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# regression output for the following equation

4. The following is the regression output for the following equation, which was estimated for a large sample of people:

log(wage) = &#945; + &#946;1Schooling + &#946;2Age + &#946;3Female + &#946;4Non-white

Variable Coefficient estimate (&#946;-hat) Standard error

Schooling (years) .134 .024

Age (years) 0.009 0.002

Female -0.021 0.001

Non-white -0.014 0.003

(a) Calculate the t-statistics and discuss which variables are statistically significant.

(b) What do the estimates imply is the percent wage increase associated with an additional year of schooling?

(c) Why might the estimated effects of some of the variables be overstated? Provide some examples of what might lead to the overstatement.

(d) What if one could fully deal with the problems in (c) by adding variables to the estimation equation? Is there any reason to believe that the resulting estimates of the effect of schooling would then be understated?

(e) Explain why estimating the following regression equation might fail to capture the sheepskin effect.

#### Solution Preview

labor economics
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4. The following is the regression output for the following equation, which was estimated for a large sample of people:

log(wage) = α + β1Schooling + β2Age + β3Female + β4Non-white

Variable Coefficient estimate (β-hat) Standard error

Schooling (years) .134 .024

Age (years) 0.009 0.002

Female -0.021 0.001

Non-white -0.014 0.003

(a) Calculate the t-statistics and discuss which variables are statistically significant.

Ans:
With the given information,

t- Statistics = coefficient of the estimate / standard error.

(i) t^ β1 = .134 /.024

= 5.583

Since the estimation is for larger samples, the t-table value at  degrees of freedom for 5% significance level is 1.645.

As the estimated value (t^ β1) is greater than the table value, the variable β1 is statistically significant & positively related with the dependent variable (wage).

(ii) t^ β2 = 0.009 / 0.002

...

#### Solution Summary

Examine a regression output for the following equation.

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