From Correlation to Granger Causality

A rough draft of a new paper so don't cite it but comments are welcome. I have posted a couple of sections already on the blog. It's written for a workshop where I meant to present on "From correlation to causality" and I think I need to talk about both major approaches - instrumental variables and Granger causality. Then I do a Granger causality analysis of a bunch of variables with 150 year time series from Sweden to illustrate the points but also to contribute to the literature on energy and growth. The results support causality from energy to output but that relationship appears to have weakened or reversed in the second half of the 20th Century. Or maybe it is just harder to find anything significant in a shorter time series. Energy prices have a more significant impact on GDP than energy quantity in a model of GDP, energy price, and energy quantity, but again the relationship seems to weaken.

Representative Concentration Pathways

Everyone in the climate policy field is familiar with the SRES - Special Report on Emissions Scenarios developed by the IPCC more than a decade ago. It was time for an update and we now have the new RCP's. The primary focus here is on atmospheric concentrations of greenhouse gases and other radiatively active substances. There are four pathways with radiative forcing of 2.6, 4.5, 6, and 8.5 Wm^-2. The new scenarios are being published as a special (open access) issue of Climatic Change. The overview article is authored by Detlef van Vuuren et al. I'll focus here on the related emissions pathways.



The figures compare the new scenarios to each other, the general literature, and the 4 main SRES pathways. The main thing to note is that the 2.6 RCP has much stronger climate action than any of the SRES scenarios on both CO2 and CH4 emissions. For local air pollutants, the new pathways show much lower levels than any of the SRES pathways, especially for sulfur:



This makes sense and is in-line with new understanding on both historical and likely future sulfur emissions. This will make controlling global warming harder than would have been thought with the old scenarios.

Granger Causality Testing

More from my paper in progress. It's for an audience that isn't so familiar with econometrics but has a reasonable background in statistics. This is very rough, comments are very welcome!

A variable x is said to Granger cause another variable y if past values of x help predict the current level of y given all other appropriate information. This definition is based on the concept of causal ordering. Two variables may be contemporaneously correlated by chance but it is unlikely that the past values of x will be useful in predicting y, given all the past values of y, unless x does actually cause y in a philosophical sense. Similarly, if y in fact causes x, then given the past history of y it is unlikely that information on x will help predict y. Granger causality is not identical to causation in the classical philosophical sense, but it does demonstrate the likelihood of such causation or the lack of such causation more forcefully than does simple contemporaneous correlation (Geweke, 1984). However, where a third variable, z, drives both x and y, x might still appear to drive y though there is no actual causal mechanism directly linking the variables. The simplest test of Granger causality requires estimating the following two regression equations:



where p is the number of lags that adequately models the dynamic structure so that the coefficients of further lags of variables are not statistically significant and the error terms e are white noise. The error terms may, however, be correlated across equations. If the p parameters are jointly significant then the null that x does not Granger cause y can be rejected. Similarly, if the p parameters are jointly significant then the null that y does not Granger cause x can be rejected. This test is usually refereed to as the Granger causality test. There are several variants including the Sims (1972) causality test and the Toda and Yamamoto (1995) procedure discussed below.

There has been much criticism of Granger causality testing in the econometrics literature. Roberts and Nord (1985) found that the functional form of the time series affected the sensitivity of both Granger's and Sims' tests. Data that had undergone logarithmic transformation showed no sign of causality while the untransformed data yielded significant results. This stands to reason, as logarithmic transformation tends to reduce heteroscedasticity and increase the stationarity of the variables. However Chowdhury (1987) found more disturbing results that give support to those who have doubted whether Granger causality was related to philosophical causality or economic exogeneity in any meaningful way. He found that a Granger test indicated that GNP caused sunspots! A Sims test showed that prices caused sunspots! None of the alternative hypotheses were validated. Prices and income may be exogenous in the sunspot equations, but sunspots are not endogenous in any meaningful philosophical or economic way. But because sunspots are quite predictable prices and income might have anticipated them. The forward-looking behavior of human agents can be an obstacle to Granger causality testing.

