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Empirical investigation of the long-term movement of resource prices
Economics Letters 7 (1981) 95% 103 North-Holland Publishing Company
95
EMPIRICAL INVESTIGATION OF THE LONG-TERM MOVEMENT OF RESOURCE PRICES A Preliminary Report
Geoffrey HEAL * University of Essex, Colchester CO4 3SQ, UK
Michael BARROW * University of Sussex, Falmer, Brightott BNI 9RH, UK Received
6 May 1980
This note reports the results of an investigation into the long-run movements of natural resource prices and their relationship to interest rates and extraction costs. The results do not support the equilibrium type Hotelling rule but rather a more general asset market approach.
1. Introduction
The aim of this paper is to report briefly on an extension of the analysis of Heal and Barrow (1979), which was performed on twelve years of monthly data, to a time series of annual data covering the last century. A fuller discussion is in Heal and Barrow (1980). The analysis is concerned specifically with exhaustible resources, and it is assumed that the supply of and demand for such resources depend not only on the current price, but also on the expected rate of capital gain on the resource and on the expected rate of return available from holding other assets. Thus if p is the resource price, r, =p/p (2 = dx/dt), r is the return elsewhere and f= and i are traders’ expectations of rc and r, market
* We are grateful to Mina Toksoz for research assistance, and to David Hendry for making available to us the computer programs on which this work is based. We have also received valuable comments from Graciela Chichilmsky, David Gulley, Joe Farrell, Donald Hanson and V. Kerry Smith The research was supported by grants from the U.K. Social Science Research Council and from U.N.I.T.A.R.
0165-1765/81/0000-0000/$02.50
0 1981 North-Holland
96 G. Heal, M. Burrow / Empirical inve&tigcrtion of long-term resource prices movement
clearing requires that
The inclusion of variables other than price is of course in the spirit of the classic analysis of Hotelling (193 l), which sees an exhaustible resource as an asset, the demand for which will depend inter alia on the return that it offers relative to returns elsewhere. Differentiating (1) logarithmically with respect to time, assuming the demand and supply functions to be of constant elasticity, and that expectations are formed adaptively, leads to the following differential equation:
r,{E(S,P) -E(D,P)}
++(S,FJ-E(D,Q) c
=;{E(D,?)--E(S,?)}, c
(2)
where E(i, j) is the elasticity of i with respect toj. It should be noted that here the rate of return on the resource, r,, appears both in level and rate of change form, whereas, the return on the other asset appears only in rate of change form. This follows from the fact that (1) contains terms in p, which is in effect the integral of r,, but no equivalent terms for r. Analysis of equations similar to (1) and (2) and their discrete transformations lead Heal and Barrow (1979) to estimate the following difference equation:
+A,r(t-l)+A,r(t-2)+c(t),
(3)
where x(t) is the value of variable x in period t, c(t) is a serially correlated error process and the interest rate coefficients A,, A, and A, satisfy the restriction: A, +A,
+A,
=O.
(4)
(4) can readily be seen to imply that it is the rate of change of the interest
rate, and not its level, that features in (3), and this in turn follows from
G. Heul, M. Barrow / Empirical inve>tigution of long-term resource prices movement
91
the fact that (2) contains only terms in the rate of change of r, and not terms in its level. In all of the work on monthly post-war data reported in Heal and Barrow, the hypothesis of a relationship of the form suggested by (3) and (4) received considerable support. One would not of course expect exactly the same equations to give an equally good fit over the long term, as there are factors that can be neglected over this shorter period that become influential in the long term. Changes in extraction costs and the discovery of new resource deposits might be expected to have significant effects on price movements. The present study therefore begins by using the model of the earlier study [i.e., (3) and (4)] on long-run data [see Manthy (1978) for a similar study see Smith (1979)], and then adds in variables to allow for the effects of cost changes. Unfortunately there are no reliable time series on any aspect of extraction costs over this period, so it has proved necessary to adapt techniques from the latent or unobservable variable literature to this problem. The conclusions that emerge are that a model of the type outlined above, supplemented by data on extraction costs, is capable of giving a significant explanation of the long-run movement of the prices of various exhaustible resources. These results imply a picture which differs from the conventional one in two major respects- the relatively less important role of the level of industrial output as an influence on prices, and the major role of interest rate changes.
