Testing the household Euler equation with consumption data faces econometric challenges caused by large measurement errors in the data and a short time span. We adopt a framework to test the Euler equation with stock market data to alleviate the measurement error and short time span issues. Utilizing a data-driven group panel data method, we identify a heterogeneous pattern of Euler equation failure among different groups of listed firms. The identified degree of Euler equation failure is significantly related to firm characteristics that are associated with famous stock anomalies. We show that the correlations between the degree of Euler equation failure and firm characteristics provide a new set of stylized facts that can help us distinguish between different economic theories on Euler equation failures and asset pricing anomalies, and identify challenges facing current theories.