You are interested in the influence of education on hourly wages.Table 1: Description of VariablesVariable Descriptionwage Hourly wage (in €)educ Education in yearsSelect the population model with which the interpretation below is possible.The hourly wage of a person increases by x € if the education of the person increases by one percent (ceteris paribus).Answer 1Answer 2Answer 3Answer 4
Question
You are interested in the influence of education on hourly wages.Table 1: Description of VariablesVariable Descriptionwage Hourly wage (in €)educ Education in yearsSelect the population model with which the interpretation below is possible.The hourly wage of a person increases by x € if the education of the person increases by one percent (ceteris paribus).Answer 1Answer 2Answer 3Answer 4
Solution
The question is asking for a model that would allow for the interpretation that an increase in education by one percent leads to an increase in hourly wage by x €, all other things being equal (ceteris paribus).
This implies a model where the dependent variable (wage) is influenced by the independent variable (educ) in a way that a percentage change in education leads to a change in wage. This is typically represented by a log-linear model, where the natural logarithm of the dependent variable is regressed on the independent variable.
However, without the specific models provided in the options (Answer 1, Answer 2, Answer 3, Answer 4), it's impossible to select the correct one.
In general, the model would look something like this:
ln(wage) = β0 + β1*educ + ε
Where:
- ln(wage) is the natural logarithm of the wage
- β0 is the intercept of the model
- β1 is the coefficient for education
- educ is the years of education
- ε is the error term
In this model, β1 can be interpreted as the percentage change in wage for a one unit increase in education, holding all other variables constant.
Similar Questions
In this exercise we examine which factors might influence the wages of employees. To do so, the variable wage is regressed on the variables educ, tenure, tensq, female, married, and m_female.Table 1: Descriptive StatisticsVariable Explanationwage Average hourly wage (in €)educ Years of educationtenure Employment duration (current employer)tensq = tenure × tenurefemale dummy (= 1 if female)married dummy (= 1 if married)m_female Interaction term (= married × female)The corresponding Stata output is:Source | SS df MS N. of obs. = 526 + F(6, 519) = 57.23 Model | 2851.181 6 475.197 Prob > F = 0.000 Residual | 4309.233 519 8.303 R-squared = 0.398 + Adj. R-sq. = 0.391 Total | 7160.414 525 13.639 Root MSE = 2.882 wage | Coef. S. Err. t-stat. P > |t| [95% Conf. Int.] + educ |0.522 0.046 ? ? ? ? tenure | 0.263 0.046 5.69 0.000 0.172 0.354 tensq | -0.005 0.002 -2.77 0.006 -0.008 -0.001 female | -0.321 0.408 -0.79 0.431 -1.123 0.480 married | 1.807 0.389 4.65 0.000 1.043 2.571 m_female | -2.326 0.526 ? ? ? ? _cons | -2.012 0.662 -3.04 0.002 -3.313 -0.711 Reference: Wooldridge, J. (2013). Introductory Econometrics, 5E. © 2013 South-Western, a part of Cengage, Inc. Reproduced by permission. www.cengage.com/permissions.Does educ have a significant relationship with the outcome wage? State the associated null hypothesis and alternative hypothesis for the coefficient βeduc. Also, determine its statistical significance at the 5 percent significance level in a two-sided test. Which one is the correct answer?Answer 1H0: vs. H1: c(0.05, 526-6-1) = 1.645⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 2H0: vs. H1: c(0.05, 526-6-1) = 1.645⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 3H0: vs. H1: c(0.05, 526-6-1) = 1.960⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.Answer 4H0: vs. H1: c(0.05, 526-6-1) = 1.960⇒ t > c⇒ H0 can be rejected at the 5 percent significance level.
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