An analysis of the stylized facts of economic growth for
good and bad outputs
Adalmir Marquetti
Departamento de Economia, PUCRS, Brasil
aam@pucrs.br
Gabriel Mendoza Pichardo,
Facultad de Economía, UNAM, Mexico
gamp@servidor.unam.mx
Abstract
In the paper, we investigate the regularities of the economic growth, considering that the process of
production involves joint production of good and bad outputs. Kaldor (1957, 1961) pointed to the stylized
facts of economic growth of the good output. The good output is the GDP and the bad output is the
emission of carbon dioxide from burning fossil fuels. It is possible to summarize the results in four
regularities: i) the production of the good and bad outputs increase in the process of economic growth; the
production of good output raises with the employment of labor and capital inputs, the production of bad
output expands with the employment of capital input; ii) labor productivity and capital labor ratio increases,
while capital productivity declines in the process of economic growth; iii) both emissions per unit of output
and per unit of labor increase in the early stages of economic growth, declining after some threshold. This
result is consistent with the hypothesis of an environmental Kuznets curve; iv) there are large differences
both in the levels and in the growth rates of bad and good outputs, labor productivity and CO2 efficiency
among countries.
JEL Code: E01, E23
Key words: Stylized facts, Pollution
Resumo
No texto analisamos as regularidades do crescimento econômico, considerando que o processo produtivo
envolve a produção conjunta de um bom e um mau produto com a utilização de capital e trabalho como
insumos. Kaldor (1957, 1961) considera os fatos estilizados do crescimento econômico do bom produto.
O PIB é o bom produto e a emissão de CO2, a partir da queima de combustíveis fosseis, é o mau produto.
É possível sumarizar os resultados em quatro regularidades: i) a produção do bom e do mau produto
aumenta com o processo de crescimento econômico; o PIB se expande com o emprego de trabalho e
capital, enquanto a produção de CO2 aumenta com a utilização de capital; ii) a produtividade do trabalho e
razão capital-trabalho aumentam, enquanto a produtividade do capital declina com o crescimento
econômico; iii) as emissões de CO2 por unidade de produto e por unidade de trabalho aumentam em um
primeiro estágio, para declinar após um certo nível de desenvolvimento. Esse resultado é consistente com
uma curva de Kuznets ambiental; iv) existem grandes diferenças nos níveis e nas taxas de crescimento do
bom e do mau produto, da produtividade do trabalho e da emissão de CO2 por unidade de produto entre os
países.
Código JEL: E01, E23
Palavras Chaves: Fatos Estilizados, Poluição
Área ANPEC: Área 5 - Crescimento, Desenvolvimento Econômico e Instituições
1. Introduction
The large scale of production in the capitalist society has had impressive impact in the
environment with negative consequences in the ecosystems. Global warming and its
effects over the next generations are among the highest scientific and political concerns
of the present time. It is linked to the emission of anthropogenic greenhouse gases,
particularly carbon dioxide, from the burning of fossil fuel and deforestation (Stern et al.,
2006).
While the process of production normally involves joint production of good and
bad outputs the analysis of the regularities or the stylized facts of economic growth
pioneered by Kaldor (1957, 1961) considered just the good output. The present paper
investigates the stylized facts considering that production process results in a good
output, the GDP, and a bad output, the emission of carbon dioxide from burning fossil
fuels for an unbalanced data panel of countries over the 1963-2006 period. The good and
bad outputs are produced by labor and physical capital. The good output is distributed as
wage and profit and it can be consumed or invested.
Therefore, the paper will not only provide a fresh look at the Kaldor’s stylized
facts, but also observe some regularities relating production of carbon dioxide to the
economic growth. The generation of CO2 is a by-product of the GDP production. It is a
joint production process as suggested by Sraffa (1960) and Pasinetti, with the proviso that
the economic process does not determine a price, positive or negative, of the bad output
and the whole society must cope with its negative effects.
The source of the data on GDP, its components and the capital stock is the
Extended Penn World Tables, and for the emission of carbon dioxide it is Boden,
Marland and Andres (2010).
The paper is organized as follow. In section 2 we present Kaldor´s stylized facts.
In section 3 we discuss a simple system for analyzing the regularities of economic
growth. In section 4 we investigate the relationship between inputs and outputs. Then, in
section five we look at the technical change and the stylized facts. In section six we
investigate the evolution of the production of both good and bad outputs and their
technique of production for the world economy between 1973 and 2006.
2. Kaldor’s stylized facts
Kaldor (1961, p. 178) introduced the conception that the theorist must start the models
from hypothesis based on stylized facts that summarizes the “broad tendencies, ignoring
individual details, and proceed on the “as if” method”. From this perspective the
“stylized facts” should inform the researcher the central features of the phenomenon in
study, guiding her in the construction of the model. Moreover, if the stylized facts are
observable phenomenon of the nature, the final model should also be capable of
reproducing them or most of them. In this sense, the stylized facts are the departure and
the arrival points of the model.
2
Kaldor (1961) suggested six stylized facts of economic growth in capitalist
societies, as a starting point for the construction of economic growth models:
1) Production and labor productivity have increased at a more or less constant growth rate
over long run;
2) Capital per worker has also growth at a more or less constant rate over long run;
3) The rate of profit has been stable in the long run, particularly, in developed capitalist
societies;
4) The capital-output ratio has also been stable over the long run;
5) Distribution of income between wage and profits has been stable;
6) There are appreciable differences in the rates of growth of output and labor
productivity among countries.