2. The influence of interest rates
Table 1 presents the results of estimating eq. (3). As a general point, it should be noted that all of the variables used in regressions reported in this paper are in the real terms. The general goodness of fit, as measured by the R2,is usually low, though it is worth emphasising that we have a very long time series covering two world wars, the great depression, the Korean war and the 1973/1974 commodity boom, and that this series is in first difference form. High values of R2 are therefore not to be expected. However, three positive features stand out from these results: (1) at least one of the lagged endogenous variables usually has a coefficient significantly different from zero. (2) At least one of the interest rate coefficients is usually significantly different from zero, in spite of the probable multicollinearity between the three interest rate variables. (3) A, +A, +A,, the sum of
98
G. Heal, M. Barrow / Empirical investigation of long-term resource prices movement
G. Heal, M. Barrow / Empirical investigation
of long-term resource prices movement
99
the coefficients on the interest rates, is invariably not significantly different from zero. So once again it is the change in the rate of interest, and not its level, that matters. 3. The effect of cost changes We adopt a formulation in which it is assumed that extraction costs are a function of two other observable variables, namely the current level of output L(t) and cumulative output to date, Z(f): Z(t)
=j,lL(T)d7,
i(t)
=I$),
with marginal extraction costs C given by C( Z(t),L( t)). The reasons for including Z and L here should be quite clear. Z is intended to capture the diminishing returns effect of increases in cumulative output forcing operators to use lower quality or deeper deposits, and L should reflect the increases in costs associated with a movement towards short-run capacity limits. The model is reformulated to take account of costs by assuming the supply and demand functions depend not on the gross return to the resource, but on the net return, given by the rate of change of the difference between price and marginal extraction costs. r,(=j/p) is therefore to be replaced by (p - c)/( p - c). Obviously the dependence of c and d on Z and L will pose problems of non-linear estimation here, and we have chosen, given that the data is anyway only an approximation to the variables concerned, to simplify and replace e/p = rc, and C/( p - c) by either k/p or t/c. The results of both approaches are reported in Heal and Barrow (1980): both provide interesting results with the t/p variable performing marginally the better, so this is the case reported here. Let x = C/p: then if x is an argument of S and D, the equivalent of (2) includes terms in a/x. Once again we reduce this to 1 to avoid nonlinearities, and note that
The appearance of a term in (t/p) (p/p) is unfortunate, as it introduces a non-linearity in the dependent variable. In order to derive general conclusions about the form of the equation to be tested, we shall neglect
100
G. Heal, M. Barrow / Empirical inoedgation of long-term resource prices movement
,
-0.01
G,H
-0.001
B
64-104
ZAZ/P
Interest
Obs.
0.36
52-104
G,H
0.0002
-0.005
0.33
2.00
0.001
-0.008
-0.004
52-104
G,H
0.001
-0.001
0.45
3.42
-0.0004
-0.007
0.01 b (2.90)
52-104
G,H
64-104
-0.00003
-0.00001
0.006
0.34
2.15
0.0002
0.00
-0.001
B
-0.002
0.67
6.01
0.0003
-0.007b (-2.50)
0.006b (2.55)
52- 104
G,H
-0.003
0.008
0.42
3.00
-0.001
0.02
0.12b (2.59)
a PI= pig iron, Cu = copper, Pb= lead, Zn = zinc, Fu= fuel oil, Bx= bauxite, Mn = manganese. LEVI,LE V2= endogenous variable lagged once, twice; R,RI,R2= current interest rate, same lagged once, twice; XR = sum of interest rate coefficients; ZA Z = sum of coefficients on AZ variables; Interest=identity of the interest rate used in the regression; B=interest rate on 3 month U.S. Treasury Bills, O.M.R., N.Y.C.; H=interest rate on U.S. Treasury Bonds; G=interest rate on corporate bonds-AAA (Moody’s); F=F statistic of a regression, with the degrees of freedom indicated in brackets below. b Denotes coefficient significantly different from zero at 5% level.
