Unemployment Compensation Amendment of 1998

Unemployment Compensation Amendment of 1998 - Amends the Federal-State Extended Unemployment Compensation Act of 1970 to: (1) repeal certain State law requirements under the extended unemployment compensation benefit program; (2) establish certain mandatory triggers based on total unemployment; (3) revise requirements for supplemental benefits during high unemployment periods; and (4) modify provisions for alternative triggers that States may establish. Amends title IX (Employment Security Administrative Financing) of the Social Security Act (SSA) to modify the ceiling on the Federal Unemployment Account. Provides for special distributions of funds to the States under SSA title IX. Directs the Secretary of Labor to reserve specified amounts for grants to States to assist in implementing alternative base periods for determining the eligibility of claimants for unemployment compensation. Requires States to achieve or make substantial progress toward achieving certain solvency targets for their unemployment compensation accounts. Directs the Secretary to transfer to other States' accounts the amount that would otherwise be transferred to the account of a State that violates such requirement under SSA title IX. Revises SSA title IX requirements for distribution to States of certain excess amounts in the Employment Security Administration Account as of the close of FY 2002. Amends the North American Free Trade Agreement Implementation Act to extend the self-employment assistance program. Amends the Federal Unemployment Tax Act (FUTA) under the Internal Revenue Code to set forth requirements for treatment of short-time compensation programs.