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Forecasting

In the volume, Consumer Demand in the United States: Analyses and Projections
(Cambridge, Mass.: Harvard University Press, 1970), H.S. Houthakker and L.D. Taylor presented the following results for their estimated demand equation from 1929 to 1961 (excluding the 1942 through 1945 war year in the United States:

Qt = 19.575 + 0.0289Xt - 0.0923Pt - 99.568Ct - 4.06Dt
(9.3125) (-1.7682) (-9.8964) (23.50)
R² = 0.857 D-W = 1.86

Where Qt = per capita personal consumption expenditures on shoes and other footwear during year t, at 1954 prices

Xt= total per capita consumption expenditures during year t, at 1954 prices

Pt= relative prices of shoes in year t, at 1954 prices

St= stock of automobiles per capita in year t

Dt= dummy variable to separate pre-from post-World war II years:
Dt= 0 for year 1929 to 1941 and
Dt= 1 for years 1946 to 1961

The number of parentheses below the estimated slope coefficients refer to the estimated t statistics.

Using the above estimated regression equation, forecast the demand for shoes for (a) 1962 and (b) 1972 if the forecasted values of the independent or explanatory variables are those given in the following table. (c) Why would you expect the error for the 1972 forecast to be larger than for the 1962 forecast?

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Qt = 19.575 + 0.0289Xt - 0.0923Pt - 99.568Ct - 4.06Dt

(a) For 1962 we are given the following values:
X = 1,646
P=20
C=0.4
D=1
Putting these numbers in the regression equation we get:
Q(1962) = 19.575 + ...

Solution Summary

The solution performs demand analysis and forecasting for the scenarion provided in the question. It also goes in a lot more detail about other aspects of regression analysis.

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