeying the Rule of Law or Morals, then we will have to go after it. Sorry, I have no quantitative model to offer.
For some excellent reference on prominent research concerning extra legal trade see
Article SIMULTANEITY, MULTI-PLEXITY, EXTRA-LEGAL – Emerging Ideas in...
Look into colonial histories when colonial governments enforced such measures.
The Guardian reported just recently on the seizure of Pangolin bound for these markets - not successful though as the animals were already dead. See
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