52-104
-0.005
0.48
-0.0003
ZR
2.33
-0.001
-0.01
0.03
R2
2.79
-0.12b (-2.24)
A L/P2
F
-0.12
0.51
A L/P1
AL/P
102
the term in p/p, C==aZ+j3L
and also assume the cost function
giving
YL=~+
pi; ----P
(Yi P
pi P’
to be linear:
(6)
On the basis of this, we included terms in (.Z( t) - Z( t - l))/p(t - 1) and (L(t) - L(t - l))/p(t - 1) in the estimating difference equation. The results are reported in table 2 and in general show an improvement in the specification of the model. The cost-related variables prove to be particularly relevant in the cases of zinc and fuels and in general it is the variable related to cumulative extraction (AZ/p) which is the more important. The sum of the AZ/p variables is invariably insignificant from zero and, with the exception of copper, at least an order of magnitude smaller than the individual co-efficients. Although the inclusion of variables involving AZ/p and AL/p are only partial proxies for true marginal extraction costs they do improve the performance of the model. A more accurate measure of marginal extraction costs would have to include the effects of technical progress and new resource discoveries. Although not included in the tables reported here, it is worth mentioning that the growth rate of manufacturing output also performed well as an explanatory variable in some cases, and certainly better than in the study of short-run data reported in Heal and Barrow (1979). For a fuller discussion of this, see Heal and Barrow (1980). A point which is probably worth examining explicitly is the relationship between the models discussed in this section, and the Hotelling rule of price net of marginal extraction cost rising at the interest rate. Formally this requires
p-c
-=r P--C
which gives
r, =I
This will relate r, to interest rates and changes in extraction costs. In fact we found rC to be related to changes in interest rates and to the second difference of extraction costs, as predicted by supply and demand functions of the form D( p, Fc,P,t/c) and S( ~,?~,F,t/c). So the simple equilibrium version of Hotelling’s rule is again nested within the model tested, and is rejected. But of course the study as a whole confirms the more general idea that resource markets have some of the characteristics of asset markets, with rates of return being important variables.
G. Heal, M. Barrow / Empirical invebtigation of long-rerm resource prices movement 103
References Heal, G.M. and M.M. Barrow, 1979, The relationship between interest rates and metal price movements, Review of Economic Studies, Jan. Heal, G.M. and M.M. Barrow, 1980, Empirical investigation of the long-term movement of resource prices, to appear in V. Kerry Smith, ed., Sussex University Economics Working Paper. Hotelling, H., 193 1, The economics of exhaustible resources, Journal of Political Economy 39, 137- 175. Manthy, R.S., 1978, Natural resource commodities-A century of statistics (Johns Hopkins Press for Resources for the Future, Washington, DC). Smith, V. Kerry, 1979, An econometric analysis of the behaviour of natural resource prices (Johns Hopkins Press for Resources for the Future, Washington, DC).
95
EMPIRICAL INVESTIGATION OF THE LONG-TERM MOVEMENT OF RESOURCE PRICES A Preliminary Report
Geoffrey HEAL * University of Essex, Colchester CO4 3SQ, UK
Michael BARROW * University of Sussex, Falmer, Brightott BNI 9RH, UK Received
6 May 1980
This note reports the results of an investigation into the long-run movements of natural resource prices and their relationship to interest rates and extraction costs. The results do not support the equilibrium type Hotelling rule but rather a more general asset market approach.
1. Introduction
The aim of this paper is to report briefly on an extension of the analysis of Heal and Barrow (1979), which was performed on twelve years of monthly data, to a time series of annual data covering the last century. A fuller discussion is in Heal and Barrow (1980). The analysis is concerned specifically with exhaustible resources, and it is assumed that the supply of and demand for such resources depend not only on the current price, but also on the expected rate of capital gain on the resource and on the expected rate of return available from holding other assets. Thus if p is the resource price, r, =p/p (2 = dx/dt), r is the return elsewhere and f= and i are traders’ expectations of rc and r, market
* We are grateful to Mina Toksoz for research assistance, and to David Hendry for making available to us the computer programs on which this work is based. We have also received valuable comments from Graciela Chichilmsky, David Gulley, Joe Farrell, Donald Hanson and V. Kerry Smith The research was supported by grants from the U.K. Social Science Research Council and from U.N.I.T.A.R.
0165-1765/81/0000-0000/$02.50
0 1981 North-Holland
96 G. Heal, M. Burrow / Empirical inve&tigcrtion of long-term resource prices movement
clearing requires that
The inclusion of variables other than price is of course in the spirit of the classic analysis of Hotelling (193 l), which sees an exhaustible resource as an asset, the demand for which will depend inter alia on the return that it offers relative to returns elsewhere. Differentiating (1) logarithmically with respect to time, assuming the demand and supply functions to be of constant elasticity, and that expectations are formed adaptively, leads to the following differential equation:
r,{E(S,P) -E(D,P)}
++(S,FJ-E(D,Q) c
=;{E(D,?)--E(S,?)}, c
(2)
where E(i, j) is the elasticity of i with respect toj. It should be noted that here the rate of return on the resource, r,, appears both in level and rate of change form, whereas, the return on the other asset appears only in rate of change form. This follows from the fact that (1) contains terms in p, which is in effect the integral of r,, but no equivalent terms for r. Analysis of equations similar to (1) and (2) and their discrete transformations lead Heal and Barrow (1979) to estimate the following difference equation:
+A,r(t-l)+A,r(t-2)+c(t),
(3)
where x(t) is the value of variable x in period t, c(t) is a serially correlated error process and the interest rate coefficients A,, A, and A, satisfy the restriction: A, +A,
+A,
=O.
