Ambo University School of Graduate Studies Department of Economics Assignment on Advanced Econometrics Total mark allowed: 20% Submission: On final examination day Note: The assignment should be hand written Part I: Theory Section 1. In a regression, explain why we include a disturbance term. 2. Briefly explain how ordinary least squares (OLS) works and derive OLS estimator. 3. Briefly discuss the assumptions underlying the Classical Linear Regression Mode and the properties of OLS estimator. 4. Concisely discuss the classical linear regression model diagnostics focusing on causes, consequences, and solutions for Heteroscedasticity, autocorrelation, multicollinearity, non-normality and omitted variable bias as well as model specification error. 5. What is the difference between fixed effect and random effect estimators? Which test will assist you to choose between the two estimators? Outline the stata command helpful for identifying an appropriate estimator for estimating regression that uses panel data 6. Distinguish logistic/probit estimator from tobit estimator. How do would you decide whether logistic/probit or tobit is an appropriate estimator to apply. 7. What is a spurious regression? When does such a regression possibly occur? 8. What do we mean by a non-stationary variable? Identify a statistical test which is commonly used to determine whether a variable is stationary or non-stationary. If a variable is non-stationary at level, how do you transform it to stationary one? Explain. Part II: Application Section 1. Write down a stata command for generating a new variable 2. Write down a stata command useful for calculating summary statistics for a continuous variable 3. Write down a stata command useful for drawing a scatter plot between two variables say Y and X 4. Indicate a stata command for determining functional form of a continuous variable say Y 5. Write down a stata command to run a regression based on the following information - Dependent variable : y - Independent variables : x1, x2, x3, z1, z2 - Suppose that z’s enter the model in logarithmic form while the x’s enter the model in their level form. - Use robust option 6. Repeat question (5) if the dependent variable’s values range between two values (𝛾 and 𝛿) such that 𝛾 ≤ 𝑦 ≤ 𝛿. 7. Write down procedures for Breusch-Pagan / Cook-Weisberg and White tests for heteroskedasticity 8. Show procedures for Durbin-Watson test for autocorrelation in stata. Clearly indicate how to interpret the results. 9. Show the steps you need to follow to test for multicollinearity using stata command 10. How do you test for omitted variable bias using a stata command? 11. Outline Hausaman’s test for choosing between fixed and random effect estimators. Part III: Interpreting regression results The following table summarizes regression results obtained by regressing logarithm of wage [𝑙𝑜𝑔(𝑤𝑎𝑔𝑒)] on a number of covariates. OLS, Random Effects as well as Fixed effects results are reported in the table. The right hand side variables include: educ (respondent’s education level in years); black (dummy variable = 1 if the respondent is black; 0 otherwise); Hispanic (dummy variable = 1 if the respondent is Hispanic; 0 otherwise); exper (work experience in years); exper2 (square of work experience in years); married (a dummy variable =1 if the respondent is married; 0 otherwise); union (a dummy variable =1 if the respondent is a member of a labour union; 0 otherwise). Numbers in the paranthesis are standar erros. Table 1: Estimation of Wages Earned 1. Identify statistically significant variable in the thee regressions 2. Interpret statistically significant coefficients. You could refer to theories, previous studies as well as your intuition whenever necessary. Table 2: Estimations of Annual Hours Worked where kidslt6 denotes the number of children less than six years old and kidsge6 stands for number of kids between 6 and 18 years of age. age is age in years and nwifeinc is the woman’s nonwage income and the other variables are as explained before. 1. Identify statistically significant variable in the thee regression 2. Interpret statistically significant coefficients. You could refer to a theory and/or previous studies as well as your intuition.
