Chapter 8 - Appendixes
Appendix 8.1. Individual Preferences for Growth, Environment,
and Income Distribution
Funds to be invested
in projects that
will stimulate
economic growth
Funds to be invested
in projects to
reduce environmental
damages
Funds to be invested
in projects that
will reduce income
inequality
Average
3.85
4
2
Standard
Error
Source: Author calculations.
1.34
1.46
0.87
8-2
Appendix 8.2. Composition of the Wealth of Nations (Figures in
per Capita USD current)
Population
Argentina
7,914,690
117,787,000
Bangladesh
Belgium
8,063
199,794
168,482
13,352
17,960
17,982
404,903
272,244
67,193
65,466
25,307
364,960
272,918
77,749
14,292
220
31,837
24,142
2,161
5,534
23,001
360,777
299,137
61,625
15
376
36,206
28,556
4,015
3,634
770
53,924
33,906
8,980
11,038
2,800
124,898
98,663
15,473
10,762
3,370
125,813
96,758
15,902
13,154
302
20,824
14,327
2,169
4,327
149
14,564
8,893
2,165
3,506
686
48,044
27,459
8,286
12,298
19,656
443,272
312,191
66,608
64,474
370
33,374
17,704
3,136
12,535
193
23,308
11,278
1,752
10,279
3,507
207,640
163,084
17,203
27,353
5,246,000
Bolivia
7,237,000
Botswana
1,443,000
159,143,000
Brazil
Burkina
Faso
Burundi
10,046,000
6,209,000
Cameroon
12,871,000
Canada
Central African
Republic
Chad
Chile
29,120,700
3,235,000
6,183,000
14,044,000
1,190,920,000
China
Colombia
530
50,757
40,297
5,989
4,471
1,620
119,294
97,056
11,691
10,546
635
44,917
27,684
9,295
7,939
2,400
135,499
106,588
14,635
14,277
N/A
31,426
18,219
6,214
6,993
28,285
375,477
285,331
71,264
18,882
1,319
97,060
73,955
8,079
15,026
1,311
97,158
62,970
14,480
19,708
700
72,236
51,883
16,246
4,106
1,478
56,951
50,186
4,675
2,090
18,874
315,301
194,587
90,190
30,524
23,552
381,318
296,078
70,435
14,805
359
25,873
19,277
2,725
3,870
25,698
353,006
279,785
65,596
7,626
422
38,022
30,718
3,921
3,383
7,723
182,722
142,440
30,777
9,505
36,330,100
Congo
2,516,000
Rica
3,304,000
Cote D’Ivoire
(Ivory Coast)
Denmark
Dominican
Republic
Ecuador
Finland
7,684,000
5,641,000
5,082,570
France
Germany
5,172,770
57,556,000
Salvador
Gambia,
13,780,000
11,220,000
Egypt
Greece
Natural
Produced Capital
Capital
10,080,400
Benin
Ghana
Human
Capital
17,841,400
Austria
El
Total
Wealth
34,180,000
Australia
Costa
GNP
57,726,200
The
1,081,000
81,140,800
16,944,000
10,408,000
8-3
Guatemala
Guinea-Bissau
Haiti
Honduras
72,164
62,469
6,630
3,064
239
28,580
11,733
2,351
14,496
219
17,998
13,534
2,947
1,517
607
49,998
35,528
8,099
6,371
320
28,364
17,098
4,366
6,900
1,050,000
7,035,000
India
5,493,000
913,600,000
Indonesia
189,907,000
Ireland
1,190
10,322,000
882
86,053
65,143
7,927
12,983
13,738
296,895
224,199
38,911
33,784
3,542,940
8-4
Population
Italy
Jamaica
Japan
Jordan
Total
Wealth
Human
Capital
Natural
Produced Capital
Capital
19,258
323,081
250,091
67,005
5,985
57,154,200
2,496,000
1,421
64,832
38,832
20,004
5,996
124,782,000
34,680
380,290
282,326
93,768
4,196
1,330
91,522
74,195
15,653
1,674
250
26,971
16,536
7,168
3,267
8,200
224,826
192,908
26,702
5,216
681
39,414
32,849
4,805
1,760
230
24,476
11,222
1,392
11,862
123
10,236
6,612
2,068
1,556
3,551
193,048
149,510
24,729
18,809
250
18,755
7,963
1,822
8,970
480
35,666
21,700
4,280
9,686
3,212
134,514
114,065
18,209
2,240
3,865
159,175
127,965
19,313
11,898
1,145
76,597
63,074
9,481
4,042
84
13,083
7,939
3,100
2,043
1,981
101,573
79,204
9,894
12,475
196
23,074
15,488
2,379
5,207
21,955
344,549
267,504
71,066
5,979
13,048
391,725
230,660
63,208
97,857
321
39,529
28,576
4,042
6,911
227
37,013
12,511
2,178
22,324
26,599
386,796
243,072
99,253
44,472
440
48,171
40,894
3,957
3,321
2,698
136,810
108,955
16,151
11,704
1,158
58,205
37,470
6,445
14,291
1,556
88,379
64,939
10,268
13,172
1,882
84,447
61,329
14,815
8,303
972
62,844
51,296
6,780
4,768
9,437
226,000
184,769
33,893
7,337
4,217,000
Kenya
26,017,000
Korea, Republic of
Lesotho
44,563,000
1,996,000
Madagascar
Malawi
13,101,000
10,843,000
Malaysia
Mali
19,498,000
9,524,000
Mauritania
Mauritius
Mexico
Namibia
21,360,000
Netherlands
Zealand
Nicaragua
Niger
Pakistan
Panama
3,530,930
4,275,000
4,317,630
126,284,000
2,585,000
Papua New Guinea
Paraguay
Peru
4,205,000
4,830,000
23,331,000
Philippines
Portugal
66,188,000
9,831,980
80
Rwanda
3,740
2,010
2,030
7,365
7,781
280,099
109,721
30,112
140,266
622
46,578
32,838
4,016
9,724
144
16,403
9,373
1,558
5,472
2,963
116,194
91,559
16,793
7,841
13,143
257,873
204,181
43,300
10,392
7,750,000
Arabia
Senegal
Spain
15,391,200
8,846,000
Norway
South
16,613,900
1,500,000
Nepal
Sierra
1,104,000
26,488,000
Mozambique
Saudi
2,217,000
91,858,000
Morocco
New
GNP
17,497,600
8,102,000
Leone
Africa
4,587,000
41,591,000
39,550,900
8-5
Sri
Lanka
Sweden
65,273
51,309
7,806
6,158
23,753
334,488
237,074
69,638
27,777
36,487
441,132
324,347
111,166
5,620
90
12,762
4,388
4,170
4,205
2,382
163,446
133,349
16,658
13,439
320
25,854
17,457
3,613
4,784
3,749
174,291
120,607
38,537
15,147
8,735,350
Switzerland
Tanzania
7,126,850
28,846,000
Thailand
58,718,000
