Problem Description:
The STATA assignment aims to investigate the potential correlation between the variable "choiceyrs" and the error term in a regression model. This correlation arises due to endogeneity, indicating a need for careful examination. The dataset comprises 990 students, with varying experiences related to school vouchers and private school attendance.
 Endogeneity of "choiceyrs": The correlation between "choiceyrs" and the error term is attributed to endogeneity. This suggests that "choiceyrs" is endogenous in the equation, and further analysis is required to address this issue.

Descriptive Statistics: Out of 990 students:
 468 students were never awarded vouchers.
 522 students had vouchers available for four years.
 470 students attended a choice school for four years.
 Regression Analysis:The regression of "choiceyrs" on "selectyrs" is conducted to explore the relationship. The coefficient on "selectyrs" is 0.7668, indicating that a unit increase in the number of years a student is selected for a voucher correlates with a 0.7668 increase in the number of years spent in a private school. The positive relationship is evident, but the endogeneity of "selectyrs" is tested, and results suggest nonrejection of the null hypothesis.
 Impact on Academic Performance: Regression of "mnce" (math score) on "choiceyrs" reveals a negative relationship. The coefficient of 1.8370 implies that an increase in the number of years a student attends a private school leads to a decrease in math scores.
 Instrumental Variable (IV) Analysis: A regression of "mnce" on "choiceyrs" is performed with "selectyrs" as the instrumental variable. However, the use of IV does not demonstrate a positive effect of attending a private school on math scores, as indicated by the coefficient on "choiceyrs."
 Improved Effect through Instrumenting: The coefficient on "choiceyrs" in the IV analysis provides a refined understanding of the effect of attending a private school on math scores. This instrumental variable approach enhances the precision of the estimation and contributes to a more accurate assessment of the impact of school choice on academic performance.
Table 1: The coefficients of choiceyrs
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