Finally, we have a revised version of the meta-analysis paper I presented in Perth in September out as a working paper.

So what's it all about? There is a massive literature on Granger causality testing of whether energy use causes economic growth or vice versa. We collected more than 400 papers. Yet the literature is very inconclusive. In fact we found that about 40% of tests for each direction of causation in our sample of 70 or so papers have statistically significant results at the 5% level. 40% is a lot more than 5% so either there must be a real effect or some kind of biases. On the other hand, it's not overwhelming evidence.

A recent paper conducted the first meta-analysis of this field of research. When we noticed this paper, we were initially worried that we had been "scooped". But, it turned out that the analysis in Chen

We do this separately for tests of energy causes output and output causes energy. Overall there is no genuine effect in the literature but there do seem to be some genuine effects in subsets of the literature. Specifically, if we control for energy prices then income causes energy use. This is the energy demand function relationship, which Stern and Enflo also found was very strong in the Swedish data. Energy use might cause income but only if we control for employment and the VAR model passes a cointegration test. So, this is pretty tentative. There were some things we would have liked to test but simply had too little data. For example, does adjusting for energy quality make a difference?

There is a whole other story in the paper, which is about dealing with the econometric pitfalls associated with these kind of time series models. Initially, we found that the greater the degrees of freedom the more negative the test statistics were. Significantly so. It turns out that there is a tendency to included too many lags of the variables in small sample sizes. And these over-fitted models result in spurious rejections of the null hypothesis of no Granger causality. We control for this issue by including the number of degrees of freedom lost in fitting the model as an independent variable. This is likely to be important in other meta-analyses of Granger causality tests. We have a further econometric theory paper in preparation on this topic.

In some ways this is a silly question. We know that energy is used to produce things and we know that in theory income is a determinant in the demand function for energy. But observing that in the data in a consistent way doesn't seem to be that easy.

So what's it all about? There is a massive literature on Granger causality testing of whether energy use causes economic growth or vice versa. We collected more than 400 papers. Yet the literature is very inconclusive. In fact we found that about 40% of tests for each direction of causation in our sample of 70 or so papers have statistically significant results at the 5% level. 40% is a lot more than 5% so either there must be a real effect or some kind of biases. On the other hand, it's not overwhelming evidence.

A recent paper conducted the first meta-analysis of this field of research. When we noticed this paper, we were initially worried that we had been "scooped". But, it turned out that the analysis in Chen

*et al*. is fairly exploratory. Our paper tries to see if the effects found in the literature are genuine or simply the results of various biases. We do this by exploiting the "statistical power trace" - if an effect is non-zero then the test statistic associated with restricting it to zero should be greater in absolute value the greater the degrees of freedom associated with the model estimate. So we regress the test statistics for the Granger causality tests - after converting them all to normal test statistics - on the square root of the degrees of freedom. The way we have set things up, if we can reject the null that the regression coefficient on the square root of degrees of freedom is non-positive then there is a real Granger causality effect in the underlying literature.We do this separately for tests of energy causes output and output causes energy. Overall there is no genuine effect in the literature but there do seem to be some genuine effects in subsets of the literature. Specifically, if we control for energy prices then income causes energy use. This is the energy demand function relationship, which Stern and Enflo also found was very strong in the Swedish data. Energy use might cause income but only if we control for employment and the VAR model passes a cointegration test. So, this is pretty tentative. There were some things we would have liked to test but simply had too little data. For example, does adjusting for energy quality make a difference?

There is a whole other story in the paper, which is about dealing with the econometric pitfalls associated with these kind of time series models. Initially, we found that the greater the degrees of freedom the more negative the test statistics were. Significantly so. It turns out that there is a tendency to included too many lags of the variables in small sample sizes. And these over-fitted models result in spurious rejections of the null hypothesis of no Granger causality. We control for this issue by including the number of degrees of freedom lost in fitting the model as an independent variable. This is likely to be important in other meta-analyses of Granger causality tests. We have a further econometric theory paper in preparation on this topic.

In some ways this is a silly question. We know that energy is used to produce things and we know that in theory income is a determinant in the demand function for energy. But observing that in the data in a consistent way doesn't seem to be that easy.

I don't think the question you explore here is "silly" at all. There is a reason that mainstream growth theory primarily relies on functional form models, even though it might seem you could just "go to the data" and use time series comparisons and regressions; there are just so many ways to get spurious correlations with the latter approach.

ReplyDeleteYour paper was just what I was looking for. Economic historians (such as Kander and Malanima's Princeton-published "Power to the People") have been resorting to time series regressions in ways that I found pretty puzzling. When I tried to understand this usage I stumbled upon the multitudinous "Energy Consumption and Economic Growth" cointegration articles you refer to. So I was glad to find the overview offered in some of your papers. You have saved a layman some serious thrashing around in matters that are way over his head!

I should clarify my earlier comment. My search was actually kicked off by an handbook entry by Paolo Malanima that referenced a graph correlating energy consumption and GDP growth in Kander, Malanima, and Warde's book. Kander herself actually seems much more in the energy-as-production-function-input tradition (as in her article with you) than in the time series comparison tradition.

ReplyDeleteThe Malanima "Energy in History" contains an interesting equation, Y/P = (E/P)*(Y/E) (where "E" might as well be the number of students taking an econometrics class at ANU!). He defines rate of growth E/P as e-dot and of Y/E as pi-dot, and then states that the growth of Y/P = e-dot plus pi-dot. he then shows a diagram correlating Y/P and E/P time series and says (in the working paper) "The difference between the interpolating exponential curves was filled through the rise in the efficiency of energy use". That last comment gets dropped, thank goodness, from the published article - but it seems to me that the whole scheme, even allowing for some extreme algebraic simplification, is nonsense.

I like the "role of energy" article a lot. I'm still digesting the details but the approach (if one accepts the thought that a single production function can describe pre-modern and modern economies) makes sense to me. I'm skeptical about the part in brackets - the differences between historically pre-industrial and industrial economies may not be the same as the differences between poor and rich nations today - but I'm more than willing to see where this goes.

Great blog, TB