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## problem 1 a. b. c. d. Econometrics questionECO 321 Fall 2016Homework 3Due Friday Oct 28 by 5 pmPleas

problem 1 a. b. c. d. Econometrics questionECO 321 Fall 2016Homework 3Due Friday Oct 28 by 5 pmPlease also cut and paste at the end of your submission the R code you have usedin problem 2 to show your work. 1. We would like to obtain an estimator of ?1 from the following regression model withonly one independent regressor:yi = ?0 + ?1 x1i + ui . (1) However, there is another variable x2i , which is missing from the model and potentially correlated with x1i . That is, the true model would beyi = ?0 + ?1 x1i + ?2 x2i + vi (2) where vi is an observation error, which satisfies E (vi |x1i , x2i ) = 0.(a) Show that the OLS estimator of ?1 obtained from model (1) is biased.(b) When is this bias equal to 0?(c) Derive the OLS estimators of ?1 and ?2 from model (2).(d) Show that, when the sample covariance between x1i and x2i is equal to 0, thenthe OLS estimator of ?1 derived in (c) is the same as the OLS estimator of ?1derived in (a).2. We are using data to investigate the the relationship between workersâ education(educ) and their wage (wage). The data can be found on Blackboard under thefolder Homework 3. The file wage data.zip contains a database wage data.csvfor full-time, full-year workers aged 28-38. A description of the data is providedin the pdf file wage data descr. You can find a sample code for fitting a linearregression model in R on Blackboard.(a) Suppose that all assumptions for OLS are satisfied and estimate the followingregression model:wagei = ?0 + ?1 educi + ui , i = 1, . . . , n. Report the value of ?Ë1 , and of its heteroskedasticity robust standard error. (b) We conjecture that IQ can also have an impact on the workerâs wage and it ispotentially correlated with the workerâs education. We thus now estimate thefollowing model,wagei = ?0 + ?1 educi + ?2 IQi + ui , i = 1, . . . , n. Report the value of ?Ë1 , and of its heteroskedasticity robust standard error.(c) How has your estimator of ?1 changed compared to (a)? Explain using youranswer to question 1, part (a).