In data visualization posts #21 and #22, I referred to the results of simple multivariate linear regressions where I examined the statistical relationships between the cost of electricity across European Union countries and the market penetration of renewable energy sources, and a cost-of-living index. Here are the regression results that form the source data for the predictive plots in those blog posts.
First, with the price of electricity as the dependent variable (DV):
## Here is the R code for the linear regression (using the generalized linear models (glm) framework:
glm.1<-glm(Elec_Price~COL_Index+Pct_Share_Total,data=eu.RENEW.only,family="gaussian") # Electricity Price is DV
Dependent Variable: Price of Household Electricity (in Euro cents)
Type: Linear regression
χ²(2) = 306.82, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.40
Pseudo-R² (McFadden) = 0.08
AIC = 166.04, BIC = 171.37
Standard errors: MLE
Est. S.E. t val. p
------------------------------ ------ ------ -------- ------
(Intercept) 4.10 3.59 1.14 0.26
Cost-of-Living Index 0.22 0.06 3.59 0.00
Renewables (% share of total) 0.03 0.04 0.74 0.46
We can see that the cost-of-living index is positively correlated with the price of household electricity, and it is statistically significant at conventional (p=0.05) levels. The market penetration of renewables (on the other hand) is not statistically significant (once controlling for cost-of-living.
Now, we use the pre-tax price of electricity (there are large differences in levels of taxation of household electricity across EU countries) as the DV. Here are the regression code (R) and the model results of the multivariate linear regression.
## Here is the R code for the linear regression (using the generalized linear models (glm) framework:
glm.2<-glm(Elec_Price_NoTax~COL_Index+Pct_Share_Total,data=eu.RENEW.only,family="gaussian") # Elec Price LESS taxes/levies is DV
Dependent Variable: Pre-tax price of Household Electricity (Euro cents)
Type: Linear regression
χ²(2) = 100.13, p = 0.00
Pseudo-R² (Cragg-Uhler) = 0.44
Pseudo-R² (McFadden) = 0.12
AIC = 130.11, BIC = 135.43
Standard errors: MLE
Est. S.E. t val. p
----------------------------- ------- ------ -------- ------
(Intercept) 5.20 1.89 2.75 0.01
Cost-of-Living Index 0.14 0.03 4.41 0.00
Renewables (% share of total) -0.03 0.02 -1.44 0.16
Here, we see an even stronger relationship between the cost-of-living and the pre-tax price of household electricity, while there is (once the cost-of-living is controlled for) a negative (though not quite statistically significant) relationship between the pre-tax cost of electricity and the market penetration of renewables across EU countries.
One of the first things that is (or should be) taught in a quantitative methods course is that “correlation is not causation.” That is, just because we establish that a correlation between two numeric variables exists, that doesn’t mean that one of these variables in causing the other, or vice versa. And to step back ever further in our analytical process, even when we find a correlation between two numerical variables, that correlation may not be “real.” That is, it may be spurious (caused by some third variable) or an anomaly of random processes.
I’ve seen the chart below (in one form or another) for many years now and it’s been used by opponents of renewable energy to support their argument that renewable energy sources are poor substitutes for other sources (such as fossil fuels) because, amongst other things, they are more expensive for households.
In this example, the creators of the chart seem to show that there is a positive (and non-linear) relationship between the percentage of a European country’s energy that is supplied by renewables and the household price of electricity in that country. In short, the more a country’s energy grid relies on renewables, the more expensive it is for households to purchase electricity. And, of course, we are supposed to conclude that we should eschew renewables if we want cheap energy. But is this true?
No. To reiterate, a bivariate (two variables) relationship is not only not conclusive evidence of a statistical relationship truly existing between these variables, but we don’t have enough evidence to support the implied causal story–more renewbles equals higher electricity prices.
Even a casual glance at the chart above shows that countries with higher electricity prices are also countries where the standard (and thus, cost) of living is higher. Lower cost-of-living countries seem to have lower electricity prices. So, how do we adjudicate? How do we determine which variables–cost-of-living, or renewables penetration–is actually the culprit for increased electricity prices?
