Aggregation of price risk over commodities: an economic index number approach.

(10) To be more precise, standard chained output price indexes [P.sub.t]/[P.sub.t-1] (Tornqvist, Fisher, Laspeyres) are constructed, and then corresponding implicit output quantity indexes [Y.sub.t]/[Y.sub.t-1] are constructed from the product test equation (1).

(11) Autoregressive distributed lag models of investment for Manitoba crop machinery and equipment were estimated using alternative indexes for price risk aggregated over commodities (Coyle 2005). Econometric results indicate that the index number procedures such as [VP.sup.Torn] developed here have greater explanatory power in these investment models than does a variance of a Tornqvist price index ([VP.sup.B]).

Barry Coyle is associate professor, Department of Agribusiness and Agricultural Economics, University of Manitoba, Canada.

The author thanks the Editor and two anonymous referees for helpful comments and the Organization for Economic Cooperation and Development (Paris) for financial support. Table 1. Correlations between Market Prices, 1950-2002 (Annual Data)

Oats Coef. of

Wheat Barley Canola Flax Variation Wheat 0.4645 Barley 0.9483 0.4598 Canola 0.9072 0.8922 0.5389 Oats 0.8583 0.9319 0.8749 0.5101 Flax 0.8919 0.8819 0.8714 0.8482 0.5126 Rye 0.9267 0.9332 0.9012 0.8792 0.4621 Table 2. Correlations between Output Quantity Indexes (Annual Data)

[Y.sup.Torn] [Y.sup.Fish] [Y.sup.Fish] 0.99000 [Y.sup.Lasp] 0.9912 0.9992 Table 3. Correlations between Indexes of Aggregate Price Risk from Naive Models (Annual Data)

[VP.sup.Torn] [VP.sup.Fish] [VP.sup.Fish] 0.9846 [VP.sup.Lasp] 0.9871 0.9997 [VP.sup.L] 0.9678 0.9897 [VP.sup.B] 0.5129 0.4930

[VP.sup.Lasp] [VP.sup.L] [VP.sup.Fish] [VP.sup.Lasp] [VP.sup.L] 0.9873 [VP.sup.B] 0.4959 0.4656 Table 4. Correlations between Market Prices, 1990-2(M5 (Monthly Data)

Coef. of

Wheat Barley Canola Oats Variation Wheat 0.2519 Barley 0.9096 0.2234 Canola 0.6785 0.6096 0.1758 Oats 0.7449 0.8387 0.5249 0.2790 Flax 0.4906 0.4953 0.4951 0.4014 0.3130 Table 5. Correlations between Indexes of Aggregate Price Risk from Multivariate GARCH Models (Monthly Data)

[VP.sup.Torn] [VP.sup.Fish] [VP.sup.Fish] 0.9981 [VP.sup.Lasp] 0.9978 0.9994 [VP.sup.L] 0.9536 0.9563 [VP.sup.B] 0.8043 0.7988

[VP.sup.Lasp] [VP.sup.L] [VP.sup.Fish] [VP.sup.Lasp] [VP.sup.L] 0.9568 [VP.sup.B] 0.7986 0.7810 Table 6. Correlations between Indexes of Aggregate Price Risk from Multivariate GARCH Models with Dummies (Monthly Data)

[VP.sup.Torn] [VP.sup.Fish] [VP.sup.Fish] 0.9989 [VP.sup.Lasp] 0.9985 0.9993 [VP.sup.L] 0.9605 0.9667 [VP.sup.B] 0.6663 0.6745

[VP.sup.Lasp] [VP.sup.L] [VP.sup.Fish] [VP.sup.Lasp] [VP.sup.L] 0.9657 [VP.sup.B] 0.6819 0.6774