Togo
Trinidad
Tobago
631
18,125,000
4,010,000
and
1,292,000
8-6
Population
Tunisia
GNP
Total
Wealth
Human
Capital
Natural
Produced Capital
Capital
1,790
114,292
86,679
16,584
11,029
2,453
109,396
91,014
11,329
7,052
200
22,911
13,315
5,633
3,963
18,507
338,466
278,536
51,253
8,677
25,872
524,887
419,396
76,468
29,023
4,644
174,046
133,121
13,377
27,548
2,734
165,234
93,114
31,759
40,362
189
26,336
17,572
1,719
7,044
350
22,388
8,802
3,582
10,004
480
43,236
28,784
9,743
4,708
8,815,300
Turkey
60,771,000
18,592,000
Uganda
United
Kingdom
United
States
Uruguay
Venezuela
Viet Nam
Zambia
Zimbabwe
58,087,600
260,529,000
3,167,000
21,378,000
72,500,000
9,196,000
11,002,000
8-7
Appendix 8.3. Introduction to the Random Field Two Dimensional
Estimator
This Appendix has been reproduced with minor notational changes from Quah
(1992). Define the distance between two points z1 and z2 in Z2, where z1 =
(j1,t1) and z2 = (j2,t2) as:
z1 − z 2 = max ( j 1 − j 2 , t1 − t 2 ) .
Similarly, the distance between any two subsets A1 and A2 in Z2 is
def
d(A1 , A2 ) = zinf
∈A
z1 − z 2 .
1
1
z 2 ∈ A2
Fix a probability space (Ω, F, Pr). For p > 0, denote the p-norm of a
random variable (rv) X on (Ω, F, Pr) by X
def
p
= E 1/ p X
p
(
p
= ∫ Ω X (ω d Pr(Ω)
As usual, if G⊂ F is an σ-algebra, then X ∈ G indicates that X is Gmeasurable.
Definition 7.1: A random field is a collection of rv’s
( Ω, F, Pr).
{u
z
)
1/ p
.
}
| z ∈ Z 2 on
For F1 and F2 two sub-σ-algebra of F, define the α-mixing coefficient
def
α (F1,F2 ) = sup Pr( F1 ∩ F2 ) − Pr( F1 ). Pr( F2 ) ,
F1 ∈F1
F2 ∈F2
and the symmetric φ-mixing coefficient
def
(
)
φ s (F1,F2 ) = sup Pr (F1 F2 ) − Pr(F1 ) ∨ Pr (F2 F1 ) − Pr(F2 ) ,
where the sup in φ is taken over F1 in F1 and F2 in F2 such that Pr(F1) > 0
and Pr(F2) > 0. The s superscript (denoting symmetric) distinguishes
s
φ s from the usual φ-mixing coefficient.
Both α and
and
φ s quantify dependence between two σ-algebra of events: α
φ s equal zero whenever F and F are independent.
1
2
σ -algebra of events generated by {u z | z in A} .
2
For m ≥ 1 , and A1 and A2 subsets of Z , define the sequences:
2
For A ⊂ Z , let S (A ) be the
8-8
def
αm =
def
φ ms =
sup
d ( A1 , A 2 ) ≥m
sup
d ( A1 , A2 ) ≥m
α (S (A1 ), S (A 2 )),
φ s (S (A1 ), S (A 2 )). .
Using the same symbols α and φ
is without loss of clarity. It is
straightforward now to extend the usual time series discussion to random
s
α -mixing (φ s -mixing) if α m → 0(φ ms → 0) as
λ
is of size –q if α m = O (m ) for some λ < − q , so
fields.
The random field u z is
m →∞ .
The sequence
that
∑
αm
1
m
α m q < ∞ ; similarly for the sequence φ ms . The smaller
(algebraically) is the size, the faster is the sequence of mixing
coefficients required to vanish.
It is easy to see that
φ s dominates α ,
φ s mixing implies α mixing.
s
The sequences α and φ
above are natural counterparts of the usual
so that
mixing coefficients in time series econometrics: they specialize
appropriately when the index set is restricted to be one-dimensional, and
A1 and A2 in the definitions are half-lines.
Sharp probability inequalities are the basis for useful consistency and
asymptotic distribution results. For random fields, the following Hölderrelated inequalities, already familiar in the time series applications, are
immediate from probability theory:
LEMMA 7.2:
X 2 ∈ S (A2 ) .
(i)
Let A1 and A2
2
be subsets of Z , and let X 1 ∈ S (A1 ) and
For p and q real numbers such that p>1,
−1
−1
if p + q < 1 , then
EX 1 X 2 − EX 1 X 2 ≤ 15α (S (A1 ), S (A2 ))
1− p − 1 − q − 1
(ii)
X1
p
⋅ X2 q.
−1
−1
if p + q = 1 , then
EX 1 X 2 − EX 1 X 2 ≤ 2φ s (S (A1 ), S (A2 )) X 1
p
⋅ X2 q.
The first result is also known as Davydov’s inequality. It is
convenient to give slightly different regularity conditions for different
results.
, j = 1,2,...., N ; t = 1,2,...., T = kN }, with k a fixed
positive number, be (part of) a random field. Assume Eu jt = 0 for all j and
Assumption
A0: Let
{u
jt
t.
8-9
This assumption builds in the restriction that the time and crosssection dimensions are of the same order of magnitude; the zero mean
property will be guaranteed under the hypothesis of interest.
{ }is α-mixing,
∑ u <∞ .
Assumption A1: The random field u jt
(a.) sup jt u jt
r
and for some r > 2,
T
< ∞ and (b.) sup jT T −1 / 2
jt
t =1
Requiring mixing rules out common factors and “fixed effects”.
Suppose that in A1, we require the α-mixing sequence to have size –r
(
−1 / 2
/ (r –2) and further assume lim t→ ∞ Var T
−1 / 2
j, as T → ∞ , the quantity T
degenerate normal rv.
∑
T
t= 1
∑
T
t= 1
)
u jt > 0 .
Then for each fixed
u jt converges in distribution to a non-
The limiting rv then has moments of all orders.
−1 / 2
fact, for each j, (T
∑t =1 u jt )2 is uniformly integrable in T. Uniform
In
T
integrability holds across j as well, under this stronger mixing
assumption. Part (b.) of A1 strengthens this conclusion by requiring a
