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Energy and the economy— A reply to Smil and Kuz
54
Long Range Planning Vol. 10
February 1977
Energy and the EconomyA Reply to Smil and Kuz L. G. Brookes
In the June 1976 edition of this journal Smil and Kuz discussed the case for saying that there are quite firm relationships between energy consumption and GDP. They argued broadly that there was no general relationship, but, instead, the individual countries are locked into individuaf patterns of energy consumption. The proponents of the ‘there is a relationship’ school of thought include the author of this reply who is employed in the Economics and Programmes Branch of the U.K. Atomic Energy Authority.
This version of the work of Smil and Kuz* is open to less objection than earlier versions in other journals-partly, I suspect, because they have profited by the criticism that their earlier publications evoked-but it is still a very inadequate piece of work in the following respects: (1) It completely misses the point of the work of the people it claims to refute. Their object was to see whether general relationships existed, not to produce curve or line fits with high Y values, which Smil and Kuz seem to regard as the be-all and end-all. Neither, given their aims is there anything wrong in selecting data provided the researcher starts with some intellectually derived hypothesis that he wishes to test and explains why it is sensible to limit the data used in his tests, or otherwise all that results is a mindless curve fitting exercise. It would, for example, be pointless to look at the energy GDP relationships of tropical islands living entirely on the export of bananas if one wanted to examine how energy contributes to GDP in industrial societies; indeed any form of national specialization- for example in light, high technology industry, whilst importing all heavy energy dependent industrial products, like steel-produces a country which will not exhibit the features that the researcher is trying to examine. This is only a way of saying that a high level of disaggregation results in macro-effects being lost and if it is macroeffects that are being examined the researcher must either aggregate or be selective.) Energy and The Economy-A L.R.P. June 1976.
l
Global
and National
Analysis
To be brutally frank Smil and Kuz do not seem to understand what they themselves have done, any more than they have understood what the people they are criticizing have done. Far from their results refuting others, they in fact support them. Their lack of understanding is, however, at an even more unsophisticated level than this. They simply do not seem to know enough about elementary mathematics to appreciate the significance of some of the results they obtained from their rather mechanical application of simple linear regression. There are more examples of this in some of their other publications, but there are enough examples in the article under discussion to make it possible to make this charge. (2)
(3) In the end all they have done is to say that simple linear regressions produce fairly good short term forecasts of energy requirements, using GDP as the independent variable. So what? This is where most tyro forecasters start. There is not even any evidence that they have made any actual projections of their own. In other words they do not seem to have tested the predictive capability of the straight lines they have found, they say only that a good value of r is obtained from a straight line fitted to the points for the whole period they examined. There is moreover no analysis that justifies the rejection of the hypotheses advanced and tested by other people (includmg myself) or for their claim that individual countries are all locked into individual patterns of energ consumption. The only evidence they have is that tK e value of I for cross-sections covering groups of countries is lower than that for time series for individual countries. Given all the dif?iculties in obtaining comparability between countries (differences in exchange rates, differences in fuel mixes and so on) this is precisely what we should have expected. It tells us nothing about basic underlying relationships between energy consumption and GDP. First we have to give some marks to Smil and Kuz for producing a fairly complete list of all the problems and pitfalls facing energy statisticians-the difhculty of finding suitable ‘exchange rates’ behveen fuels that are very different in nature and application, the difficulties that
Energy and the Economy-A arise because external exchange rates do not reflect internal purchasing powers etc. As I have said earlier, I suspect that critics of some of their earlier paper deserve the credit for some of the items in this list. More importantly, however, there is no evidence whatever that they heeded their own warnings about these problems when they came to do their own analyses. The fairly low value of r for cross-section regressions is attributed to the absence of any basic relationship between energy consumption and GDP: the effects of differences in fuel mixes and the problem of purchasing power parities is just not considered as a reason why the regressions based on time series for individual countries could produce much better values for r than regressions based on crosssections using groups of countries. Let us look for a moment at the regressions based on groups of countries, because it provides an example of