7/25/2019 ETC1010 S12015 Solution Part 1

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Question 1: Spreadsheet Modelling

Murdock realty manages real estate investment properties, such as, condominiums and com-mercial real estat. For each rental property, the company has two associated revenue streams:administrative fees assocaited with maintaining the investment properties and fees associatedwith managing each investment property. In addition to the revenue streams, Murdock realty

has several cost outlays associated with managing each individual property: labor costs, leasingcosts for the building Murdock realty operates out of, marketing costs associated with the Mur-dock realty website, and additional expenses. Use the above information and Figure 1 to answerthe following questions.

(A) Murdock realty is currently trying to expand into new markets. To do so, they need toraise new capital, which will require borrowing money from a bank. As part of their loanapplication the bank has asked Murdock realty to explain their business model, includingall revenue and cost streams. Dram an influence diagram that accurately represents thisinformation and how these different pieces relate to company profit. (4 pt)

(B) Consider the spreadsheet model in Figure 1. Currently, Murdock realty charges a flat

management fee per managed property. The current fee is 250$. Determine, using Figure1, how profit will change if the management fee is increased to 325$ (assuming the samenumber of clients is retained). Do you expect the same number of clients to be retainedafter Murdock realty increases the management fee? (5 pt)

(2pt) Revenue will increase and costs will stay the same, therefore profit will increase.

(2pt) old = 500, new= 1250 which yields a percentage increase of 150%

(1pt) However, basic economics says that, ceteris parabus, as price increases quantity de-manded decreases. Therefore, it is unlikely that the same number of clients will beretained with the new pricing scheme.

(C) Murdock realty currently has labor costs and revenues given in Figure 1. Murdock realtywould like to give its employees a raise. Using Figure 1, determine how much Murdockrealty can increase their employees hourly wage before earning zero profit (holding every-thing else constant). Explain how this can be answered using native spreadsheet functionsin excel. (6 pt)

The simplest way to solve this is to use guess and verify. I showed them howthat if x [a, b] and f() is continuous on [a, b], with f(a) > 0, f(b) < 0, f()crosses zero at a value (Rolls theorem, aka, mean value theorem). If we start

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off with 18$ we get a positive number, going to 19$ we get a negative. Theanswer must therefore lie somewhere in the middle. The actual answer is 18.57.So, Murdock realty can increase the wage of every employee by 3.57. If theyget close to this, and state how they obtained the answer, the student shouldreceive full credit. This can easily be answered in excel using the goal seekfunction.

(3pt) They should recognize that this is similar to what I have done in the review lectureand so they should mention somthing like: ifx [a, b] andf() is continuous on [a, b],with f(a)>0, f(b)

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(A) From the output given in Figure 2, state the regression model that is being estimated. (1pt)

Ans: ln(wage) =0+1 age+2 exp+3 educ+ they either get it or they dont.

Figure 2: Awesome Image

(B) What percentage of the variation in ln(wage) is explained by this model and state whetheror not this model is a good fit? (2 pt)

About 15% of the variation can be explained by the three covariates. Withonly 428 observations the model fit is adequate but not spectacular.

(1pt) for correct percentage: 15% of the variation can be explained by the three covariates

(1pt) for correct interpretation of fit. Accept statements that say fit is adequate or notgreat.

(C) Calculate the coefficient estimate of education. (3 pt)

The coefficient has not been given so it will need to be backed-out usingtval =/std. Using this formula we have that educ= 7.69489 .014201 .10927.

(2pt) for those who get the right formula to back out the coefficient.

(1pt) for correct answer.

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(D) Using the information in Figure 2 and your knowledge of the student t-distribution, andstandard normal distribution, report an approximate 95% confidence interval for the co-efficient of experience (3pt). Please state why you are only able to build an approximate95% confidence interval (2 pt). (total = 5pt)

By design, the t table will not be given so the students will not be able to get

the exact critical value. However,in this example we can use tLarge,.0251.96 forthe critical value to obtain the approximate interval:

(.11 1.96 .0142, .11 + 1.96 .0142) = (.082168, .137832)

(1pt) for correct approximation for t-distribution of 1.96.

(1pt) for correct formula for confidence interval using approximation 1.96.

(1pt) for correct answer (.082168, .137832).

(1pt) for knowing that the interval is approximate because they are using a normal whenthey should be using a student-t

(1pt) for knowing that the correct degrees of freedom for the student-t is 42831 = 424.

