What I want to decipher is if irregular migration is something to be blamed on the migrant (criminalization) or is it a state policy given the gap between the actual demand of immigrant labour (for instance in the US) and the number of visas issued in a certain period. In order to make the problem a bit more complex, it might be interesting to consider the root causes not in the sending country in isolation, but in the relationships among sending and receiving country.
This is a complex, multifaceted question. First, on terminology. I assume that by irregular you mean illegal. An entry to a country without visa when visas are required would be a breach of that country's law, hence illegal. It's a better term than irregular, which I find a bit fuzzy (e.g., "irregular" migration could conceivably be caused by a one-off green card lottery campaign officially launched by the USA). Second, policy. I worked for the gov't (in fact, for 3 gov'ts) and in all cases "policy" is smth codified, i.e. written on paper, announced and distributed electronically and by other means. May or may not be published, but definitely has to be uniformly communicated to civil servants charged with its implementation. As far as I know, there is no state policy in this sense of the word that would encourage or somehow bet on illegal immigration to fulfill the labor market demand. However, you are right about the push-pull dynamics and the relationship between the sending and the receiving country. If illegal immigration is your focus of interest, this relationship is better described in terms of unregulated market exchange than in terms of any sort of policy. Finally, the question on how to estimate (the numbers) of illegal migration -- I suppose, a difference between the estimated size of the actual labor force in any particular region and the number of people paying income taxes off their wages, or smth like that.
I don't know much about the United States, in Italy data about several regularization programs were very useful to make a rough (very rough) estimation of the phenomenon. It is also quite easy to get data on detected irregular entries, and maybe also on overstayers/loss of status (e.g. visas expired and not renewed), together with entry quotas stabilised for a year.
Maybe the results of the Clandestino project (http://www.gla.ac.uk/media/media_147171_en.pdf), or a publication of the European Migration Network on Irregular migration* (Chapter 5) can give you some useful idea, even if the latter is much more a policy report than an academic researches.
If your question is about the labour force, the results of specific labour inspections could be used (I know that it is done and published - I think regularly - in Italy). Of course usuallythese inspections do not cover the whole economy, but on national level they can provide very useful and quite specific information.
*http://ec.europa.eu/dgs/home-affairs/what-we-do/networks/european_migration_network/reports/docs/emn-studies/irregular-migration/it_20120105_practicalmeasurestoirregularmigration_en_version_final_en.pdf
The publications listed here may be of interest to you:
http://www.pewhispanic.org/topics/unauthorized-immigration/
Dr. Passel is the expert in the US
http://www.pewresearch.org/staff/jeffrey-s-passel/
May be it has a relation with the uncertantity, drougt ie., and political problems.
Regarding the question that I framed several weeks ago, it is interesting to notice in the case of Mexico-US labour migration: