Please refer to FERTIL1 dataset (see "Course Resources" in "Modules" → "Welcome to Class: Your Journey Begins Here!"). Use Excel’s regression data analysis tool first and then Stata to compute the answers to the questions asked. Excel and Stata should give you the same answers.

Consider the following model: kidsit = β0 + β1ageit + γ0y82it + uit, where kids is the total number of kids born to a woman, age is her age and y82 = 1 if year = 1982, 0 if year = 1972. Please estimate that, holding age fixed, a woman had on average [Fill in the blank],
less children in 1982 than in 1972; then further estimate whether it is statistically significant at the 5% level: [Fill in the blank],
.

NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands. For your second answer, write either YES or NO.

HINT: only use data from years 1972 and 1982 to run your regression. Excel for this question is straightforward--see the incomplete solution here Q3 Excel-incomplete.xls; please finish by yourself. For Stata program, refer to Example 13.1 and make changes as needed--you may need the following command that is not in the Stata program for Example 13.1: regress y x1 x2 if year==? | year==?

Question

Please refer to FERTIL1 dataset (see "Course Resources" in "Modules" → "Welcome to Class: Your Journey Begins Here!"). Use Excel’s regression data analysis tool first and then Stata to compute the answers to the questions asked. Excel and Stata should give you the same answers.

Consider the following model: kidsit = β0 + β1ageit + γ0y82it + uit, where kids is the total number of kids born to a woman, age is her age and y82 = 1 if year = 1982, 0 if year = 1972. Please estimate that, holding age fixed, a woman had on average [Fill in the blank],
 less children in 1982 than in 1972; then further estimate whether it is statistically significant at the 5% level: [Fill in the blank],
.

NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Add a leading minus sign symbol, a leading zero and trailing zeros when needed. Use a period for the decimal separator and a comma to separate groups of thousands. For your second answer, write either YES or NO.

HINT: only use data from years 1972 and 1982 to run your regression. Excel for this question is straightforward--see the incomplete solution here Q3 Excel-incomplete.xls; please finish by yourself. For Stata program, refer to Example 13.1 and make changes as needed--you may need the following command that is not in the Stata program for Example 13.1: regress y x1 x2 if year==? | year==?

BlackTom AI · Accepted Answer

The problem asks us to interpret a linear regression model and extract two pieces of information from the estimated parameters.

First, restating the setup: the model is kidsit = β0 + β1 ageit + γ0 y82it + uit, where y82 = 1 for year = 1982 and y82 = 0 for year = 1972. Holding age fixed means we are comparing the expected number of kids born to a woman in 1982 versus 1972 at the same age. The coefficient γ0 on the indicator y82 captures this difference in expected kids between the two years, because when y82 goes from 0 to 1 (moving from 1972 to 1982) the predicted change in kids is γ0.

Now, analyze the statement: “estimate that, holding age fixed, a woman had on average [Fill in the blank], less children in 1982 than in 1972.” This phrasing is asking for the amount by which the average number of children in 1982 is lower than in 1972. If γ0 is negative, then the difference E[kids | year=1982, age] − E[kids | year=1972, age] = γ0 is negative, indicating fewer children in 1982. In that case, the magnitude of the difference is |γ0| and the sign of γ0 indicates which year has more children. Therefore, the fill-in value should reflect a negative difference when 1982 has fewer children, i.e., the number entered should be −(|γ0|). If the expected difference is 0.56 fewer children, the correct way to express it would be −0.56. If someone enters 0.56 without the minus sign, this would correspond to more children in 1982 than in 1972, which contradicts the phrasing “less children in 1982.”

For the second fill-in: “then further estimate whether it is statistically significant at the 5% level: [YES/NO].” This requires testing whether γ0 is statistically different from zero. The usual test is a t-test: t = γ0 / SE(γ0), where SE(γ0) is the standard error of the γ0 estimate. If |t| is greater than the critical value from the t-distribution (or, equivalently, if the p-value is less than 0.05), we declare the difference statistically significant at the 5% level, and the correct response would be YES. If the p-value is ≥ 0.05, the correct response would be NO.

Now, evaluate potential interpretations of the provided answers:
- If the regression output yields γ0 = −0.56 with SE(γ0) such that |t| ≥ 2 (typical for a 5% two-sided test with moderate degrees of freedom), then the magnitude 0.56 represents the absolute difference, and the sign indicates fewer children in 1982. The proper fill for the magnitude would be −0.56 when the instruction asks for the number with the sign that reflects the direction of the difference. If the system accepts just the magnitude with a minus sign to reflect the direction, the entry should be −0.56.
- The YES/NO response depends on the t-test result. If the p-value associated with γ0 is below 0.05, the correct choice is YES (the difference is statistically significant at the 5% level); if not, it is NO.

Common pitfalls and misconceptions to avoid:
- Mixing up the sign: remember that y82 = 1 for 1982, so a negative γ0 means fewer kids in 1982 relative to 1972. The question asks for how much fewer, so the sign matters for the first blank.
- Confusing statistical significance with practical significance: even a sizable −0.56 difference might not be statistically significant if the standard error is large; always check the t-statistic or p-value.
- Assuming the magnitude is always negative when 1982 has fewer children; the actual sign depends on the estimated γ0 from the data, so you must rely on the regression output.

In summary, the first fill-in asks for the directional difference in expected kids between 1982 and 1972 at fixed age, which should reflect the sign and magnitude of γ0 (e.g., if the difference is 0.56 fewer children, the appropriate numeric entry should be −0.56, not 0.56). The second fill-in requires determining whether γ0 is statistically significant at the 5% level by examining the t-statistic or p-value for γ0. If the test rejects zero at 5%, answer YES; otherwise, NO.

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