Abstract Prior research finds that Dodd–Frank Act’s regulations on credit rating agencies (CRAs) increase rated firms’ risk of downgrades, regardless their quality. Our difference-in-difference estimates suggest after Dodd–Frank, low-rated firms, which face steep costs from a further downgrade, significantly reduce debt issuance and investments compared to similar unrated firms. results are not...

We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce squarefree criteria for polynomials in several variables.