Sargent (1979) and Sims (1980) introduced the vector autoregression or VAR modeling approach as a method of carrying out econometric analysis with a minimum of a priori assumptions about economic theory (Qin, 2011). The VAR model generalizes the model given by equations (1) and (2) to a multivariate setting. A multivariate Granger causality test can be identical to that described above but simply with more control variables in the regression but tests can also be constructed to exclude the lags of variables from multiple equations (Sims, 1980). The VAR approach to econometrics has been much criticized, but the critics, such as Epstein (1987) and Darnell and Evans (1990), argue that multivariate Granger causality tests are a (or the only) useful application of VARs. The advantage of multivariate Granger tests over bivariate Granger tests is that they can help avoid spurious correlations and can aid in testing the general validity of the causation test. This is through adding additional variables that may be responsible for causing y or whose effects might obscure the effect of x on y (Lütkepohl, 1982; Stern, 1993). There may also be indirect channels of causation from x to y, which VAR modeling could uncover.

Though a VAR cannot, due to limits on degrees of freedom, include all variables that may be causally related to the principal variable under investigation, some attempt can be made to include as many as possible. Of course, failure to reject the null hypothesis that x does not cause y, does not necessarily mean that there is in fact no causality. A lack of sensitivity could be due to a misspecified lag length, insufficiently frequent observations, too small a sample, or the lack of Granger causality even if philosophical causation occurs.

Engle and Granger (1987) introduced the notion of cointegration and tied it closely to the VAR model. Time series that must be differenced in order to render them stationary are referred to as integrated or stochastically trending series. The simplest case is the classic random walk where the current value of a variable is equal to its previous value plus a white noise error term. Typically, linear combinations of integrated process also are integrated. The residual from a regression of the two variables will be non-stationary. This violates the classical conditions for a linear regression. Such a regression is known as a spurious regression (Granger and Newbold, 1974). However, if a group of integrated variables share a common stochastic trend the linear combination will be non-integrated. This phenomenon - the elimination of a stochastic trend by an appropriate linear function - is known as cointegration (Engle and Granger, 1987). If two variables share a common trend, there will be Granger causality in one or more directions between them (Cuthbertson et al., 1992). Cointegration tests themselves cannot establish the direction of causality but tests can be applied to cointegrating VARs such as those estimated using the Johansen procedure (Johansen and Juselius, 1990).

An advantage of cointegration analysis is that if any integrated variables are omitted from the cointegrating relationship, which should be included in it, then the remaining variables will fail to cointegrate. Thus, if we can reject the null of non-causality in a cointegrated model, we can be more confident that this is not a spurious causality due to omitted variables.

References
Chowdhury, B. 1987. Are causal relationships sensitive to causality tests. Applied Economics 19: 459-465.

Cuthbertson, K., S. G. Hall, and M. P. Taylor. 1992. Applied Econometric Techniques. University of Michigan Press, Ann Arbor MI.

Darnell, A. and J. Evans. 1990. The Limits of Econometrics. Gower, Aldershot, Hampshire.

Engle, R. E. and C. W. J. Granger. 1987. Cointegration and error-correction: representation, estimation, and testing. Econometrica 55: 251-276.

Epstein, R. 1987. A History of Econometrics. North-Holland, Amsterdam.

Geweke, J. 1984. Inference and causality in economic time series models. In: Z. Griliches and M. D. Intriligator (eds.) Handbook of Econometrics. Elsevier Science Publishers, Amsterdam, 1101-1144.

Granger, C. W. J. 1969. Investigating causal relations by econometric models and cross-spectral methods. Econometrica 37: 424-438.

Granger, C. W. J. and P. Newbold. 1974. Spurious regressions in econometrics. Journal of Econometrics 2: 111-120.

Johansen, S. and K. Juselius. 1990. Maximum likelihood estimation and inference on cointegration with application to the demand for money. Oxford Bulletin of Economics and Statistics 52: 169-209.

Lütkepohl, H. 1982. Non-causality due to omitted variables. Journal of Econometrics 19: 367-378.

Qin, D. 2011. Rise of VAR modeling approach. Journal of Economic Surveys 25(1): 156-174.

Roberts D. and S. Nord (1985) Causality tests and functional form sensitivity, Applied Economics 17, 135-141.

Sargent, T. 1979. Estimating vector autoregressions using methods not based on explicit economic theories. Federal Reserve Bank of Minneapolis, Quarterly Review 3(3): 8-15.

