Statistical Modeling and Hypothesis Testing of State-Level Unemployment in the United States: Distribution Fitting, Structural Breaks, and Interstate Heterogeneity Based on BLS-LAUS Data, 19762025

Unemployment has always been one of the most important signals of how well an economy is working, but at the state level, it tells a much richer story than national averages alone. This paper uses monthly unemployment data from 1976 to 2025, provided by the Bureau of Labor Statistics through the FRED database, to study both long-run trends and short-term shocks across all 50 states and the District of Columbia. The analysis begins with descriptive statistics and probability distribution fitting, showing that unemployment rates often depart from the standard normal distribution and are better captured by heavy-tailed alternatives such as the lognormal or gamma distribution. Building on this, structural break tests highlight 2020 as a turning point when the COVID-19 pandemic produced the sharpest rise in unemployment in decades, with recovery paths diverging widely across states. States such as New York, with service-oriented economies, experienced slower rebounds, while Texas, supported by its energy and manufacturing sectors, recovered more quickly. Hypothesis testing and principal component analysis further confirm that U.S. labor market dynamics reflect both nationwide shocks and persistent regional differences. Taken together, the results show that unemployment is not only a national issue but also a local story shaped by industrial structure and policy response. The findings suggest that future economic strategies should combine broad countercyclical measures with targeted, state-specific policies that account for structural heterogeneity.