Chapter 8 - Appendixes

Chapter 8 - Appendixes Appendix 8.. Individual Preferences for Growth, Environment, and Income Distribution Funds to be invested in projects that Funds to be invested in projects to Funds to be invested in projects that will stimulate reduce environmental will reduce income economic growth damages inequality Average 3.85 4 Standard.34.46 0.87 Error Source: Author calculations. 8-

Appendix 8.. Composition of the Wealth of Nations (Figures in per Capita USD current) Population GNP Total Human Natural Wealth Capital Produced Capital Capital Argentina 34,80,000 8,063 99,794 68,48 3,35 7,960 Australia 7,84,400 7,98 404,903 7,44 67,93 65,466 Austria 7,94,690 5,307 364,960 7,98 77,749 4,9 Bangladesh 7,787,000 0 3,837 4,4,6 5,534 Belgium 3,00 360,777 99,37 6,65 5 0,080,400 Benin 376 36,06 8,556 4,05 3,634 5,46,000 Bolivia 770 53,94 33,906 8,980,038 7,37,000 Botswana,800 4,898 98,663 5,473 0,76,443,000 Brazil 59,43,000 3,370 5,83 96,758 5,90 3,54 Burkina Faso 0,046,000 30 0,84 4,37,69 4,37 Burundi 6,09,000 49 4,564 8,893,65 3,506 Cameroon,87,000 686 48,044 7,459 8,86,98 Canada 9,0,700 9,656 443,7 3,9 66,608 64,474 Central African 3,35,000 370 33,374 7,704 3,36,535 Republic Chad 6,83,000 93 3,308,78,75 0,79 Chile 4,044,000 3,507 07,640 63,084 7,03 7,353 China,90,90,000 530 50,757 40,97 5,989 4,47 Colombia Congo Costa Rica Cote D Ivoire (Ivory Coast) Denmark Dominican Ecuador Egypt El Salvador Finland France Gambia, Germany Ghana Greece The Republic 36,330,00,56,000 3,304,000 3,780,000 5,7,770 7,684,000,0,000 57,556,000 5,64,000 5,08,570 57,76,00,08,000 8,40,800 6,944,000 0,408,000,60 9,94 97,056,69 0,546 635 44,97 7,684 9,95 7,939,400 35,499 06,588 4,635 4,77 N/A 3,46 8,9 6,4 6,993 8,85 375,477 85,33 7,64 8,88,39 97,060 73,955 8,079 5,06,3 97,58 6,970 4,480 9,708 700 7,36 5,883 6,46 4,06,478 56,95 50,86 4,675,090 8,874 35,30 94,587 90,90 30,54 3,55 38,38 96,078 70,435 4,805 359 5,873 9,77,75 3,870 5,698 353,006 79,785 65,596 7,66 4 38,0 30,78 3,9 3,383 7,73 8,7 4,440 30,777 9,505 8-3

Guatemala 0,3,000,90 7,64 6,469 6,630 3,064 Guinea-Bissau,050,000 39 8,580,733,35 4,496 Haiti 7,035,000 9 7,998 3,534,947,57 Honduras 5,493,000 607 49,998 35,58 8,099 6,37 India 93,600,000 30 8,364 7,098 4,366 6,900 Indonesia 89,907,000 88 86,053 65,43 7,97,983 Ireland 3,54,940 3,738 96,895 4,99 38,9 33,784 8-4