In statistics, we have a tool called multiple regression analysis. It is a numerical method, in which competing variables “fight it out” to see which has more impact (numerically) on the variation in the dependent (in this case, cost of electricity) variable. I won’t get into the details of how this works, as it’s complicated. But it is a standard statistical method.
So, what do we notice when we perform a multivariate linear regression analysis (note: a non-linear method actually strongly the case below even more strongly, but we’ll stick to linear regression for ease of interpretation and analysis) where we “control for” each of the two independent variables–cost-of-living and renewables penetration)?
The image below shows (contrary to the implied claim in the chart above) that once we a country’s cost of living, there is little influence on the price of household electricity of renewables penetration in a country Moreover, the impact is not “statistically significant (see table at the end of the post).” That is, based on the data it is highly likely that the weak relationship we do see is simply due to random chance. We see this weak relationship in the chart below, which is the predicted cost of electricity in each country based on different levels of renewables penetration, holding the cost-of-living constant.
At only 10% of renewable penetration in a country the predicted price of electricity is about 17.5 ct/kWh (the shaded grey areas are 95% confidence bands, so we see that even though our best estimate of the price of electricity for a country that gets only 10% of its energy from renewables is 17.5 ct/kWh, we would expect the actual result to be between 14.5 ct/kWh and 20.5 ct/kWh 95% of the time. Our best estimate of the predicted cost of electricity in a country that gets 80% of its energy from renewables is expected to be about 19.5 ct/kWh. So, an 800% increase in renewables penetration leads only to only a 14.5% increase in the predicted price of electricity.
Now, what if we plot the predicted price of household electricity based on the cost-of-living after controlling for renewables penetration in a country? We see that, in this case, there is a much stronger relationship, which is statistically significant (highly unlikely for these data to produce this result randomly).
There are two things to note in the chart above. First, the 95% confidence bands are much closer together indicating much more certainty that there is a true statistical relationship between the “Cost-of-Living Index (COL)” and the predicted price of household electricity. And, we see that a 100% increase in the COL leads to a ((15.5-9.3)/9.3)*100%, or 67% increase in the predicted price of electricity in any EU country. (Note: I haven’t addressed the fact that electricity prices are a component of the COL, but they are so insignificant as to not undermine the results found here.
Stay tuned for the next post, where I’ll show that once we take out taxes and levies the relationship between the predicted price of household electricity and the penetration of renewables in an EU country is actually negative.
Here is the R code for the regression analyses, the prediction plots, and the table of regression results.
## This is the linear regression.
library(stargazer) # needed for prediction cplots
## Here is the code for the two prediction plots.
## First plot
cplot(reg1,"COL_Index", what="prediction", main="Cost-of-Living Predicts Electricity Price (ct/kWh) across EU Countries\n(Holding Share of Renewables Constant)", ylab="Predicted Price of Electricity (ct/kWh)", xlab="Cost-of-Living Index")
## Second plot
cplot(reg1,"Pct_Share_Total", what="prediction", main="Share of Renewables doesn't Predict Electricity Price (ct/kWh) across EU Countries\n(Holding Cost-of-Living Constant)", ylab="Predicted Price of Electricity (ct/kWh)", xlab="Percentage Share of Renewables of Total Energy Use")
The table below was created in LaTeX using the fantastic stargazer (v.5.2.2) package created for R by Marek Hlavac, Harvard University. E-mail: hlavac at fas.harvard.edu
We used the last session of IS450 as a chance to hold a mock United Nations climate conference simulation. The participants brought forward many intriguing and instructive topics, and I applaud them for putting in the time and energy to make the simulation as successful as I, at least, judged it to be. At some point during the proceedings, there was majority agreement (finally!) on one small element of the overall framework resolution. Interestingly, though, immediately upon the successful passing of that small piece of the framework a couple of delegates put forward a motion to make the obligations legally binding. A heated discussion ensued debating the merits and disadvantages of such an approach.
“Some may fear that commitments that are not internationally legally-binding may lack credibility,” he said.
“That, in my view, is a serious mistake. The sanctions available under the Kyoto Protocol, for example, were notionally legally-binding but were simply not credible and failed to guarantee domestic implementation of commitments.”