the apparent deficiencies of Smil and Kuz in the field of elementary mathematics. They linearized the expression Y = aXb (where Y is energy and X is GDP) by taking simple logarithms to produce the linear expression log Y = log a + b log X. The fact that linearization of this sort produces a somewhat bastard fit that is not the best least squares fit to the original function is probably too complicated for Smil and Kuz so I will pass over it. Their more elementary failing is in apparently attributing great significance to the fact that the poorer groups of countries produced negative intercepts on the log Y axis whilst the richer ones produced positive intercepts. There is in fact no significance whatever about the sign of these intercepts. They could have been made all positive or all negative simply by choosing different units. If there is any significance in these intercepts it is that their antilog is larger for richer countries than for poorer countries, and the richer they get the bigger it gets. Now this antilog is simply the value of a in the expression Y = aX* ; and all that they have learned is that, for any given energy elasticity, rich countries consume more commercial energy per unit of output than poor countries do. Did we need all this pseudo-erudition to tell us this? The significant point about these regressions-that, in general, as countries get richer the intercept gets larger and the slope smaller -is dismissed, although it in fact supports one of the hypotheses they are claiming to dismiss, namely that energy elasticities are not constant (Y = aXb is the wrong model, in other words); as countries become more affluent they move along a path that forms a curve on a double log scale with just the properties that Smil and Kuz found. In this version of their work (unlike some others) they go so far as to say that ‘an audacious interpretation of these statistics would be to suggest a general process model where different stages of economic development would correspond to various positions of regression lines . . . as they rotate clockwise from negative intercepts and steep slope to positive intercepts and shallow slopes.’ Would it be audacious however to develop an a priori hypothesis that the energy GDP relationship should change in this way; then to test it statistically and, having found that there was no statistically significant difference between the expected and actual results to offer the hypothesis as
Reply to Smil and Kuz
55
one that had been reasonably tested. This is precisely what I did (reported in ]ourrzal of Industrial Economics (November 1972) and in Long Range Planning (September 1973)) and this is what Smil and Kuz claim to have rebutted by tests which in fact lend support to it! I would not myself attach a lot of importance to this support because the exercise was not conducted on a yer capita basis. In other words increases in production due to increases in population were lumped along with increases due to higher levels of industrialization as if they were all the same thing. Such a chaotic analysis can hardly be expected to tell us anything about the underlying relationships between energy consumption and GDP. But equally it cannot be advanced as having given us any reason for rejecting the idea of any such relationship-especially as the indications, for what they are worth, are in entirely the opposite direction. Having erected this very ramshackle Aunt Sally and formed the mistaken impression that they had knocked it down, Smil and Kuz then moved on to look at individual country regressions over time. They paused for a moment to use the simple linear equation Y = u + bX on a total GDP basis (i.e. not using per capita figures) just to give, to their own satisfaction at any rate, the final coup de grace to my thesis that the per cllpita use&l energy coefficient tends asymptotically to a value of unity. Why on earth they should think this exercise produces anything to refute my hypothesis it is hard to imagine. Consider the following : (1) Only per capita studies can tell us anything about the basic relationships between energy and GDP. Total GDP studies-especially for poor countries with high population growths-introduce the complication of extra output due to a larger labour force. In any case my hypothesis was about per capita elasticities, not total GDP elasticities. (2) Through time studies introduce the complication of changes in fuel mixes over time. They do not tell you anything about useful energy elasticities (i.e. elasticities which exclude such time dependent effects). (3) The simple linear expression Y = a + bX does not produce an estimate of the energy elasticity in any event. It produces an estimate of the marginal energy content per unit of output. Ironically, however, the choice of this model has implications which support my hypothesis, as I will explain below. Having paused for this brief pointless exercise, Smil and Kuz then switched to per capita figures in order to demonstrate the stability of their own thesis-namely that individual countries are locked into very firm energy GDP relationships of their own. They are quite right to use per capita figures. Those of us whose work Smil and Kuz claim to have dismissed by their naive and woolly analysis would have appreciated the same courtesy being shown to the examination of their work. Let us consider for a moment the significance of the choice by Smil and Kuz of the very elementary model
