Spending Natural Resource Revenues in an Altruistic Growth Model

Transcription

1 Spending Natural Resource Revenues in an Altruistic Growth Model Elisabeth Hermann Frederiksen University of Copenhagen, FAME y and EPRU z Please, consider for the young economist session. Preliminary draft. Comments welcome. May 8, 2006 Abstract This paper examines how revenues from a natural resource interact with growth and welfare in an overlapping generations model with altruism. Spending policies determine the allocation of resource revenues between public services and direct transfers to members of society. It is well-known that the growth dynamics depend on whether the bequest motive is operative. We analyze the role of spending policies in how bequests and savings respond to higher resource revenues, and derive solutions which imply that growth can be harmed. Furthermore, we examine spending policies that may lead to multiplicity of equilibria, and illustrate that growth and welfare can be oppositely a ected by changes in the resource revenue. Finally, we provide the socially optimal spending policies. The analysis suggests that variation in spending policies, and in the strength of the bequest motive, may be part of the reason why resource revenues seem to a ect economic performance across nations di erently. Keywords: Natural Resources, Economic Growth, Welfare, Altruism JEL Classi cations: D64, O4, Q33, Q38 I wish to thank Carl-Johan Dalgaard, Massimo Franchi, Christian Groth, Christian Schultz, Ragnar Torvik, seminar participants at the University of Copenhagen, and at the 2005 annual DGPE workshop for their helpful discussions and suggestions. Correspondence: Elisabeth Hermann Frederiksen, Department of Economics, University of Copenhagen, Studiestræde 6, 455 Copenhagen - K, Denmark. ehfecon.ku.dk. y FAME (Fisheries & Aquaculture, Management & Economics) is a network and resource school within resource and sheries management and economics connecting universities, research institutions and researchers. z The activities of EPRU (Economic Policy Research Unit) are nanced through a grant from The Danish National Research Foundation.

2 Introduction An important hypothesis in the growth literature is the notion of a resource curse ; a notion that is not new but dates back in history. The decline of Spain s prosperity after it s colonization of the New World and discovery of large amounts of gold and other precious metals is a classical example. Also within the last decades has the resource curse hypothesis received support by a large body of empirical literature (see Auty 993, 200; Sachs and Warner 995, 999, 200 among others) 2. Nevertheless, recent empirical studies have begun to question an unconditional negative relationship between natural resources and growth. Stijns (2005) reexamines the e ect of natural resource abundance on growth rates in a cross-country study by decomposing natural resources into four groups, namely oil and gas, coal, minerals and land. He concludes that only land is negatively correlated with economic growth. Sala-i-Martin et al. (2004) investigate overall determinants of growth rates; also by means of cross-country regressions. Among the robust and signi cant variables contributing positively to economic growth is the fraction of GDP in mining. Moreover, the classical counterexample to the resource curse is oil-rich Norway. Larsen (2005) concludes that resources are a blessing for Norway s economy 3. Motivated by what could look like an empirical rejection of a pandemic resource curse, this paper takes a closer look at how the variation across nations in the relationship between growth performance and natural resources can be explained 4. We use the term resource curse to describe the situation where resource abundant nations grow slower than nations endowed with fewer resources. In the literature the term is sometimes used in a more general way to describe poor economic performance. However, in our model, it is important to distinguish between growth and welfare e ects. 2 For a recent survey of the literature, consult Stevens (2003). 3 He notes, however, a slow-down in growth after the mid-90s. 4 The theoretical literature has traditionally focused on how to link poor growth performance to natural resource abundance. Classical explanations include the Dutch disease theory (Corden and