In Lima, negotiators are trying to hammer out the format that mitigation efforts should take. By the end of March next year countries have to declare their hands, but they have yet to formalize what will be included in these commitments and what will not.
Lord Stern believes that grounding the process in the laws and promises that countries undertake by themselves is a better model for a deal than a top-down process like Kyoto.
“It will be enforceable and deliverable through the arrangements and laws in the countries themselves.
“That way you will get stronger ambition as countries won’t be tempted to be hesitant about some type of international sanction.”
What do you think about Lord Stern argument? Would you support voluntary obligations over mandatory ones?
Here is an interview with Lord Stern from earlier this week in Lima, wherein he speaks on the link between economic growth, development, and better climate responsibility?
Host Peter Mansbridge, of the Canadian Broadcasting Coroporation’s (CBC) evening news program, The National, interviewed United Nations Secretary-General Ban Ki-Moon earlier this week on issues related to climate change and the Alberta oil sands. (I’ll have more next week about the anti-pipeline protests on Burnaby Mountain (in the vicinity of SFU) next week.)
Here are some excerpts:
Ban Ki-Moon: I know the domestic politics in Canada and Australia…but this is a global issue.
Peter Mansbridge: But the Canadian argument has always been, if everybody’s not in, we’re not in. [This obviously refers to the Kyoto Protocol’s division of countries into those that are required to make cuts (so-called Annex I countries) and those (mostly ‘developing’ countries) that do not.]
Ban Ki-Moon: China and [the] United States have taken such a bold initiative, Germany has been a leading country now, and [in] the European Union, twenty-eight countries have shown solidarity and unity. Therefore, it is only natural that Canada as one of the G-7 countries should take a leadership role.
The Secretary-General also spoke about the Alberta oil sands, which have been in the news lately in our part of the world as the result of protests aimed at Kinder Morgan over its plans to increase (three-fold) the flow of tar sands oil (bitumen) through an existing pipeline that runs through Burnaby Mountain to waiting oil tankers in Vancouver’s Burrard Inlet, to almost one million barrels per day.
Peter Mansbridge: Should Canadians, or the Canadian government, look beyond the oil sands to make its decisions about climate change?
Ban Ki-Moon: Energy is a very important, this is a cross-cutting issue. There are ways to make transformative changes from a fossil fuel-based economy to a climate-resilient economy by investing wisely in renewable energy resources.
Peter Manbridge: So back away from…
Ban Ki-Moon: Yes, Canada is an advanced economic country…you have many technological innovations, so with the technological innovation and financial capacity, you have many ways to make some transformative changes.
This is the key; the political and societal will has to be created and sustained to force our leaders to make the requisite changes, which will move our country towards an economy that is climate-resilient. An economically-sustainable future and economic well-being are not mutually exclusive. Indeed, there is every reason to believe that not not only are they not mutually exclusive, but that that each is necessary for the other. If we don’t start moving away from our “extractivist economic structure”, we in Canada face the prospect of a future with tremendous ecological and environmental degradation coupled with economic despair, when our leaders finally realize that rather than using our current wealth to innovate away from the extraction and toward energy innovation, we have squandered our wealth on fining ever cheaper ways to dig up crap that the world no longer wants to buy.
“Polluted and poor”–how’s that for a political campaign slogan?
This blog is back from an end-of-semester-induced slumber with some important posts. Here is post, the first:
Here’s an intriguing map, posted on the spatialities.com web site. It shows what Vancouver would look like with an expected 80-meter sea-level rise, which is what the United States Geological Survey predicts would happen were the Antarctic and Greenland ice sheets to melt completely (remember that these are land-based ice sheets).
Most of the current global land ice mass is located in the Antarctic and Greenland ice sheets (table 1). Complete melting of these ice sheets could lead to a sea-level rise of about 80 meters, whereas melting of all other glaciers could lead to a sea-level rise of only one-half meter.
Don’t go and sell your Fairview condo just yet, however, as this scenario is not projected to complete for between 1,000 and 10,000 years. Of course, this is a process that develops incrementally (though not linearly) over time and the city would be deeply affected adversely with only a fraction of that projected rise in sea levels.