uniform bound on the r-th absolute moment for all T and j. Alternatively,
notice that if u jt were normally distributed to begin, then the normalized
−1 / 2
partial sum T
∑
T
t= 1
u jt is again normally distributed, and so would have
finite absolute moments of all orders.
At times, it will be necessary to use stronger conditions than
provided in A1.
These are given in the following.
Assumption A2: For some r > 2, sup u jt
r
j, t
< ∞ and {
u jt }is mixing with either
φ s coefficients of size –2 or α coefficients of size –2r/ (r – 2).
Assumption A3: The field
{u }obeys:
jt
(a.) for some r > 4,
sup T −1 / 2 ∑ u jt
T
t= 1
j, T
{ } is
and u jt
mixing with either
r
<∞
φ s coefficients of size –r/2 (r – 2) or α
coefficients of size –r/ (r – 4), and (b.) the sequence of variances
def
(
v N2 = Var N −1 / 2 ∑
N
j= 1
(T −1 / 2 ∑ u jt ) 2
T
t =1
)
2
satisfies lim N →∞ v N > 0 .
Assumptions A2 and A3 strengthen A1 in different ways. Both impose
an explicit size requirement on the mixing coefficients whereas in A1 the
mixing coefficients are only assumed to tend to zero. In A2 and A3, the
8-10
decay rate is explicitly linked to the existence of different higher order
moments. As usual, the slower is the decay rate, the greater is the number
of higher order moments that are required to be finite. Condition (b.) of
A3 is equivalent to a bound on the information matrix in likelihood-based
models, and is standard.
The assumptions above will typically be sufficient for consistent
estimation. For inference, we will impose:
{ } is such
< ∞ , sup T
∑ u
Assumption A4: The random field u jt
sup u jt
j, t
{ } is
and u jt
−1 / 2
r
that (a.) for some r > 4,
T
t= 1
j, T
jt
r
<∞ ,
φ 2 coefficients of size –2 or α coefficients
mixing with either
of size -2r/ (r – 4), and (b.) as in A3.
Notice that assumption A4 implies A1, A2, and A3 because for r >
4, we have -2r/ (r – 4)≤ min (-r/ (r – 4), -2r/ (r – 2)) and -2 ≤ -1 ≤
-r/ 2 (r – 2).
Our first result will be useful for the consistency proofs below.
Let
{X },
with N ≥ 1, j = 1,2,...., N , and t = 0,1,...., T = kN
jt
Define the field data regression coefficient of X
def
βN =
(∑
N
j =1
∑
T
t= 1
X
2
j, t −1
) (∑
−1
N
j =1
∑
T
t= 1
jt
X jt X
be observed data.
on X
j, t −1
j, t −1
as:
);
field data regression distinguishes this from time series (N = 1) and
panel data (T small and fixed ) regressions.
The first main result is a consistency proposition for field data
regression with unit roots.
Theorem 7.11: Suppose
X
(ii)
β 0 = 1;
(iii) sup j≥1 X j 0
(iv)
(v)
Then
jt
generated by:
= β 0 X j ,t −1 + u jt , j = 1,...., N , t ≥ 1;
(i)
jt
{X }is
2
< ∞;
{u }satisfies A0 and A1;
inf T ∑ Var (T
∑ u )> 0.
jt
j, T
−1
T
−1 / 2
t =1
Pr
β N →
1 as
t
s =1
js
N → ∞.
The consistency result above is similar to that for time series
regression with unit roots (see for example Phillips, 1987). However,
whereas the asymptotic distribution for the least squares regression
8-11
coefficient with the time series data is non-normal, that for
appropriately standardized, is normal.
βN
here,
The proof of this theorem is rather long, and the reader is referred to
Quah (1992, Section 9).
8-12
Appendix 8.4.
Basic Mathematics for the Analysis of the Linkage
Between Social Capital and Technology Diffusion: Gibbs States
and Markov Random Fields
In this Appendix, I introduce briefly the concepts of Gibbs states and
Markov fields respectively developed by Gibbs (1902) and Dobrushin (1968).
For a more complete introduction to these concepts I refer the readers to
Preston (1974), and Kemeny et al. (1966). The main application of these
tools is to characterize the probability of observing different
configurations or states of a system/model determined by a finite set of
interconnected agents.
Basic definitions
Field of sets: Consider the set Λ for which the elements are in this case
economic agents. We define the field F ( Λ ) as the set of subsets of Λ .
Hence
F ( Λ ) can be viewed as all the combinations of agents in Λ .
Configurations and size: Let’s define
in
A ∈ F ( Λ ) as one of the combinations
F ( Λ ) such that all agents in A are in some state +w (e.g., informed or
using a technology 1) while the agents in
Λ − A are in some state –w
uniformed or not using technology 1). We say that A represents a
configuration of the system or some state of the system and refer to its
size by its number of elements denoted
A.
Graph: To add structure to the set of agents
Λ , we introduce the concept
of graph. A graph G(V,E) is constituted by a set of vertices V (points that
in this case represent agents) and a set of edges E (lines that join some
of the agents). Most models work with the assumption that
V ⊆ Z 2 . We say
that two agents represented by vector i and j ∈ V are connected if (i,j) ∈
E. We also say that two agents that are connected are neighbors. In our
application, we associate the set Λ with the graph G ( Λ,e) .
Boundary: Let’s define:
8-13
c : Λ × Λ → {0,1}
1 if (i, j ) ∈ e ,