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February 1977
Y = a + 6X. Presumably they chose it because they thought it was a better model than the constant elasticity for their too-ready model Y = aXb. Unfortunately dismissal of the case for saying that energy elasticities converge ultimately to a value of unity, the model they have chosen has precisely this property ! This can easily be demonstrated as follows : 1 XdY elasticity c = - = YdX W+1’ which tends to 1 as X tends to infinity. In other words by demonstrating (to their own rather dubious standards at any rate) a high degree of conformity to this simple model they have lent support to my hypothesis whilst, at the same time claiming to have disproved it ! They go on however to draw all sorts of unwarranted conclusions from the fact that different values of the parameters cl and b emerge for different countries. They assume that these differences are due to real differences between the energy GDP patterns of the countries themselves. They ignore all the warnings they uttered in the first part of their article about factors (like the inadequacy of exchange rates to reflect internal purchasing powers, the d&&y of putting different fuels on a common footing, the special problem of countries with a high proportion of hydra-electricity etc.) which they found. Indeed some of these differences have been analysed and evaluated by Darmstadter (whose work they mention) and by Adams and Miovic-whose work they do not mention in this article but which is referred to in other articles of theirs. There is no attempt to quantify any of these effects (although Adams and Miovic did a man-sized job in quantifying some of them) and the entirely unscientific conclusion is drawn that the differences in the regressions are due to ‘individual countries being locked into individual patterns of energy consumption.’ One could more easily forgive this sort of thing if it was not combined with entirely unfounded and manufactured criticism of other people. Earlier in their article they say ‘misuse of statistical inference and tests of significance is compounded by the careless treatment of correlation coefficients’. They talk learnedly about the dangers of handling small groups with non-homoscedastic distributions. Yet they themselves apply least squares fits (which imply homoscedastic distributions) to logarithmic transformations (which result in loss of homoscedasticity). This is alright if one can convince oneself that random variations take a percentage rather than a linear form but nowhere do they make this stipulation, nor is there any corresponding statement that the linear equations were fitted by percentage least squares rather than linear least squares (which would be the consistent thing to do). These are rather hairsplitting points but they need to be made to people who make wild accusations about the rigorousness of other people’s work. It is especially galling in this case that the accusations are based not on what Darmstadter and I respectively did, but on what Smil and Kuz did with our data !
At one point they say ‘Brookes and Darmstadter normalized distributions by converting to decadic logarithms . . .’ and they then go on to produce some results based on the principle of constant energy elasticities. I did not convert figures to decadic logarithms or any other sort of logarithms.* Neither Darmstadter nor I, in our separate ways, subscribe to the idea of a constant elasticity relationship between energy and GDP. What purpose, then, is served by ascribing constant elasticity equations to us and then criticizing them? Smil and Kuz must be hard up for material to complain about it if they have to manufacture it. Let us now consider what Smil and Kuz have actually done. They have put their telescopes to their blind eyes and have said ‘We see no general relationships. Therefore anyone who does must be wrong.’ They have then gone on to say ‘But when-ignoring all the warnings we have given to other people at the beginning of our article-we fit simple linear equations to time series for individual countries we get quite good straight line tits whose slopes and intercepts differ from country to country. Again ignoring all the warnings that we have given to other people at the beginning of our article, we conclude that these differences are highly significant (although we apply no tests of significance) and they are due to individual countries being locked into individual patterns of energy consumption. Moreover we claim, on the basis of the correlation coefficients we found, excellent predictive properties for the individual straight lines that we found, although we have never made any predictions with them and do not understand why this particular modelt should explain the relationship between energy and GDP for the countries concerned. Everyone else is a sissy and their work is no good for forecasting.’ Let me now say briefly, by way of contrast, what I did. It was very far from perfect and I would dearly like to find the time to pursue these studies further, but I am not lucky enough to be a university research worker; I have a full time job to do. This will be a very brief account. The work is explained in more detail in the September 1973 issue of Long Range Planning and in even more detail in the Journal of In&rtrial Econorrrics for November 1972. I formed the very simple view that increasing GDP per capita was mainly due to the harnessing of more and more mechanical slaves per man in the shape of fuel consuming machines of one sort or another. This led to the conclusion (explained in detail elsewhere)
