In a macroeconomic model with drifting long-run inflation expectations, the anchoring of inflation expectations manifests in two testable predictions. First, expectations about inflation far in the future should no longer respond to news about current inflation. Second, better anchored inflation expectations weaken the relationship between unemployment and inflation, flattening the reduced-form Phillips curve. We evaluate both predictions and find that the Federal Reserve’s communication of a numerical inflation objective, first through its Summary of Economic Projections and later through the announcement of a 2% target in 2012, better anchored inflation expectations. Moreover, inflation expectations in the United States have remained anchored amid the volatility of the COVID-19 pandemic. In contrast, similar analysis reveals no evidence of anchoring in Japan despite the adoption of a numerical inflation target.

The H-1B Visa Reform Act of 2004 dictates an annual allocation of 85,000 visas with 20,000 reserved for advanced-degree applicants. We represent the main requirements of this legislation as formal axioms and characterize visa allocation rules consistent with the axioms. Despite the precise number reserved, we show that the range of implementations satisfying these axioms can change the allocation of advanced-degree visas by as much as 14,000 in an average year. Of all rules satisfying these axioms, the 2019 rule imposed by executive order is most favorable to advanced-degree holders. However, two earlier modifications resulted in larger changes, possibly unintentionally.