c(i, j ) = 
0 otherwise
We define the boundary of A by the set
A =  j ∈ Λ − A; c(i, j ) = 1 for some i ∈ A .


Hence,
the
boundary of A is the
set of all agents connected to some agent in A.
Simplex: We define a simplex by the set
B = i, j; c(i, j ) = 1, i ≠ j  . This is a


set of all the interconnected agents.
Probability measure and probability space: We define a probability measure
as a function
µ : F ( Λ ) → ℜ such that µ ( A) ≥ 0, ∀A and
∑ µ ( A) = 1 .
We define
A⊂ Λ
the set
℘( Λ ) as the set of all probability measures µ, and call this set
the probability space.
Potential: We call potential a function
Gibbs state potential:
V : F ( Λ ) → ℜ such that V (∅) = 0
We call Gibbs state potential or the potential of a
state A the function:


π ( A) =  ∑ exp V ( B) .exp V ( A) .
 B⊂ Λ

Proposition 1: The probability measure µ is a Gibbs state potential with
potential
 µ ( A) 
V ( A) = log 
,
 µ ( ∅) 
Proof: Given V(A) and the definition of potential we have:
−1
−1



u( B)  u( A)
u ( A)
π ( A) =  ∑ exp V ( B) .exp V ( A) =  ∑
= µ ( ∅)
= µ ( A) . CQFD.
 .
µ ( ∅)
 B⊂ Λ