In fact I fitted the above two equations directly, i.e. without linearization (no mean feat in itself I) because they have the properties that I was hypothesizing. t Where the intercepts are positive the model is a nonsense because it implies energy consumption at zero GDP. Where they are negative-as they are in most cases-the model crudely supports my hypothesis that the energy coefficient falls asymptotically to zero from above. l
Energy and the Economy-A that as a country moves from a primitive state to a state of fully industrialized development its per capita energy coefficient must fall from some very high initial value, asymptotically approaching unity. The two functions mentioned in the footnote have this property. Provisos had to be made, however, about the definition of energy usage. Adams and Miovic had shown that to substitute oil or primary electricity for coal was equivalent, in its effect on GDP, to making large increases in primary energy consumption. But to use their findings in testing my hypothesis would introduce circularity. I overcame the difficulty by making the assumption (and it was no more than an assumption) that there was no trend in the mix of fuels at any point in time between the richer and poorer countries in the sample I took. Then by concentrating upon cross-section analysis I could eliminate time dependent effects like improvements in thermal efficiency over time and changes in fuel mixes over time. By producing a time series of such cross-section analyses I could perhaps learn something about the time dependent effects. The point was that the two-co-ordinate approach gave me some chance to disentangle underlying effects from time dependent effects. I make no apologies for being selective in the choice of my sample, I deliberately excluded countries with lopsided econo-
Enagy 4
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mies and lopsided energy systems. The outcome of this work was 32 ‘world lines’ (two different functions for each of 16 years). But they were all very close to one another and differences between them could very credibly be explained by slow time dependent effects. Much of the dispersion about the lines could also be explained (qualitatively only) by differences in climate (resultin in a different requirement for space heating) and di P erences between official exchange rates and purchasing power parities. The trend of the world cross-section energy coefficient for the whole of the 22 countries and for the richer and poorer 10 (there was some changing of position in the middle) was also examined. Statistical tests showed that the world cross-section energy coefficient was approaching asymptotically a value that was not statistically significantly different from 1. The poorer 10 countries had an average energy coefficient for the l&year period of l-464 with a standard deviation of only 0.121 and, for the richer 10, the figure was 1.037 with a standard deviation of 0.0413. In other words there was a good deal of evidence (by no means perfect it is true) for saying that the original hypothesis was born out by facts about world energy usage in practice. The hypothesis could, with care, be used as a basis for forecasting. Its
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Vol. 10
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great advantage lay in the fact that the user could claim some understanding about the mechanisms at work and make allowance for future changes in fuel mixes by applying the foldings of Adams and Miovic to assumptions about changes in fuel mixes. Moreover, because the ‘world lines’ were produced independently from time series of the experience of individual countries and because the world line for 1950 was not significantly different from that for 1965 (or indeed for any of the years in between) the predictive ability of the world line could be tested against the experience of individual countries, converting their fuel usage into units of useful energy by applying the work of Adams and Miovoc. This was done for the U.K. and U.S.A. with the results shown in Figures 1 and 2. The values of r were collectively as good as those found by Smil and Kuz for their simple linear model (significantly better for the U.K., not quite so good for the U.S.A.) but with the very big difference that the line with which the points were being compared was produced quite inde-
1977 pendently of the points with which it was being compared. In other words r quite genuinely measures the predictive capability of the model. This is quite different from the situation with the lines produced by Smil and Kuz. In their case r measures the dispersion of points about a line that was derived from those very same poirits. This is no test of predictive power. It is simply a test of linearity. I would claim from all this that I can have much more confidence in the ability of my model to predict the energy requirements of some future level of GDP; and, what is more, can, using the work of Adams and Miovic, incorporate the likely differences in the prediction that could arise from changes in the proportions of the different fuels. I will say no more.
.&knowledgement-The work on which this reply is based was conducted as part of the author’s duties as a member of the staff of the UKAEA, but the opinions expressed are his own.
