The Beveridge curve shows a fairly stable empirical relationship between job openings and unemployment. There is nothing political about it, and there is really no theory behind it either, it just shows over time a stable relationship in the data between two macroeconomic aggregates. The other you might be interested in is "Okun's Law" which shows a 2:1 relationship between GDP growth rates and changes in employment.
Both the Beveridge curve and Okun's Law have held up fairly well in this recession, suggesting that they are A) good predictors and that B) there is nothing particularly unusual about hiring/firing in this recession and recovery, as some have argued.
Homer: [looking at watch] Two hours? Why'd they build this ghost town so far away?
Lisa: Because they discovered gold over there!
Homer: It's because they're stupid, that's why. That's why everybody does everything.