(E) We know from class that 95% CIs can be used to conduct two-sided hypothesis tests. Is atwo-sided hypothesis test for education appropriate in this example (2 sentence maximumplease)? (3 pt)

A two-sided hypothesis test does not account for any prior information wehave about the effect of the variable of interest on the outcome variable. Ifthis were the case with education, we would be saying that an additional yearof education could have a negative impact on wages. No, a two-sided test isnot appropriate

(1pt) for those who note the stem of the question gives prior information about the sign ofeducation in this regression, and hence the appropriateness of the two-sided test.

(1pt) for those who acknowledge that testingeduc= 0 implies the effect of this sign couldbe negative.

(1pt) for those who just answer no.

(F) Conduct a one-sided approximate hypothesis test for a positive educational affect at the95% level (please state all testing steps) (4 pt). Why is the test approximate? (1 pt) (total= 5)

(1pt) for those who answer something like: Since t428,.05 is not given we can use thecorresponding z.05 = 1.645 value to conduct the test. This is why the testis approximate.

(1pt) for each of the following four pieces of the test. These are either correct or not, nopartial credit.

(1) Hypothesis. Ans: H0: educ= 0 vs. Ha : educ> 0

(2) T.S.Ans: teduc= 7.69489

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(3) C.V. Ans: The critical value is t428,.05 since we are not given this value we canuse Use 1.645(since N is large).

(4) Decision rule: RejectH0 ifteduc> tC.V.. Ans: Reject teduc> 1.645.

(G) In the observed sample there are many missing values for wages, as not all individuals inthe sample were employed at the time the sample information was collected.

(G.1) State the missing data method used to generate the regression results in Figure 2. (1pt)

(1pt) Discarding individuals from the sample that are unemployed.

(G.2) Does the missing data method in [G.1] place any restrictions on how the coefficientsin the regression output can be interpreted? (3 pt)

Yes, similar to the College football revenue example in class, the regressionestimates can only be interepreted accurately for individuals in the sample.Which means that these results are only valid for individuals who wereemployed at the time of the sample, which is a rather sever restriction in

terms of policy impact.(2pt) for knowing that the coefficients can only be interpreted for individuals who were

employed.

(1pt) for noting that this is a severe restriction.

(G.3) State two possible ways of dealing with the missing values for lwage. For one of thetwo methods, give a short description as to why this method may be appropriate. (2pt)

As in the previous regression results, we could simply throw out thoseindividuals for which the data are missing. In addition, we could imputevalues for the missing observations using some model. If they give reason-able answers give them the points.

(H) Figure ?? contains regression output associated with an alternative way of dealing withthe missing values.

(H.1) From the given output, obtain and interpret the coefficient estimate for education (3pt)

Unlike the previous regression output, it seems now we are given even lessinformation. But we are now given the excel confidence intervals whichtells us

CIl= 1.96 std = =CIl+ 1.96std .0615.

The coefficient can be interpreted in the standard way since we have im-puted the missing values (Note that N=753).

(1pt) for noting that they have to use the normal approximation here.

(1pt) for correct formula to obtain coefficient estimate. It must include the normalvalue since they wont have the t-value memorized

(1pt) for the correct approximate answer. Anything close to .0615 give them the points.

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(H.2) Using the regression output in Figure ??, test the null hypothesis that there is noeffect of education on wages. (please include all testing steps) (3pt)

(1) Hypothesis. Ans: H0: exper = 0 vs. Ha : exper = 0

(2) T.S.Ans: Must use the confidence interval since no exact t-stat is given

(3) Decision rule: RejectH0 if 0 (CIl, CIh). Ans: Reject H0

(2pt) for listing all testing steps correctly. Their can be variations in the above sincewe are using the confidence interval approach to testing the null.

(1pt) for correct conclusion

(H.3) Compare and contrast the coefficient estimates from education and experience acrossthe two methods for dealing with the missing data. What do these results say aboutthe appropriateness of the two missing data methods? (4 pt)

The first thing they will need to do is back out, using the same methodas above, the coefficient from experience. Which is about exper .0065(1pt). Both coefficient estimates are smaller than their corresponding

counterparts obtained when simply throwing out the observations of non-employed individuals. However, they are not strikingly different (2pt).The second method yields coefficient estimates that are about half as largeas those obtained by the first method, but both sets are significant and theyhave the same sign. The coefficient on age and the intercept change, butneither are significant. This says that both methods may be appropriate,depending on how you interpret large (1pt)

(1pt) for backing out the additional coefficient correctly

(2pt) for correctly comparing the coefficient estimates.

(1pt) for correctly interpreting what this means in terms of the missing data methods.

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