Long Range Planning Vol. 10
February 1977
Energy and the EconomyA Reply to Smil and Kuz L. G. Brookes
In the June 1976 edition of this journal Smil and Kuz discussed the case for saying that there are quite firm relationships between energy consumption and GDP. They argued broadly that there was no general relationship, but, instead, the individual countries are locked into individuaf patterns of energy consumption. The proponents of the ‘there is a relationship’ school of thought include the author of this reply who is employed in the Economics and Programmes Branch of the U.K. Atomic Energy Authority.
This version of the work of Smil and Kuz* is open to less objection than earlier versions in other journals-partly, I suspect, because they have profited by the criticism that their earlier publications evoked-but it is still a very inadequate piece of work in the following respects: (1) It completely misses the point of the work of the people it claims to refute. Their object was to see whether general relationships existed, not to produce curve or line fits with high Y values, which Smil and Kuz seem to regard as the be-all and end-all. Neither, given their aims is there anything wrong in selecting data provided the researcher starts with some intellectually derived hypothesis that he wishes to test and explains why it is sensible to limit the data used in his tests, or otherwise all that results is a mindless curve fitting exercise. It would, for example, be pointless to look at the energy GDP relationships of tropical islands living entirely on the export of bananas if one wanted to examine how energy contributes to GDP in industrial societies; indeed any form of national specialization- for example in light, high technology industry, whilst importing all heavy energy dependent industrial products, like steel-produces a country which will not exhibit the features that the researcher is trying to examine. This is only a way of saying that a high level of disaggregation results in macro-effects being lost and if it is macroeffects that are being examined the researcher must either aggregate or be selective.) Energy and The Economy-A L.R.P. June 1976.
l
Global
and National
Analysis
To be brutally frank Smil and Kuz do not seem to understand what they themselves have done, any more than they have understood what the people they are criticizing have done. Far from their results refuting others, they in fact support them. Their lack of understanding is, however, at an even more unsophisticated level than this. They simply do not seem to know enough about elementary mathematics to appreciate the significance of some of the results they obtained from their rather mechanical application of simple linear regression. There are more examples of this in some of their other publications, but there are enough examples in the article under discussion to make it possible to make this charge. (2)
(3) In the end all they have done is to say that simple linear regressions produce fairly good short term forecasts of energy requirements, using GDP as the independent variable. So what? This is where most tyro forecasters start. There is not even any evidence that they have made any actual projections of their own. In other words they do not seem to have tested the predictive capability of the straight lines they have found, they say only that a good value of r is obtained from a straight line fitted to the points for the whole period they examined. There is moreover no analysis that justifies the rejection of the hypotheses advanced and tested by other people (includmg myself) or for their claim that individual countries are all locked into individual patterns of energ consumption. The only evidence they have is that tK e value of I for cross-sections covering groups of countries is lower than that for time series for individual countries. Given all the dif?iculties in obtaining comparability between countries (differences in exchange rates, differences in fuel mixes and so on) this is precisely what we should have expected. It tells us nothing about basic underlying relationships between energy consumption and GDP. First we have to give some marks to Smil and Kuz for producing a fairly complete list of all the problems and pitfalls facing energy statisticians-the difhculty of finding suitable ‘exchange rates’ behveen fuels that are very different in nature and application, the difficulties that
Energy and the Economy-A arise because external exchange rates do not reflect internal purchasing powers etc. As I have said earlier, I suspect that critics of some of their earlier paper deserve the credit for some of the items in this list. More importantly, however, there is no evidence whatever that they heeded their own warnings about these problems when they came to do their own analyses. The fairly low value of r for cross-section regressions is attributed to the absence of any basic relationship between energy consumption and GDP: the effects of differences in fuel mixes and the problem of purchasing power parities is just not considered as a reason why the regressions based on time series for individual countries could produce much better values for r than regressions based on crosssections using groups of countries. Let us look for a moment at the regressions based on groups of countries, because it provides an example of the apparent deficiencies of Smil and Kuz in the field of