__QUESTION__** : – In the question two alternative regression models have been given. The students are required to estimate both the models using OLS method and subsequently answer a series of questions. It is needed that students answer the questions and also submit the GRETL output.**

__SOLUTION__** : –**

**Q1. Model A & Model B**

(1) Provide a summary report for each model by writing down the estimated equation and

relevant statistics including the standard errors.

**MODEL A**

(…) Standard errors of coefficients estimates

*R²=23.98% and adj-R²= 23.366%*

*F=39.037 (Significant at 1% level)*

*LL=-2163.016*

*AIC= 4336.032*

*N=500 *

**MODEL B**

(…) Standard errors of coefficients estimates

*R²=30.047% and adj-R²= 29.482 %*

*F=53.155 (significant at 1% level)*

*LL=-252.7880*

*AIC= 515.5759*

*N=500*

(2) Discuss whether each of the estimated coefficients has the expected sign

**Model A and Model B**

- EDUC have the expected + (positive) sign. We expect that more educated workers have a higher WAGE.
- EXP and EXP² have the expected + (Positive) and – (negative) signs respectively. EXP have a positive impact on WAGE. The negative sign of EXP² indicate a turnaround effect of experience on wage.
- CTEST have the expected + (positive) sign. Best score has positive impact on WAGE.

For the two models A and B, the coefficients estimates have the expected signs.

**Q2. Model A**

Interpret the estimated coefficients. (N.B. Do not try to interpret α3 and α4 separately, but

interpret the marginal effect of experience on wage rate, which includes both α3 and α4.)

- Coefficient of EDUC:

The estimated coefficient of the EDUC suggests that, when the number of years of education goes up by 1 year, and other variables are held constant*(ceteris paribus)*, the average hourly wage will increase by the amount 2.888 $.

- Coefficients of EXP and EXP²:

The estimated coefficient of the EXP and EXP² suggests that we have decreasing marginal effect of Experience (EXP) on RHW. Estimates values of show the presence of Turning point (or turnaround value) at :

We say, that when experience exceed 31 years, an additional year of experience will have negative impact on rate of wage. We agree that is unrealistic!

The estimated response of RHW to EXP is:

WhenEXP is at its minimum value in thesample of 0.055 year, the marginal effect of EXP on Wageis 1,488$. WhenEXP is 18 years (the sample mean value), the marginal effect is 0.607$. when EXP exceed 31 years, say 35 years, the marginal effect become negative (-0.224$).

- Coefficient of CTEST:

The estimated coefficient of the CTEST suggests that, when the score of the cognitive test goes up by 1 point, and other variables are held constant*(ceteris paribus)*, the average hourly wage will rise by 0.196 $.

- Constant Coefficient :

The intercept suggests the real Hourly wage for someone with no educational year, no experience and zero in the cognitive test is -31.5 $. However, this figure is unreliable or unrealistic, since there would be no one with a zero score (minimum sample score is 2), no one with no experience (minimum sample experience is 0.055).

**Q3. MODEL A**

(1) Test if each regression coefficient is significantly different from zero. Use the 5%

significance level. For your tests, clearly state the hypotheses, test statistic, its

distribution under the null hypothesis, the observed value of the test statistic, the critical

value (or p-value), decision to reject or not to reject the null hypothesis, and

interpretation of the test result.

- Coefficient of EDUC:

**the null hypothesis is:**

This null hypothesis state that the independent variable EDUC do not explain the RHW.

**The alternative hypothesis** is that EDUC has a significant effect on RHW:

Assuming the classical Linear Model Gauss-Markov Assumption, and the normality assumption hold:

The assumption of normality of distribution is necessary for statistical inference. This hypothesis is justified by the ** Central Limit Theorem and the large size of our sample (N = 500).** This result is very important because it allows us to perform the t-tests, the fisher tests, the confidence intervals and the construction of the forecast intervals.

**Q4. Model A**

(1) Estimate and interpret the elasticity of wage rate with respect to education, evaluated at

the sample mean values of the variables.

The Elasticity of wage rate with respect to education, evaluated at the sample mean values of the variables

**Q5. Model A**

Test if the model as a whole is significant. Use the 5% significance level. For your test,

clearly state the hypotheses, test statistic, its distribution under the null hypothesis, the

observed value of the test statistic, the critical value (or p-value), decision to reject or not to

reject the null hypothesis, and interpretation of the test result. (Assume that the random error

term follows a normal distribution.)

The estimated model is

**Q6. Model A**

Assume that, in another data set, wage rate is measured in hundreds of dollars and education

is measured in months. Explain what would happen to (i) the estimate of α2, (ii) its standard

error, (iii) R2, (iv) the unexplained variation (SSE), and (v) the sample mean of the dependent

variable, if the model were estimated using this data set.

When rescaling dependent and/or independent variables, some change occur in the estimated results.

MODEL B

Q3

Q4

Q5

Q6

RHWH=RHW/100

EDUM=EDU*12

Q7

Q8

Q9

Q10