1. Suppose that we are interested in measuring the relationship between hourly wage and output productivity in the U.S economy. Variables hrwage, and outphr, denote the average hourly wage and output productivity in the U.S economy for year t. We start by estimating the model specification shown in equation (1) below log(hrwage) = -5.2 +1.53 log(outphr.), (0.033) (0.09) n = 41, R² = 0.967. i. Briefly comment on the value of the coefficient of determination, R², as shown in (2). ii. Test the null hypothesis that the elasticity of output productivity on hourly wage is zero against its two-tailed alternative at the 95% significance level. iii. Show how you can use the coefficient of determination, R², to test the null hypothesis that B₁ is equal to zero against ₁0 at the 95% significance level. How does your answer compare to that in (ii)?

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1. Suppose that we are interested in measuring the relationship between hourly wage
and output productivity in the U.S economy. Variables hrwage, and outphr, denote
the average hourly wage and output productivity in the U.S economy for year t. We
start by estimating the model specification shown in equation (1) below
log(hrwage) = -5.2 +1.53 log(outphr.),
(0.033) (0.09)
n = 41, R² = 0.967.
i. Briefly comment on the value of the coefficient of determination, R², as
shown in (2).
ii. Test the null hypothesis that the elasticity of output productivity on hourly
wage is zero against its two-tailed alternative at the 95% significance level.
iii. Show how you can use the coefficient of determination, R², to test the null
hypothesis that B₁ is equal to zero against $₁0 at the 95% significance
level. How does your answer compare to that in (ii)?
Transcribed Image Text:| 1. Suppose that we are interested in measuring the relationship between hourly wage and output productivity in the U.S economy. Variables hrwage, and outphr, denote the average hourly wage and output productivity in the U.S economy for year t. We start by estimating the model specification shown in equation (1) below log(hrwage) = -5.2 +1.53 log(outphr.), (0.033) (0.09) n = 41, R² = 0.967. i. Briefly comment on the value of the coefficient of determination, R², as shown in (2). ii. Test the null hypothesis that the elasticity of output productivity on hourly wage is zero against its two-tailed alternative at the 95% significance level. iii. Show how you can use the coefficient of determination, R², to test the null hypothesis that B₁ is equal to zero against $₁0 at the 95% significance level. How does your answer compare to that in (ii)?
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