Population GNP Total Human Natural Wealth Capital Produced Capital Capital Italy 57,54,00 9,58 33,08 50,09 67,005 5,985 Jamaica,496,000,4 64,83 38,83 0,004 5,996 Japan 4,78,000 34,680 380,90 8,36 93,768 4,96 Jordan,330 9,5 74,95 5,653,674 4,7,000 Kenya 50 6,97 6,536 7,68 3,67 6,07,000 Korea, Republic of 8,00 4,86 9,908 6,70 5,6 44,563,000 Lesotho 68 39,44 3,849 4,805,760,996,000 Madagascar 30 4,476,,39,86 3,0,000 Malawi 3 0,36 6,6,068,556 0,843,000 Malaysia 3,55 93,048 49,50 4,79 8,809 9,498,000 Mali 50 8,755 7,963,8 8,970 9,54,000 Mauritania 480 35,666,700 4,80 9,686,7,000 Mauritius 3, 34,54 4,065 8,09,40,04,000 Mexico 3,865 59,75 7,965 9,33,898 9,858,000 Morocco,45 76,597 63,074 9,48 4,04 6,488,000 Mozambique 84 3,083 7,939 3,00,043 6,63,900 Namibia,98 0,573 79,04 9,894,475,500,000 Nepal 96 3,074 5,488,379 5,07,360,000 Netherlands,955 344,549 67,504 7,066 5,979 5,39,00 New Zealand 3,048 39,75 30,660 63,08 97,857 3,530,930 Nicaragua 3 39,59 8,576 4,04 6,9 4,75,000 Niger 7 37,03,5,78,34 8,846,000 Norway 6,599 386,796 43,07 99,53 44,47 4,37,630 Pakistan 6,84,000 440 48,7 40,894 3,957 3,3 Panama Papua New Guinea Paraguay Peru Philippines Portugal Rwanda Saudi Senegal Sierra South Spain Arabia Leone Africa,585,000 4,05,000 4,830,000 3,33,000 66,88,000 9,83,980 7,750,000 7,497,600 8,0,000 4,587,000 4,59,000 39,550,900,698 36,80 08,955 6,5,704,58 58,05 37,470 6,445 4,9,556 88,379 64,939 0,68 3,7,88 84,447 6,39 4,85 8,303 97 6,844 5,96 6,780 4,768 9,437 6,000 84,769 33,893 7,337 80 3,740,00,030 7,78 7,365 80,099 09,7 30, 40,66 6 46,578 3,838 4,06 9,74 44 6,403 9,373,558 5,47,963 6,94 9,559 6,793 7,84 3,43 57,873 04,8 43,300 0,39 8-5

Sri Lanka Sweden Switzerland Tanzania Thailand Togo Trinidad and Tobago 8,5,000 8,735,350 7,6,850 8,846,000 58,78,000 4,00,000,9,000 63 65,73 5,309 7,806 6,58 3,753 334,488 37,074 69,638 7,777 36,487 44,3 34,347,66 5,60 90,76 4,388 4,70 4,05,38 63,446 33,349 6,658 3,439 30 5,854 7,457 3,63 4,784 3,749 74,9 0,607 38,537 5,47 8-6

Population GNP Total Human Natural Wealth Capital Produced Capital Capital Tunisia 8,85,300,790 4,9 86,679 6,584,09 Turkey 60,77,000,453 09,396 9,04,39 7,05 Uganda 8,59,000 00,9 3,35 5,633 3,963 United Kingdom 8,507 338,466 78,536 5,53 8,677 58,087,600 United States 60,59,000 5,87 54,887 49,396 76,468 9,03 Uruguay 4,644 74,046 33, 3,377 7,548 3,67,000 Venezuela,734 65,34 93,4 3,759 40,36,378,000 Viet Nam 89 6,336 7,57,79 7,044 7,500,000 Zambia 9,96,000 350,388 8,80 3,58 0,004 Zimbabwe,00,000 480 43,36 8,784 9,743 4,708 8-7

Appendix 8.3. Introduction to the Random Field Two Dimensional Estimator This Appendix has been reproduced with minor notational changes from Quah (99). Define the distance between two points z and z in Z, where z = (j,t ) and z = (j,t ) as: z z = max ( j j, t t ). Similarly, the distance between any two subsets A and A in Z is d( A, A) def = inf z z A z A z. Fix a probability space ( Ω, F, Pr). For p > 0, denote the p-norm of a p p / Ω F, Pr) by ( ) p / p random variable (rv) X on (, X = E X = X ( d Pr( Ω) p Ω ω. As usual, if G F is an σ-algebra, then X G indicates that X is G- measurable. Definition 7.: A random field is a collection of rv s { u z Z } z ( Ω, F, Pr). def on For F and F two sub-σ-algebra of F, define the α-mixing coefficient ( ) α F,F def = sup F F F F Pr( F F ) Pr( F ).Pr( F ), and the symmetric φ-mixing coefficient φ s ( ) def ( F,F ) = sup Pr( F F) Pr( F) Pr( F F) Pr( F), where the sup in φ s is taken over F in F and F in F such that Pr(F ) > 0 and Pr(F ) > 0. The s superscript (denoting symmetric) distinguishes s φ from the usual φ-mixing coefficient. and φ s Both α and φ s quantify dependence between two σ-algebra of events: α equal zero whenever F and F are independent. A Z (), let A S be the σ { } -algebra of events generated by z in A For For m, and A and A subsets of Z, define the sequences: u z. 8-8

