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make sure to copy the table shown below at the beginning of your answers and provide this information. Name ID number Tutor Tutorial day & time Tutorial location ECOM20001 Intro Econometrics Semester 1, 2017 2/5 1. (10 marks total) Question from a previous year’s exam: For a sample of 5 observations the following model was estimated: 2 01 2 y     x xe (1.1) The Eviews output for this estimation is given in Table 1.1. Table 1.1 However, it is suspected that the restriction given by    2 1 holds in equation (1.1). That is, that the model should be specified as: 2 01 1 y     x xe (1.2) 1.a (5 marks) Using the data given in Table 1.2, estimate the parameters of equation (1.2). (Note that the last column of this table is based on the estimated parameters for equation (1.2).) 1.b (5 marks) Define a test to see if the restriction holds and perform the test. To get credit for this question you must show your work – remember on an exam you will not have access to a computer. Table 1.2 obs y x 2 x   2 x  x   2 x  x   2 x  x y   2 x  x y  2 2 x  x  2 2 x  x yˆ (from 1.2) 1 1 0 0 0 0 0 0 0 0 0.992336 2 1.2 0.3 0.09 0.21 0.39 0.252 0.468 0.0441 0.1521 1.276283 3 1.4 0.5 0.25 0.25 0.75 0.35 1.05 0.0625 0.5625 1.330369 4 1.2 0.8 0.64 0.16 1.44 0.192 1.728 0.0256 2.0736 1.208677 5 1 1 1 0 2 0 2 0 4 0.992336 sum 5.8 2.6 1.98 0.62 4.58 0.794 5.246 0.1322 6.7882 mean 1.16 0.52 0.396 0.124 0.916 0.1588 1.0492 0.02644 1.35764 Dependent Variable: Y Sample: 1 5 Variable Coefficient Std. Error t-Statistic Prob. C 0.981556 0.070343 13.95395 0.0051 X 1.374640 0.326153 4.214707 0.0519 X^2 -1.354467 0.309784 -4.372292 0.0485 S.E. of regression 0.072819 R-squared 0.905311 Sum squared resid 0.010605 Adjusted R-squared 0.810622 ECOM20001 Intro Econometrics Semester 1, 2017 3/5 2. (25 marks total) The Econometrician Checks his Electricity Usage In mid-2009 the instillation of smart meters was begun in Victoria and by now most residences in Victoria have them. These meters can measure electricity usage in 30 minute intervals and to transmit this information to the company that distributes the power to enable the retail firm to generate bills. Previously the meters at each residence used a meter where electricity use turned a counter that was read at the end of the billing period. Besides the obvious advantage of the smart meter to eliminate the expense to have a meter reader travel to each house,1 the other advantage of the smart meter is the ability to determine when the electricity was being used and to charge for it at a time differentiated rate. This is important because electricity, for the most part, cannot be stored thus the time at which it is being used determines the cost to generate it. 2 In Victoria the usual peak for energy use is in the late afternoon and early evening due to air conditioning and meal preparation. To meet this peak demand, it is necessary to generate power using more expensive methods or buy power from neighbouring states at higher prices than the cost of electricity at nonpeak periods. Thus in order to price electricity at the marginal cost (as would be most economically efficient) it would be necessary to charge households different prices at different times of the day. This option is now available for households with smart meters. These customers can choose Time-of-Day pricing or Flexible pricing plans from their retailers that allow for different prices at different times of the day. In this way they can benefit by shifting some of their electricity use to off-peak times when prices are lower. Since the instillation of smart meters households can access the data that describes their energy usage for up to the last 2 years. Data files for these observations are available on-line and can be downloaded once the householder has created an account with their distributer. These files can be read with a spreadsheet program such as Excel and can be used to determine how a household might benefit from a time differentiated rate. 3 The data for this assignment was assembled by combining the electricity usage for a house with weather data from an electronic weather monitor at the house. The 30 minute electricity use data is aggregated by hour and the weather data are averaged over 10 minute observations for each hour. There are 744 observations (31 days by 24 hours) the variables in data set e_house.wf1 are listed below: Description Mnemonic Mean Max Min SD. Barometric pressure (hPa) BAROMETR 1008.61 1024.00 993.00 5.23 Start time of Hour (0 to 23) HR 11.50 23.00 0.00 6.93 Indoor humidity (%) INDOORHU 50.35 67.00 36.17 5.87 Indoor temperature (ºC) INDOORTE 24.12 29.44 17.98 2.35 kWh used in hour KWHH 0.71 2.26 0.27 0.39 Outdoor humidity (%) OUTDOORH 69.31 99.00 18.67 23.82 Outdoor temperature (ºC) OUTDOORT 21.19 42.06 5.11 7.57 Cumulative Rain fall (mm) RAIN 443.59 471.42 432.05 13.59 Wind average (km/hr) WINDAVER 3.81 14.60 0.00 3.44 Day of week (Sun = 1,.., Sat = 7) WD 4.06 7.00 1.00 2.08 1 Although both gas and water meters still need to be read in this manner. 2 The expense of household batteries still means that they are quite rare. 3 You can access the data for your own house by checking with your distributer (this is not necessarily your retailer) at: http://www.victorianenergysaver.vic.gov.au/bills-pricing-and-meters/smart-meters-in-home-displays-and-web-portals ECOM20001 Intro Econometrics Semester 1, 2017 4/5 2.a (5 marks) A graphical examination of the data. i. (1 mark) Generate three side-by-side box-plots by hour of the outdoor temperature, the average wind speed, and the kWh. (see appendix A for how this can be done) ii. (2 marks) How closely do we find that the variation of electricity use follows the variation in the wind and the outdoor temperature? iii. (2 marks) Can you conclude whether a solar (assume the outside temperature matches the solar radiation) generator or a wind generator would be able to provide energy at the right hours of the day to power the house during the period of peak use? 2.b (6 marks) Estimate the two regressions: i. (1 mark) Using dummy variables for the day of the week and the hour of the day as regressors, estimate a regression with kWh used in that hour as the dependent variable.4 ii. (1 mark) Using the same regressors estimate a regression with the log of the kWh used in the day as the dependent variable. iii. (3 marks) On the basis of the results of a White (with no interactions), Ramsey RESET (use only one predicted term), and the Jarque-Bera test which model would you prefer? iv. (1 mark) Is there any advantage for prediction of one over the other? 2.c (6 marks) Estimate a new regression: i. (2 marks) As an alternative to the hourly dummy variables use 3rd order polynomials in the hour of the day to account for the hourly activity of the household for the model you have fit in part 2.b.ii Comment on the results of this estimation. ii. (2 mark) How does this model compare to the model fit in 2.b.ii? Can you see any advantages in using this alternative model? iii. (2 marks) Can you find a weather variable that when added to this specification that can improve the fit of this model? (Don’t try more than 3-4 alternatives). Justify your choice of variable. 2.d (5 marks) Using the model specification you estimated in part 2.c.i (not from part 2.c.iii) write the code for an EViews program to do the following. Make sure to add comments to your code. i. (1 mark) Read the data and Estimate the model from part 2.c and save result. ii. (1 mark) Test that all the day of the week dummies are equal to each other and save result. iii. (1 mark) Test that the day of the week dummies for Monday to Friday are equal to each other and save result. iv. (1 mark) Test that the day of the week dummies for Saturday and Sunday are equal to each other and save result. v. (1 marks) Estimate the marginal effect of time at 5pm (hr =17) and save result.