In their volume Consumer Demand in the United States: Analyses and Projection (Cambridge, Mass: Harvard University Press, 1970), p. 119, H. S. Houthakker and L. D Taylor presented the following results for their estimated demand equation for local bus service over the period from 1929 to 1961 (excluding the 1942 through 1945 war years) in the United States. Qt = 22. 819 + 0. 0159 Xt – 0. 1156 Pt – 86. 106 St – 0. 9841 Dt Qt = per capita personal consumption expenditures on bus transportation during year t. Xt = total per capita consumption expenditure during year t.
Pt = relative price of bus transportation in year t. St = car stock per capita in year t. Dt = Dummy variable to separate pre-from post-world war 2 years: Dt = 0 for years 1929 to 1941, and Dt = 1 for years 1946 to 1961. a. Evaluate the sign and values of the coefficient. Qt = 22. 819 + 0. 0159 Xt – 0. 1156 Pt – 86. 106 St – 0. 9841 Dt From the estimated demand equation for local bus service above indicate that: 1% increase in total per capita consumption expenditure (Xt) would increase 0. 0159% per capita personal consumption expenditures on bus transportation.
1% increase in relative price of bus transportation (Pt) would decrease 0. 1156% per capita personal consumption expenditures on bus transportation. 1% increase in car stock per capita (St) would decrease 86. 106% per capita personal consumption expenditures on bus transportation. 1% increase in Dummy variable (Dt) would decrease 0. 9841% per capita personal consumption expenditures on bus transportation. The Value of the Durbin –Watson (D-W) statistic indicates that the hypothesis of no autocorrelation cannot be rejected. b.
Evaluate the statistical significant of the coefficients and the explanatory power of the regression. n = 29, k= 5, df = n – k, df = 29 – 5 = 24 Assumption: the level of significance = 5% ? critical t value = 2. 064. b1 = 12. 23, b2 = 16. 84, b3 = 15. 83, b4 = 3. 22 Since the t statistic for b1, b2, b3 and b4 exceeds the critical value of 2. 064 for 24 df, both slope coefficient are statistically significant at 5%. Since the value of the calculated t statistic exceeds the critical t value of 2. 064, we conclude that both parameters are statistically different from 0 at the 5% level of significance.
R2 = 0. 996 = 0. 995 This means that the variation in total per capita consumption expenditure, relative price of bus transportation and car stock per capita explains 99. 5% of the variation in demand for local bus service when adjustment is made and 99. 6% when no adjustment is made. c. Evaluate the presence of possible econometric problems. n = 29, k’ = 5, dl = 1. 05, du = 1. 84 D-W = 1. 11, ranges of d is 0 and 4 Based on the graph above, the value of D-W is falls between du and dl, we can conclude that the test is inconclusive. Its means that there is no error between variables that correlated.
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