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This paper shows that standard RD estimation using a rounded discrete running variable leads to inconsistent estimates of treatment effects, even when the true functional form relating the outcome and the running variable is known and is correctly specified. This paper provides simple formulas to correct for this discretization bias. The proposed approach does not require instrumental variables, but instead uses information regarding the distribution of rounding errors, which is easily obtained and often close to uniform. Bounds can be obtained without knowing the distribution of the rounding error. The proposed approach is applied to estimate the effect of Medicare on insurance coverage in the USA, and to investigate the retirement\u2010consumption puzzle in China, utilizing the Chinese mandatory retirement policy. 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