Question 2 [15 marks in total] The Department of Energy is interested in methods

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Question 2 [15 marks in total] The Department of Energy is interested in methods of reducing household energy consumption and in particular electricity consumption. One demand-side management scheme that is currently being considered for adoption involves energy audits. This involves an expert visiting the home and advising on potential energy saving initiatives The crucial policy question is: How effective are audit programs in promoting energy savings? The Department has collected data for a sample of 296 households in order to conduct this analysis. The available variables are number of people in household people number of rooms in dwelling where household lives rooms household income s'000 income audit dummy if household was audited, 0 otherwise dummy -1 if household has gas, -0 otherwise gas audit gas interaction of audit and gas annual electricity expenditure elec /elec log(elec) Table 1 provides Stata output including summary statistics and results from two regression models. The first regression simply provides a convenient way to estimate the difference in electricity expenditure for those who were audited and those who were not. This model can be represented as (1) elec Po Biaudit u The second model is given by (2) log (elec) po B1 audit B2 gas B3 audit. gas B4people Bsrooms B6 u income The results from mode 1) indicate a very large impact of energy audits on electricity expenditure. Why might you have concerns about the reliability of the estimated impact obtained from this regression? 12 marks] (ii) n what ways does model (2) address the concerns you expressed in (i) 12 marks (iii) Explain how the impact of an energy audit is being modelled in equation (2) Note: this explanation should be in terms of the population parameters of the model and thus without reference to the actual estimates.) [3 marksl (iv) Use the results from model (2) to give a full description of the impact of energy audits on electricity expenditure. In particular comment on a. whether the impact is large in an economic sense; b. whether the estimates of the impact are statistically significant; and c. how the estimates of the impact from model (2) compare with those provided by model (1). [8 marks]

Explanation / Answer

i) In the first model, the singinficance F i.e. Prob > F is very low, we might think that the model is significant and energy audit has a very large impact on electricity expenditure. But, you shouldn't judge a model's performance by only one factor. If you notice the R-Square or Adjusted R-sqaure, you will realize that it 5.93%, which is very low to explain the variability in the electricity expenditure. So, you should have cncern seeing the R-square of the model.

ii) In the 2nd model, the adjusted R-square has significantly gone up and it is pretty decent one to explain the variability in the data. So, the concern of R-sqaure has been mitigated by the 2nd model.

iii) The impact of energy audit has been modelled as an exponential relationship with electricity expenditure.

iv) The sign if the coefficient of audit os negative. Which senses that, if the audit is 1, then expenditure on electricity will go down by exp(-0.1822) units. So in an ecenomic sense, the audit program plays a significant role in lowering the expenditure on electricity. the p-value of the coefficient of audit in the 2nd model is 0.014 < 0.05, which says that 5% level, there is significant impact of audit on the electrivity expenditure

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