Assignment 231541251
Assignment 2
This assignment is based on the data set in “CHARITY.RAW”, see also tutorial exercises C2.7 and C7.14. The definitions of variables are in the file “CHARITY.DES”. To examine what influence individuals’ decisions on donations, the linear regression model respond = β0 + β1 resplast + β2 avggift + β3 propresp + β4 mailsyear +u is used. For hypothesis-testing questions, please always present hypotheses, test statistic and its distribution under the null, decision rule and conclusion.
a) Why the model is known as a linear probability model (LPM)? What is the meaning of β1?
b) Suppose that MLR.1-4 hold for the model when all variables are correctly measured. Further suppose that respond is measured with error: respond = respond* + e (i.e., observed = truth + error). Would the OLS estimators of ’s still be unbiased and consistent and why?
c) Suppose that MLR.1-4 hold for the model when all variables are correctly measured. Further suppose that one regressor, mailsyear, is measured with an additive error and the error is uncorrelated with the truth mailsyear*. How would the OLS estimator of, say, β1 be affected by the measurement error and why?
d) Estimate the model, using OLS, and interpret the estimate of β4. Find “het.-robust” standard errors and compare these with the usual OLS standard errors.
e) Test for the presence of heteroskedasticity, using the Breusch-Pagan LM test.
f) Suppose that MLR.1-4 hold for the model. Find the expression for Var(u|all regressors).
g) Given your answer to f), how would you use weighted least squares (WLS) to estimate the model? What would be the weights for the WLS? Practically, what may prevent you from implementing the WLS?
h) Re-estimate the model, using FGLS with the textbook equation (8.32). Compare the estimates with those in d).
i) Test for possible model misspecifications, using the RESET. What does your conclusion suggest?
Notes on Assignment 2
Your answers to the above questions must
This assignment is based on the data set in “CHARITY.RAW”, see also tutorial exercises C2.7 and C7.14. The definitions of variables are in the file “CHARITY.DES”. To examine what influence individuals’ decisions on donations, the linear regression model respond = β0 + β1 resplast + β2 avggift + β3 propresp + β4 mailsyear +u is used. For hypothesis-testing questions, please always present hypotheses, test statistic and its distribution under the null, decision rule and conclusion.
a) Why the model is known as a linear probability model (LPM)? What is the meaning of β1?
b) Suppose that MLR.1-4 hold for the model when all variables are correctly measured. Further suppose that respond is measured with error: respond = respond* + e (i.e., observed = truth + error). Would the OLS estimators of ’s still be unbiased and consistent and why?
c) Suppose that MLR.1-4 hold for the model when all variables are correctly measured. Further suppose that one regressor, mailsyear, is measured with an additive error and the error is uncorrelated with the truth mailsyear*. How would the OLS estimator of, say, β1 be affected by the measurement error and why?
d) Estimate the model, using OLS, and interpret the estimate of β4. Find “het.-robust” standard errors and compare these with the usual OLS standard errors.
e) Test for the presence of heteroskedasticity, using the Breusch-Pagan LM test.
f) Suppose that MLR.1-4 hold for the model. Find the expression for Var(u|all regressors).
g) Given your answer to f), how would you use weighted least squares (WLS) to estimate the model? What would be the weights for the WLS? Practically, what may prevent you from implementing the WLS?
h) Re-estimate the model, using FGLS with the textbook equation (8.32). Compare the estimates with those in d).
i) Test for possible model misspecifications, using the RESET. What does your conclusion suggest?
Notes on Assignment 2
Your answers to the above questions must