3 We argue that one possibility is that countries may be in di erent economic stages of development, or what we refer to as di erent economic growth regimes, when more natural resources are discovered. In particular, if economic factors such as private savings di er in the way they are generated across economic development stages, it seems natural to hypothesize that economies respond di erently to resource in ows depending on the dynamics of the particular growth regime by which they are con ned, even when natural resource revenues are allocated in the same ways. Yet, resource revenues are typically managed by governments. Therefore, economic policies, institutions (Mehlum et al. 2006), and political economic factors are likely to in uence spending policies that, in turn, possibly matters for how resource revenues impact economic performance. Classical political economy explanations are based on an idea that easy revenues corrupt and bring about con icts (Ross 2004, 2006) and encourage economically ine cient - but politically important - projects (Robinson and Torvik 2005). As a solution to such problems, Sala-i-Martin and Subramanian (2003) suggest, at least for the case of Nigeria, to decentralize revenues by distributing them directly to the people, by which the government is forced to nance public services by taxes. Taxes may be costly to collect, but Neary 982; Torvik 200; van Wijnbergen 984), rent seeking problems (Tornell and Lane 999; Torvik 2002), and political economy explanations (Ross 2004, 2006; Robinson and Torvik 2005). Rodriguez and Sachs (999) suggest that natural resource rich countries are overshooting their consumption levels and consequently converge to their steady states from above, which results in slow rates of economic growth. Only a limited number of theoretical studies have tried to explain the diverging experiences in resource impact on economic performance. One exception, however, is Mehlum et al. (2006). The paper argues that growth performance varies with how resource rents are distributed between grabbing and production, which, in turn, depends on the type of institution. The paper empirically supports that the resource curse is weaker or completely missing in countries with producer friendly institutional quality. Another paper by Torvik (200) proposes a Dutch disease model that explains the variation in resource impact on economic outcomes by di erences in learning-by-doing e ects and spillovers across traded and non-traded sectors. 2

4 overall society gains in that collecting taxes is claimed to incorporate a disciplining mechanism that protects against wasteful projects 5. We argue that nations that follow this recommendation and allocate (a least a share of) the resource revenues directly to their inhabitants, may experience different economic outcomes due to di erent economic growth regimes. Moreover, is not at all clear whom within society the resources should be given to. Papyrakis and Gerlagh (2004) study a two-generation overlapping generations model where resource revenues are given exclusively to the retired old generation 6. They show that the higher the resource revenues, the less the young generation saves, and therefore the economy is resource cursed. In general, while there has been intense focus on analyzing natural resources in positive settings, an important aspect, namely how best to manage the resource revenues despite potentially harmful e ects on growth has been largely ignored 7. This paper combines the possibility of di erent growth regimes and the possibility of di erent spending policies in a uni ed framework in which the natural resource impact on economic growth and welfare is analyzed. We use a two-period overlapping generations model where individuals are altruistic in that parents care about the welfare of their children. Parents have the possibility to leave bequests, 5 A similar proposal is made by Sandbu (2004). He argues that tax revenues di er from resource revenues in that the rst is considered as out-of-pocket losses and the latter as forgone gains by members of society. In general, he argues, members of society are more likely to hold the government accountable for out-of-pocket losses than for forgone rents. 6 The authors consider in an appendix a situation where all individuals equally divide the resource revenue and nd that resource revenues are less harmful to savings than when only given to the old. 7 One exception is Matsen and Torvik (2005). They analyze an optimal intertemporal consumption path in a Dutch Disease model, and show that the growth maximizing policy di ers from the welfare maximizing policy. In their framework, this means some Dutch Disease is optimal. Within the literature of exhaustible natural resources, the literature of how optimally to manage resource revenues in order to achieve intergenerational equity is well established, see e.g. Hartwick (977), and Solow (974, 986). 3

5 which they will do when their altruism is su ciently high. In this case, the economy is dynastic and behaves like an in nitely-lived agent s model, whereas the economy behaves like an overlapping generations model when altruism is not intense enough and bequests are absent (cf. Barro 974). Natural resource revenues enter the model in every period as a xed fraction of man-made output. They are allocated by a given spending policy as direct transfers to members of society and as expenditures on a public service that works as input in production (in the sense of Barro 990). As rst pointed out by Weil (987), there is a threshold level of altruism that separates the two growth environments. Our paper shows that this threshold level of altruism is determined endogenously by the allocation of natural resource revenues and by the size of the resource ows. Nations with identical spending policies, but di erent resource in ows, and nations with identical resource in ows, but di erent spending policies, may therefore experience di erences in how the resource impacts economic development. We show by use of exogenous policies that the resource curse may occur when the bequests motive is not operative. In this case, under spending policies that allocate resources to the oldest generation, more resources may cause a drop in savings of the young and a subsequent decline in the economic growth rate. Yet, the e ect of a resource curse on welfare is ambiguous as spending policies exist for which the growth rate declines but welfare of the young generation is increased. An increase in consumption that follows from higher in ows of natural resource revenues may (more than) compensate for reduced growth rates. When the bequest motive is operative the resource curse is non-existing and 4