While 1) and 2) are generally accepted as observable facts in the process of
economic development, facts 3) and 4) are controversial both empirically and
theoretically. The enormous literature on the neoclassical growth model suggest a pattern
of declining capital productivity, measured by the capital output ratio, in the process of
convergence to the steady state in a stable production–function relationship between
capital and labor inputs (Solow, 1970, Mankiw et al., 1992) The much smaller literature
putting forward a classical-Marxian alternative to the neoclassical production function
suggests that the declining capital productivity results from biases in technical change
rather than movements along a stable production function isoquant (Duménil and Lévy,
1995, Foley and Michl, Marquetti, 2003).
3. A system for studying the stylized facts
In studying the stylized facts of economic growth we consider a single process of production with
constant returns to scale that produces a good output, X, and a bad one, B, using homogeneous
physical capital, K, and labor as inputs, N. The good output corresponds to gross domestic
product of the whole economy, GDP, which is equal to total gross production including
fixed capital depreciation, D, valued at monetary prices less intermediary inputs of
production, raw and auxiliary materials. The intermediary inputs are ignored in Kaldor’s
analysis, the main source of pollution stems from the productive use of specific
intermediary inputs such as oil, coal and chemical in the process of production. A fraction
d of the capital stock is depreciated every period of production and total depreciation is equal to
D = dK. Table 1 specifies how production takes place in this economy.
Table 1: The input-output production process
Inputs
Outputs
Capital
Labor
Good
bad
Capital
K
N
X
B
K-D
A technique of production is describe by the intensity of capital, k, the ratio between
stock of capital and labor inputs; the labor productivity, x, the ratio between the good output and
labor inputs; the “labor emission”, b, the ratio between the bad output and labor inputs; and the
depreciation rate, d, respectively (k, x, b, d). It is possible to compute the capital productivity, p,
as the ratio between the good output and the capital stock. The emission intensities are measured
3
as the capital emission, a, the ratio between the bad output and the capital stock; and the output
emission, o, the ratio between the bad and the good output. Table 2 presents the input-output
matrix of this economy.
Table 2: The input-output coefficients
Inputs
Outputs
capital
labor
Good
bad
Capital
k
1
x
b
(1-d)k
The good output is distributed as wage, W, and gross profit, Z. The wage share, 1- π,
represents the percentage of the good output accruing to wage earners. The real wage, w, is
measured as the ratio between total wage and labor inputs. The gross profit rate, v, is measured
as the profit share, π, multiplied by the capital productivity. The good output is used either for
consumption by wage earners and capitalists or investment, mainly by capitalists. The
accumulation of capital raises the capacity of production of both outputs. The bad output is
dispersed in the atmosphere and it has been accumulated over time to the point that now is
generating health problems, climate changes, and economic costs.
It is possible to compute the growth rate of any of the variables discussed above. We will
investigate the growth rates of labor productivity, gx = Δx/x, capital productivity, gp = Δ p/p ,
capital intensity, gk = Δk/k, labor emissions, gb = Δb/b, capital emissions, gc = Δc/c, and output
emissions, go = Δo/o.
4. Empirical Analysis between outputs and inputs
In order to investigate the stylized facts we employ a panel data for 142 countries during
the 1963-2006 period. The good output is the Gross Domestic Product measured in 2005 PPP
international dollars obtained from Heston, Summers, and Aten (2009). The labor input is
measure as the number of workers and it also obtained from Heston, Summers, and Aten
(2009). The standardized fixed capital stock is measured in the same monetary units that
the good output. The bad output is the carbon dioxide, CO2, emitted in the process of
production and it is obtained from Boden, Marlan and Andres (2009) of the Carbon
Dioxide Information Analysis Center (CDIAC). The methodology for calculating
variables employed in the paper is described in the Appendix 1.
We begin by looking at the growth rates of the good and bad outputs reported at
Appendix 2. It presents the average growth rate of X, B, K and N for 142 countries that
data is available for a part or all the period 1963-2006. As it is possible to observe, only
Liberia, Zimbabwe, Somalia and Lebanon had a decline in the good output. The
production of the bad output fell in three developed European countries, five former
communist European countries, four African countries and Cuba.
Next we investigate the relationship between the good and bad outputs and the
inputs. Figure 1 displays the scatterplot matrix between the logarithms of X, B, K and N
for all 123 countries and years which the data is available for any part of the period 1963-
4
2006. Some outliers were removed from the sample. It is possible to observe that raising
capital stock increases the amount produced of both outputs. Expanding labor inputs also
raises the good output, but it is less evident the link between the number of workers and
CO2 emission. Moreover, there is a positive association between the good and the bad
outputs and between capital and labor inputs.
Figure 2 is a three dimensional plot of the logarithms of the outputs and inputs.
We utilize the non-parametric local regression method (Cleveland, 1993, and Loader,
1999) to estimate both graphs. The analysis of the upper graph reveals that the
production of the good output increases with the employment of either input, while the
lower graph shows that the production of the bad output, CO2, rises only with the use of
capital input. Therefore, for a given capital stock, the higher employment of labor inputs
expands the production of the good output with no effect in the production of the bad
output1.
Figure 1: The scatter plot of the logaritms of the good and bad output and the inputs.
Source: Appendix 1.
1
The least square regressions between the outputs and the inputs confirms that the expansion of the
number of workers has a negligible effect on the bad output (t-statistic in brackets).
log(B) = -15.1545 + 0.0070log(N) + 0.9546 log(K)
(-18.23)
(0.061)
(20.33)
log(X) = 3.4567 + 0.2461 log(K) + 0.7115 log(N)
(11.17) (10.84)
(40.69)
5
log(X), 2005 PPP
28 30
18 20 22 24 26
20
18
30
log 16
(N
), w
28
12
20
26
24 PPP
5
0
22 K), 20
log(
0
2
log(B), Kg of CO
10
5
15
1
ork 4
ers
20
18
30
log 16
(N
), w
28
ork 14
ers
12
20
26
24 PPP
05
22 (K), 20
log
Figure 2: The three dimensional plot of the logarithms of the outputs and inputs.
