Consider the following OLS regression line obtained from a random sample of 500 workers:

^
log(wage)
=0.3+0.1educ+0.005exper+0.02tenure

(0.1) (0.005) (0.001) (0.003)

where wage is hourly wage (measured in dollars), educ is years of formal education, exper is years of labor market experience, and tenure is years with the current employer. Standard errors appear in parentheses below the estimated coefficients. Assume the classical linear model (CLM) assumptions are satisfied. The lower bound of the 95% confidence interval (CI) for the population parameter βeduc is [lower].

Note: please write your 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.

HINT: Use Table G.2 in your text if the table is printed correctly. Otherwise, see below (ignore highlighted or circled parts that are for other questions):

Question

Consider the following OLS regression line obtained from a random sample of 500 workers:

^
log(wage)
=0.3+0.1educ+0.005exper+0.02tenure

(0.1)    (0.005)        (0.001)               (0.003)

where wage is hourly wage (measured in dollars), educ is years of formal education, exper is years of labor market experience, and tenure is years with the current employer. Standard errors appear in parentheses below the estimated coefficients. Assume the classical linear model (CLM) assumptions are satisfied. The lower bound of the 95% confidence interval (CI) for the population parameter βeduc is [lower].

Note: please write your 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.

HINT: Use Table G.2 in your text if the table is printed correctly. Otherwise, see below (ignore highlighted or circled parts that are for other questions):

BlackTom AI · Accepted Answer

We start by identifying the relevant values for constructing a 95% confidence interval for the population parameter β_educ from the OLS output.
The estimated coefficient on educ is 0.1, and its standard error is 0.005, as shown beneath the coefficient in parentheses in the regression output.
To form a 95% CI under the CLM assumptions, we use the appropriate critical value from the t-distribution. With a large sample size (n = 500) and the usual CLM framework, the t_{0.025, df} is approximately 1.96, which coincides with the standard normal z-value for 95% in large samples.
The formula for the lower bound of the CI is:
beta_hat − t_{0.025} * SE(betahat).
Plugging in the numbers: 0.1 − 1.96 * 0.005 = 0.1 − 0.0098 = 0.0902.
Rounding to two decimal places as requested yields 0.09.
Thus, the lower bound of the 95% CI is calculated to be 0.09.
Note that if one used a slightly different critical value due to a smaller degrees of freedom, the result might differ marginally, but with a sample this large the difference would be negligible and the rounded value would still be 0.09.

AS.440.606.80.SP25 M05: Assignment

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