In their article, “The Demand for Coffee in the United States: 1963-1977” (Quarterly Review of Economics and Business, Summer 1980 pp.36-50), C.J. Huang, J.J. Siegfried, and F. Zardoshty estimated the following regression equation using quarterly data for the 58 quarters running from the first quarter of 1963 through the second quarter of 1977:
ln Qr = 1.2789 – 0.1647ln Pt + 0.5115ln It + 0.1483ln P’t1 - 0.0089T – 0.0961D1t – 0.1570D2t – 0.0097D3t
                          (-2.14)              (1.23)            (0.55)                 (-3.36)       (-3.74)             (-6.03)           (-0.37)
                           R^2 = 0.50 D-W=2.08
Where Qt = quantity (in pounds) of coffee consumed per capita (for population over 16 years of age) in quarter t
Pt = relative price of coffee per pound in quarter t, at 1967 prices
It = per capita disposable income in quarter t, in thousands of 1967 dollars
P’t = relative price of tea per quarter pound in quarter t, at 1967 prices
T = time trend; T=1 for first quarter (spring) and 0 otherwise
D1t = dummy variable equal to 1 for first quarter (spring) and 0 otherwise
D2t = dummy variable equal to 1 for second quarter (summer) and 0 otherwise
D3t = dummy variable equal to 1 for third quarter (fall) and 0 otherwise
The numbers in parenthesis below the estimated regression coefficients are t statistics.
Using the above estimated regression equation for the seasonal demand for coffee in the United States and predicting that the values of the independent or explanatory variables in the demand equation from the third quarter of 1977 to the second quarter of 1978 are those indicated in the following table, forecast the demand for coffee (a) the third quarter of 1977, (b) the fourth quarter of 1977, (c) the first quarter of 1978, (d) the second quarter of 1978. (e) How much confidence can we have in these forecasts?  What could cause the large forecasting error to be very large?
Quarter
P
Y
P’
1977.3
1.86
3.57
1.10
1977.4
1.73
3.60
1.08
1978.1
1.60
3.63
1.07
1978.2
1.46
3.67
1.05
Y = per capita disposable personal income
* Please change the variable of per capita disposable personal income from It to Yt. For the fourth quarter of 1977 forecast, D1t=D2t=D3t=0
Solution:
lnQ=1.2789-0.1647(1.86)+0.5115(3.57)+0.1483(1.10)-0.0089(59)-0.0961(0)-0.1570(0)-0.0097(1)
=1.2789-0.1647(0.62)+0.5115(1.27)+0.1483(0.10)-0.089(59)-0.0097(1)
= -3.42