For those who may doubt that the world’s glaciers are melting, here is video of the largest glacier ‘calving’ event ever caught on film. The end of the clip demonstrates the extent of change in the rate of melting and glacial retreat over the last century. Just watch!
You may also have awoken this morning to reports of a potentially ‘game-changing’ deal between the United States and China, which pledges to reduce greenhouse gas (GHG) emissions. [Note: the US media likes to use the sports-derived phrase ‘game-changing’ to refer to significant events.] This is certainly a significant development in the politics of climate change. Indeed, the two countries are the world’s largest emitters of GHGs and until today the two have been engaged in a game of what Paul Harris has called “you go first!” From the looks of it, they have both chosen to ‘go first’.
[President] Obama is setting a new target for the U.S., agreeing to cut greenhouse gas emissions to 26 to 28 percent below 2005 levels by 2025. The current U.S. target is to reach a level of 17 percent below 2005 emissions by 2020…
[President] Xi committed China to begin reducing its carbon dioxide emissions, which have risen steadily, by about 2030, with the intention of trying to reach the goal sooner, according to a statement released by the White House.
China, the world’s largest greenhouse-gas emitter, also agreed to increase its non-fossil fuel share of energy production to about 20 percent by 2030, according to the White House.
Is the negotiated agreement ideal? Not nearly. China will still be increasing its total GHG emissions until about 2030. Despite this, however, the deal has been met with some praise from environmental groups for the symbolic significance of the deal, which makes the potential for getting a positive deal agreed in Paris next year more likely.
Jake Schmidt, director of international programs for the Natural Resources Defense Council, a Washington-based environmental group, said no other countries can have as big an impact on the climate debate as the U.S. and China.
“They shape how the market invests,” he said. “They’ve also been two of the most difficult players in the history of the climate negotiations so the fact that they are coming out and saying they are going to take deep commitments will be a powerful signal to the rest of the world.”
Of course, not everyone is happy. Soon-to-be US Senate Majority Leader, Mitch McConnell (R-KY) is outraged:
Election results in the United States are mostly final and the Republican Party has had a big night, capturing control of the US Senate, which combined with a Republican-controlled House of Representative means that President Barack Obama will face a united (in party name, at least) Republican Congress upon the opening of the new Congressional session–the 114th–which meets for the first time in early January of next year.
The New York Times has a handy graphic, summarizing the disconcerting results (from the perspective of climate change politics) of exit polls earlier today. This seems to be disheartening news to those who wish to see the United States government become more proactive in the are of climate politics and climate change. As you can see, while six in 10 voters said that climate change is a problem, fully 83\% of the partisans of the majority party in Congress believe the same.
In a couple of weeks time, we will be finishing up the course with a UN simulation. Each of the participants will be required to give a 1-minute (maximum!) opening presentation to the conference. Here is the opening statement of Honourable Leona Aglukkaq, Minister of the Environment, Minister of the Canadian Northern Economic Development Agency and Minister for the Arctic Council, to the 19th Conference of the Parties (COP19) to the United Nations Framework Convention on Climate Change (UNFCCC) held in Warsaw, Poland in 2013. Your opening statements should follow a similar structure (but not length!).
Last week we discussed the role of domestic politics–institutions, electoral systems, partisanship, etc.,–on national political leaders’ attitudes towards and policies on climate change. We noted that the Canadian federal governments stance toward mitigation and adaptation changed dramatically upon the ascension of the Conservatives to power in 2006 (a minority government). The majority government that Harper was able to win in 2011 signalled the death knell for Canada’s involvement in the Kyoto process as Harper’s government reneged on Canada’s obligations quickly thereafter.
The United States, meanwhile, enters the final week of the biennial “midterm elections”, with most candidates (and the public) focused on issues other than climate change. When climate change is mentioned, however, the candidates responses are not reassuring. Have a look at this video for an impressive compilation of candidates’ responses to whether they believe in the existence of anthropogenic climate change. Incidentally, for a comprehensive debunking of Representative Steve Pearce’s claim that 31,000 scientists signed a petition claiming that there was no global warming, click here.