Source: Appendix 1.
5. Technical change and the stylized facts
There are three stylized facts regarding to technical change: labor productivity and capital
per worker had grown and capital-output ratio had been stable over the long run (Kaldor,
6
1961). The data on Appendix displays a much more complex story. The labor
productivity and the capital labor ratio declined, respectively, in 34 and 37 countries,
around 25% of our sample. The output-capital ratio also shows large fluctuation in the
periods of study, the standard deviation of its growth rate among the countries was 1.78%
and it fell in 83 countries. There were large differences in the growth rates of labor
productivity and capital per worker among countries.
Other related technical variables are the labor, capital and output emissions. The
Appendix also presents the growth rates of these variables. There is no clear cut answer
to the long run behavior of these variables2. The labor and output emissions rose in most
countries, while the capital emission declined half of the sample and there was large
variance among the countries.
The data set allows us to examine the patterns of technical change along the
economic growth path. In Figure 3, the upper graphs display the relationship between
labor productivity and capital-labor ratio on the right hand side and between labor
productivity and capital productivity on the left hand side for the data available in the
period 1963-2006. In the lower graphs, labor productivity is replaced by labor emissions.
The data shows that in the course of economic growth there is a positive
correlation between labor productivity and capital labor ratio and a negative one between
labor and capital productivities. There are some exceptions represented by data points
outside of the main clusters; these outliers are mainly observations from the oil export
countries. It is equally clear that there are substantial variations in the exact paths that
national economies follow in the course of economic development as demonstrated by
the growth rates of these variables. Poor countries are characterized by low labor
productivity, low capital labor ratio and high capital productivity while rich countries
have high labor productivity, high capital labor ratio and low capital productivity.
In the trajectory of economic growth, the evolution of labor emission seems
consistent with an environmental Kuznets curve; first it raises with capital intensity, then
after some threshold level it stabilizes and start[s] to decline. However, CO2 emissions per
worker in high capital labor ratio countries are greater than in low capital labor countries. It
is consistent with the negative correlation between labor emission and capital
productivity observed in the lower left hand side of the Figure.
2
The development stage, geographical location and growth rate of the good output seems to play a role in
technical change over the long run.
7
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p
Figure 3: The scatter plot of the technical variables.
Source: Appendix 1.
Figure 4 further investigates the environmental Kuznets curve by looking at the
output and capital emissions related to labor productivity and the capital labor ratio. The
data was fitted employing robust local regression. The local regression calculates a
weighted least-squares fit to the data at each point on a grid, with weights that decline
sharply with the distance of the data point from the grid point. The local regression fit is
made robust by calculating robustness weights that decline sharply with the size of the
residual for each data point from the local regression fit, and then iterating the local
regression fit with these robustness weights.
In the upper graphs, the output emissions show an inverted U-shaped curve in the
trajectory of economic growth consistent with the environmental Kuznets curve. There
are a series of outliers; they are basically observations from the rich oil countries. It is
consistent with the conception that cheaper energy has its cost in higher pollution. The
lower graphs present the data on the pairs (a, x) and (a, k) and the local linear fits. The
support for the environment Kuznets curve hypothesis is weaker in these cases. The
capital emissions appear to be lower at high capital labor ratio and high labor productivity
countries.
8
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0
x, 2005 PPP/worker
20000
40000
60000
80000 100000
k, 2005 PPP/worker
Figure 4: The environmental Kuznets curve.
Source: Appendix 1.
6. World patterns of growth and technical change
The production of the good and bad output is a social production. However, while the
good output belongs to a specific country and it is distributed to its inhabitants, the bad
output is not attached to a specific country; it belongs to the world population. Therefore,
it makes sense to investigate the data on production and technical change for the world
economy. In the present section we investigate it for the period 1973-2006.
The world economy is formed by 82 countries; the major drawback is the
exclusion of most of the former real socialist countries and Germany. The Russian
Federation and Germany were the fourth and the sixth greatest producers of CO2 in 2007.
The countries in our world economy were responsible for 75% of the total emission of
CO2 in 2006.
Figure 5 shows the production of good and bad output and the inputs employed in
their production. It is possible to observe an expansion in the production of both outputs
during the whole period in study. However, the production of GDP was multiplied by
3.3, while the production of CO2 doubled. The number of workers also doubled and the
use of physical capital expanded 3.7 times over the period 1973-2006.
9
B, 1000 m3 ton
X, 2005 PPP
8000000
60000000000000
6000000
40000000000000
4000000
20000000000000
2000000
N, workers
120000000000000
3000000000
80000000000000
2000000000
40000000000000
2005
2001
1997
1993
1989
1985
1981
1973
2005
2001
1997
1993
1989
1985
1981
1977
1000000000
2005
2001
1997
1993
1989
1985
1981
0
1977
2005
2001
1997
1993
1989
1985
1981
1977
1973
0
1973
1973
K, 2005 PPP
1977
0
0
Figure 5: The production of good and bad output and the employment of the physical
capital and labor inputs in the world economy.
Source: Appendix 1.
Next figure displays the evolution of the technique of production, (k, x, b), and
emission intensities, (o, a) for the world economy over the period 1973-2006. As it is
possible to observe, labor productivity and the capital labor ratio increased, while capital
productivity declined over the period of study. It indicates that the world economy is still
in a process of mechanization, raising the capital stock above the output. The CO2
emission per worker was relatively stable over the period of study. The emission
intensities have declined during the 1973-2006 period, capital emission declined at 1.5%
and output emission at 1.9% per year.