(4)
(4) can readily be seen to imply that it is the rate of change of the interest
rate, and not its level, that features in (3), and this in turn follows from
G. Heul, M. Barrow / Empirical inve>tigution of long-term resource prices movement
91
the fact that (2) contains only terms in the rate of change of r, and not terms in its level. In all of the work on monthly post-war data reported in Heal and Barrow, the hypothesis of a relationship of the form suggested by (3) and (4) received considerable support. One would not of course expect exactly the same equations to give an equally good fit over the long term, as there are factors that can be neglected over this shorter period that become influential in the long term. Changes in extraction costs and the discovery of new resource deposits might be expected to have significant effects on price movements. The present study therefore begins by using the model of the earlier study [i.e., (3) and (4)] on long-run data [see Manthy (1978) for a similar study see Smith (1979)], and then adds in variables to allow for the effects of cost changes. Unfortunately there are no reliable time series on any aspect of extraction costs over this period, so it has proved necessary to adapt techniques from the latent or unobservable variable literature to this problem. The conclusions that emerge are that a model of the type outlined above, supplemented by data on extraction costs, is capable of giving a significant explanation of the long-run movement of the prices of various exhaustible resources. These results imply a picture which differs from the conventional one in two major respects- the relatively less important role of the level of industrial output as an influence on prices, and the major role of interest rate changes.
2. The influence of interest rates
Table 1 presents the results of estimating eq. (3). As a general point, it should be noted that all of the variables used in regressions reported in this paper are in the real terms. The general goodness of fit, as measured by the R2,is usually low, though it is worth emphasising that we have a very long time series covering two world wars, the great depression, the Korean war and the 1973/1974 commodity boom, and that this series is in first difference form. High values of R2 are therefore not to be expected. However, three positive features stand out from these results: (1) at least one of the lagged endogenous variables usually has a coefficient significantly different from zero. (2) At least one of the interest rate coefficients is usually significantly different from zero, in spite of the probable multicollinearity between the three interest rate variables. (3) A, +A, +A,, the sum of
98
G. Heal, M. Barrow / Empirical investigation of long-term resource prices movement
G. Heal, M. Barrow / Empirical investigation
of long-term resource prices movement
99
the coefficients on the interest rates, is invariably not significantly different from zero. So once again it is the change in the rate of interest, and not its level, that matters. 3. The effect of cost changes We adopt a formulation in which it is assumed that extraction costs are a function of two other observable variables, namely the current level of output L(t) and cumulative output to date, Z(f): Z(t)
=j,lL(T)d7,
i(t)
=I$),
with marginal extraction costs C given by C( Z(t),L( t)). The reasons for including Z and L here should be quite clear. Z is intended to capture the diminishing returns effect of increases in cumulative output forcing operators to use lower quality or deeper deposits, and L should reflect the increases in costs associated with a movement towards short-run capacity limits. The model is reformulated to take account of costs by assuming the supply and demand functions depend not on the gross return to the resource, but on the net return, given by the rate of change of the difference between price and marginal extraction costs. r,(=j/p) is therefore to be replaced by (p - c)/( p - c). Obviously the dependence of c and d on Z and L will pose problems of non-linear estimation here, and we have chosen, given that the data is anyway only an approximation to the variables concerned, to simplify and replace e/p = rc, and C/( p - c) by either k/p or t/c. The results of both approaches are reported in Heal and Barrow (1980): both provide interesting results with the t/p variable performing marginally the better, so this is the case reported here. Let x = C/p: then if x is an argument of S and D, the equivalent of (2) includes terms in a/x. Once again we reduce this to 1 to avoid nonlinearities, and note that
The appearance of a term in (t/p) (p/p) is unfortunate, as it introduces a non-linearity in the dependent variable. In order to derive general conclusions about the form of the equation to be tested, we shall neglect
100
G. Heal, M. Barrow / Empirical inoedgation of long-term resource prices movement
,
-0.01
G,H
-0.001
B
64-104
ZAZ/P
Interest
Obs.