def ( S( A ), S( A )), α m = sup α def d( A, A ) m ( S( A ), S( A )). s s φ m = sup φ. d ( A, A ) m Using the same symbols α and φ s is without loss of clarity. It is straightforward now to extend the usual time series discussion to random s fields. The random field u is α -mixing ( φ -mixing) if α 0( φ 0) as m. The sequence m that m α q m < z α is of size q if α O( m ) λ ; similarly for the sequence φ s m m = m for some λ < q, so. 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, so that φ s mixing implies α mixing. The sequences α and φ s above are natural counterparts of the usual mixing coefficients in time series econometrics: they specialize appropriately when the index set is restricted to be one-dimensional, and A and A 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.: Let A and A be subsets of X S( A ). For p and q real numbers such that p>, (i) if p + q <, then Z, and let S( ) X A and s m EX X EX X p q ( S ( A ), S( A ) X X. 5α p q (ii) if p + q =, then EX ( S( A ), S( A ) X X. s X EX X φ p q The first result is also known as Davydov s inequality. It is convenient to give slightly different regularity conditions for different results.,, with k a fixed positive number, be (part of) a random field. Assume Eu jt = 0 for all j and t. Assumption A0: Let { u jt j =,,..., N; t =,,..., T = kn} 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. Assumption A: The random field { u jt } is α-mixing, and for some r >, (a.) / sup < and (b.) sup T <. jt u jt r T u jt t = jt Requiring mixing rules out common factors and fixed effects. Suppose that in A, we require the α-mixing sequence to have size r lim / T Var T >. Then for each fixed t u t = jt / (r ) and further assume ( ) 0 T / j, as T, the quantity T u t = jt converges in distribution to a nondegenerate normal rv. The limiting rv then has moments of all orders. In fact, for each j, / T ( T u ) t = jt is uniformly integrable in T. Uniform integrability holds across j as well, under this stronger mixing assumption. Part (b.) of A 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 / T partial sum T u t = 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 A. These are given in the following. Assumption A: For some r >, sup u jt < and { u jt } is mixing with either s φ coefficients of size or α coefficients of size r/ (r ). Assumption A3: The field {} u jt obeys: (a.) for some r > 4, sup T j, T j, t / T t = and { u jt } is mixing with either φ s coefficients of size r/ (r ) or α coefficients of size r/ (r 4), and (b.) the sequence of variances satisfies lim N v > 0 N. v def N = Var r u jt r < / N / T ( N ( T u jt ) ) j= t = Assumptions A and A3 strengthen A in different ways. Both impose an explicit size requirement on the mixing coefficients whereas in A the mixing coefficients are only assumed to tend to zero. In A and A3, the 8-0

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: Assumption A4: The random field { u jt } is such that (a.) for some r > 4, sup u jt <, sup T / u <, j, t r j, T T t = and { u jt } is mixing with either φ coefficients of size or α coefficients of size -r/ (r 4), and (b.) as in A3. Notice that assumption A4 implies A, A, and A3 because for r > 4, we have -r/ (r 4) min (-r/ (r 4), -r/ (r )) and - - -r/ (r ). Let { jt } Our first result will be useful for the consistency proofs below. X, with N, j =,,..., N, and t = 0,,..., T = kn be observed data. Define the field data regression coefficient of X jt on X j, t as: jt r β N N T N T ( X t )( X jt X j, t ); j def = j = t=, j = t= field data regression distinguishes this from time series (N = ) 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.: Suppose { X jt } is generated by: (i) X jt = β 0 X j, t + u jt, j =,..., N, t ; (ii) β = 0 ; (iii) sup j X j 0 < ; (iv) {} u jt satisfies A0 and A; T / t (v) inf T T Var( T u js ) j, > 0. t = s = Then β Pr N as N. The consistency result above is similar to that for time series regression with unit roots (see for example Phillips, 987). However, whereas the asymptotic distribution for the least squares regression 8-