10
x, 2005 PPP/worker
b, Kg/worker
3000
24000
18000
2000
12000
1000
6000
2005
2001
1997
1993
1989
1985
1981
1973
2005
2001
1997
1993
1989
1985
1981
1977
1973
1977
0
0
o, Kg/2005 PPP
k, 2005 PPP/worker
0.20
45000
0.15
30000
0.10
15000
0.05
2005
2001
1997
1993
1989
1985
1981
1977
2005
2001
1997
1993
1989
1985
1981
1977
1973
1973
0.00
0
a, Kg/2005 PPP
p
0.12
0.8
0.08
0.6
0.04
2005
2001
1997
1993
1989
1985
1981
1977
2005
2001
1997
1993
1989
1985
1981
1977
1973
1973
0.00
0.4
Figure 6: Patterns of technical change and emission intensity in the world economy,
1973-2006
Source: Appendix 1.
7. Conclusion
One of the major scientific and political concerns at the present is the possible effects of
global warming over the next generations. Its main cause is the emission of
anthropogenic greenhouse gases, particularly carbon dioxide, from burning fossil fuel in
the process of production.
In the paper, we investigate the regularities of the economic growth, considering
that the process of production involves the joint production of good, the GDP, and bad
outputs, the emission of carbon dioxide from burning fossil fuels. Kaldor (1957, 1961)
pointed to the stylized facts of economic growth of the good output.
11
It is possible to summarize our results in the following regularities:
1) the production of the good and bad outputs increase in the process of economic
growth; the production of good output raises with the employment of labor and capital
inputs; the production of bad output expands with the employment of capital inputs;
2) labor productivity and capital labor ratio increases, while capital productivity declines
in the process of economic growth;
3) output emissions and labor emission increase in the firsts phases of economic growth,
declining after some threshold. It is consistent with the hypothesis of an environmental
Kuznets curve;
4) there are large differences in the growth rates of output and labor productivity among
countries.
These preliminary findings suggest a number of avenues for further research. It
would be useful to categorize these evidences for level of development, geographic, size
of national economies. Such studies could lead to a deeper understanding of the
relationship between emission of greenhouse gases and the process of economic
development.
7. References
Blades, D. 1993. Comparing capital stocks. In: Explaining economic growth: essays in
honor of Angus Maddison, eds. Adam Szirmai, bar Van Ark, and Dirk Pilat. Amsterdam:
North-Holland.
Boden, T., Marland, G., Andres, B. (2010). Global, Regional, and National Fossil-Fuel
CO2 Emissions. Carbon Dioxide Information Analysis Center, Oak Ridge National
Laboratory, Oak Ridge. Available on: http://cdiac.ornl.gov/trends/emis/tre_glob.html,
Downloaded: 3/2/2010.
Cleveland, W.S., 1993. Visualizing Data. Hobart Press, Summit.
Duménil, G., Lévy, D., 1995. A stochastic model of technical change: an application to
the US economy (1869–1989). Metroeconomica, 46, 213–245.
Heston, A., Summers, R., and Bettina, A. (2010). Penn World Table Version 6.3. Center
for International Comparisons of Production, Income and Prices at the University of
Pennsylvania, 2010. Available in: http://pwt.econ.upenn.edu8. Downloaded: 3/3/2010.
Hulton, C., Wycoff, F. (1981). The measurement of economic depreciation. In:
Depreciation, inflation, and the taxation of income from capital, ed. Charles Hulten.
Washington: Urban Institute Book.
Kaldor, N. (1957). A model of economic growth. The Economic Journal, 67, 591-624.
12
Kaldor, N. (1961), 'Capital Accumulation and Economic Growth.' In: Lutz, Hague (eds.).
The Theory of Capital, London, 177-222.
Mankiw, G., Romer, D., Weil, D. (1992). A contribution to the empirics of economic
growth. Quarterly Journal of Economics, 152, 407–437.
Marquetti, A. (2003). Analyzing historical and regional patterns of technical change from
a classical-Marxian perspective. Journal of Economic Behavior & Organization, 52, 2,
191-202.
OECD. (2001). Measuring Capital: OECD Manual. Paris.
Solow, R. (1970). Growth Theory: An Exposition. New York: Oxford University Press.
Stern, N. et al. 2006. The Stern Review of the Economics of Climate Change. Available
on: http://www.hm-treasury.gov.uk, Downloaded: 3/4/2010.
Appendix 1: Data Source and Methodology
This appendix presents the data source and a description of the methodology used to
calculate the data set. The data set basically employs the Penn World Table 6.2, PWT
6.3. The PWT 6.3 displays a basic set of national accounts, relative prices, and
demographic data which allows comparisons between countries and over time. It covers
the 1950-2007 period for some countries and for others it starts after 1950 and/or finishes
before 2004. For the list of variables and the exposition of the PWT methodology, see
Summers, Heston, Aten (2006).
The procedures to calculate the variables that compose this data set and are not
obtained directly in the PWT 6.2 are described below. The variable N represents the
number of workers. It is obtained dividing the variable X by the real GDP per worker,
rgdpw, in the PWT 6.3. The variable X ($/year) represents the GDP in 2005 purchasing
power parity (2005 PPP). It is obtained multiplying the variables population and the real
GDP per capital in 2005 PPP (chain index), respectively, pop (000s) and rgdpch in PWT
6.3. The result is multiplied by 1000.
The variable K ($/year) is our estimated net fixed standardized capital stock. It is
obtained by the Perpetual Inventory Method (PIM) using the investment series computed
from the variable real investment share (ki) of GDP presented in the PWT 6.3. There are
two major problems in our attempt to estimate the capital stock that involves strong
simplifications. First, the investment data is not presented by categories of gross fixed
capital formation and it includes the gross residential capital formation as well as change
in stocks. Second, the investment variable is reported for a short period of time. The
solution for these problems is to consider not only that all categories of gross capital
formation have the same asset life, but also that the asset life is very short.