elementary mathematics. They linearized the expression Y = aXb (where Y is energy and X is GDP) by taking simple logarithms to produce the linear expression log Y = log a + b log X. The fact that linearization of this sort produces a somewhat bastard fit that is not the best least squares fit to the original function is probably too complicated for Smil and Kuz so I will pass over it. Their more elementary failing is in apparently attributing great significance to the fact that the poorer groups of countries produced negative intercepts on the log Y axis whilst the richer ones produced positive intercepts. There is in fact no significance whatever about the sign of these intercepts. They could have been made all positive or all negative simply by choosing different units. If there is any significance in these intercepts it is that their antilog is larger for richer countries than for poorer countries, and the richer they get the bigger it gets. Now this antilog is simply the value of a in the expression Y = aX* ; and all that they have learned is that, for any given energy elasticity, rich countries consume more commercial energy per unit of output than poor countries do. Did we need all this pseudo-erudition to tell us this? The significant point about these regressions-that, in general, as countries get richer the intercept gets larger and the slope smaller -is dismissed, although it in fact supports one of the hypotheses they are claiming to dismiss, namely that energy elasticities are not constant (Y = aXb is the wrong model, in other words); as countries become more affluent they move along a path that forms a curve on a double log scale with just the properties that Smil and Kuz found. In this version of their work (unlike some others) they go so far as to say that ‘an audacious interpretation of these statistics would be to suggest a general process model where different stages of economic development would correspond to various positions of regression lines . . . as they rotate clockwise from negative intercepts and steep slope to positive intercepts and shallow slopes.’ Would it be audacious however to develop an a priori hypothesis that the energy GDP relationship should change in this way; then to test it statistically and, having found that there was no statistically significant difference between the expected and actual results to offer the hypothesis as
Reply to Smil and Kuz
55
one that had been reasonably tested. This is precisely what I did (reported in ]ourrzal of Industrial Economics (November 1972) and in Long Range Planning (September 1973)) and this is what Smil and Kuz claim to have rebutted by tests which in fact lend support to it! I would not myself attach a lot of importance to this support because the exercise was not conducted on a yer capita basis. In other words increases in production due to increases in population were lumped along with increases due to higher levels of industrialization as if they were all the same thing. Such a chaotic analysis can hardly be expected to tell us anything about the underlying relationships between energy consumption and GDP. But equally it cannot be advanced as having given us any reason for rejecting the idea of any such relationship-especially as the indications, for what they are worth, are in entirely the opposite direction. Having erected this very ramshackle Aunt Sally and formed the mistaken impression that they had knocked it down, Smil and Kuz then moved on to look at individual country regressions over time. They paused for a moment to use the simple linear equation Y = u + bX on a total GDP basis (i.e. not using per capita figures) just to give, to their own satisfaction at any rate, the final coup de grace to my thesis that the per cllpita use&l energy coefficient tends asymptotically to a value of unity. Why on earth they should think this exercise produces anything to refute my hypothesis it is hard to imagine. Consider the following : (1) Only per capita studies can tell us anything about the basic relationships between energy and GDP. Total GDP studies-especially for poor countries with high population growths-introduce the complication of extra output due to a larger labour force. In any case my hypothesis was about per capita elasticities, not total GDP elasticities. (2) Through time studies introduce the complication of changes in fuel mixes over time. They do not tell you anything about useful energy elasticities (i.e. elasticities which exclude such time dependent effects). (3) The simple linear expression Y = a + bX does not produce an estimate of the energy elasticity in any event. It produces an estimate of the marginal energy content per unit of output. Ironically, however, the choice of this model has implications which support my hypothesis, as I will explain below. Having paused for this brief pointless exercise, Smil and Kuz then switched to per capita figures in order to demonstrate the stability of their own thesis-namely that individual countries are locked into very firm energy GDP relationships of their own. They are quite right to use per capita figures. Those of us whose work Smil and Kuz claim to have dismissed by their naive and woolly analysis would have appreciated the same courtesy being shown to the examination of their work. Let us consider for a moment the significance of the choice by Smil and Kuz of the very elementary model