coefficient with the time series data is non-normal, that for β N here, appropriately standardized, is normal. The proof of this theorem is rather long, and the reader is referred to Quah (99, Section 9). 8-

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 (90) and Dobrushin (968). For a more complete introduction to these concepts I refer the readers to Preston (974), and Kemeny et al. (966). 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 A F ( Λ ) as one of the combinations in F ( Λ) such that all agents in A are in some state +w (e.g., informed or using a technology ) while the agents in Λ A are in some state w uniformed or not using technology ). 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. 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: 8-3

c : Λ Λ 0, { } if (, i j) e, ci (, j)= 0 otherwise We define the boundary of A by the set A = j Λ A; c( i, j) = 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) =, 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)=. We define the set ( ) A Λ Λ as the set of all probability measures µ, and call this set the probability space. Potential: We call potential a function V : F ( Λ) Rsuch that V( )= 0 Gibbs state potential: We call Gibbs state potential or the potential of a state A the function: π ( A )= V ( B ) exp.expv( A). B Λ Proposition : The probability measure µ is a Gibbs state potential with potential ( A) VA ( )= log µ, µ ( ) Proof: Given V(A) and the definition of potential we have: ub ua ua π( A)= V B V A µ µ A ( ) ( ) = B B µ ( ) µ ( ) = ( ) ( ) exp ( ).exp ( ). µ ( ) = ( ) Λ Λ. CQFD. 8-4

Interaction Potential: We define an interaction potential as the function A X J V : F ( Λ) Rsuch that JV ( A)= ( ) V( X) X A Nearest Neighborhood Potential: A potential V is called a nearest neighborhood potential if J ( A) 0 only if A is simplex of the graph. V 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 A: (Preston, 974). If µ ( Λ ) is a nearest neighborhood state t µ ( Λ ) is a Markov random field. 8-5

Appendix 8.5. Proofs of Propositions,, and 3, in Section 5 Proof of proposition The proof of this proposition is trivial. Let s define * f ki f ki k = maxk f( ( ki )= ) ( ). Then it is possible to find c, c such that ki c c k * >. Because k* is a maximum we know that f <0 if k>k* and f >0 if p * c c k<k*. Then we can find kmin < k such that f( kmin) k k * max > and p c c f( kmax). p Proof of proposition First, observe that for each agent i there is a function ϕ( ) that gives the minimum of number of connections with users of technology that are required to choose that technology given the number of connections of users of technology, and the level of spillover effects of each connection: * Jw = ϕ i Jw ij, (8.) j v i ij j v() i () Then, I need to prove that I can construct at least one type of each typologies. I construct a typology of type ξ (the construction of a typology in ξ' is identical). Define S ; k = k n k( n) max + ε as the set of agents such that k < k < max i k. Set n= and for each element i of S create a subset of neighbors vi ) ()={ j i ( ji, ) Ek, k () j k} and a sub-set ( vi ()={ j i ( ji, ) Ek, j > k} such that vi ) () vi ( ()= vi () and restriction (8.) holds. Repeat for all n such that kn ( ) K. The resulting typology ensures that the high productivity technology will dominate the market. Indeed, at time t= the agents in S εk observe their neighbors. Because of restriction (8.) they all switch to technology. But then, diring the next time 8-6

