homework using EVIEWS (FOR ANYONE WHO CAN USE EVIEWS)
hanxiao
a_5_s-15_revised_answers.docYOURLASTNAME, YourFirstName
Assignment 5 - REVISED
Save this document as A5-YourLastNameFirstName.doc. Type or copy and paste your responses to the instructions and questions into this document following each instruction or question.
1. You want to estimate a model for the demand for electricity by households in the U.S. States of the following form: Quantity of electricity consumed= f (Price of electricity, Price of gas, Income, Housing).
FOR THE REVISION YOU SHOULD USE QELEC/HOUSING AS THE DEPENDENT VARIABLE AND INCOME/HOUSING AS THE INDEPENDENT VARIABLE AND OMIT HOUSING AS AN INDEPENDENT VARIABLE. COMPARE THE RESULTS OF THIS REVISION WITH YOUR ORIGINAL RESULTS.
Obtain the most up-to-date data for sales of electricity, the residential price of electricity and the price of natural gas from the website of the U.S. Energy Information Administration ( http://www.eia.gov/electricity/ and http://www.eia.gov/naturalgas/ ) . Obtain data on the number of housing units from the U.S. Bureau of the Census http://www.census.gov/popest/data/housing/totals/2012/index.html )
and personal Income from the U.S. Bureau of Economic Analysis ( http://www.bea.gov/regional/index.htm )
Add each series to an EViews workfile and change the names to QELEC, PELEC, PGAS, INCOME and HOUSING:
a. Carefully identify the series including providing the url for the data.
b. Tell why you think the data series is or is not exactly what you should use in your estimation.
c. Paste the variable names for each series and only the first and the last observations into your assignment.
The Excel file Assignment 5 data contains all the identifying information for the data I used. You mayhave found some slightly different data.
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STATE |
QELEC |
PELEC |
PGAS |
INCOME |
HOUSING |
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1 |
Alabama |
3256.000 |
10.99000 |
12.54000 |
181816.0 |
2189545. |
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51 |
Wyoming |
313.0000 |
10.28000 |
8.540000 |
32018.00 |
265162.0 |
2. Type the equation you will estimate and explain it including your theory and the expected signs for each estimated coefficient.
Theory of demand QELEC = C(1)*PELEC + C(2)*PGAS + C(3)*INCOME +C(4)HOUSING + C(5)
C(1) –
C(2) +
C(3) +
C(4)+
C(5) no expectation
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Dependent Variable: QELEC |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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PELEC |
-94.46757 |
53.30388 |
-1.772246 |
0.0831 |
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PGAS |
39.22659 |
51.56934 |
0.760657 |
0.4508 |
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INCOME |
-0.008121 |
0.003297 |
-2.463220 |
0.0177 |
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HOUSING |
0.001853 |
0.000400 |
4.628823 |
0.0000 |
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C |
994.6281 |
356.9909 |
2.786144 |
0.0078 |
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R-squared |
0.876198 |
Mean dependent var |
2726.780 |
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Adjusted R-squared |
0.865193 |
S.D. dependent var |
2541.893 |
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S.E. of regression |
933.2830 |
Akaike info criterion |
16.60993 |
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Sum squared resid |
39195776 |
Schwarz criterion |
16.80114 |
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Log likelihood |
-410.2483 |
Hannan-Quinn criter. |
16.68274 |
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F-statistic |
79.62067 |
Durbin-Watson stat |
1.967556 |
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Prob(F-statistic) |
0.000000 |
Wald F-statistic |
21.47470 |
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Prob(Wald F-statistic) |
0.000000 |
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REVISED: THEORY OF DEMAND QELEC/HOUSING = C(1)*PELEC + C(2)*PGAS + C(3)*INCOME/HOUSING + C(4)
C(1) –
C(2) +
C(3) +
C(4) no expectation
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Dependent Variable: QELEC/HOUSING |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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PELEC |
-6.94E-05 |
1.46E-05 |
-4.750072 |
0.0000 |
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PGAS |
2.06E-05 |
1.41E-05 |
1.466870 |
0.1492 |
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INCOME/HOUSING |
-0.000327 |
0.002383 |
-0.137055 |
0.8916 |
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C |
0.001784 |
0.000217 |
8.223864 |
0.0000 |
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R-squared |
0.549799 |
Mean dependent var |
0.001091 |
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Adjusted R-squared |
0.520438 |
S.D. dependent var |
0.000341 |
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S.E. of regression |
0.000236 |
Akaike info criterion |
-13.78950 |
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Sum squared resid |
2.56E-06 |
Schwarz criterion |
-13.63654 |
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Log likelihood |
348.7375 |
Hannan-Quinn criter. |
-13.73125 |
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F-statistic |
18.72553 |
Durbin-Watson stat |
2.016181 |
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Prob(F-statistic) |
0.000000 |
Wald F-statistic |
18.67201 |
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Prob(Wald F-statistic) |
0.000000 |
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3. Re-estimate the equation to see if there is a quadratic effect for income and paste the output in your assignment.