13
The PIM procedure employed follows Hulton and Wycoff (1981). The
depreciation takes a geometric form. Hulton and Wycoff (1981, p. 94) calculated the rate
of depreciation (d) with the expression (d= R/T) where R is the factor that defines the
degree of declining balance due to depreciation, and T is the average asset life. The
average value found by Hulton and Wycoff (1981) for R is 1.65 for equipment categories,
and 0.91 for structure categories. The R employed for us is 1.05. t was calculated
considering that equipment categories represent 20 percent and structure categories 80
percent of the gross capital formation. The asset life considered was 14 years, hence the
depreciation rate was 7.5 percent. The net capital stock was computed using the
T
( T i )
expression K t  ( 1  0.075 / 2 )I   ( 1  0.075 )
i
I T i , i = 2, …, 14, where I is the
investment series calculated from the variables real investment share of GDP, real GDP
per capita in constant dollars (chain index), and population in the PWT 6.3. This
procedure considers that new assets are placed in service at midyear. Thus, depreciation
on these assets in year 1 is equal to half of the depreciation on the other assets. The first
observation for capital stock is 1963 for countries whose first observation for investment
is 1950. This is basic procedure adopted by BEA. An example of this procedure is
explained on OECD (2001, p. 100).
Our capital stock estimate is the cumulated, depreciated sum of the past aggregate
investment. Certain problems are inherent in this attempt to extend the PWT data. First,
there is the problem of data quality on investment of the PWT table. Srinivasan (1995)
calls the attention for this problem. Second, our methodological procedure implies in
considering a common and high rate of depreciation across countries. However, the
assumption of common rate of depreciation or common asset life is considered a first step
to enhance international comparability of capital stock estimates (Groote, Albers and de
Jong, 1996). The effect of using a short service life is to understate the size of capital
stock and to increase the variance of the capital stock growth rate. But, as Blades (1993,
p. 404) remarks the "use of erroneous service lives does not introduce any systematic bias
into capital stock growth rates".
The variable k is the capital labor ratio calculated as the ratio of the estimated
capital stock to the variable N, its units are $ 2005 PPP/worker. The variable x represents
labor productivity and it has $ 2005 PPP/worker as units. It is the variable real GDP per
worker-year, rgdpw, in the PWT 6.3. The variable p is the productivity of capital
(output-capital ratio) which has the units 1/year. It was obtained dividing X per the
estimated capital stock.
The variable B is the CO2 emission obtained in Boden, T., G. Marland, and B.
Andres (2010). It is measured in quilograms of CO2 emissions.
This data set contains information on national CO2 emissions from fossil-fuel
burning, cement manufacture, and gas flaring. The variable a is the ratio between CO2
emissions and our capital stock, it is expressed in Kg CO2/$ 2005 PPP. The variable o is
the ratio between CO2 emissions and X. It is also expressed in Kg CO2/$ 2005 PPP. The
variable b is the ratio between B and X, it has the unit of Kg CO2/worker.
14
Appendix 2: Growth rate of the variables by country.
Country
Year
gB
gX
gK
gN
Gabon
Albania
Mozambique
Poland
Luxembourg
Bulgaria
Singapore
Zambia
Romania
Hungary
Congo
China
Belgium
Iceland
United Kingdom
France
Sweden
Bahamas
Malawi
Tanzania
Mali
Denmark
United States
Ireland
Tunisia
Mongolia
Guinea
Somalia
Macao
Netherlands
Austria
Solomon Islands
Colombia
Angola
Sudan
Hong Kong
Canada
Cuba
Chad
Norway
Switzerland
Chile
Sri Lanka
Uruguay
Panama
Samoa
Republic of Korea
Guinea-Bissau