period, the agents in S εk ( ) switch to technology. 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(-,t) we can find a process φ() that will generate connections that guarantee that S(,t)=S(,t-) U S. We need to prove that for each agent in I, the probability of observing connections that verify (3.5) is positive. We first observe that the probability that a given agent in S will have h connections with members of S() is given by: k Ψ N c k x Pr ( ψi ΨN )= φ( β i j ). [ φ( β i z )] ; j J z Z c x = j z x, (8.) where ψ i is a by N c vector that characterizes the set of connections of agent i, Ψ N k C is the set of possible connection states where k agents are connected and N c k agents are not connected, J x is the set of agents that k are connected in permutation x within Ψ, and Z x N is the set of agents C that are not connected in the same permutation. This probability is clearly positive, and increases with S(,) t and decreases with β. On the other hand, the probability that an agent in S is connected with an agent in S US(-,t) is given by: k Ψ N c k x Pr ( ψi ΨN )= φ( β i j ). [ φ( β i z )] ; j J z Z c x = j z x, (8.3) This probability is also positive and increases with S(,) t and β. 8-7

Finally, the probability that the connections of agent i are such that they promote switching is given by: Pr( i S' ) = ι I ι I i yι Pr( ψi Ψ Pr S t ) ψ Ψ ' i yι Pr( ψi Ψ Pr S t ) ψ Ψ ( ) ( ) x ι (,) i S(,) t S' x ι (,) i S(,) t S', (8.4) This probability is also positive, and is inverted U-shapped in β. The same exercise can be performed for S(,t+n). By the same token, we can prove that there are neighborhoods of S(,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. 8-8

Appendix 8.6. Dynamics of Fossil Fuel Depletion Rates A: Depletion Rates (Rents/GNP) Country 970 97 97 973 974 975 976 977 978 979 ALGERIA 6.8% 7.8% 8.09% 7.33% 4.7% 8.80% 0.% 9.98% 6.65% 3.9% ARGENTINA 0.44% 0.53% 0.58% 0.40%.30%.44%.73%.8%.74% 5.59% BAHRAIN.................... BANGLADESH 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.0% 0.0% 0.00% 0.0% BARBADOS 0.0% 0.00% 0.00% 0.00% 0.5% 0.4% 0.9% 0.4% 0.45%.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%.7%.43%.7% 5.84% 4.00% 4.06% 3.4%.83% 7.85% BRAZIL 0.9% 0.