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Dependent Variable: QELEC |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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PELEC |
-137.1613 |
52.17824 |
-2.628706 |
0.0118 |
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PGAS |
80.63222 |
49.84062 |
1.617801 |
0.1129 |
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INCOME |
-0.000579 |
0.003924 |
-0.147580 |
0.8833 |
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INCOME^2 |
-2.01E-09 |
7.26E-10 |
-2.770709 |
0.0082 |
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HOUSING |
0.001283 |
0.000387 |
3.314235 |
0.0018 |
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C |
806.2214 |
314.7208 |
2.561703 |
0.0139 |
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R-squared |
0.894377 |
Mean dependent var |
2726.780 |
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Adjusted R-squared |
0.882375 |
S.D. dependent var |
2541.893 |
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S.E. of regression |
871.7807 |
Akaike info criterion |
16.49112 |
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Sum squared resid |
33440071 |
Schwarz criterion |
16.72056 |
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Log likelihood |
-406.2780 |
Hannan-Quinn criter. |
16.57849 |
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F-statistic |
74.51553 |
Durbin-Watson stat |
2.059782 |
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Prob(F-statistic) |
0.000000 |
Wald F-statistic |
19.59777 |
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Prob(Wald F-statistic) |
0.000000 |
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Dependent Variable: QELEC/HOUSING |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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PELEC |
-6.93E-05 |
1.47E-05 |
-4.722351 |
0.0000 |
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PGAS |
2.07E-05 |
1.41E-05 |
1.465375 |
0.1498 |
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INCOME/HOUSING |
0.001132 |
0.018876 |
0.059950 |
0.9525 |
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(INCOME/HOUSING)^2 |
-0.006353 |
0.082070 |
-0.077403 |
0.9386 |
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C |
0.001703 |
0.001061 |
1.605227 |
0.1154 |
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R-squared |
0.549894 |
Mean dependent var |
0.001091 |
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Adjusted R-squared |
0.509885 |
S.D. dependent var |
0.000341 |
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S.E. of regression |
0.000239 |
Akaike info criterion |
-13.74971 |
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Sum squared resid |
2.56E-06 |
Schwarz criterion |
-13.55851 |
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Log likelihood |
348.7428 |
Hannan-Quinn criter. |
-13.67690 |
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F-statistic |
13.74414 |
Durbin-Watson stat |
2.023571 |
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Prob(F-statistic) |
0.000000 |
Wald F-statistic |
13.82124 |
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Prob(Wald F-statistic) |
0.000000 |
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4. Interpret the coefficients for income and calculate where the parabola turns.
When income changes by one unit(one million dollars) ( I chose to do it from the means of all the data to the mean + 1 for income), QELEC changes by .001739 million kilowatthours
GENR CHANGE_QELEC2 = (c(3)*@mean(INCOME)+c(4)*@mean(INCOME)^2)-(c(3)*(@mean(INCOME) +1)+c(4)*(@mean(INCOME)+1)^2)
To find where the parabola turns take the partial derivative wrt incomeand set it equal to 0 and solver for INCOME=-5.28E-13 (very slightly below the origin)
Revised: When income changes by one unit(one million dollars) ( I chose to do it from the means of all the data to the mean + 1 for income), QELEC changes by 3664.19 million kilowatthours per household.