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Y = a + 6X. Presumably they chose it because they thought it was a better model than the constant elasticity for their too-ready model Y = aXb. Unfortunately dismissal of the case for saying that energy elasticities converge ultimately to a value of unity, the model they have chosen has precisely this property ! This can easily be demonstrated as follows : 1 XdY elasticity c = - = YdX W+1’ which tends to 1 as X tends to infinity. In other words by demonstrating (to their own rather dubious standards at any rate) a high degree of conformity to this simple model they have lent support to my hypothesis whilst, at the same time claiming to have disproved it ! They go on however to draw all sorts of unwarranted conclusions from the fact that different values of the parameters cl and b emerge for different countries. They assume that these differences are due to real differences between the energy GDP patterns of the countries themselves. They ignore all the warnings they uttered in the first part of their article about factors (like the inadequacy of exchange rates to reflect internal purchasing powers, the d&&y of putting different fuels on a common footing, the special problem of countries with a high proportion of hydra-electricity etc.) which they found. Indeed some of these differences have been analysed and evaluated by Darmstadter (whose work they mention) and by Adams and Miovic-whose work they do not mention in this article but which is referred to in other articles of theirs. There is no attempt to quantify any of these effects (although Adams and Miovic did a man-sized job in quantifying some of them) and the entirely unscientific conclusion is drawn that the differences in the regressions are due to ‘individual countries being locked into individual patterns of energy consumption.’ One could more easily forgive this sort of thing if it was not combined with entirely unfounded and manufactured criticism of other people. Earlier in their article they say ‘misuse of statistical inference and tests of significance is compounded by the careless treatment of correlation coefficients’. They talk learnedly about the dangers of handling small groups with non-homoscedastic distributions. Yet they themselves apply least squares fits (which imply homoscedastic distributions) to logarithmic transformations (which result in loss of homoscedasticity). This is alright if one can convince oneself that random variations take a percentage rather than a linear form but nowhere do they make this stipulation, nor is there any corresponding statement that the linear equations were fitted by percentage least squares rather than linear least squares (which would be the consistent thing to do). These are rather hairsplitting points but they need to be made to people who make wild accusations about the rigorousness of other people’s work. It is especially galling in this case that the accusations are based not on what Darmstadter and I respectively did, but on what Smil and Kuz did with our data !
At one point they say ‘Brookes and Darmstadter normalized distributions by converting to decadic logarithms . . .’ and they then go on to produce some results based on the principle of constant energy elasticities. I did not convert figures to decadic logarithms or any other sort of logarithms.* Neither Darmstadter nor I, in our separate ways, subscribe to the idea of a constant elasticity relationship between energy and GDP. What purpose, then, is served by ascribing constant elasticity equations to us and then criticizing them? Smil and Kuz must be hard up for material to complain about it if they have to manufacture it. Let us now consider what Smil and Kuz have actually done. They have put their telescopes to their blind eyes and have said ‘We see no general relationships. Therefore anyone who does must be wrong.’ They have then gone on to say ‘But when-ignoring all the warnings we have given to other people at the beginning of our article-we fit simple linear equations to time series for individual countries we get quite good straight line tits whose slopes and intercepts differ from country to country. Again ignoring all the warnings that we have given to other people at the beginning of our article, we conclude that these differences are highly significant (although we apply no tests of significance) and they are due to individual countries being locked into individual patterns of energy consumption. Moreover we claim, on the basis of the correlation coefficients we found, excellent predictive properties for the individual straight lines that we found, although we have never made any predictions with them and do not understand why this particular modelt should explain the relationship between energy and GDP for the countries concerned. Everyone else is a sissy and their work is no good for forecasting.’ Let me now say briefly, by way of contrast, what I did. It was very far from perfect and I would dearly like to find the time to pursue these studies further, but I am not lucky enough to be a university research worker; I have a full time job to do. This will be a very brief account. The work is explained in more detail in the September 1973 issue of Long Range Planning and in even more detail in the Journal of In&rtrial Econorrrics for November 1972. I formed the very simple view that increasing GDP per capita was mainly due to the harnessing of more and more mechanical slaves per man in the shape of fuel consuming machines of one sort or another. This led to the conclusion (explained in detail elsewhere)