Sims, C. A. 1972. Money, income and causality. American Economic Review 62: 540-552.

Sims, C. A. 1980. Macroeconomics and reality. Econometrica 48: 1-48.

Stern, D. I. 1993. Energy use and economic growth in the USA: a multivariate approach. Energy Economics 15: 137-150.

Toda, H, Y. and T. Yamamoto. 1995. Statistical inference in vector autoregressions with possibly integrated processes. Journal of Econometrics 66: 225-250.

Update on Potential Chinese Energy and Climate Policy Developments

This article clarifies what I referred to a few days ago. Setting an energy cap before an emissions cap would follow the Chinese pattern of setting energy intensity reduction targets before they set emissions intensity reduction targets. Setting an energy consumption cap might seem odd. At the meeting in India it was argued that this might be done for "social" reasons. The level of development in Europe and Japan is seen as desirable and adequate and the Chinese government doesn't want its society to become like the United States. Of course, it might be desirable to limit energy use for environmental reasons. Though some energy production and consumption processes are more environmentally damaging than others, in the end all energy use is used to transform nature in some way.

P.S. 21 August

Actually, none of this is news. I and most other people missed this news item back in March. The target didn't appear in the 5 year plan but it still seems to be under discussion as a potential future policy.

Correlation and Causality

I'm writing a paper on the topic of "From correlation to causal inference" for a workshop I'm planning to attend next month at the University of Michigan. A couple of recent papers featured on blogs which are nice examples to use in my paper.

Basically, we can only make causal statements based on a simple regression analysis if:

1. We can establish from theory that an explanatory variable is exogenous. In other words, it isn't itself caused to some degree by the variable we are trying to explain.

2. We are sure we haven't omitted any variables from the regression that might be correlated with those that are included in the regression.

Instrumental variables and Granger causality testing are two approaches that go beyond the simple regression model to try to make causal statements.

In some instances, though, exogeneity and causality are obvious. For example, in a joke paper discussed by Andrew Gelman, Bezimeni (2011) claims * to regress individual ages from survey data on responses to a survey question on trust, a factor derived from a factor analysis of various variables, and the percentage of overqualified women in national parliaments’ cafeterias. Clearly, individual age is exogenous and cannot be caused by any of the explanatory variables. Therefore, the supposed regression is nonsense. Instead, age might explain some of the responses. But average age in a location might be an endogenous variable and researchers need to be cautious of using it as an explanatory variable in a regression. For example, if we regressed income per capita in local government areas in Australia on average age, we could not necessarily interpret the results causally as the age composition of a location will depend to some degree on the economic opportunities available and vice versa.

Then there are cases where an explanatory variable is clearly exogenous and appears to have a significant effect on the dependent variable and yet theory suggests that the relationship is spurious and due to omitted variables that happen to be correlated with the explanatory variable in question. In a paper discussed by the blog Economic Logic, Westling (2011) regresses national economic growth rates on average reported penis lengths and other variables and finds that shorter penises are correlated with more rapid economic growth in the period. Penis length would seem to be exogenous but obviously this relationship would not have held in earlier periods when economic growth was more rapid in Europe and its Western offshoots and slower in Asia. So, it seems that the result is likely due to omitted variables bias unless the effect should only have become relevant in recent decades.

* Though regression results are reported, it is obvious from the variables named that no regression analysis was in fact conducted.

Career Update

Some of you have known about this for a while, but as I just signed the contract it is now official: My position at ANU in the Crawford School is being converted from a one-year fixed term position to a continuing position (the closest we get to tenure in Australia) and I am also being promoted from Associate Professor to Professor. This follows my presentation and interview on 27th June as part of a search in the area of environmental management and environmental economics. Several positions were advertised and, in fact, Crawford will interview for (a) further position(s). Anyway, the bottom line is I'll now be staying at ANU and no longer looking for a job. I thank everyone who helped me out in this job search including writing recommendations, passing on job opportunities, and giving me the opportunity to interview at various places.