The parabola turns at 3.59E-06
5. Describe the procedure you should use to determine how high a power of income should be included in the equation.
Start with the highest power you think could be in the equation (I use 4th power). Test to see if the highest powers is statistically significantly different form zero (is the p-value below .05). If not drop that power and re-estimate with a lower power. Test the highest power coefficient,. Etc. until you have found the highest significant power. The fourth power is significant.
Revised. The fourth power is not significant but the third power is.
6. Re-estimate the equation of #3 in log-log form and paste the results in your assignment.
With my data the income squared term caused multicollinearity so I deleted it.
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Dependent Variable: LOG(QELEC) |
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Method: Least Squares |
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Date: 04/09/15 Time: 12:40 |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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LOG(PELEC) |
-1.014908 |
0.147823 |
-6.865699 |
0.0000 |
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LOG(PGAS) |
0.058667 |
0.128630 |
0.456089 |
0.6505 |
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LOG(INCOME) |
-0.063944 |
0.208747 |
-0.306321 |
0.7608 |
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LOG(HOUSING) |
1.058285 |
0.212936 |
4.969967 |
0.0000 |
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C |
-4.542955 |
0.748159 |
-6.072176 |
0.0000 |
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R-squared |
0.968086 |
Mean dependent var |
7.447635 |
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Adjusted R-squared |
0.965249 |
S.D. dependent var |
1.069879 |
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S.E. of regression |
0.199443 |
Akaike info criterion |
-0.291940 |
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Sum squared resid |
1.789983 |
Schwarz criterion |
-0.100738 |
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Log likelihood |
12.29850 |
Hannan-Quinn criter. |
-0.219129 |
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F-statistic |
341.2581 |
Durbin-Watson stat |
2.079090 |
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Prob(F-statistic) |
0.000000 |
Wald F-statistic |
477.6741 |
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Prob(Wald F-statistic) |
0.000000 |
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Dependent Variable: LOG(QELEC/HOUSING) |
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Method: Least Squares |
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Date: 04/11/15 Time: 10:12 |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
-4.631142 |
0.587478 |
-7.883086 |
0.0000 |
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LOG(PELEC) |
-1.014415 |
0.147011 |
-6.900267 |
0.0000 |
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LOG(PGAS) |
0.059788 |
0.127858 |
0.467613 |
0.6423 |
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LOG(INCOME/HOUSING) |
-0.065418 |
0.204341 |
-0.320142 |
0.7503 |
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R-squared |
0.686380 |
Mean dependent var |
-6.873730 |
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Adjusted R-squared |
0.665927 |
S.D. dependent var |
0.341443 |
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S.E. of regression |
0.197351 |
Akaike info criterion |
-0.331050 |
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Sum squared resid |
1.791576 |
Schwarz criterion |
-0.178088 |
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Log likelihood |
12.27625 |
Hannan-Quinn criter. |
-0.272801 |
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F-statistic |
33.55814 |
Durbin-Watson stat |
2.064927 |
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Prob(F-statistic) |
0.000000 |
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7. Evaluate your results including your estimate of the own price elasticity of demand
1a. Own price elasticity is just coefficient of LOG(PELEC) = -1.04, so demand is elastic.
1b. The r-quare is 0.968086, which improved a lot BUT because the dependent variables are different the two R-squareds are not comparable.
Revised 1 The own elasticity is just coefficient of log(PELEC) = -1.014415, so demand is elastic
Revised 2. The r-square is 0.686380, which improved from the previous regression. BUT because the dependent variables are different the two R-squareds are not comparable.
8. Which is better, the linear model or the log-log model? Calculate the predicted values of consumption for each of the states and use these values to construct an approximate R-square to compare with the one from the linear model.
