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We study asset-tested unemployment insurance in an incomplete markets model with moral hazard during job search. Optimal asset testing is weak and yields negligible welfare gains. The optimal replacement rate of an unemployed worker with zero liquidity is 9 percentage points higher than that of the median worker. Welfare rises by 0.03 percent in consumption equivalent terms. We develop a general welfare decomposition for heterogeneous agent models with transitional dynamics. Asset testing creates welfare gains due to redistribution and additional consumption during the transition phase, and welfare losses due to reduced consumption smoothing, lower consumption, and higher effort levels.