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A researcher in Namibia estimated a wage equation for small enterprises using recent data from the Namibia

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A researcher in Namibia estimated a wage equation for small enterprises using recent data from the Namibia Labor Force Survey (LFS) for year 2018. The dependent variable (In_wage) is the logarithm of wage. The explanatory variables are as follows: age (age), age squared (age_2), type of neighborhood in which employed is living (rural: 0 urban area, 1 rural area), sex (sex: 0 male, 1 female), education (educ: 0

primary, 1 vocational education, 2 secondary, 3 higher), working time (w_time: 0 part- time, 1 full-time), interaction between gender and working time and marital status (status: 0 single, 1 married, 2 widow/widower, 3 divorced). Significance level to be used in testing 𝛼 = 0.05 and test results should be justified with respective p-values.

 

The empirical econometric model was specified as follows:

𝐼𝑛 − π‘€π‘Žπ‘”π‘’π‘– = 𝛽0 + 𝛽1π‘Žπ‘”π‘’ + 𝛽2π‘Žπ‘”π‘’2 + 𝛽3π‘Ÿπ‘’π‘Ÿπ‘Žπ‘™ + 𝛽4𝑠𝑒π‘₯ + 𝛽5𝑒𝑑𝑒𝑐 + 𝛽6𝑀 − π‘‘π‘–π‘šπ‘’

+ 𝛽7𝑠𝑒π‘₯ ∗ 𝑀 − π‘‘π‘–π‘šπ‘’ + 𝛽8π‘ π‘‘π‘Žπ‘‘π‘’π‘  + πœ‡π‘–

Using the estimation results as reported below, answer the following question.

1. Are the explanatory variables jointly significant? Explain. [4]

2. Give an interpretation to coefficient of determination. [4]

3. What would you say about the constant term in the model and the constant term in the empirical results on the table? [5]

4. Verify which explanatory variables are statistically significant, while stating their levels of significance. [12]

5. Interpret the results on the table below. [25]

6. What is the importance of adding the square of age (π‘Žπ‘”π‘’2) and the interaction term of gender and working time (sex*w_time) in the model above? [8]

7. Is the heteroscedasticity problem present in the estimated results? Explain [4]

8. Is the error term normal in the estimated model? Explain [4]

9. Check whether the linear functional form of the model is valid. Explain. [4]

10. If estimated model does not satisfy the assumptions of CLRM:

a. which assumptions of CLRM are invalid? [5]

b. what consequences does it have on statistical inference for this model? [10]

c. how the problems indicated by diagnostic tests could be solved? [15]

 

 

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