Suggested Solutions to Assignment 4 (Optional) - Trent University

is forecasted, the more the estimated regression equation is likely to lead to
error because it does not reflect the structural changes (i.e., changes in the values
of the estimated coefficients) that usually occur over time.
11. (a) The reduced-form equation for C t is obtained by substituting Equation 6-23 for GNP t
into Equation 6-21 for C t . That is:
Substituting Equation 6-23 for GNP t into Equation 6-21 for C t (and omitting u 1t
because its expected value is zero), we get
C t = a 1 + b 1 (C t + I t + G t )
(6-24')
C t = a 1 + b 1 C t + b 1 I t + b 1 G t (6-24")
By then substituting Equation 6-22 for I t into Equation 6-24" (and omitting u 2t ), we have
C t = a 1 + b 1 C t + b 1 (a 2 + b 2 FS) + b 1 G t
(6-25')
C t = a 1 + b 1 C t + b 1 a 2 + b 1 b 2 π t − 1 + b 1 G t (6-25")
Collecting the C t terms to the left in Equation 6-25" and isolating C t , we have
C t (1 − b 1 ) = a 1 + b 1 a 2 + b 1 b 2 π t − 1 + b 1 G t
(6-26')
Dividing both sides of Equation 6-26' by 1 − b 1 , we finally obtain
C t = a 1 + b 1 a 2 + b 1 b 2 π t − 1 + b 1 G t (6-27')
1 − b 1 1 − b 1 1 − b 1 1 − b 1
Equation 6-27' is the reduced-form equation for C t . It is expressed only in terms
of π t − 1 and G t (the exogenous variables of the model) and can be used in forecasting
C t + 1 by substituting the known value of π t and the predicted value of G t+1 into
Equation 6-27' and solving for C t + 1 .
(b) Equation 6-22 is already in reduced form because π t − 1 is exogenous (i.e., it is
known in period t). The lagged (and therefore known) value of a variable is
sometimes known as a predetermined variable.
12. Wait for June 2011 when the 2011/1 issue of the OECD Economic Outlook will be out and
compare the forecasts presented in Table 6-10 in the text with the actual results reported
for 2010 in June 2011.
13. Prepare a table similar to Table 6-10 in the text of the macroforecasts in the 2011/2 issue of
the OECD Economic Outlook.
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