Taiwan
Japan
Egypt
1973-2006
1983-2006
1973-2006
1983-2006
1963-2006
1983-2006
1973-2006
1973-2006
1973-2006
1983-2006
1973-2006
1973-2006
1963-2006
1963-2006
1963-2006
1963-2006
1963-2006
1983-2006
1973-2006
1973-2006
1973-2006
1963-2006
1963-2006
1963-2006
1983-2006
1983-2006
1973-2006
1983-2006
1983-2006
1963-2006
1963-2006
1983-2006
1963-2006
1983-2006
1983-2006
1973-2006
1963-2006
1983-2006
1973-2006
1963-2006
1963-2006
1964-2006
1963-2006
1963-2006
1963-2006
1983-2006
1973-2006
1973-2006
1964-2006
1963-2006
1963-2006
-2.85
-2.49
-1.69
-1.23
-0.03
-2.74
2.95
-1.88
-1.17
-1.78
0.55
5.58
0.03
1.23
-0.14
0.32
-0.20
0.25
1.84
1.58
2.28
0.66
1.38
2.74
3.11
1.30
1.60
-2.03
5.16
1.43
1.54
0.99
2.54
3.16
4.42
4.35
2.20
-0.17
2.72
2.30
0.84
2.93
3.59
1.08
3.93
1.42
5.68
2.82
6.62
3.21
4.76
2.37
2.65
3.41
3.02
4.15
1.42
6.81
1.92
2.43
1.70
3.63
8.64
2.81
3.97
2.54
2.95
2.39
2.80
4.11
3.82
4.35
2.68
3.34
4.68
4.92
3.05
3.33
-0.44
6.74
3.00
3.02
2.46
4.00
4.59
5.85
5.70
3.53
1.13
4.02
3.51
2.04
4.04
4.69
2.14
4.97
2.42
6.60
3.70
7.45
4.02
5.46
3.82
0.21
4.61
2.17
3.41
-0.77
6.42
0.15
1.78
1.88
2.93
9.25
3.16
4.08
3.23
3.38
2.20
6.94
0.60
4.13
4.31
3.63
4.06
5.20
1.55
-0.34
3.70
-0.02
6.07
3.14
3.58
1.76
4.00
2.55
6.78
6.19
4.05
-2.85
7.32
2.92
2.48
3.26
4.03
1.45
5.35
-1.30
9.19
1.42
9.69
5.41
5.84
2.78
0.66
1.92
0.06
2.17
-1.49
3.15
2.89
-0.05
-0.65
3.07
1.79
0.48
2.03
0.41
0.76
0.51
2.14
2.59
2.76
1.88
0.67
1.68
1.38
2.64
3.01
2.64
1.96
3.68
1.52
0.52
3.69
3.10
2.23
2.27
2.11
2.15
1.52
3.15
1.14
0.90
2.24
1.87
0.89
2.90
1.22
2.25
2.29
2.10
0.81
2.70
gx
-0.40
1.99
1.49
2.96
1.98
2.91
3.65
-0.97
2.48
2.35
0.56
6.85
2.33
1.94
2.13
2.19
1.87
0.66
1.52
1.06
2.47
2.02
1.66
3.30
2.28
0.04
0.69
-2.40
3.06
1.48
2.50
-1.23
0.90
2.36
3.58
3.59
1.38
-0.40
0.88
2.37
1.13
1.80
2.82
1.25
2.07
1.20
4.36
1.40
5.35
3.21
2.76
gp
-1.45
2.43
-1.20
0.85
0.74
2.19
0.38
1.77
0.65
-0.18
0.70
-0.61
-0.35
-0.11
-0.69
-0.44
0.19
-4.14
3.51
-0.31
0.04
-0.94
-0.72
-0.52
3.37
3.39
-0.37
-0.42
0.67
-0.14
-0.57
0.69
0.00
2.04
-0.93
-0.49
-0.52
3.97
-3.30
0.58
-0.44
0.78
0.66
0.69
-0.38
3.72
-2.58
2.28
-2.24
-1.39
-0.38
gk
gb
go
ga
1.04
-0.44
2.69
2.11
1.24
0.72
3.27
-2.74
1.83
2.53
-0.14
7.46
2.68
2.06
2.82
2.62
1.69
4.80
-1.99
1.37
2.43
2.96
2.38
3.82
-1.09
-3.35
1.06
-1.98
2.39
1.62
3.06
-1.93
0.90
0.32
4.51
4.08
1.90
-4.37
4.18
1.78
1.57
1.02
2.15
0.56
2.45
-2.52
6.94
-0.88
7.59
4.60
3.14
-5.63
-3.15
-3.61
-1.29
-2.20
-1.26
-0.20
-4.77
-1.13
-1.13
-2.52
3.79
-0.45
-0.80
-0.55
-0.44
-0.71
-1.89
-0.75
-1.18
0.40
-0.01
-0.30
1.37
0.47
-1.71
-1.04
-3.99
1.48
-0.09
1.02
-2.70
-0.56
0.93
2.16
2.24
0.06
-1.70
-0.43
1.16
-0.06
0.69
1.72
0.19
1.03
0.20
3.43
0.52
4.52
2.40
2.06
-5.22
-5.14
-5.10
-4.25
-4.18
-4.16
-3.85
-3.79
-3.60
-3.49
-3.08
-3.06
-2.78
-2.74
-2.68
-2.63
-2.58
-2.55
-2.27
-2.24
-2.06
-2.02
-1.95
-1.93
-1.81
-1.75
-1.73
-1.59
-1.57
-1.57
-1.48
-1.46
-1.46
-1.43
-1.42
-1.35
-1.33
-1.30
-1.30
-1.21
-1.19
-1.11
-1.10
-1.06
-1.04
-0.99
-0.93
-0.88
-0.84
-0.81
-0.70
-6.67
-2.71
-6.30
-3.40
-3.44
-1.97
-3.47
-2.02
-2.95
-3.66
-2.38
-3.68
-3.13
-2.85
-3.37
-3.06
-2.40
-6.69
1.23
-2.54
-2.03
-2.97
-2.68
-2.46
1.56
1.64
-2.10
-2.01
-0.91
-1.71
-2.04
-0.77
-1.45
0.61
-2.35
-1.84
-1.85
2.67
-4.60
-0.63
-1.63
-0.33
-0.43
-0.37
-1.41
2.73
-3.51
1.40
-3.08
-2.20
-1.08
15
Australia
Cote d`Ivoire
New Zealand
Venezuela
Italy
South Africa
Vanuatu
Finland
Kenya
Peru
Brazil
Papua New Guinea
Senegal
Cyprus
Philippines
Central African Rep.
Cape Verde
Qatar
Djibouti
Argentina
Israel
Mexico
Fiji
Jamaica
Malta
Comoros
Spain
India
Portugal
Cameroon
Indonesia
Malaysia
Madagascar
Niger
Uganda
Mauritania
Dominican Republic
Bahrain
United Arab Emir.
Guatemala
El Salvador
Vietnam
Suriname
Zimbabwe
Barbados
Swaziland
Ghana
Saudi Arabia
Paraguay
Sierra Leone
Greece
Burundi
Turkey
Honduras
Belize
Syria
Sao Tome and Princ.
