This paper implements a time series econometric model to determine the timing of full convergence of incomes and output per capita and total factor productivity in the North and South of Cyprus, regardless of whether there is a political settlement or not. A significant dimension of the paper is its emphasis on institutional convergence, going beyond econometric or statistical convergence. Our results reveal that North Cyprus needs 17 years to catch up to full per capita income convergence, 16 years for per capita output convergence and 17 years for full total factor productivity (technological) convergence. The time-series findings demonstrate that statistical convergence is occurring quite rapidly as the North is catching up to the average income and productivity levels of the South, which may confirm evidence of unconditional (beta) or absolute convergence, but there are significant differences between North and South in savings, tastes, population growth and technology. Most significantly, there are institutional differences highlighted in the study with a Two-sector model of gate-keeping and rent-seeking which validates the premises of conditional convergence. Put differently, there are strong forces of divergence hidden behind our statistical findings.