Variation in the value of mineral resources. Part I. The USA |
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| Authors: | J C Griffiths W D Menzie |
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| Institution: | 1. Department of Geosciences, Pennsylvania State University, University Park, Pennsylvania, USA
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| Abstract: | The value of mineral resources produced in the USA during the 93 years, 1880–1972, deflated to 1967=100, totals 921 billions of dollars; this yields a value of $303,289 per mi2 for the conterminous 48 states. Alaska has aggregated some 4160 millions of dollars during the same period, an average yield of some 7107 deflated dollars per mi2. If we assume Alaska will achieve the average level of the “lower 48,”the potential value of its mineral resources is 178 billions of deflated 1967 dollars. Fuels account for about two-thirds of this value followed by about 20 percent for each of the aggregates, nonmetals and metals. The deflated dollar value of these four aggregate figures, fuels, nonmetals, metals, and total, during the period 1880–1972 are four time series and the economic processes which produced these series may be modelled through Box-Jenkins procedures. The value of fuels has steadily increased through the period, except for the depression years of the 1930s; this series may be represented as a multiplicative seasonal ARIMA(1,1,0)(1,0,1) model with periods at 4 and 3 yr for the autoregressive (AR) and moving average (MA) terms. Forecasts for 1973 to 1980, using the model, show the value of fuels produced to be about 20 billions of dollars per annum. The value of nonmetals also increased throughout the period except for a somewhat larger drop during the depression years of the 1930s. A multiplicative seasonal ARMA(1,0,0)(1,0,1) model with period at 7 yr for both the AR (autoregressive) and MA (moving average) terms appears to best reflect this series; the forecasts with this model fluctuate around their present annual value of some 6 billions of dollars. The value of metals behaves less consistently; it was much more strongly affected by the Great Depression and its subsequent growth is slower and less consistent than those of the fuels and nonmetals. It is appropriately represented by a multiplicative seasonal ARMA(1,0,0)(0,0,2) model with moving average (MA) periods at 6 and 11 yr respectively. Forecasts with this model show a decline in value for years beyond 1972; the large residual “error” \((\hat \sigma _e = 0.0925)\) , which is about twice as large as the equivalent errors for the value of fuels and nonmetals ( \(\hat \sigma _e = 0.0408\) and 0.0532, respectively), makes this forecast less firm. The total value of mineral resources is composed of all three series and, because fuels account for two-thirds of the total value, the two series closely resemble each other. The total value is not a simple aggregate of the three series; it is appropriately fitted by a multiplicative seasonal IMA(0,1,0)(0,0,2) model with periods at 7 and 11 yr (and error \(\hat \sigma _e = 0.0423\) ). Forecasts using this model imply that the total value of mineral resources produced will be over 30 billions of dollars per annum through 1980. |
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