6 resource abundance increases both welfare and growth rates. Bequests interrupt the connection between in ows of natural resource revenues and savings by allowing for o setting intergenerational transfers from the oldest to the youngest. Therefore, consumption and saving are una ected by how resource revenues are allocated across generations. These results suggest an important caveat to the general recommendations by Sala-i-Martin and Subramanian (2003) and others. While trying to escape the resource curse created by political economy reasons by distributing revenues directly to members of society, a resource curse situation may be created due to economic factors instead. It seems reasonable to think of spending policies as typically endogenously determined by a speci c economic or political agenda. We study growth maximizing policies and policies chosen to give the highest feasible welfare of either the young or the old generation and examine if under such policies, potentially a resource curse situation may be triggered. In both cases, we nd possibility of multiplicity of equilibria. This means that ex ante identical nations may end up in ex post different growth regimes; expectations about whether bequests are positive or absent are self-ful lling. The resource curse is not triggered by growth maximizing policies. When bequests are absent, any direct transfers are given only to the young in order to increase savings and thus growth. Higher in ows of natural resources merely increase direct transfers and hence savings and growth. When bequests are positive, no revenues are allocated as direct transfers, since in a dynastic regime growth expands with more public services. Public services, in turn, expand with the resource 5

7 revenue in ow. Nevertheless, the resource curse may grow out of gerontocracies with in nitesimal levels of altruism. The old may allocate direct transfers to themselves to an extent that higher resource ows lead to decreased savings. In general, however, we cannot solve the welfare maximization problem. Nevertheless, if we restrict direct transfers to accrue only to the young, we show that resource curse may happen as the regime that yields highest welfare may not yield highest growth. It turns out that the competitive equilibria are sub-optimal. The sub-optimality partly stems from an externality that works through the production process, and partly from the budget restriction on public services. The rst reason is due to the fact that rms do not take into account the e ect of production on resource in ows and private decisions lead to underaccumulation of capital in this respect. The second reason is due to the fact that the budget available for the public service, which is con ned by the resource in ow, may be sub-optimally low. The social optimum can be decentralized by means of a production subsidy that allocates resource revenues entirely to the rm. In order to nance public services a lumpsum tax is levied on consumption. On a decentralized optimal balanced growth path, parents leave bequests, or are just indi erent between leaving bequests or not. Therefore, the resource curse does not exist. The results presented here are related to those of Papyrakis and Gerlagh (2004) but more general. In particular, we show that the resource curse is not robust to variation in allocation of natural resource revenue across generations in an economy with non-dynastic dynamics. The resource curse situation occurs as a special case. Moreover, we provide a political economy explanation for when it is likely to occur, 6

8 namely when an old generation which is not very altruistic decides the spending policy. Finally, our model is related to the literature that studies e ectiveness of economic policy in an altruistic setting. Caballe (998) analyzes how taxation of labor and capital in uences not only growth performance, but also the growth regime. In his model, the level of altruism that distinguishes the growth regimes is determined itself by the tax policy. Croix and Michel (2002) analyze the neutrality of economic policy when the bequest motive is operative. The paper proceeds as follows. We present the model in section two. In section three, we explain the market equilibrium and characterize the conditions for the altruism factor that distinguishes the growth regimes. In section four, we derive di erent spending policies and analyze the impact of natural resources on growth and welfare under those policies. In section ve, we study the optimal policy and the nal section provides concluding remarks. 2 The Model The economy is closed and described by a one sided altruistic overlapping generations framework. Parents care about the welfare of their o spring and have the possibility to make intergenerational transfers to their immediate descendants in the form of bequests. Individuals live for two periods, as young and as old. Only the young generation works, the old generation is retired. There are L individuals in each generation, which remains constant over time. 7

9 2. Natural Resource Revenues In every period t; an in ow from the sale of a natural resource enters the economy. The value of the revenues is exogenously given as a xed fraction of the real value of man-made output Y t where 0 < < : We may think of as a characteristic that is country speci c 8. Let E t denote the real value of the natural resource ow, then E t Y t : () In this way, our theoretical model also applies to in ows of foreign aid and other gifts and transfers from abroad. As the resource revenues are exogenously given and grow at the same rate as output, and therefore the revenue output ratio is constant over time, we focus purely on allocation questions of the resource revenue spending policy in relation to intergenerational transfers and economic growth 9. Similar ways of modelling of the natural resource (or foreign aid) ow are found in Chatterjee et al. (2003), Lensink and White (200), Papyrakis and Gerlagh (2004), and Torvik (200) Natural Resource Revenue Applications Based on a spending policy, a government spends all resource revenues in every period on potentially two purposes. First, it allocates a share where 0 < ; 8 The revenue output ratio varies considerably across countries. For instance, Iceland, Nigeria, Norway and Venezuela have a share of primary exports in GDP above 0.2, whereas Nepal, Sweden and the US have a share of primary exports below 0.. ( 9 For a reference on optimal resource extraction consult Dasgupta and Heal (979). 0 Torvik (200) discusses alternative ways of modelling the real value of the natural resource in- ow in footnote 4, p The important assumption is that the resource ow grows over time so that, as a share of income, it does not converge towards zero. 8