% 0.7% 0.4% 0.50% 0.5% 0.47% 0.4% 0.39% 0.80% CAMEROON 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.0%.% 7.36% CHILE 0.7% 0.6% 0.4% 0.7% 0.5% 0.9% 0.68% 0.49% 0.35% 0.86% CHINA 0.4%.5% 0.87%.43% 6.08% 0.34%.49%.% 5.% 9.63% COLOMBIA.3%.70%.53%.4% 5.9% 4.74% 4.4% 3.38%.68% 4.85% CONGO 0.06% 0.04% 0.90% 4.90%.% 0.5% 3.93% 3.33% 6.% 4.% COTE D'IVOIRE 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.0% 0.34% ECUADOR 0.08% 0.%.53% 5.93% 8.45%.80% 3.6%.5%.0% 4.0% EGYPT.90%.00%.45%.6% 4.5% 4.90% 6.84% 9.79% 9.60% 5.7% GABON 4.39% 6.35% 6.99% 3.66% 36.5% 3.99% 9.80%.8% 5.7% 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% 0.0% 0.0% 0.04% 0.% INDIA 0.56% 0.75% 0.66% 0.77%.8% 3.54% 3.8% 3.35%.97% 3.75% INDONESIA 5.% 5.95% 6.96% 6.65% 7.59%.97% 3.5% 3.34%.4% 8.54% IRAN, ISLAMIC REPUBLIC OF........ 54.6% 40.77% 38.45% 33.40% 5.86% 40.94% KOREA, REPUBLIC OF 0.09% 0.3% 0.7% 0.33% 0.84%.05%.49%.0% 0.88% 0.65% MALAYSIA 0.5% 0.78% 0.98% 0.73%.9% 3.8% 5.34% 5.46% 5.48% 3.50% MEXICO 0.43% 0.57% 0.56% 0.56%.87%.80% 3.47% 4.89% 4.88% 0.93% MOROCCO 0.03% 0.04% 0.03% 0.04% 0.08% 0.8% 0.9% 0.6% 0.3% 0.% MYANMAR 0.43% 0.53% 0.69% 0.7%.65%.70%.04%.5%.% 5.5% NIGER 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% NIGERIA 3.8% 5.83% 6.65% 7.69% 6.66% 6.05% 7.08% 6.04% 3.4% 3.% NORWAY 0.0% 0.0% 0.0% 0.08% 0.7% 0.90%.44%.34%.33% 5.98% PERU 0.46% 0.44% 0.45% 0.45%.59%.07%.38%.3% 3.79%.4% PHILIPPINES 0.00% 0.00% 0.00% 0.00% 0.00% 0.0% 0.0% 0.04% 0.03% 0.79% PORTUGAL 0.0% 0.0% 0.0% 0.00% 0.0% 0.03% 0.0% 0.0% 0.0% 0.0% SAUDI ARABIA 60.89% 69.5% 57.80% 3.59% 88.65% 57.00% 6.93% 65.4% 5.90% 85.08% SOUTH AFRICA 0.36% 0.90% 0.58% 0.88%.3% 5.04% 6.% 6.% 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.74% 3.55% 3.59% 3.56% 9.89% 0.53%.04% 0.75% 9.74% 8.36% TAIWAN, CHINA 0.07% 0.7% 0.0% 0.3% 0.9% 0.57% 0.53% 0.4% 0.3% 0.30% THAILAND 0.0% 0.0% 0.0% 0.0% 0.0% 0.03% 0.03% 0.03% 0.0% 0.05% TRINIDAD AND TOBAGO 9.40%.9%.48% 3.48% 34.35% 6.77% 9.5% 7.68% 3.06% 46.96% TUNISIA.07%.49%.0%.89% 8.54% 7.0% 6.9% 6.97% 6.85% 5.77% TURKEY 0.5% 0.58% 0.5% 0.44%.08%.06% 0.9% 0.8% 0.77%.% VENEZUELA.5% 4.38%.55%.4% 38.8% 5.03% 3.8%.66% 9.9% 4.77% ZAMBIA 0.04% 0.4% 0.0% 0.6% 0.3% 0.89% 0.83% 0.77% 0.58% 0.46% ZIMBABWE 0.% 0.48% 0.3% 0.4% 0.96%.8%.8%.30%.3%.83% 8-9

