Suppose You Are Interested in Testing the Claim That Students

Essay

Suppose you are interested in testing the claim that students who participate in band perform better on standardized tests but you are worried that the results might be biased because individuals are likely to self-select into joining the band.You only have test scores for those students that participate in band.Suppose that for a sample of 14,111 6^th-grade students you estimate the Heckman selection model (marginal effects listed,standard errors in parentheses) Second-Stage:
$$\begin{aligned}Tes\widehat {t S}core _ { i } = & 58.932 +& 1.374 \lambda _ { i } +& 0.583 \text { Income } _ { i } + &2.156 \text { Male } _ { i } \\& ( 7.961 ) &( 0.358 )& ( 0.136 )&(1.679)\end{aligned}$$
First-Stage:
$$\begin{array} { l } {\widehat{\text { Band }_{i}}}=&0.261+&0.045 \text { Siblings in Band }_{i}+&0.048 \text { Income }_{i}+&0.125 \text { Male }_{i}\\&( 0.043 ) &( 0.022 ) &( 0.012 )&(0.103) \\\end{array}$$
a)Explain why OLS is inappropriate in this circumstance and how this model improves on OLS.
b)Which variable are you using to identify the model? Does this choice seem correct? Explain.
c)Discuss the results above.