 B ⊂ Λ µ ( ∅)  µ ( ∅)
8-14
Interaction Potential: We define an interaction potential as the function
JV : F ( Λ ) → ℜ such that JV ( A) =
∑ (−1)
A− X
V(X)
X⊂A
Nearest Neighborhood Potential: A potential V is called a nearest
neighborhood potential if JV ( A) ≠ 0 only if A is simplex of the graph.
Nearest Neighborhood State: We say that µ∈℘( Λ ) is a nearest neighborhood
state if µ(A)>0 for all A and, given i≠A we have:
(
)
µ( A ∪ i) µ ( A ∩ i ) ∪ i
=
.
µ ( A)
µ( A ∩ i )
This states that the conditional probability of observing agent i in state
+w given that agents in A are in +w only depends on what happens in the
neighborhood of i.
Theorem A1: (Preston, 1974).
If µ∈℘( Λ ) is a nearest neighborhood state t
µ∈℘( Λ ) is a Markov random field.
8-15
Appendix 8.5. Proofs of Propositions 1,2, and 3, in Section 5
Proof of proposition 1
The proof of this proposition is trivial. Let’s define
k * = max k f (ki ) =
f1 (ki ) − f−1 (ki )
. Then it is possible to find
ki
c1 , c−1 such that
c1 − c−1
. Because k* is a maximum we know that f’<0 if k>k* and f’>0 if
p
c − c−1
*
k<k*. Then we can find kmin < k such that f ( kmin ) ≤ 1
kmax > k * and
p
c −c
f (kmax ) ≤ 1 −1 .
p
k* >
Proof of proposition 2
First, observe that for each agent i there is a function
ϕ(
)
that gives
the minimum of number of connections with users of technology 1 that are
required to choose that technology given the number of connections of users
of technology –1, and the level of spillover effects of each connection:
∑J
j ∈v1 ( i )


w
=
ϕ
J
w
∑
−
1
i
ij −1  ,
ij
 j ∈v −1 ( i )

*
(8.1)
Then, I need to prove that I can construct at least one type of each
ξ (the construction of a
typology in ξ' is identical). Define Sk ( n ) ; k = kmax + nε as the set of agents
typologies.
I construct a typology of type
kmax < ki < k . Set n=1 and for each element i of Sk (1) create a sub)
set of neighbors v (i ) = { j ≠ i | ( j, i ) ∈ E, k j ≤ k } and a sub-set
(
)
(
v (i ) = { j ≠ i | ( j, i ) ∈ E, k j > k } such that v (i ) ∪ v (i ) = v(i ) and restriction (8.1)
such that
holds. Repeat for all n such that
k (n) ≤ K . The resulting typology ensures
that the high productivity technology will dominate the market. Indeed, at
time t=1 the agents in Sεk observe their neighbors. Because of restriction
(8.1) they all switch to technology 1.
But then, diring the next time
8-16
period, the agents in
Sεk ( 2 ) switch to technology 1. The process continues
until all agents switch. CQFD.
Proof of Proposition 3
Proof of Proposition 3 is given in the text.
Proof of Proposition 4
Now let’s prove that for a set of agents S’∈S(-1,t) we can find a process
φ () that will generate connections that guarantee that S(1,t)=S(1,t-1) U
S’. We need to prove that for each agent in I, the probability of
observing connections that verify (3.25) is positive. We first observe that
the probability that a given agent in S’ will have
h connections with
members of S(1) is given by:
(
Pr ψ i ∈ Ψ
where
ΨNk c
k
Nc
ψi
agent i,


) = ∑ ∏ φ (−β i − j ).∏[1 − φ (−β i − z )]; ∀j ∈ J
x =1

j
Ψ
k
NC

z
is a 1 by
x
∧ z ∈Zx ,
(8.2)
Nc vector that characterizes the set of connections of
is the set of possible connection states where k agents are
Nc − k agents are not connected, J x is the set of agents that
x
k
are connected in permutation x within ΨN C , and Z is the set of agents
connected and
that are not connected in the same permutation. This probability is clearly
positive, and increases with S(1, t ) and decreases with β .
On the other hand, the probability that an agent in S’ is connected with an
agent in S’US(-1,t) is given by:
(
Pr ψ i ∈ Ψ
k
Nc
ΨNk c


