Exploring the Law of Numbers: Evidence from China's Real Estate

The renowned proverb, Numbers do not lie, underscores the reliability and insight that lie beneath numbers, a concept of undisputed importance, especially in economics and finance etc. Despite the prosperity of Benford's Law in the first digit analysis, its scope fails to remain comprehensiveness when it comes to deciphering the laws of number. This paper delves into number laws by taking the financial statements of China real estate as a representative, quantitatively study not only the first digit, but also depict the other two dimensions of numbers: frequency and length. The research outcomes transcend mere reservations about data manipulation and open the door to discussions surrounding number diversity and the delineation of the usage insights. This study wields both economic significance and the capacity to foster a deeper comprehension of numerical phenomena.Comment: DS

Assessing the effect of school days and absenceson test score performance

While instructional time is viewed as crucial to learning, little is known about the effectiveness of reducing absences relative to increasing the number of school days. In this regard, this paper jointly estimates the effect of absences and length of the school calendar on test score performance. Using administrative data from North Carolina public schools, we exploit a state policy that provides variation in the number of days prior to standardized testing and find substantial differences between these effects. Extending the school calendar by ten days increases math and reading test scores by only 0.8% and 0.2% of a standard deviation, respectively; a similar reduction in absences would lead to gains of 5.8% and 3% in math and reading. We perform a number of robustness checks including utilizing u data to instrument for absences, family-year fixed effects, separating excused and unexcused absences, and controlling for a contemporaneous measure of student disengagement. Our results are robust to these alternative specifications. In addition, our findings indicate considerable heterogeneity across student ability, suggesting that targeting absenteeism among low performing students could aid in narrowing current gaps in performance

Not All Price Endings Are Created Equal: Price Points and Asymmetric Price Rigidity

There is evidence that 9-ending prices are more common and more rigid than other prices. We use data from three sources: a laboratory experiment, a field study, and a large US supermarket chain, to study the cognitive underpinning and the ensuing asymmetry in rigidity associated with 9-ending prices. We find that consumers use 9-endings as a signal for low prices, and that this signal interferes with price information processing. Consequently, consumers are less likely to notice a bigger price when it ends with 9, or a price increase when the new price ends with 9, in comparison to a situation where the prices end with some other digit. We also find that retailers respond strategically to this consumer bias by setting 9-ending prices more often after price increases than after price decreases. 9-ending prices, therefore, usually increase only if the new prices are also 9-ending. Consequently, there is an asymmetry in the rigidity of 9-ending prices: they are more rigid than non 9-ending prices upward but not downward