Please make sure that you present your output and answers in a concise and clean manner. Dont show me endless outputs. Try to summarise or edit your results where possible. QUESTION 1 (30 points) Use the data in AIRBNB for this question. (a) (8 points) Suppose that we want to find the best places in the Sydney Airbnb listing. Lets define a binary variable best for which the overall satisfaction is 4 (out of 5) or greater and also for which there are 25 or more reviews. Estimate a linear probability model relating best to price. Then estimate the same model again but controlling for room type [Hint: Interact with price]. Does it make a difference if you use the usual standard errors or the heteroskedasticity- robust standard errors? Briefly comment on your results [You can summarise your outputs in a table with the relevant estimations and statistics]. (b) (8 points) Now estimate the model of best on price controlling for room type by probit and by logit separately, and compute the marginal effects. Briefly comment and compare with part (a). (c) (6 points) Calculate and interpret the odds ratio of your logistic model in (b) for the price variable only. Show your steps. (d) (8 points) For the probit and the logit model estimated in part (d), obtain the percentage of correctly predicted outcome (or classified). This may involve several steps. Make sure you detail (succinctly) how you do it. And comment on your results. QUESTION 2 (20 points) Use the data in PENSION for this exercise. (a) (3 points) Estimate a linear model for pctstck, where the explanatory vari- ables are choice, age, educ, female, black, married, finc25,..., finc101, wealth89, and prftshr. Why might you compute heteroskedasticity-robust standard er- rors? Compare them to the usual standard errors. (b) (6 points) The sample contains separate observations for some husband-wife pairs. Compute standard errors of the estimates from the model in part a that account for the cluster correlation within family. (These should also be heteroskedasticity-robust.) Do the standard errors differ much from the usual OLS standard errors, or from the heteroskedasticity-robust standard errors? Discuss. [Suggestion: For further information about clustered sampling and clustered standard errors, see Bruce Hansen Econometrics textbook Chapter 4, Section 4.22, pages 123 - 128. Also you can revise our BUSS7904 Lab on Robust standard errors.] (c) (4 points) Estimate the model from part (a) by ordered probit and compute the marginal effects. Briefly comment and compare with the OLS results. (d) (7 points) Estimate E(pctstck|x) for a single woman with 14 years of educa- tion who is 55 years old. Assume she has net worth (in 1989) equal to $125,000 and earns $55,000 a year, and her plan is not profit sharing. Compare this with the estimate of E(pctstck|x) from the linear model. QUESTION 3 (25 points) Use the data in APPLE for this question. These are phone survey data, where each respondent was asked the amount of ecolabeled (or ecologically friendly) apples he or she would purchase at given prices for both ecolabeled apples and regular apples. The prices are cents per pound, and ecolbs and reglbs are both in pounds. (a) (4 points) For what fraction of the sample is ecolbsi = 0? Discuss generally whether ecolbs is a good candidate for a Tobit model. (b) (5 points) Estimate a linear regression model for ecolbs, with explanatory variables log(ecoprc), log(regprc), log(faminc), educ, hhsize, and num5_17. Are the signs of the coefficient for log(ecoprc) and log(regprc) the expected ones? Interpret the estimated coefficient on log(ecoprc). (c) (2 points) Obtain the OLS fitted values. How many are negative? And why? (d) (4 points) Now estimate a Tobit model for ecolbs. Are the signs and statistical significance of the explanatory variables the same as in (b)? What do you make of the fact that the Tobit estimate on log(ecoprc) is about twice the size of the OLS estimate in the linear model? (e) (6 points) Obtain the estimated partial effect of log(ecoprc) for the Tobit model. These partial effects are usually computed using this formula ? E(y|x) = F(x/s)j ?xj where the xj are evaluated at the mean values. Comment briefly. Also obtain the partial effect of the log(regprc) (at the mean values of the xj) and comment briefly. (f) (4 points) Reestimate the Tobit model dropping the variable log(regprc). What happens to the coefficient on log(ecoprc)? What kind of correlation does this result suggest between log(ecoprc) and log(regprc)?

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