P Y Q 50 9 7.1 50 9 5.7 50 10 10.3 50 10 11.8 50 11 11.9 50 11 13.9 60 11 5.7 60

Question

P Y Q 50 9 7.1 50 9 5.7 50 10 10.3 50 10 11.8 50 11 11.9 50 11 13.9 60 11 5.7 60 11 6.6 60 12 11.5 60 12 12.6 60 13 16.8 60 13 14.4 70 13 13.2 70 13 9.7 70 14 16.0 70 14 9.3 70 15 19.0 70 15 21.5 80 15 11.3 80 15 15.6 80 16 15.6 80 16 15.8 80 17 21.7 80 17 20.9 P = price per unit Y = income Q = quantity of heating oil demanded 2. Consider demand for heating oil (1) Use LS estimation method and the data file heating oildemand to estimate the following demand equation: log(Q)-A + 1 log(P) + u . Does Bi have the expected sign (in terms of negative or positive)? If not, can you think of a reason? (2) Now, cstimate thc following model log(Q) _ Ao + 1 log(P) + 2log (Y) + u . Does Bi have the expected sign now? Comparing this model with the model in p1, which one is correctly specilied? The Data File No. oI households observed 24 Variable names (he variable names are lisled in the same order as they appea in the data ile) P: price per unit of heating oil Y house hold income : units of heating oil bought by a household

Explanation / Answer

2)

using Excel

we make two new columns with log Q and log Y

coefficient for log P = 1.19362 > 0

expected sign is negative as demand is inversely proportional to price

This may have happend because price only is not able to capture the variation

b)

now coefficient (-3.0413369) is negative .

Model 2 is correctly specified

P Y Q log Q log P logY 50 9 7.1 0.851258 1.69897 0.954243 50 9 5.7 0.755875 1.69897 0.954243 50 10 10.3 1.012837 1.69897 1 50 10 11.8 1.071882 1.69897 1 50 11 11.9 1.075547 1.69897 1.041393 50 11 13.9 1.143015 1.69897 1.041393 60 11 5.7 0.755875 1.778151 1.041393 60 11 6.6 0.819544 1.778151 1.041393 60 12 11.5 1.060698 1.778151 1.079181 60 12 12.6 1.100371 1.778151 1.079181 60 13 16.8 1.225309 1.778151 1.113943 60 13 14.4 1.158362 1.778151 1.113943 70 13 13.2 1.120574 1.845098 1.113943 70 13 9.7 0.986772 1.845098 1.113943 70 14 16 1.20412 1.845098 1.146128 70 14 9.3 0.968483 1.845098 1.146128 70 15 19 1.278754 1.845098 1.176091 70 15 21.5 1.332438 1.845098 1.176091 80 15 11.3 1.053078 1.90309 1.176091 80 15 15.6 1.193125 1.90309 1.176091 80 16 15.6 1.193125 1.90309 1.20412 80 16 15.8 1.198657 1.90309 1.20412 80 17 21.7 1.33646 1.90309 1.230449 80 17 20.9 1.320146 1.90309 1.230449

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