0.36
52-104
G,H
0.0002
-0.005
0.33
2.00
0.001
-0.008
-0.004
52-104
G,H
0.001
-0.001
0.45
3.42
-0.0004
-0.007
0.01 b (2.90)
52-104
G,H
64-104
-0.00003
-0.00001
0.006
0.34
2.15
0.0002
0.00
-0.001
B
-0.002
0.67
6.01
0.0003
-0.007b (-2.50)
0.006b (2.55)
52- 104
G,H
-0.003
0.008
0.42
3.00
-0.001
0.02
0.12b (2.59)
a PI= pig iron, Cu = copper, Pb= lead, Zn = zinc, Fu= fuel oil, Bx= bauxite, Mn = manganese. LEVI,LE V2= endogenous variable lagged once, twice; R,RI,R2= current interest rate, same lagged once, twice; XR = sum of interest rate coefficients; ZA Z = sum of coefficients on AZ variables; Interest=identity of the interest rate used in the regression; B=interest rate on 3 month U.S. Treasury Bills, O.M.R., N.Y.C.; H=interest rate on U.S. Treasury Bonds; G=interest rate on corporate bonds-AAA (Moody’s); F=F statistic of a regression, with the degrees of freedom indicated in brackets below. b Denotes coefficient significantly different from zero at 5% level.
52-104
-0.005
0.48
-0.0003
ZR
2.33
-0.001
-0.01
0.03
R2
2.79
-0.12b (-2.24)
A L/P2
F
-0.12
0.51
A L/P1
AL/P
102
the term in p/p, C==aZ+j3L
and also assume the cost function
giving
YL=~+
pi; ----P
(Yi P
pi P’
to be linear:
(6)
On the basis of this, we included terms in (.Z( t) - Z( t - l))/p(t - 1) and (L(t) - L(t - l))/p(t - 1) in the estimating difference equation. The results are reported in table 2 and in general show an improvement in the specification of the model. The cost-related variables prove to be particularly relevant in the cases of zinc and fuels and in general it is the variable related to cumulative extraction (AZ/p) which is the more important. The sum of the AZ/p variables is invariably insignificant from zero and, with the exception of copper, at least an order of magnitude smaller than the individual co-efficients. Although the inclusion of variables involving AZ/p and AL/p are only partial proxies for true marginal extraction costs they do improve the performance of the model. A more accurate measure of marginal extraction costs would have to include the effects of technical progress and new resource discoveries. Although not included in the tables reported here, it is worth mentioning that the growth rate of manufacturing output also performed well as an explanatory variable in some cases, and certainly better than in the study of short-run data reported in Heal and Barrow (1979). For a fuller discussion of this, see Heal and Barrow (1980). A point which is probably worth examining explicitly is the relationship between the models discussed in this section, and the Hotelling rule of price net of marginal extraction cost rising at the interest rate. Formally this requires
p-c
-=r P--C
which gives
r, =I
This will relate r, to interest rates and changes in extraction costs. In fact we found rC to be related to changes in interest rates and to the second difference of extraction costs, as predicted by supply and demand functions of the form D( p, Fc,P,t/c) and S( ~,?~,F,t/c). So the simple equilibrium version of Hotelling’s rule is again nested within the model tested, and is rejected. But of course the study as a whole confirms the more general idea that resource markets have some of the characteristics of asset markets, with rates of return being important variables.
G. Heal, M. Barrow / Empirical invebtigation of long-rerm resource prices movement 103
References Heal, G.M. and M.M. Barrow, 1979, The relationship between interest rates and metal price movements, Review of Economic Studies, Jan. Heal, G.M. and M.M. Barrow, 1980, Empirical investigation of the long-term movement of resource prices, to appear in V. Kerry Smith, ed., Sussex University Economics Working Paper. Hotelling, H., 193 1, The economics of exhaustible resources, Journal of Political Economy 39, 137- 175. Manthy, R.S., 1978, Natural resource commodities-A century of statistics (Johns Hopkins Press for Resources for the Future, Washington, DC). Smith, V. Kerry, 1979, An econometric analysis of the behaviour of natural resource prices (Johns Hopkins Press for Resources for the Future, Washington, DC).