Country 980 98 98 983 984 985 986 987 988 989 ALGERIA 7.84% 9.70% 5.96%.3%.6% 9.64% 3.95% 5.08% 4.% 6.35% ARGENTINA 6.59% 6.07% 5.0% 3.4%.86% 3.9% 0.38% 0.93% 0.8%.09% BAHRAIN 0.96% 6.7% 4.6%.03% 0.9%.44% 7.7% 9.7% 7.04% 7.03% BANGLADESH 0.0% 0.0% 0.0% 0.0% 0.03% 0.0% 0.0% 0.0% 0.0% 0.0% BARBADOS.4% 0.66% 0.68% 0.90%.8%.% 0.35% 0.4% 0.3% 0.5% BENIN 0.5% 3.5% 3.08%.68% 3.4% 3.78% 0.85%.00% 0.5% 0.93% BOLIVIA 7.58% 5.48% 6.4% 5.05% 4.74% 3.89% 0.38% 0.94% 0.30% 0.69% BRAZIL.0%.05%.09%.67%.%.33% 0.9%.09% 0.7% 0.70% CAMEROON 9.59% 3.07% 5.34% 4.43% 8.3% 0.57% 7.09% 7.60% 5.65% 8.8% CHILE.7%.5%.55%.48%.45%.38% 0.3% 0.3% 0.09% 0.5% CHINA.0% 4.44% 3.49% 5.8% 3.0% 3.% 8.66% 9.49% 8.00% 9.05% COLOMBIA 5.0% 4.83% 4.40% 4.09% 4.50% 5.00% 3.85% 6.% 4.7% 5.74% CONGO 44.60% 44.88% 38.4% 40.46% 4.67% 39.0% 9.88% 8.06% 0.90% 8.43% COTE D'IVOIRE 0.30%.0%.30% 3.6% 3.38%.77%.03%.% 0.54% 0.% ECUADOR.65% 8.74% 9.53% 3.03% 6.0%.5% 0.9% 9.59% 3.4% 5.97% EGYPT 9.9% 6.90% 4.5% 0.7%.36% 9.4% 4.79% 9.6% 5.3% 7.5% GABON 48.4% 4.85% 39.95% 36.87% 33.60% 3.70% 8.04% 4.57% 6.6% 3.46% GHANA 0.48% 0.34% 0.35% 0.3% 0.4% 0.06% 0.0% 0.00% 0.00% 0.00% GUATEMALA 0.63% 0.56% 0.78% 0.74% 0.48% 0.34% 0.7% 0.3% 0.% 0.4% INDIA 3.44% 5.07% 5.40% 4.6% 4.3% 4.37%.7%.55%.7%.86% INDONESIA 4.55% 9.73% 4.74% 4.40% 4.6% 3.5% 6.9% 8.5% 5.3% 6.% IRAN, ISLAMIC REPUBLIC OF 9.98% 7.59%.66% 6.7% 3.69%.69% 4.6% 0.3% 9.0% 3.73% KOREA, REPUBLIC OF 0.87%.8%.0% 0.54% 0.4% 0.54% 0.4% 0.4% 0.0% 0.6% MALAYSIA 3.80%.00%.09%.35%.49% 3.% 7.35% 8.69% 6.37% 7.94% MEXICO.98%.65% 8.79% 8.9% 5.85% 3.78% 8.30% 0.7% 6.40% 6.68% MOROCCO 0.% 0.% 0.0% 0.3% 0.% 0.5% 0.08% 0.05% 0.04% 0.04% MYANMAR 6.4% 5.78% 4.76% 4.3% 4.5% 3.54%.8% 0.89% 0.44% 0.4% NIGER 0.0% 0.05% 0.09% 0.4% 0.4% 0.0% 0.09% 0.07% 0.07% 0.0% NIGERIA 8.45% 0.4% 7.65% 4.7% 5.87% 6.60% 4.60% 7.07% 8.48% 30.68% NORWAY 8.09% 7.05% 6.35% 6.53% 6.86% 6.3%.33%.3%.49% 0.77% PERU 0.64% 8.06% 7.33% 7.4% 7.68% 8.66%.73%.3%.00%.7% PHILIPPINES 0.4% 0.0% 0.33% 0.43% 0.37% 0.3% 0.5% 0.3% 0.% 0.0% PORTUGAL 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.00% 0.00% SAUDI ARABIA 80.88% 76.7% 56.48% 4.04% 37.58% 3.3% 7.38% 3.00% 9.30% 3.89% SOUTH AFRICA 4.54% 7.0% 7.88% 4.6% 4.8% 7.6% 5.64% 3.6% 3.38% 3.63% SURINAME 0.00% 0.00% 0.34% 0.34% 0.7%.6% 0.8%.8%.8% 4.06% SYRIAN ARAB REPUBLIC 8.0% 5.03%.58% 0.9% 0.96% 0.93% 6.79% 3.98% 3.84%.54% TAIWAN, CHINA 0.8% 0.8% 0.4% 0.3% 0.09% 0.09% 0.05% 0.03% 0.0% 0.0% THAILAND 0.04% 0.07% 0.08% 0.9% 0.37% 0.59% 0.6% 0.5% 0.8% 0.% TRINIDAD AND TOBAGO 4.4% 3.57%.8% 7.8%.38% 0.%.08% 5.8% 0.84% 5.7% TUNISIA 6.04% 5.8% 3.7% 3.4%.99%.87% 4.80% 5.76% 3.99% 5.09% TURKEY.40%.56%.63%.%.5%.5% 0.77% 0.56% 0.44% 0.53% VENEZUELA 40.7% 33.0% 7.0%.45% 30.57% 5.97%.67%.99% 3.78% 4.9% ZAMBIA 0.47% 0.54% 0.68% 0.34% 0.37% 0.59% 0.79% 0.34% 0.30% 0.0% ZIMBABWE.75%.89%.7%.7%.%.64%.6%.3%.34%.49% 8-0