Indian Perspective on Climate Change

I've been at the workshop on Equity, Sustainability, and Climate Change organized by the Centre for Science, Technology and Society at the Tata Institute of Social Sciences in Delhi over the last two days. The meeting was attended by both academics, NGOs, and government officials including a speech by the environment minister. It has been interesting to hear different perspectives on the climate change issue than I usually hear from Australians, Europeans, Americans, and Chinese. Though mentioned by some Chinese, there is a much stronger emphasis on historical responsibility for emissions in the context of a "carbon space" or "carbon budget" model. Developed countries have used up much of the available space in the atmosphere to absorb carbon dioxide and the question is how can the developing countries develop with the little remaining available space in the next few decades if we are to stay within a 2C maximum warming. There is still debate about whether there should be another round of Kyoto commitments or whether the "bottom up" or "pledge and review" framework that emerged from Copenhagen can be accepted. It was pointed out that it was the BASIC countries (Brazil, South Africa, India, and China) that got together with the US at Copenhagen to introduce this regime, so they can hardly complain now. And many seem to accept that Kyoto is dead and at least China has to be in any new agreement in order to have the slightest chance of the getting the Americans on board. Mukul Sanwal stated that China looks like announcing a unilateral cap on per capita emissions, perhaps at the Durban meeting and that this will change the whole game. There was a lot of exasperation with the US and amazement that they could almost default on their debt obligations just because they can't agree with each other internally.

There were also several presentations on the costs of climate mitigation, lead off by my paper on alternative cost measures. We found that the alternative approaches came to the same conclusion - that even a $50 a tonne CO2 tax is very low and would prompt switching to renewable energy on a large scale or substantial abatement in the short-term.

I met a lot of new people. Several, such as , Sivan Kartha, were at the IPCC meeting in Korea but I didn't happen to meet them there.

Bunch of New CCEP Working Papers

We have added six new working papers to the series, so far in July and August:

How Many Jobs is 23,510, Really? Recasting the Mining Job Loss Debate,
Bruce Chapman and Kiatanantha Lounkaew, July 2011, CCEP Working Paper 1106

It is commonplace in Australian policy debate for groups presumed to be adversely affected by proposed policies to provide estimates of the undesirable consequences of change. A fashionable form relates to predictions of job losses for the group affected, usually accompanied by counter-claims made by the government of the day or other groups in favour of the policy. A highly public example of the above is the claim by the Minerals Council of Australia (MCA), based on work done in 2009 by Concept Economics (2009) that the then-planned Emissions Trading Scheme (ETS) would result in 23,510 fewer jobs in Australian mining than would otherwise be the case. Our research reports on findings using three different data series and methods to put into context the supposed jobs loss figure. Our results should not be taken to mean that economic policy reform is costless to all employees who might be affected by sectoral changes in the labour market, and there remain clear roles for government to minimise the personal costs for those so disadvantaged. As well, the details of this research cannot be translated into precise analyses of the employment effects of the carbon price policy being developed by the current government. But the essential points concerning the size and meaning of mining sector employment effects should not be in dispute; the alleged Òjobs lossesÓ aspect of the climate change policy debate is not in any sense important to the overall discourse.

Nordhaus, Stern, and Garnaut: The Changing Case for Climate Change Mitigation,
Stephen Howes, Frank Jotzo, and Paul Wyrwoll, July 2011, CCEP Working Paper 1107

Today the idea that climate change requires a gradual and moderate response no longer commands consensus support among economists. A more demanding approach is gaining ground. This paper traces the changes in economic thinking concerning the case for action on climate change, through an analysis of the work of three eminent economists: William Nordhaus, Nicholas Stern and Ross Garnaut. It shows how from Nordhaus to Stern to Garnaut the case for more urgent and radical mitigation has been strengthened as temperature targets have been lowered and business-as-usual emissions projections raised. It also shows that Stern and especially Nordhaus, who has been working on this subject the longest, have changed their own views in favour of more urgent and radical mitigation. Some disagreements remain between these three economists, and some other economists have more moderate views, but the old consensus has been shattered.

