ECM308 - Econometrics Assignment

Assignment Task

Part I

The objective of the questions in this section is to check your understand of the econometric concepts introduced in the lectures. Hence, you must do all the required calculations by hand and present the working steps in detail.

1. Let the residuals from a fitted straight line be denoted by

ei = Yi − Yˆ i = Yi − a − bXi i = 1, 2, . . . , n,

where a and b denote estimates of the unknown parameters. Perform tasks (a) to (e) below based on the data given in Tables 1 and 2. 

(a) Compute the least square estimates of the unknown parameters.

(b) Compute the Coefficient of Determination and comment. 

(c) Compute the variances of the least square estimates. 

(d) Compute the 95% confidence intervals of the population parameters and provide logical interpretation.

(e) Perform the hypothesis test of significance and draw some logical connection with your answers to Question 1(d).

2. The Phillips Curve is a well-known concept in economics, which explains the systematic relationship between changes in the wage rate and the level of unemployment. Let wt be the wage rate in time t, then the percentage change in the wage rate can be formulated as %∆wt = wt−wt−1 wt−1 . Also, let dt denote the excess demand for labor and assume that the percentage change in the wage rate is proportion to the excess demand for labor. That is

%∆wt = γdt, 

where γ is an economic parameter. Moreover, let ut denote the unemployment rate. Assume that the unemployment rate is inversely related to the excess demand for labor and that the relationship can be represented by the reciprocal function

dt = α + η (1/ut),

where α and η are economic parameters. Explain how you may use a simple regression model to empirically study the relationship between changes in the wage rate and the level of unemployment. 

3. In our lecture, we have derived the normal equation

(X′X)b = X′y

(a) Specialize equation (3) to the three-variable case of the regression model. That is

Y = β1 + β2X2 + β3X3 + u,

where u is the error term.

(b) Starting from (3), solve for the least-squares estimators b2 and b3. For simplicity, you may assume (in this case) that β1 = 0. 

Part II

The objective of the questions in this section is to ensure that you can apply econometric concepts introduced in the lectures to analyze real world data and provide appropriate interpretation of the results. You may complete these questions by using Stata statistical software. The data set FERTIL2.dta contains information on a large sample of women living in Botswana in 1988. The variable children refers to the number of living children.

4. Consider the regression model where variable children is regressed on age, age2 (that is, age in quadratic form), educ, electric, urban, and the three religious affiliation dummies. 

(a) Write down this linear regression model in matrix notation. Estimate the model and report the estimation output. Describe how the software computed the coefficients of the regression.

(b) Interpret the estimated coefficient on educ. In particular, holding age, electric and urban fixed, what is the estimated effect of another year of education on fertility? How many more (or less) children are they expected to have among them if 1000 women receive another year of education?

(c) Interpret the estimated coefficient on electric. What does the estimated parameter measure? In your explanation make sure that you identify the reference group in the regression. 

(d) In this regression, is the parameter on age on its own of much interest? Explain your answer. 

5. In the regression from question 4, explain carefully how you would test the null hypothesis that having electricity does not have a statistically significant effect on the number of children against a two-sided alternative. (Be sure to write down the hypotheses and the test statistic that you are working with.) What is the p-value of the test? With the help of a graph, explain what a p-value means for this test. Last, say if you reject the null at the 1% significance level.

6. In the regression from question 4, explain carefully how you would test the null hypothesis that the religious affiliation does not have a statistically significant effect on the number of children. Say if you reject the null at the 5% significance level. 

7. To the regression in question 4 add an interaction between electric and educ; that is, add regressor electric × educ.

(a) Explain carefully what the coefficient on the interaction term measures. How does the coefficient on electric compare with that in question 4? 

(b) Explain whether you prefer regression specification in this question to the smaller model in question 4. 

This ECM308 - Statistics Assignment Help has been solved by our Statistics Experts at My Uni Paper. Our Assignment Writing Experts are efficient to provide a fresh solution to this question. We are serving more than 10000+ Students in Australia, UK & US by helping them to score HD in their academics. Our Experts are well trained to follow all marking rubrics & referencing style.