Can bank interaction during rating measurement of micro and very small enterprises ipso facto Determine the collapse of PD status?

This paper begins with an analysis of trends - over the period 2012-2018 - for total bank loans, non-performing loans, and the number of active, working enterprises. A review survey was done on national data from Italy with a comparison developed on a local subset from the Sardinia Region. Empirical evidence appears to support the hypothesis of the paper: can the rating class assigned by banks - using current IRB and A-IRB systems - to micro and very small enterprises, whose ability to replace financial resources using endogenous means is structurally impaired, ipso facto orient the results of performance in the same terms of PD assigned by the algorithm, thereby upending the principle of cause and effect? The thesis is developed through mathematical modeling that demonstrates the interaction of the measurement tool (the rating algorithm applied by banks) on the collapse of the loan status (default, performing, or some intermediate point) of the assessed micro-entity. Emphasis is given, in conclusion, to the phenomenon using evidence of the intrinsically mutualistic link of the two populations of banks and (micro) enterprises provided by a system of differential equations