) = ∑ ∏ φ (−β i − j ).∏[1 − φ (−β i − z )]; ∀j ∈ J
x =1

j
z

This probability is also positive and increases with
x
∧ z ∈Zx ,
(8.3)
S(1, t ) and β .
8-17
Finally, the probability that the connections of agent i are such that they
promote switching is given by:
Pr(i ∈ S' → 1) =
∑ Pr(ψ
∑ Pr(ψ
ι ∈I i
) (
) Pr(ψ
i
∈ Ψ Syι(1, t ) Pr ψ i ∈ Ψ Sxι( −1, t ) ∪ S'
i
∈ Ψ Syι(1, t )
ι ∈I i'
i
∈ Ψ Sxι( −1, t ) ∪ S'
)
,
)
This probability is also positive, and is inverted U-shapped in
(8.4)
β . The
same exercise can be performed for S(1,t+n).
By the same token, we can prove that there are neighborhoods of S(1,t) for
which existing connections force them to never switch. The resulting
function is U-shapped in β .
Proof of Proposition 5
Proposition 5 follows directly from Proposition 4.
8-18
Appendix 8.6.
Dynamics of Fossil Fuel Depletion Rates
A: Depletion Rates (Rents/GNP)
Country
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
ALGERIA
6.81%
7.28%
8.09%
7.33%
24.71%
18.80%
20.12%
19.98%
16.65%
32.92%
ARGENTINA
0.44%
0.53%
0.58%
0.40%
1.30%
1.44%
1.73%
1.82%
1.74%
5.59%
..
..
..
..
..
..
..
..
..
..
BANGLADESH
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.01%
0.01%
0.00%
0.01%
BARBADOS
0.01%
0.00%
0.00%
0.00%
0.15%
0.24%
0.29%
0.24%
0.45%
1.08%
BENIN
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
BOLIVIA
0.74%
1.27%
1.43%
1.71%
5.84%
4.00%
4.06%
3.42%
2.83%
7.85%
BRAZIL
0.19%
0.21%
0.17%
0.14%
0.50%
0.51%
0.47%
0.41%
0.39%
0.80%
CAMEROON
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.10%
1.21%
7.36%
CHILE
0.17%
0.16%
0.14%
0.17%
0.52%
0.92%
0.68%
0.49%
0.35%
0.86%
CHINA
0.41%
1.25%
0.87%
1.43%
6.08%
10.34%
12.49%
12.21%
15.21%
19.63%
COLOMBIA
1.32%
1.70%
1.53%
1.41%
5.29%
4.74%
4.24%
3.38%
2.68%
4.85%
CONGO
0.06%
0.04%
0.90%
4.90%
22.12%
10.52%
13.93%
13.33%
16.11%
42.12%
COTE D'IVOIRE
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.01%
0.34%
ECUADOR
0.08%
0.12%
2.53%
5.93%
18.45%
12.80%
13.62%
11.52%
11.01%
24.01%
BAHRAIN
EGYPT
1.90%
2.00%
1.45%
1.16%
4.51%
4.90%
6.84%
9.79%
9.60%
25.17%
GABON
14.39%
16.35%
16.99%
13.66%
36.52%
23.99%
19.80%
22.81%
25.27%
64.49%
GHANA
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.09%
0.37%
GUATEMALA
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.02%
0.01%
0.04%
0.22%
INDIA
0.56%
0.75%
0.66%
0.77%
1.81%
3.54%
3.82%
3.35%
2.97%
3.75%
INDONESIA
5.12%
5.95%
6.96%
6.65%
17.59%
12.97%
13.52%
13.34%
11.41%
28.54%
IRAN, ISLAMIC REPUBLIC OF
..
..
..
..
54.16%
40.77%
38.45%
33.40%
25.86%
40.94%
KOREA, REPUBLIC OF
0.09%
0.31%
0.17%
0.33%
0.84%
2.05%
1.49%
1.20%
0.88%
0.65%
MALAYSIA
0.15%
0.78%
0.98%
0.73%
2.91%
3.28%
5.34%
5.46%
5.48%
13.50%
MEXICO
0.43%
0.57%
0.56%
0.56%
2.87%
2.80%
3.47%
4.89%
4.88%
10.93%
MOROCCO
0.03%
0.04%
0.03%
0.04%
0.08%
0.18%
0.19%
0.16%
0.13%
0.11%
MYANMAR
0.43%
0.53%
0.69%
0.71%
1.65%
1.70%
2.04%
2.51%
2.21%
5.15%
NIGER
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
NIGERIA
3.18%
5.83%
6.65%
7.69%
26.66%
16.05%
17.08%
16.04%
13.42%
32.21%
NORWAY
0.01%
0.02%
0.10%
0.08%
0.27%
0.90%
1.44%
1.34%
1.33%
5.98%
PERU
0.46%
0.44%
0.45%
0.45%
1.59%
1.07%
1.38%
2.13%
3.79%
11.24%
PHILIPPINES
0.00%
0.00%
0.00%
0.00%
0.00%
0.02%
0.02%
0.04%
0.03%
0.79%
PORTUGAL
0.01%
