The CO2 emissions in Finland, Norway and Sweden: a dynamic relationship

In this paper a dynamic relationship between the CO2 emissions in Finland, Norway and Sweden is presented. With the help of a VAR(2) model, and using the Granger terminology, it is shown that the emissions in Finland are affecting those in Norway and Sweden. Other aspects of this dynamic relationship are presented as well.


Introduction
In this paper we consider the CO2 emissions in Norway, Sweden and Finland, three countries in the Nord of Europe.
The CO2 emissions is a subject of concern for goverments in Europe and the rest of the World due to its influence in the climate change. The Conference of Paris 2015 has established clear goals to slow the deterioration of the World Climate.
The selection of the three Nordic states for our analysis is due to the fact that they are three developed economies, that have also signed the Paris 2015 Agreement, and due to their location in the North of Europe, the three countries are facing similar problems in order to fulfill the Paris Agreement.
To get a first view of the situation, we represent in figure 1, the 55 years evolution of the CO2 emissions of the three countries: Figure 1. CO2 emissions in Finland, Norway andSweden: 1960-2014 The picture reflects the efforts of Finland, Norway and Sweden for reducing the CO2 emissions in their economies.
The basic statistics for these series are in for simplicity, let us use: (The reason for this ordering is alphabetical.) After some exploratory analysis, the VAR appropriate for our case is a VAR(2) model. In symbols, With t a as a sequence of independent and identically distributed (iid) random vectors, with mean zero and covariance matrix a  which is positive-definite.

Impulse response functions
The VAR formulation of models allow us to establish dynamic relationships between the variables of the system, but at the same time, it is possible to consider this relationship from other points of view. That is: the impulse response and the forecast error variance decomposition.
With the impulse response function it is posible to evaluate the effects of inducing a shock or unitary impulse in one of the variables on its own evolution and on the evolution of the other variables of the system.
The effect is better understood in the MA versión of the VAR model. There is a problem involved with Cholesky decomposition of a  , worth of mentionning. That is, the order of variables in the vector t z has consequences, however this is not the place for more details, and we could consider this artificiality as the cost for clarifying the impulse response of the system to the new uncorrelated t e .
Coming to our case, and using the software RATS, the impulse responses, ten steps ahead, for Finland, Norway and Sweden are, in tables 3, 4, and 5.   In the first column of these tables are printed the estimated standard errors of the predictions, here 10 steps ahead. Each column shows the percentage of error due to each of the variables; as a consequence the total of each row is 100. Once again, these tables are in agreement with the three estimated models.

Forseeing the future
Once we get a validated model, we could attemp to forseen the future. From our simplified model, and using RATS package, we forecast the future from 2015 to 2020. The results are in table 8.    1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008  The picture shows that the Norvegian series is falling down, while the oher two series show a light rising path.

Conclusions
Our VAR(2) model has established a classification among our series of CO2 emissions, with the Finnish case been independent of the other two as well as affecting the CO2 emissions in Norway and Sweden. Apart from the data series alone, the strong economy of Norway shows a decreasing evolution in the inmediate near future.