The introduction of a small UBI does not cancel out the value of unemployment insurance.

"We now want to compare both policies. As previously noted, both UI and UBI programs are significant improvements over the laissez-faire, i.e., self-insurance shown in the first lines of Tables 3 and 4. The UBI policy around its optimum may appear as a credible alternative to UI in both periods. However, for the shirking success probability considered in Table 3 (π = 0.20) and the monitoring cost calibrated to Oregon, the optimal UI policy is socially more desirable, as a comparison of average welfare across Tables 3 and 4 suggests. For both calibrations, UI is clearly a better insurance mechanism against idiosyncratic employment shocks than UBI, and the inefficiency caused by monitoring costs and cheating behavior do not offset this fact in our simulations."