R-squared from the linear regression = 0.876198, for the log-log model a roughly comparable R-Square is computed as follows:
GENR LOG_QELEC_HAT= -1.01490807904*LOG(PELEC) + 0.0586667432728*LOG(PGAS) - 0.0639435179339*LOG(INCOME) + 1.05828529565*LOG(HOUSING) - 4.54295469693
GENR QELEC_HAT=EXP( LOGQELEC_HAT)
GENR R_squared = 1 - @SUMSQ(QELEC-QELECHAT)/@SUMSQ(QELEC-@MEAN(QELEC))=.934672 which is better
REVISED R-squared from the linear regression = 0.558977, from the log-log model a roughly comparable R-Square is computed as follows:
GENR LOG_QELEC_P_HAT -1.01441518281*LOG(PELEC) + 0.0597882688648*LOG(PGAS) - 0.0654180887821*LOG(INCOME/HOUSING) - 4.63114153304
GENR QELEC_P_HAT=EXP( LOG_QELEC_P_HAT)
GENR R_squared_REVISED= 1 - @SUMSQ(QELEC/HOUSING-QELEC_p_HAT)/@SUMSQ(QELEC/HOUSING-@MEAN(QELEC/HOUSING))=.662213 which is better
9. Re-estimate the linear model using the ratio of electric to natural gas prices and paste the results in your assignment.
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Dependent Variable: QELEC |
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Method: Least Squares |
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Date: 04/11/15 Time: 14:14 |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
1108.287 |
630.1472 |
1.758776 |
0.0853 |
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PELEC/PGAS |
-752.8126 |
477.4749 |
-1.576654 |
0.1217 |
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INCOME |
-0.008921 |
0.003179 |
-2.806252 |
0.0073 |
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HOUSING |
0.001955 |
0.000395 |
4.942812 |
0.0000 |
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R-squared |
0.871187 |
Mean dependent var |
2726.780 |
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Adjusted R-squared |
0.862786 |
S.D. dependent var |
2541.893 |
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S.E. of regression |
941.5783 |
Akaike info criterion |
16.60961 |
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Sum squared resid |
40782209 |
Schwarz criterion |
16.76257 |
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Log likelihood |
-411.2403 |
Hannan-Quinn criter. |
16.66786 |
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F-statistic |
103.7021 |
Durbin-Watson stat |
2.001158 |
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Prob(F-statistic) |
0.000000 |
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Dependent Variable: QELEC/HOUSING |
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Method: Least Squares |
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Date: 04/11/15 Time: 14:14 |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
0.002021 |
0.000225 |
8.985315 |
0.0000 |
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PELEC/PGAS |
-0.000421 |
0.000154 |
-2.737523 |
0.0087 |
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INCOME/HOUSING |
-0.003864 |
0.002411 |
-1.602961 |
0.1156 |
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R-squared |
0.278478 |
Mean dependent var |
0.001091 |
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Adjusted R-squared |
0.247775 |
S.D. dependent var |
0.000341 |
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S.E. of regression |
0.000295 |
Akaike info criterion |
-13.35783 |
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Sum squared resid |
4.10E-06 |
Schwarz criterion |
-13.24311 |
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Log likelihood |
336.9458 |
Hannan-Quinn criter. |
-13.31414 |
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F-statistic |
9.070038 |
Durbin-Watson stat |
2.089905 |
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Prob(F-statistic) |
0.000467 |
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10. Evaluate this model in comparison with the original one.
R-squared does not change too much.
R-squared decreased significantly.
11. Is the consumption behavior different (i.e., do prices, incomes and housing units have different effects) in sates with incomes higher than the average? Estimate an equation that will let you determine this and paste the results in your assignment.