In fact I fitted the above two equations directly, i.e. without linearization (no mean feat in itself I) because they have the properties that I was hypothesizing. t Where the intercepts are positive the model is a nonsense because it implies energy consumption at zero GDP. Where they are negative-as they are in most cases-the model crudely supports my hypothesis that the energy coefficient falls asymptotically to zero from above. l
Energy and the Economy-A that as a country moves from a primitive state to a state of fully industrialized development its per capita energy coefficient must fall from some very high initial value, asymptotically approaching unity. The two functions mentioned in the footnote have this property. Provisos had to be made, however, about the definition of energy usage. Adams and Miovic had shown that to substitute oil or primary electricity for coal was equivalent, in its effect on GDP, to making large increases in primary energy consumption. But to use their findings in testing my hypothesis would introduce circularity. I overcame the difficulty by making the assumption (and it was no more than an assumption) that there was no trend in the mix of fuels at any point in time between the richer and poorer countries in the sample I took. Then by concentrating upon cross-section analysis I could eliminate time dependent effects like improvements in thermal efficiency over time and changes in fuel mixes over time. By producing a time series of such cross-section analyses I could perhaps learn something about the time dependent effects. The point was that the two-co-ordinate approach gave me some chance to disentangle underlying effects from time dependent effects. I make no apologies for being selective in the choice of my sample, I deliberately excluded countries with lopsided econo-
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mies and lopsided energy systems. The outcome of this work was 32 ‘world lines’ (two different functions for each of 16 years). But they were all very close to one another and differences between them could very credibly be explained by slow time dependent effects. Much of the dispersion about the lines could also be explained (qualitatively only) by differences in climate (resultin in a different requirement for space heating) and di P erences between official exchange rates and purchasing power parities. The trend of the world cross-section energy coefficient for the whole of the 22 countries and for the richer and poorer 10 (there was some changing of position in the middle) was also examined. Statistical tests showed that the world cross-section energy coefficient was approaching asymptotically a value that was not statistically significantly different from 1. The poorer 10 countries had an average energy coefficient for the l&year period of l-464 with a standard deviation of only 0.121 and, for the richer 10, the figure was 1.037 with a standard deviation of 0.0413. In other words there was a good deal of evidence (by no means perfect it is true) for saying that the original hypothesis was born out by facts about world energy usage in practice. The hypothesis could, with care, be used as a basis for forecasting. Its
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February
great advantage lay in the fact that the user could claim some understanding about the mechanisms at work and make allowance for future changes in fuel mixes by applying the foldings of Adams and Miovic to assumptions about changes in fuel mixes. Moreover, because the ‘world lines’ were produced independently from time series of the experience of individual countries and because the world line for 1950 was not significantly different from that for 1965 (or indeed for any of the years in between) the predictive ability of the world line could be tested against the experience of individual countries, converting their fuel usage into units of useful energy by applying the work of Adams and Miovoc. This was done for the U.K. and U.S.A. with the results shown in Figures 1 and 2. The values of r were collectively as good as those found by Smil and Kuz for their simple linear model (significantly better for the U.K., not quite so good for the U.S.A.) but with the very big difference that the line with which the points were being compared was produced quite inde-
1977 pendently of the points with which it was being compared. In other words r quite genuinely measures the predictive capability of the model. This is quite different from the situation with the lines produced by Smil and Kuz. In their case r measures the dispersion of points about a line that was derived from those very same poirits. This is no test of predictive power. It is simply a test of linearity. I would claim from all this that I can have much more confidence in the ability of my model to predict the energy requirements of some future level of GDP; and, what is more, can, using the work of Adams and Miovic, incorporate the likely differences in the prediction that could arise from changes in the proportions of the different fuels. I will say no more.
.&knowledgement-The work on which this reply is based was conducted as part of the author’s duties as a member of the staff of the UKAEA, but the opinions expressed are his own.