1963-2006
1973-2006
1963-2006
1963-2006
1963-2006
1963-2006
1983-2006
1963-2006
1963-2006
1963-2006
1963-2006
1973-2006
1973-2006
1963-2006
1963-2006
1973-2006
1973-2006
1983-2006
1983-2006
1963-2006
1963-2006
1963-2006
1973-2006
1973-2006
1983-2006
1973-2006
1963-2006
1963-2006
1963-2006
1973-2006
1973-2006
1973-2006
1973-2006
1973-2006
1963-2006
1973-2006
1964-2006
1983-2006
1983-2006
1963-2006
1963-2006
1983-2006
1983-2006
1973-2006
1973-2006
1983-2006
1973-2006
1983-2006
1964-2006
1983-2006
1964-2006
1973-2006
1963-2006
1963-2006
1983-2006
1973-2006
1983-2006
3.03
2.31
2.12
2.60
2.46
3.09
2.22
2.88
3.37
3.09
4.29
3.74
3.06
4.81
4.12
1.32
4.84
6.13
1.46
2.89
5.00
4.38
2.84
1.16
4.08
3.33
4.16
5.31
4.16
4.24
5.80
7.19
2.94
3.16
4.26
3.84
5.84
4.13
5.97
4.76
4.06
7.41
2.49
0.54
3.11
5.74
3.99
3.75
5.29
1.59
4.73
3.01
5.76
5.38
6.77
6.55
2.71
3.73
2.90
2.56
2.95
2.76
3.33
2.45
3.07
3.46
3.11
4.27
3.67
2.98
4.69
3.93
1.11
4.63
5.92
1.23
2.66
4.76
4.11
2.54
0.85
3.71
2.84
3.68
4.82
3.63
3.65
5.19
6.46
2.19
2.40
3.50
3.06
5.01
3.29
4.98
3.73
2.96
6.28
1.36
-0.61
1.91
4.53
2.76
2.49
4.01
0.31
3.40
1.64
4.35
3.97
5.35
5.10
1.23
4.16
1.42
3.02
1.90
3.01
3.55
3.82
2.70
3.26
1.70
4.32
3.91
5.20
3.50
4.25
-0.53
4.29
6.79
3.18
2.39
4.80
4.51
2.64
1.48
3.34
0.27
4.73
5.65
4.91
3.66
7.08
7.95
1.38
2.02
4.64
2.80
6.13
1.84
3.35
4.16
3.96
10.14
4.85
1.49
1.31
3.46
1.08
1.37
5.50
-2.66
3.80
3.80
5.95
5.03
3.76
5.18
5.53
1.99
3.25
1.95
3.63
0.27
2.42
2.58
0.45
3.36
3.25
3.11
2.63
2.93
1.17
2.81
2.18
1.78
5.02
2.17
1.89
2.93
3.28
2.25
1.26
1.13
3.16
1.10
2.05
1.10
2.57
2.60
2.99
3.11
2.84
2.85
2.38
3.31
2.97
6.27
2.59
2.64
2.19
1.78
2.29
1.59
2.58
2.84
4.53
3.35
2.20
0.73
2.59
1.35
3.11
4.21
4.06
3.10
1.74
-0.34
0.61
-0.68
2.50
0.92
-0.13
2.62
0.10
-0.14
1.16
1.04
0.05
3.51
1.12
-1.06
2.85
0.90
-0.94
0.77
1.83
0.83
0.30
-0.41
2.58
-0.31
2.58
2.77
2.52
1.08
2.59
3.48
-0.92
-0.44
0.65
0.69
1.70
0.32
-1.29
1.15
0.32
4.09
-0.42
-2.90
0.32
1.94
-0.08
-2.04
0.66
-1.89
2.67
-0.94
3.00
0.86
1.14
1.04
-1.87
-0.43
1.48
-0.46
1.05
-0.25
-0.22
-1.37
0.37
0.20
1.41
-0.05
-0.24
-2.22
1.19
-0.33
1.64
0.34
-0.87
-1.95
0.26
-0.05
-0.40
-0.10
-0.62
0.37
2.58
-1.05
-0.83
-1.29
0.00
-1.90
-1.49
0.80
0.38
-1.14
0.26
-1.12
1.45
1.63
-0.43
-1.01
-3.86
-3.49
-2.10
0.60
1.07
1.68
1.12
-1.50
2.97
-0.40
-2.16
-1.60
-1.06
1.59
-0.08
-4.30
2.17
-1.82
1.07
-1.73
2.75
1.14
1.24
2.25
-0.10
-1.55
1.21
1.28
2.27
2.32
1.44
-2.71
2.51
1.77
1.01
0.51
1.87
1.24
0.40
0.21
2.21
-2.89
3.63
3.60
3.81
1.08
4.49
4.97
-1.72
-0.83
1.79
0.43
2.81
-1.13
-2.92
1.58
1.32
7.95
3.07
-0.80
-0.28
0.87
-1.75
-3.16
2.16
-4.86
3.07
1.21
4.60
1.92
-0.45
1.12
2.43
1.04
-0.93
0.17
-1.03
2.19
0.67
-0.36
2.43
0.01
-0.16
1.19
1.11
0.13
3.63
1.31
-0.86
3.06
1.11
-0.70
1.00
2.07
1.10
0.59
-0.11
2.95
0.17
3.06
3.26
3.06
1.67
3.20
4.20
-0.17
0.31
1.41
1.46
2.53
1.16
-0.29
2.17
1.43
5.22
0.71
-1.75
1.51
3.16
1.15
-0.78
1.94
-0.61
4.00
0.42
4.41
2.27
2.56
2.48
-0.38
-0.70
-0.59
-0.44
-0.35
-0.30
-0.24
-0.23
-0.19
-0.10
-0.02
0.03
0.07
0.08
0.12
0.20
0.21
0.21
0.22
0.23
0.23
0.24
0.27
0.30
0.30
0.36
0.48
0.49
0.49
0.53
0.59
0.62
0.73
0.75
0.76
0.76
0.78
0.83
0.84
1.00
1.02
1.11
1.13
1.13
1.15
1.20
1.21
1.23
1.26
1.28
1.28
1.33
1.37
1.41
1.41
1.42
1.45
1.49
-1.13
0.89
-0.90
0.70
-0.56
-0.46
-1.60
0.18
0.10
1.39
-0.02
-0.17
-2.14
1.31
-0.13
1.85
0.55
-0.65
-1.72
0.50
0.20
-0.13
0.19
-0.32
0.73
3.06
-0.57
-0.34
-0.75
0.59
-1.28
-0.76
1.56
1.14
-0.38
1.03
-0.28
2.30
2.62
0.59
0.10
-2.73
-2.36
-0.95
1.79
2.28
2.91
2.38
-0.22
4.25
0.93
-0.79
-0.20
0.35
3.01
1.37
-2.82
16
Gambia
Costa Rica
Morocco
Togo
Nicaragua
St. Lucia
Libya
Iran
Oman
Nepal
Ecuador
Mauritius
Benin
Brunei
St.Vincent & Grenad.
