Is panel Currency Demand equation homogeneous, why not, and what it means for shadow economy measurement

Currency Demand Analysis – one of the most popular macroeconometric techniques of shadow economy (SE) measurement – builds on equation explaining the share of cash in circulation in broader monetary aggregates, estimated as time series or panel regression. In the latter case, the homogeneity of slopes between panel units is usually assumed. We demonstrate that the data clearly reject this assumption with Pesaran-Yamagata test, and the resulting peril is using estimates obtained from inconsistent estimation for SE calculation. Due to an adverse T/N ratio, we refrain from using random coefficient or mean group estimators and propose the application of Regression Clustering and Classifier-Lasso procedures, splitting the sample in cross-sectional dimension into a limited number of homogeneous-coefficient groups, considerably smaller than N, whose number or composition remain unknown in advance. For both 2-group and 3-group partitioning, we find substantial differences between the relevant slopes, including the slopes of SE determinants impactful for SE measurement. Notably, a group dominated by Sub-Saharian and Central Asian economies exhibits higher sensitivity to all potential SE determinants: unemployment & inactivity rate, self-employment frequency and government effectiveness.