Challenges in Mitigating Indonesia's CO2 Emission: The Importance of Managing Fossil Fuel Combustion,
Budy P. Resosudarmo, Frank Jotzo, Arief A, Yusuf, and Ditya A. Nurdianto, August 2011, CCEP Working Paper 1108

Indonesia is among the largest 25 carbon dioxide emitting countries when considering only fossil fuels, and among the top three or five when emissions due to deforestation and land use change are included. Emission per capita from fossil fuels are still low in comparison with other countries, but have been growing fast, and are likely to overtake those from deforestation and land use change in the future. This paper argues the importance for Indonesia to start developing strategies to mitigate its emissions from fossil fuel combustion. It analyses the main drivers of the increase in emissions, identifies the options and challenges in reducing the future growth in emissions. Policy options are reviewed that would enable the Indonesian economy to keep on growing, but with a much lower carbon output.


Green Fiscal Policy and Climate Mitigation in Indonesia,
Budy P. Resosudarmo and Abdurohman, August 2011, CCEP Working Paper 1109

In common with other archipelagic countries, Indonesia is vulnerable to such impacts of climate change as prolonged droughts, increased frequency in extreme weather events, and heavy rainfall resulting in floods. These threats, coupled with the fact that Indonesia has been declared one of the three biggest greenhouse gases emitters, has induced the Indonesian government to place a high priority on climate change issues. In particular, the government considers its fiscal policy to be a key instrument in both mitigating against and adapting to climate change. This paper reviews Indonesia's implementation of green fiscal policies and discusses recent Indonesian fiscal policy responses to its commitment to reduce its emissions by 2020. In general, one can conclude that although progress has been made in the area of green fiscal policy in Indonesia, a more vigorous approach is needed to protect Indonesia's environment and to cope with the new challenges of controlling CO2 emission in the era of climate change.

Five Perspectives on an Emerging Market: Challenges with Clean Tech Private Equity,
Eric R. W. Knight, August 2011, CCEP Working Paper 1110

Private equity investment in technologies which deliver low carbon energy has grown as an area of both economic and social performance. This article offers a perspective on some of the challenges in the industry. It relies on case studies drawn from thirty five interviews with leading clean tech investment managers across Silicon Valley, New York and London. The findings suggest that despite the long-term growth opportunities, some investors have struggled to find attractive risk-reward premiums in early stage investments.

Where in the World is it Cheapest to Cut Carbon Emissions? Ranking Countries by Total and Marginal Cost of Abatement,
David I. Stern, John C. V. Pezzey, N. Ross Lambie, August 2011, CCEP Working Paper 1111

Countries with low marginal costs of abating carbon emissions may have high total costs, and vice versa, for a given climate mitigation policy. This may help to explain different countries' policy stances on climate mitigation. We hypothesize that, under a common percentage cut in emissions intensity relative to business as usual (BAU), countries with higher BAU emissions intensities have lower marginal abatement costs, but total costs relative to output will be similar across countries; and under a common carbon price, relative total costs are higher in emissions-intensive countries. Using the results of the 22nd Energy Modeling Forum, we estimate marginal abatement cost curves for the US, EU, China, and India, which we use to estimate marginal and total costs of abatement under a number of policy options currently under international debate. The results of this analysis provide support for our hypotheses.

Handbook of Economic Growth: Working Paper Edition

I was just looking for a reference to support a point I was making in the revision I'm doing of a paper on economic growth and remembered that all the working paper versions of the chapters in the Handbook of Economic Growth have been helpfully linked to this webpage at Stanford. It's a great resource.

2nd Climate Change Adaptation National Congress

Readers might be interested in the 2nd Climate Change Adaptation National Congress to be held in Melbourne from Thursday 13th October 2011 to Friday 14th October 2011.

CSTS-TISS Workshop

I don't think I've mentioned on the blog that I am going to India next week to a workshop on "Equity, Sustainability, and Climate Change" organized by the Centre for Science, Technology and Society at the Tata Institute of Social Sciences. Though TISS is in Mumbai the workshop will be in Delhi at the India International Centre. The workshop focuses on balancing the need for sustainability and hence a limited global carbon emissions budget with the desire for equity in dividing the remaining allowed emissions among developing and developed countries. I have written a couple of papers* relevant to India's climate policy, hence my invitation to participate.

I haven't been to India before, so it will be my second new country this year, though I'm not planning on going anywhere but Delhi.

* We will post a new version of "Where is it Cheapest to Cut Carbon Emissions?" soon. This semester I have also been working with a student (Jack Gregory) on a paper on rural energy use in India and hopefully we'll turn that into a working paper fairly soon too.