GENR DUMMY=0
SMPL IF INCOME>@MEAN(INCOME)
GENR DUMMY=1
SMPL @ALL
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Dependent Variable: QELEC |
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Method: Least Squares |
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Date: 04/11/15 Time: 14:14 |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
1109.788 |
362.2704 |
3.063425 |
0.0037 |
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PELEC |
-109.6877 |
51.59186 |
-2.126066 |
0.0391 |
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PGAS |
50.00712 |
50.39281 |
0.992346 |
0.3265 |
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INCOME |
-0.007551 |
0.002904 |
-2.600184 |
0.0126 |
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HOUSING |
0.001689 |
0.000376 |
4.496999 |
0.0000 |
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DUMMY |
763.8297 |
428.3546 |
1.783172 |
0.0815 |
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R-squared |
0.884855 |
Mean dependent var |
2726.780 |
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Adjusted R-squared |
0.871771 |
S.D. dependent var |
2541.893 |
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S.E. of regression |
910.2296 |
Akaike info criterion |
16.57744 |
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Sum squared resid |
36454785 |
Schwarz criterion |
16.80688 |
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Log likelihood |
-408.4359 |
Hannan-Quinn criter. |
16.66481 |
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F-statistic |
67.62556 |
Durbin-Watson stat |
1.934518 |
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Prob(F-statistic) |
0.000000 |
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Dependent Variable: QELEC/HOUSING |
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Method: Least Squares |
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Date: 04/11/15 Time: 14:14 |
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Sample (adjusted): 1 51 |
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Included observations: 50 after adjustments |
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White heteroskedasticity-consistent standard errors & covariance |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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C |
0.001778 |
0.000230 |
7.720086 |
0.0000 |
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PELEC |
-6.94E-05 |
1.48E-05 |
-4.704281 |
0.0000 |
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PGAS |
2.06E-05 |
1.41E-05 |
1.462455 |
0.1506 |
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INCOME/HOUSING |
-0.000229 |
0.002652 |
-0.086406 |
0.9315 |
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DUMMY |
-1.28E-05 |
7.56E-05 |
-0.168668 |
0.8668 |
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R-squared |
0.550068 |
Mean dependent var |
0.001091 |
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Adjusted R-squared |
0.510074 |
S.D. dependent var |
0.000341 |
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S.E. of regression |
0.000238 |
Akaike info criterion |
-13.75010 |
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Sum squared resid |
2.56E-06 |
Schwarz criterion |
-13.55889 |
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Log likelihood |
348.7524 |
Hannan-Quinn criter. |
-13.67729 |
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F-statistic |
13.75376 |
Durbin-Watson stat |
2.014425 |
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Prob(F-statistic) |
0.000000 |
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12. Are there a differences? (Interpret all of the coefficients)
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Wald Test: |
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Equation: BEHAVIOR_DIFFERENCE |
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Test Statistic |
Value |
df |
Probability |
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t-statistic |
1.783172 |
44 |
0.0815 |
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F-statistic |
3.179701 |
(1, 44) |
0.0815 |
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Chi-square |
3.179701 |
1 |
0.0746 |
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Null Hypothesis: C(6)=0 |
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Null Hypothesis Summary: |
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Normalized Restriction (= 0) |
Value |
Std. Err. |
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C(6) |
763.8297 |
428.3546 |
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Restrictions are linear in coefficients. |
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Wald Test: |
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Equation: BEHAVIOR_DIFFERENCE_REVI |
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Test Statistic |
Value |
df |
Probability |
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t-statistic |
-0.168668 |
45 |
0.8668 |
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F-statistic |
0.028449 |
(1, 45) |
0.8668 |
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Chi-square |
0.028449 |
1 |
0.8661 |
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Null Hypothesis: C(5)=0 |
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Null Hypothesis Summary: |
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Normalized Restriction (= 0) |
Value |
Std. Err. |
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C(5) |
-1.28E-05 |
7.56E-05 |
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Restrictions are linear in coefficients. |
Wald test doesn’t reject h0 that dummy=0 at 5% significant level, indicating that there is no difference in consumer behavior. However, it does reject h0 at 10% significant level, which suggests there is a difference.
Wald test doesn’t reject h0 that dummy=0 at 5% significant level, indicating that there is no difference in consumer behavior.
13. Save your workfile as YourLastNameFirstName.wf1. Send a copy to the assistant.
