You have the following data: The (natural) logs of aggregate annual US electrici

Question

You have the following data: The (natural) logs of aggregate annual US electricity sales, of average electricity price, and of income (GNP), for the years 1951-84. 1. Under the Data Analysis submenu, choose the "Regression" option to fit the following partial-adjustment model for 1952-84,     while requesting the residuals: LNKWHt = 0 + 1*LNKWH(t-1) + 2*LNPEt + 3*LNGNPt. 2. Use the regression results to calculate the partial adjustment coefficient, , as (1-1); also calculate the long run price elasticity 2 as 2/,     and the long run income elasticity 3 as 3/. YEAR LNKWH LNKWH (t-1) LNPE LNGNP 1951 5.7991 #N/A 1.1378 6.3620 1952 5.8749 5.7991 1.1282 6.3983 1953 5.9814 5.8749 1.1019 6.4355 1954 6.0497 5.9814 1.0886 6.4234 1955 6.2086 6.0497 1.0116 6.4884 1956 6.3026 6.2086 0.9594 6.5097 1957 6.3561 6.3026 0.9439 6.5277 1958 6.3767 6.3561 0.9517 6.5234 1959 6.4723 6.3767 0.9163 6.5816 1960 6.5352 6.4723 0.9746 6.6029 1961 6.5834 6.5352 0.9670 6.6288 1962 6.6567 6.5834 0.9361 6.6850 1963 6.7250 6.6567 0.9042 6.7244 1964 6.7979 6.7250 0.8671 6.7758 1965 6.8607 6.7979 0.8286 6.8344 1966 6.9422 6.8607 0.7701 6.8924 1967 7.0022 6.9422 0.7372 6.9191 1968 7.0926 7.0022 0.6780 6.9642 1969 7.1808 7.0926 0.6313 6.9917 1970 7.2385 7.1808 0.6043 6.9899 1971 7.2930 7.2385 0.6098 7.0232 1972 7.3746 7.2930 0.6206 7.0783 1973 7.4459 7.3746 0.6152 7.1343 1974 7.4419 7.4459 0.7701 7.1279 1975 7.4657 7.4419 0.8416 7.1161 1976 7.5258 7.4657 0.8459 7.1687 1977 7.5747 7.5258 0.8920 7.2223 1978 7.6098 7.5747 0.8961 7.2714 1979 7.6358 7.6098 0.8920 7.2994 1980 7.6470 7.6358 0.9746 7.2957 1981 7.6719 7.6470 1.0260 7.3150 1982 7.6432 7.6719 1.0852 7.2998 1983 7.6737 7.6432 1.0716 7.3361 1984 7.7312 7.6737 1.0716 7.4020 You have the following data: The (natural) logs of aggregate annual US electricity sales, of average electricity price, and of income (GNP), for the years 1951-84. 1. Under the Data Analysis submenu, choose the "Regression" option to fit the following partial-adjustment model for 1952-84,     while requesting the residuals: LNKWHt = 0 + 1*LNKWH(t-1) + 2*LNPEt + 3*LNGNPt. 2. Use the regression results to calculate the partial adjustment coefficient, , as (1-1); also calculate the long run price elasticity 2 as 2/,     and the long run income elasticity 3 as 3/. YEAR LNKWH LNKWH (t-1) LNPE LNGNP 1951 5.7991 #N/A 1.1378 6.3620 1952 5.8749 5.7991 1.1282 6.3983 1953 5.9814 5.8749 1.1019 6.4355 1954 6.0497 5.9814 1.0886 6.4234 1955 6.2086 6.0497 1.0116 6.4884 1956 6.3026 6.2086 0.9594 6.5097 1957 6.3561 6.3026 0.9439 6.5277 1958 6.3767 6.3561 0.9517 6.5234 1959 6.4723 6.3767 0.9163 6.5816 1960 6.5352 6.4723 0.9746 6.6029 1961 6.5834 6.5352 0.9670 6.6288 1962 6.6567 6.5834 0.9361 6.6850 1963 6.7250 6.6567 0.9042 6.7244 1964 6.7979 6.7250 0.8671 6.7758 1965 6.8607 6.7979 0.8286 6.8344 1966 6.9422 6.8607 0.7701 6.8924 1967 7.0022 6.9422 0.7372 6.9191 1968 7.0926 7.0022 0.6780 6.9642 1969 7.1808 7.0926 0.6313 6.9917 1970 7.2385 7.1808 0.6043 6.9899 1971 7.2930 7.2385 0.6098 7.0232 1972 7.3746 7.2930 0.6206 7.0783 1973 7.4459 7.3746 0.6152 7.1343 1974 7.4419 7.4459 0.7701 7.1279 1975 7.4657 7.4419 0.8416 7.1161 1976 7.5258 7.4657 0.8459 7.1687 1977 7.5747 7.5258 0.8920 7.2223 1978 7.6098 7.5747 0.8961 7.2714 1979 7.6358 7.6098 0.8920 7.2994 1980 7.6470 7.6358 0.9746 7.2957 1981 7.6719 7.6470 1.0260 7.3150 1982 7.6432 7.6719 1.0852 7.2998 1983 7.6737 7.6432 1.0716 7.3361 1984 7.7312 7.6737 1.0716 7.4020

Explanation / Answer

Answer:

The (natural) logs of aggregate annual US electricity sales, of average electricity price,

LNKWHt = 0 + 1*LNKWH(t-1) + 2*LNPEt + 3*LNGNPt.

From the data analysis, we can compare the equation and find that 0 = -0.685, 1 = 0.758, 2 = -0.130, and 3 = 0.367

2. Compute the partial adjustment coefficient, , as (1-1) = ( 1 - 0.758) = 0.242

Calculate the long run price elasticity 2 as 2/ = -0.130/0.242 = -0.537

Now find the long run income elasticity 3 as 3/ = 0.367/0.242 = 1.51

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