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

To begin, restate the setup in your own words so the interpretation is clear: the model is kidsit = β0 + β1*ageit + γ0*y82it + uit, where y82 is an indicator that equals 1 for the year 1982 and 0 for 1972. The coefficient γ0 therefore captures the average difference in the number of children (kids) between the year 1982 and the year 1972 when age is held fixed.

Now, examine the first blank: the prompt asks you to estimate how many fewer children a woman had on average in 1982 than in 1972, holding age fixed. This is the same as the difference in the conditional mean of kids between the two years, which is precisely γ0. If the regression yields a negative γ0, that means fewer children in 1982 relative to 1972. If γ0 is positive, it would imply more children in 1982. Therefore, the sign matters critically: a negative value indicates fewer children in 1982, while a positive value indicates more.

In the context of the placeholder instruction about formatting, you’re told to write the first answer as a number with two decimals, including a leading minus sign if appropriate, and with a period as the decimal separator. The magnitude is the estimated difference in means, holding age fixed. When you fill this in from the regression output, you’ll report γ0 interpreted as the average difference (1982 minus 1972) in the number of children, with the sign indicating the direction of the difference.

Turning to the second blank, you’re asked to assess whether that estimated difference is statistically significant at the 5% level. This requires using the standard error of the γ0 estimate from the regression and forming a t-statistic: t = γ0_hat / SE(γ0_hat). The two-sided 5% critical value (for a large sample) is about 1.96. If |t| ≥ 1.96, you reject the null hypothesis that γ0 = 0 at the 5% level and would say YES the difference is statistically significant; otherwise, you would say NO. In practice, you’d look at the regression output (the coefficient on y82 and its standard error) to determine this.

Consider potential pitfalls or clarifications that can affect interpretation:
- Because the model controls for age only linearly through β1, any nonlinear effect of age that is not captured could bias γ0 if age and year interact in affecting kids. If you suspect that age matters differently across years, you might consider including an interaction term between age and y82, though that is not in the specified model.
- The instruction to use data only from 1972 and 1982 means γ0 captures the simple year effect within that restricted sample. If the data structure or sample sizes differ by year, standard errors could be impacted, which in turn affects the significance test.
- Formatting and reporting conventions matter for the assignment: ensure you present the numeric difference with two decimals and the sign correctly, and report YES/NO in all caps for significance as requested. When calculating SE and t, ensure you’re using the regression output corresponding to the restricted sample.

If you come out with a negative γ0_hat, that aligns with the narrative that 1982 had fewer children on average than 1972, all else equal. The significance decision (YES vs NO) depends on whether the ratio γ0_hat/SE(γ0_hat) exceeds the critical threshold in absolute value. Remember: the conclusion about significance follows directly from the t-statistic and its comparison to 1.96 for a two-tailed test at the 5% level.

AS.440.606.50.SP25 M12: Assignment

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