Bolivia
Maldives
Jordan
Kuwait
Thailand
Haiti
Bangladesh
Ethiopia
Tonga
Bhutan
Cambodia
Laos
Nigeria
Lebanon
Trinidad &Tobago
Liberia
Rwanda
Equatorial Guinea
Botswana
1973-2006
1963-2006
1963-2006
1973-2006
1963-2006
1983-2006
1983-2006
1973-2006
1983-2006
1973-2006
1964-2006
1963-2006
1973-2006
1983-2006
1983-2006
1963-2006
1983-2006
1973-2006
1983-2006
1963-2006
1973-2006
1973-2006
1963-2006
1983-2006
1983-2006
1983-2006
1983-2006
1963-2006
1983-2006
1963-2006
1983-2006
1973-2006
1973-2006
1973-2006
5.08
5.98
5.67
3.36
3.81
5.71
2.62
3.88
7.41
6.18
6.38
6.78
6.36
3.40
6.92
5.21
12.30
6.79
6.04
9.05
4.42
6.70
6.18
4.43
11.15
10.47
9.01
6.75
3.21
7.55
0.43
7.38
15.15
13.73
3.54
4.34
3.95
1.63
1.99
3.85
0.57
1.83
5.21
3.98
4.12
4.38
3.94
0.90
4.40
2.62
9.71
4.19
3.35
6.24
1.50
3.66
3.13
1.32
8.00
7.26
5.74
3.43
-0.20
3.44
-4.18
2.31
9.63
7.44
5.76
5.56
5.29
0.88
3.05
6.03
-2.41
3.81
4.34
7.77
3.22
3.95
3.58
7.08
4.84
2.04
9.81
5.98
2.05
7.45
3.73
6.24
3.12
1.82
8.94
7.88
10.09
2.83
1.28
2.82
-8.53
4.84
15.79
8.02
3.41
3.27
2.61
2.96
3.45
2.42
3.64
3.08
4.57
2.48
3.13
2.06
3.62
3.60
1.56
2.65
5.01
4.58
3.30
2.19
1.28
2.48
2.92
2.75
2.32
3.00
2.93
2.43
1.55
1.71
1.78
2.57
2.20
3.37
0.13
1.08
1.34
-1.33
-1.46
1.43
-3.07
-1.25
0.65
1.50
0.98
2.33
0.32
-2.69
2.84
-0.03
4.70
-0.39
0.05
4.06
0.22
1.18
0.21
-1.43
5.68
4.27
2.82
1.00
-1.75
1.73
-5.95
-0.26
7.44
4.07
-2.22
-1.21
-1.34
0.75
-1.06
-2.18
2.98
-1.98
0.88
-3.79
0.89
0.43
0.37
-6.18
-0.44
0.58
-0.10
-1.78
1.30
-1.21
-2.23
-2.58
0.01
-0.50
-0.94
-0.62
-4.34
0.60
-1.48
0.62
4.35
-2.53
-6.16
-0.58
2.35
2.29
2.68
-2.08
-0.40
3.62
-6.05
0.73
-0.23
5.29
0.09
1.89
-0.05
3.49
3.29
-0.61
4.80
1.40
-1.25
5.26
2.45
3.76
0.20
-0.93
6.62
4.88
7.16
0.40
-0.27
1.10
-10.30
2.27
13.60
4.65
1.67
2.71
3.06
0.39
0.36
3.29
-1.03
0.80
2.84
3.70
3.25
4.72
2.74
-0.20
5.36
2.56
7.29
2.21
2.74
6.86
3.14
4.22
3.26
1.68
8.84
7.47
6.08
4.31
1.66
5.83
-1.35
4.81
12.96
10.36
1.55
1.63
1.72
1.72
1.82
1.85
2.04
2.05
2.19
2.20
2.27
2.39
2.42
2.49
2.51
2.59
2.59
2.60
2.69
2.81
2.92
3.04
3.05
3.11
3.15
3.21
3.26
3.31
3.41
4.11
4.60
5.07
5.52
6.29
-0.67
0.42
0.38
2.48
0.76
-0.33
5.03
0.07
3.07
-1.59
3.16
2.82
2.78
-3.68
2.07
3.17
2.49
0.81
3.99
1.60
0.69
0.46
3.06
2.61
2.22
2.59
-1.08
3.91
1.94
4.73
8.95
2.54
-0.64
5.71
17