How do economists quantify black market operations? I was doing a lot of research into organized crime in East Asia for a project as a favor to an author-friend of mine, and I noticed that there were noted economists and journalists who, in conjunction, estimate the value of black market operations worldwide. 
What is the methodology for this? How do these numbers come together? Are these numbers captured in traditional market models?
 A: They're not usually captured in traditional market models and some of the ways of estimating shadow markets can be a bit esoteric.
First, definitions: 


*

*informal markets, or shadow markets, are those which fall outside of formal financial systems; these are not necessarily illegal, but cater to sub-economic or very poor communities; however, it can also be local community markets or exchanges - the principle is that these are legal activities which would normally be reported for tax purposes but which are (for whatever reason) not;

*black markets, or illegal markets, are more normally associated with illicit market activity (drugs, stolen merchandise, etc.);


The UN World Drug Report (2011) lists a variety of illicit drugs and estimates the value based on tillage (aerial surveylance of agricultural areas), production, and various prices sampled throughout the supply-chain by law-enforcement services.  It's a reasonable approach, given the difficulties.
In many ways, this type of estimation is similar to the way in which Population Censuses are conducted in many emerging markets and informal settlements.  Aerial photographs are used to calculate population density and economic activity.  Sampling can estimate product range, constituency and pricing.  Supply-chains can be tracked and all of this can be used to estimate a total market size.
And many of these systems come from Wildlife Management.
A: There are many possible ways to estimate the size of the illegal sector. One particular clever way, I think, is to see how much energy a country uses compared to its official output. If this number is higher than you would expect, you might believe that other, illegal outputs are being created.
To measure drug use, researchers have measured concentrations of the drugs in sewage water.
See Schneider and Estne, "Shadow Economies: Size, Causes, 
and Consequences" from the Journal of Economic Literature for a listing of various methods and a summary IMF document here.
