Search frictions and labor market dynamics in a real business cycle model with undeclared work

We study the effects of undeclared work (UDW) on labor market dynamics in a real business cycle (RBC) model with search and matching frictions in the labor market. Distinction is made between the wages paid and the hours worked in regular and in undeclared types of activity. Calibrating the model on the US economy, we show that a greater size of UDW implies lower average employment, higher volatility of employment and lower volatility of regular wages. These volatilities are affected by the steady-state ratio between the minimum value of the regular wage that can be accepted by a worker and the maximum value that can be paid by a firm in the Nash bargaining process, which occurs when a labor match is realized. The greater the ratio, the higher the volatility of employment and the lower the volatility of wages. We demonstrate that, due to a social stigma attached to UDW, an increase in undeclared hours raises this ratio by reducing the numerator less than the denominator. This suggests that the introduction of UDW may improve the ability of RBC models to match the empirical volatilities of labor market variables.