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Now we are ready to calculate (6). The commands are:
.generate lambda0 = (-normden(cutoff1-zhat))/(norm(cutoff1-zhat)-norm(-zhat))
.generate lambda1 = (normden(cutoff1-zhat)-normden(cutoff2-zhat))/(norm(cutoff2-zhat)-norm(cutoff1-zhat))
.generate lambda2 = (normden(cutoff2-zhat)-normden(cutoff3-zhat))/(norm(cutoff3-zhat)-norm(cutoff2-zhat))
.generate lambda3 = (normden(cutoff3-zhat)-normden(cutoff4-zhat))/(norm(cutoff4-zhat)-norm(cutoff3-zhat))
.generate lambda4 = (normden(cutoff4-zhat)-normden(cutoff5-zhat))/(norm(cutoff5-zhat)-norm(cutoff4-zhat))
.generate lambda5 = (normden(cutoff5-zhat)-normden(cutoff6-zhat))/(norm(cutoff6-zhat)-norm(cutoff5-zhat))
.generate lambda6 = (normden(cutoff6-zhat))/(1-norm(cutoff6)-norm(cutoff5-zhat))
.generate lambda = m170*lambda0 + m171a*lambda1 + m172a*lambda2 + m171b*lambda3 + m172b*lambda4 + m221a*lambda5+m221b*lambda6
One thing to notice in these calculations is that cutoff0 is assumed to be and cutoff7 is assumed to be
10. Now we are ready to estimate our regression explaining the grade that each individual received in intermediate microeconomics. Use Table 8 to report the regression results for four specifications of the model. The first question is can the null hypothesis of sample selection bias be rejected? How does this conclusion compare with BFS's conclusions? (See Table 9.) Second, since many of the potential explanatory variables like class size and scores on the SATs do not seem to be statistically significant, it is reasonable to focus our comments on the results reported in column (4) of Table 8.
What can you conclude about the impact of calculus on how well a student will do in intermediate microeconomics? Do the final grades earned in a majority of the math classes impact the grade earned in intermediate microeconomics? Do the grades earned in any of the math classes positively and significantly affect the grade earned in intermediate microeconomics? Can you explain the impact of the freshman GPA on the grade earned in intermediate microeconomics? What, if any, is your bottom line conclusions about what matters in determining the grades earned in intermediate microeconomics?
| Explanatory variables | Model (1) | Model (2) | Model (3) | Model (4) |
| Lambda | — | — | ||
| Sophomore | — | — | ||
| Senior | — | — | ||
| Same | ||||
| Skip | — | — | ||
| M171a | ||||
| M172a | ||||
| M171b | ||||
| M172b | ||||
| M221a | ||||
| M221b | ||||
| GE100 | ||||
| GDE100 | ||||
| GE101 | ||||
| GDE101 | — | |||
| GDE231 | ||||
| Size | — | |||
| FGPA | ||||
| Female | ||||
| MSAT | — | |||
| VSAT | — | |||
| Grade in highest Math | — | — | — | |
| class | ||||
| GM170 | — | |||
| GM171a | — | |||
| GM172a | — | |||
| GM171b | — | |||
| GM172b | — | |||
| GM221a | — | |||
| GM221b | — | |||
| Intercept | ||||
| F( 28, 580) | — | — | — | |
| Prob>F | — | — | — | |
| F( 27, 581) | — | — | — | |
| Prob>F | — | — | — | |
| F( 20, 588) | — | — | ||
| Prob>F | — | — | ||
| F( 19, 589) | — | — | — | |
| Prob>F | — | — | — | |
| R-Squared | ||||
| Root MSE | ||||
| Sample Size | 609 | 609 | 609 | 609 |
| MICRO-2 | |||
| Variable a | Expected sign | Mean (SD) | Coefficient(t-value) |
| Intercept | — | — | -1.64 |
| (3.48) | |||
| Selection bias correction | + | -0.00 | 0.10 |
| (Predicted residual) | (0.92) | (1.29) | |
| Level of calculus attained: | |||
| Math 171A | + | 0.08 | 0.39 |
| (0.27) | (1.04) | ||
| Math 172A | + | 0.02 | -0.18 |
| (0.13) | (0.21) | ||
| Math 171B | + | 0.37 | 1.02 b |
| (0.48) | (3.49) | ||
| Math 172B | + | 0.07 | 1.52 b |
| (0.25) | (3.53) | ||
| Math 221A | + | 0.05 | 1.33 c |
| (0.22) | (2.27) | ||
| Math 221B or 222 | + | 0.14) | 0.75 c |
| (0.35 | (1.67) | ||
| Grade in last calculus course: | |||
| Math 170 | + | 3.06 | 0.36 b |
| (0.70) | (4.36) | ||
| Math 171A | + | 2.22 | 0.26 c |
| (0.86) | (2.21) | ||
| Math 172A | + | 2.94 | 0.42 |
| (0.80) | (1.54) | ||
| Math 171B | + | 2.62 | 0.10 c |
| (0.93) | (1.85) | ||
| Math 172B | + | 2.63 | -0.01 |
| (0.90) | (0.10) | ||
| Math 221A | + | 3.10 | -0.09 |
| (0.77) | (0.55) | ||
| Math 221B or 222 | + | 3.15 | 0.11 |
| (0.76) | (1.04) | ||
| Grade deflator of instructor in intermediate theory | + | -0.16 | 0.88b |
| course | (0.27) | (8.28) | |
| Taken in Sophomore year | ? | 0.32 | 0.07 |
| (0.47) | (0.94) | ||
| Taken in Senior year | - | 0.06 | -0.02 |
| (0.24) | (0.13) | ||
| MICRO-1 and MICRO-2 in same academic year | + | 0.35 | 0.04 |
| (0.48) | (0.46) | ||
| At least one semester between MICRO-1 and | - | 0.27 | 0.13 |
| MICRO-2 | (0.44) | (1.85) | |
| Grade in MACRO-1 | + | 2.73 | 0.20 b |
| (0.73) | (3.93) | ||
| Grade in MICRO-1 | + | 2.67 | 0.29 b |
| (0.74) | (5.93) | ||
| Instructor's grade deflator: | |||
| MACRO-1 | - | -0.32 | -0.33 c |
| (0.20) | (2.20) | ||
| MICRO-1 | - | -0.29 | -0.11 |
| (0.16) | (0.53) | ||
| Class size (intermediate theory course) | ? | 28.2 | -0.002 |
| (5.5) | (0.45) | ||
| Freshman Grade Point Average | + | 2.79 | 0.29 b |
| (0.46) | (3.04) | ||
| Sex (female = 1; male = 0) | ? | 0.39 | 0.13 c |
| (0.49) | (2.09) | ||
| SAT-Math score x 10 -2 | + | 6.25 | 0.12 c |
| (0.60) | (1.75) | ||
| SAT-Verbal score x 10 -2 | + | 5.56 | 0.04 |
| (0.67) | (0.78) | ||
| OVERALL RESULTS | |||
| Mean (SD) of dependent variable | |||
| Adjusted R 2 | 0.44 | ||
| Number of observations | 609 |
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