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Use the data in APPLE for this exercise. These are telephone survey data attempting to elicit thedemand for a (fictional) "ecologically friendly" apple. Each family was (randomly) presented with aset of prices for regular apples and the ecolabeled apples. They were asked how many pounds of eachkind of apple they would buy.(i) Of the 660 families in the sample, how many report wanting none of the ecolabeled apples atthe set price?(ii) Does the variable ecolbs seem to have a continution over strictly positive values?What implications does your answer have for the suitability of a Tobit model for ecolbs?(iii) Estimate a Tobit model for ecolbs with ecoprc, raminc, and hhsize as explanatoryvariables. Which variables are significant at the 1$\%$ level?(iv) Are faminc and hisize jointly significant?(v) Are the signs of the coefficients on the price variables from part (iii) what you expect? Explain.(vi) Let $\beta_{1}$ be the coefficient on ecoprc and let $\beta_{2}$ be the coefficient on regprc. Test the hypothesis $\quad \mathrm{H}_{0} :-\beta_{1}=\beta_{2}$ against the two-sided alternative. Report the $p$ -value of the test. to refer to Section $4-4$ if your regression package does not easily compute such tests.)(vii) Obtain the estimates of E(ecolbs, x) for all observations in the sample. [See equation $(17.25) .1$ Call these $\overline{e c o l b s}_{i}$ . What are the smallest and largest fitted values? (viii) Compute the squared correlation between $e c o l b s_{i}$ and $\widehat{e c o l b s}_{i}$(ix) Now, estimate a linear model for ecolbs using the same explanatory variables from part (iii). Why are the OLS estimates so much smaller than the Tobit estimates? In terms of goodness-offit, is the Tobit model better than the linear model?(x) Evaluate the following statement: "Because the $R$ -squared from the Tobit model is so small, the estimated price effects are probably inconsistent."

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(i) 248 (ii) no (iii) see video (iv) yes, in accord with demand theory (v) no (vi) .7 to 3.3 (vii) .04 (viii) Tobit no better (ix) incorrect

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Chapter 17

Limited Dependent Variable Models and Sample Selection Corrections

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Gamze Y.

December 26, 2020

can you share the r codes of the example with me?

Foster J.

December 5, 2021

Why are the OLS estimates smaller than the Tobit estimates?

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first one. There are 248 families do not want the apples at any price Or two. So distribution is not continuous, There is focal points and rounding for example. Many people report on powder and either 2/3 of a pound or one and a third pounds. This the fact that the distribution of quantity demanded is not continuous violates the underlying assumption of the topic model. Yeah. Which is the Layton error has normal distribution, but we will still explore the Tobin approach in this context. Yeah. It may work better than the linear model for estimating the expected demand function, do you? And Along with Part eight. The estimates from their topic and L. S.. Models are reported in the same table or the tablet model. The price variables ali them are Statistically significant at the one level. The sign over these prize coefficients are in accordance with the demand theory, the own price effect is negative and across price effect is positive. Cross price is the price of this substitute good, which is regular apples part Let's do part 6. 1st part six we will obtain their fitted values and we find that the ranged from 27 8 798 to you. 3.33 at five. The null hypothesis is later one plus beta two equals zero. This is something you can easily test regardless of your statistical package. Yeah. Yeah, you should get a small T statistic about minus point you and a P value of buying eight. So we are unable to reject the North part seven. The squirt correlation between it is E call B. S and it's fitted value is about .04 and that is there are square hard eight. Given the linear model estimates, even this result, we find that the old LS estimate are smaller than the top bit estimate. And in terms of our square oops, you compare the goodness of fit between the two models we look at. There are square mhm. There are squared of the topic. Model is still smaller, slightly smaller than the old LS model and serve. We can conclude that the topic is yeah, no better than the old LS. It doesnt suite the data better. The Last Part, Part nine. The statement is simply incorrect so you could run into a uh counter example. We have valid price effects, but we cannot explain much of the variation in the dependent variable. It's simply difficult to estimate the demand for a fictitious product.

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