Country 990 99 99 993 994 ALGERIA 8.53% 9.08% 8.% 6.77% 7.63% ARGENTINA.7% 0.44% 0.37% 0.3% 0.05% BAHRAIN 9.50% 7.63% 6.66% 4.85% 3.93% BANGLADESH 0.0% 0.0% 0.0% 0.0% 0.03% BARBADOS 0.40% 0.3% 0.3% 0.5% 0.% BENIN.9% 0.78% 0.66% 0.4% 0.45% BOLIVIA.45% 0.69% 0.57% 0.% 0.09% BRAZIL 0.9% 0.89% 0.9% 0.69% 0.53% CAMEROON 0.77% 7.% 6.94% 5.0% 6.70% CHILE 0.% 0.09% 0.0% 0.06% 0.04% CHINA 0.38% 8.4% 7.5% 5.45% 3.7% COLOMBIA 8.5% 5.9% 5.67% 4.36% 3.38% CONGO 6.9% 6.9% 5.57%.47% 7.80% COTE D'IVOIRE 0.48% 0.4% 0.39% 0.0% 0.00% ECUADOR 0.3% 4.95% 4.50% 0.88% 0.0% EGYPT.3% 8.4% 7.7% 4.6% 3.3% GABON.6% 4.84% 3.90% 9.47%.38% GHANA 0.00% 0.00% 0.00% 0.00% 0.00% GUATEMALA 0.39% 0.3% 0.3% 0.4% 0.6% INDIA 3.08% 3.5% 3.00%.55%.05% INDONESIA 7.9% 5.45% 5.04% 3.3%.65% IRAN, ISLAMIC REPUBLIC OF 0.80% 8.7% 0.09%.... KOREA, REPUBLIC OF 0.% 0.08% 0.06% 0.04% 0.03% MALAYSIA 9.84% 7.8% 5.95% 4.7% 3.94% MEXICO 7.55% 5.3% 4.55% 3.39% 3.% MOROCCO 0.04% 0.03% 0.03% 0.03% 0.0% MYANMAR 0.4% 0.% 0.6% 0.09% 0.07% NIGER 0.09% 0.09% 0.09% 0.08% 0.% NIGERIA 39.69% 33.56% 35.6% 3.4% 3.78% NORWAY 3.08% 0.65% 0.9% 5.6% 5.3% PERU.06%.34% 0.9% 0.70% 0.49% PHILIPPINES 0.% 0.08% 0.% 0.09% 0.04% PORTUGAL 0.00% 0.00% 0.00% 0.00% 0.00% SAUDI ARABIA 44.8% 4.6% 4.5% 37.67% 36.06% SOUTH AFRICA 3.6%.77%.38%.87%.38% SURINAME 5.6% 4.90% 7.% 6.06% 8.48% SYRIAN ARAB REPUBLIC 6.9% 9.47%...... TAIWAN, CHINA 0.0% 0.0% 0.00% 0.0% 0.0% THAILAND 0.7% 0.% 0.8% 0.0% 0.7% TRINIDAD AND TOBAGO 8.79%.43%.% 8.8% 8.6% TUNISIA 5.09% 4.33% 3.44%.97%.4% TURKEY 0.5% 0.49% 0.45% 0.30% 0.35% VENEZUELA 3.0% 5.58%.60% 8.3% 8.6% ZAMBIA 0.4% 0.% 0.% 0.4% 0.0% ZIMBABWE.46%.6%.0%.5% 0.98% 8-

B: Changes in the Growth Rate of the Fossil Fuel Depletion Rates 60.00% Average Growth Rate (984-994) Suriname 40.00% 0.00% Bangladesh 0.00% Ecuador -0.00% Myanmar -40.00% -60.00% Ghana -80.00% -50.00% 0.00% 50.00% 00.00% 50.00% 00.00% Average Growth Rate (97-984) 8-