10. In their volume Consumer Demand in the United States: Analyses and Projectio
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10. In their volume Consumer Demand in the United States: Analyses and Projections (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: Q,-22.819 + 0.0159-0.1 156P (12.23) (16.84) -86.106S,-0.9841D (15.83) (3.22) per capita personal consumption expenditures on bus transportation during year t, at 1954 prices total per capita consumption expenditures during year t, at 1954 prices where Q, x, P, - relative price of bus transportation in year t, at 1954 prices S car stock per capita in year t D,- dummy variable to separate pre- from post-World War II years; D, 0 for years 1929 to 1941 and D,= 1 for years 1946 to 1961 The numbers in parentheses below the estimated slope coefficients refer to the estimated r values. Evaluate the above results (a) in terms of the signs and values of the coefficients, (b) for the statistical significance of the coefficients and the explanatory power of the regression, and (c) for the presence of possible econometric problems. Note that a dummy variable is added to (if positive) or subtracted from (if negative) the value of the constant of the regression, thus causing the regression line to shift up or shift down, respectively, for the years to which the dummy variable refers. For a more detailed discussion of dummy variables, see D. Salvatore and D. Reagle, Statistics and Econometrics, 2nd ed. (New York: McGraw-Hill, 2002, sec. 8.2), or any other introductory econometrics textExplanation / Answer
(a) Ceteris paribus, when the total per capita consumption expenditure increases by 1 unit then on average the per capita personal consumption on bus transportation increases 0.0159 units.
Ceteris paribus, when relative price of bus transportation increases by one unit then on average the per capita personal consumption on bus transportation decreases by 0.0116 units.
Ceteris paribus, when car stock per capita increases by one unit then on average the per capita personal consumption on bus transportation decreases by 86.106 units.
Ceteris paribus, the per capita personal consumption in pre world war II years was 22.82 units and post world war II years was 21.83 units
(b) All the coefficients of the regression are statistically significant at 5% level of significance. As the parentheses shows the estimated t values which are greater than two for all coefficients. Also the R^2 being very high i.e. 99.6% shows that the explanatory variables explain the dependent variables at this rate. Hence the results of the regression will be significant and reliable.
(c) The possible econometric problems which can occur are specification errors or autocorrelation problem as the dummy is the time based variable.
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