0.01%
0.01%
0.00%
0.01%
0.03%
0.02%
0.02%
0.02%
0.01%
SAUDI ARABIA
60.89%
69.25%
57.80%
31.59%
88.65%
57.00%
61.93%
65.41%
51.90%
85.08%
SOUTH AFRICA
0.36%
0.90%
0.58%
0.88%
2.13%
5.04%
6.12%
6.22%
5.38%
4.76%
SURINAME
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
0.00%
SYRIAN ARAB REPUBLIC
2.74%
3.55%
3.59%
3.56%
9.89%
10.53%
11.04%
10.75%
9.74%
18.36%
TAIWAN, CHINA
0.07%
0.17%
0.10%
0.13%
0.29%
0.57%
0.53%
0.42%
0.32%
0.30%
THAILAND
0.01%
0.01%
0.01%
0.01%
0.02%
0.03%
0.03%
0.03%
0.02%
0.05%
TRINIDAD AND TOBAGO
9.40%
2.29%
2.48%
3.48%
34.35%
26.77%
29.15%
27.68%
23.06%
46.96%
TUNISIA
2.07%
2.49%
2.02%
1.89%
8.54%
7.20%
6.29%
6.97%
6.85%
15.77%
TURKEY
0.52%
0.58%
0.51%
0.44%
1.08%
1.06%
0.92%
0.82%
0.77%
1.12%
11.51%
14.38%
12.55%
12.42%
38.28%
25.03%
23.81%
21.66%
19.19%
42.77%
ZAMBIA
0.04%
0.14%
0.10%
0.16%
0.32%
0.89%
0.83%
0.77%
0.58%
0.46%
ZIMBABWE
0.22%
0.48%
0.23%
0.41%
0.96%
1.82%
2.82%
2.30%
2.23%
1.83%
VENEZUELA
8-19
Country
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
ALGERIA
27.84%
19.70%
15.96%
12.23%
11.61%
9.64%
3.95%
5.08%
4.21%
6.35%
6.59%
6.07%
5.02%
3.41%
2.86%
3.29%
0.38%
0.93%
0.28%
1.09%
ARGENTINA
BAHRAIN
20.96%
16.72%
14.16%
12.03%
10.91%
11.44%
7.17%
9.27%
7.04%
7.03%
BANGLADESH
0.01%
0.01%
0.01%
0.02%
0.03%
0.02%
0.01%
0.02%
0.01%
0.01%
BARBADOS
1.14%
0.66%
0.68%
0.90%
1.28%
1.21%
0.35%
0.41%
0.23%
0.25%
BENIN
0.15%
3.25%
3.08%
2.68%
3.42%
3.78%
0.85%
1.00%
0.51%
0.93%
BOLIVIA
7.58%
5.48%
6.14%
5.05%
4.74%
3.89%
0.38%
0.94%
0.30%
0.69%
BRAZIL
1.01%
1.05%
1.09%
1.67%
2.22%
2.33%
0.91%
1.09%
0.71%
0.70%
CAMEROON
9.59%
13.07%
15.34%
14.43%
18.23%
20.57%
7.09%
7.60%
5.65%
8.18%
CHILE
1.27%
1.25%
1.55%
1.48%
1.45%
1.38%
0.23%
0.31%
0.09%
0.15%
CHINA
21.02%
24.44%
23.49%
15.28%
13.20%
13.21%
8.66%
9.49%
8.00%
9.05%
5.02%
4.83%
4.40%
4.09%
4.50%
5.00%
3.85%
6.12%
4.17%
5.74%
44.60%
44.88%
38.14%
40.46%
42.67%
39.10%
9.88%
18.06%
10.90%
18.43%
0.30%
1.02%
2.30%
3.62%
3.38%
2.77%
1.03%
1.11%
0.54%
0.22%
15.97%
COLOMBIA
CONGO
COTE D'IVOIRE
ECUADOR
22.65%
18.74%
19.53%
23.03%
26.02%
22.15%
10.92%
9.59%
13.41%
EGYPT
29.29%
26.90%
24.15%
20.71%
21.36%
19.24%
4.79%
9.26%
5.13%
7.15%
GABON
48.14%
41.85%
39.95%
36.87%
33.60%
32.70%
8.04%
14.57%
6.62%
13.46%
GHANA
0.48%
0.34%
0.35%
0.32%
0.14%
0.06%
0.01%
0.00%
0.00%
0.00%
GUATEMALA
0.63%
0.56%
0.78%
0.74%
0.48%
0.34%
0.27%
0.31%
0.21%
0.24%
INDIA
3.44%
5.07%
5.40%
4.16%
4.13%
4.37%
2.71%
2.55%
2.27%
2.86%
INDONESIA
24.55%
19.73%
14.74%
14.40%
14.62%
13.51%
6.29%
8.51%
5.23%
6.22%
IRAN, ISLAMIC REPUBLIC OF
19.98%
17.59%
21.66%
16.27%
13.69%
11.69%
4.26%
10.31%
9.10%
13.73%
KOREA, REPUBLIC OF
0.87%
1.18%
1.10%
0.54%
0.41%
0.54%
0.42%
0.24%
0.20%
0.16%
MALAYSIA
13.80%
12.00%
12.09%
12.35%
12.49%
13.11%
7.35%
8.69%
6.37%
7.94%
MEXICO
12.98%
11.65%
18.79%
18.91%
15.85%
13.78%
8.30%
10.71%
6.40%
6.68%
MOROCCO
0.11%
0.21%
0.20%
0.13%
0.11%
0.15%
0.08%
0.05%
0.04%
0.04%
MYANMAR
6.42%
5.78%
4.76%
4.23%
4.51%
3.54%
1.18%
0.89%
0.44%
0.42%
NIGER
0.02%
0.05%
0.09%
0.14%
0.14%
0.20%
0.09%
0.07%
0.07%
0.10%
28.45%
20.42%
17.65%
14.72%
15.87%
16.60%
14.60%
27.07%
18.48%
30.68%
8.09%
7.05%
6.35%
6.53%
6.86%
6.23%
2.33%
1.32%
2.49%
0.77%
NIGERIA
NORWAY
PERU
10.64%
8.06%
7.33%
7.41%
7.68%
8.66%
1.73%
2.32%
2.00%
1.71%
PHILIPPINES
0.42%
0.20%
0.33%
0.43%
0.37%
0.31%
0.15%
0.13%
0.11%
0.10%
PORTUGAL
0.01%
0.02%
0.02%
0.01%
0.01%
0.01%
0.01%
0.01%
0.00%
0.00%
SAUDI ARABIA
80.88%
76.71%
56.48%
42.04%
37.58%
31.32%
27.38%
31.00%
29.30%
32.89%
SOUTH AFRICA
4.54%
7.10%
7.88%
4.16%
4.18%
7.61%
5.64%
3.16%
3.38%
3.63%
SURINAME
0.00%
0.00%
0.34%
0.34%
0.72%
1.16%
0.82%
1.18%
1.18%
4.06%
18.01%
15.03%
12.58%
10.91%
10.96%
10.93%
6.79%
13.98%
13.84%
21.54%
0.28%
0.28%
0.24%
0.13%
0.09%
0.09%
0.05%
0.03%
0.02%
0.02%
SYRIAN ARAB REPUBLIC
TAIWAN, CHINA
THAILAND
0.04%
0.07%
0.08%
0.19%
0.37%
0.59%
0.26%
0.25%
0.18%
0.21%
TRINIDAD AND TOBAGO
42.24%
31.57%
21.82%
17.82%
21.38%
20.11%
11.08%
15.28%
10.84%
15.17%
TUNISIA
16.04%
15.28%
13.71%
13.14%
12.99%
11.87%
4.80%
5.76%
3.99%
5.09%
TURKEY
1.40%
1.56%
1.63%
1.22%
1.15%
1.25%
0.77%
0.56%
0.44%
0.53%
VENEZUELA
40.17%
33.01%
27.10%
22.45%
30.57%
25.97%
12.67%
21.99%
13.78%
24.29%
ZAMBIA
0.47%
0.54%
0.68%
0.34%
0.37%
0.59%
0.79%
0.34%
0.30%
0.20%
ZIMBABWE
1.75%
1.89%
1.71%
1.27%
1.12%
1.64%
1.62%
1.32%
1.34%
1.49%
8-20
Country
1990
1991
1992
1993
1994
ALGERIA
8.53%
9.08%
8.21%
6.77%
7.63%
ARGENTINA
1.17%
0.44%
0.37%
0.13%
0.05%
BAHRAIN
9.50%
7.63%
6.66%
14.85%
13.93%
BANGLADESH
0.01%
0.01%
0.01%
0.01%
0.03%
BARBADOS
0.40%
0.31%
0.32%
0.25%
0.21%
BENIN
1.29%
0.78%
0.66%
0.41%
0.45%
BOLIVIA
1.45%
0.69%
0.57%
0.22%
0.09%
BRAZIL
0.92%
0.89%
0.92%
0.69%
0.53%
6.70%
CAMEROON
10.77%
7.11%
6.94%
5.02%
CHILE
0.22%
0.09%
0.10%
0.06%
0.04%
CHINA
10.38%
8.24%
7.15%
5.45%
3.72%
8.15%
5.91%
5.67%
4.36%
3.38%
26.29%
16.29%
15.57%
12.47%
17.80%
0.48%
0.42%
0.39%
0.02%
0.00%
ECUADOR
20.31%
14.95%
14.50%
10.88%
10.20%
EGYPT
11.31%
8.14%
7.17%
4.26%
3.31%
GABON
22.26%
14.84%
13.90%
9.47%
11.38%
GHANA
0.00%
0.00%
0.00%
0.00%
0.00%
GUATEMALA
0.39%
0.23%
0.31%
0.24%
0.26%
INDIA
3.08%
3.15%
3.00%
2.55%
2.05%
2.65%
COLOMBIA
CONGO
COTE D'IVOIRE
INDONESIA
7.91%
5.45%
5.04%
3.23%
20.80%
18.17%
20.09%
..
..
KOREA, REPUBLIC OF
0.12%
0.08%
0.06%
0.04%
0.03%
MALAYSIA
9.84%
7.28%
5.95%
4.72%
3.94%
MEXICO
7.55%
5.31%
4.55%
3.39%
3.11%
MOROCCO
0.04%
0.03%
0.03%
0.03%
0.02%
MYANMAR
0.41%
0.22%
0.16%
0.09%
0.07%
NIGER
0.09%
0.09%
0.09%
0.08%
0.11%
IRAN, ISLAMIC REPUBLIC OF
NIGERIA
39.69%
33.56%
35.16%
32.41%
23.78%
NORWAY
3.08%
0.65%
0.29%
5.16%
5.23%
PERU
2.06%
1.34%
0.92%
0.70%
0.49%
PHILIPPINES
0.12%
0.08%
0.11%
0.09%
0.04%
PORTUGAL
0.00%
0.00%
0.00%
0.00%
0.00%
SAUDI ARABIA
44.28%
41.61%
41.25%
37.67%
36.06%
SOUTH AFRICA
3.26%
2.77%
2.38%
1.87%
1.38%
SURINAME
5.61%
4.90%
7.21%
6.06%
8.48%
26.29%
19.47%
..
..
..
0.02%
0.01%
0.00%
0.01%
0.01%
SYRIAN ARAB REPUBLIC
TAIWAN, CHINA
THAILAND
0.27%
0.21%
0.18%
0.20%
0.17%
18.79%
12.43%
11.12%
8.81%
8.26%
TUNISIA
5.09%
4.33%
3.44%
2.97%
2.42%
TURKEY
0.52%
0.49%
0.45%
0.30%
0.35%
32.02%
25.58%
22.60%
18.13%
18.62%
ZAMBIA
0.24%
0.22%
0.22%
0.14%
0.01%
ZIMBABWE
1.46%
1.61%
2.01%
1.25%
0.98%
TRINIDAD AND TOBAGO
VENEZUELA
8-21
B: Changes in the Growth Rate of the Fossil Fuel Depletion Rates
Growth
Rate
(1984-1994)
60.00%
Suriname
40.00%
20.00%
Bangladesh
0.00%
Ecuador
-20.00%
Myanmar
Average
-40.00%
-60.00%
Ghana
-80.00%
-50.00%
0.00%
50.00%
Average
Growth
100.00%
Rate
150.00%
200.00%
(1971-1984)
8-22