10 directly to members of society in a lump-sum fashion. Of this share is given to the young generation and ( ) to the old (0 ). Second, the government invests the rest of the resource revenues in a public service ow G t that works as input into production. We think of the public service as a broad range of services that could be infrastructure, administration, legal and environmental services, etc. There are no externalities associated with the use of public services. In every period, the government runs a balanced budget. It cannot issue debts nor run surpluses by accumulating assets. Hence, G t ( )E t ( )Y t : (2) Summing up, the resource constraint satis es 2.3 Firms E t + ( )E t + ( )E t E t Y t : (3) A representative rm produces output Y t and uses three factors in production: labor, the average public service ow per worker g t G t L, and capital K t : Output per worker y t is produced according to the following production technology, y t Akt gt : (4) where 0 < < is the share of labor and public services in production, A is a positive constant productivity term, and k t is capital per worker. Labor productivity increases, as the public service ow per worker g t increases 2. A real example of direct transfers of resource rents is found in Alaska. One purpose of the socalled Alaska Permanent Fund is to distribute the returns of the fund, which come from minerals and oil, to all inhabitants of the state in the form of a check (Hannesson 200). 2 The public service ow per worker is non-rival but subject to congestion from L: 9

11 The representative rm maximizes pro ts taking g t ; as well as the price of output, which is the numeraire, and of inputs as given. Capital fully depreciates in each period and each factor is paid its private marginal product 2.4 Altruistic Individuals Y t gt L ( )A + r t ; (5) K t K t Y t gt L A k t w t : (6) L t K t Individuals are identical within, as well as across, generations. A parent is altruistic with respect to the welfare of her o spring in the Barro (974) sense and weights her o spring s utility in her utility function V t : Let U t denote utility derived from lifecycle consumption, so that total utility of an individual at time t can be presented as V t U t + V t+ ; (7) where 0 < < is the intergenerational discount factor, which we refer to as the altruism factor. When generations are altruistic, parents care about the welfare of their children, who in turn care about the welfare of their children and so forth. In this way, welfare of all future generations is linked. Utility from own consumption is the sum of utility from consumption as young c t ; and the discounted utility of consumption as old c 2t+. Speci cally, U t u(c t ) + u(c 2t+ ) ln(c t ) + ln(c 2t+ ); (8) where 0 < < is the intertemporal discount factor. By recursively eliminating 0

12 V t+i ; i 0; :::; in (7) we have 3 P V t i [ln(c t+i ) + ln(c 2t++i )]; (9) i0 saying that the utility of a young individual born at time t equals own life-cycle utility plus the discounted sum of life-cycle utilities of her descendants. In any period t; the young individual inelastically supplies one unit of labor for which she receives the market wage w t. When > 0 she also receives a direct transfer as a share of the natural resource revenue, and nally she may inherit bequests b t from her parents. She consumes c t and saves s t for her retirement, hence c t + s t b t + w t + e t ; (0) where e t E t L denotes the lump-sum resource revenue income of a young at time t: When old, she receives the proceeds of her saving ( + r t+ )s t ; where r t+ is the real rate of interest. In addition, if < she receives income from the natural resource, which she consumes, and possibly bequeaths to her o spring. Accordingly, her period two budget constraint can be written as c 2t+ + b t+ ( + r t+ )s t + ( )e t+ ; () where ( )e t+ is the resource revenue given lump-sum to an old person at time t +. Bequests cannot be negative, i.e. b t+ 0: This restriction prevents parents from leaving debts to their children. The dynamics of bequests are found by eliminating s t in (0) and (): b t+ ( + r t+ )(b t + w t + e t c t ) + ( )e t+ c 2t+ : (2) 3 Eq. (7) can be rewritten by induction as V t P T i0 i [u(c t+i ) + u(c 2t++i )] + T + V t++t : Taking the limit for T! and assuming that total utility satisfy the limit condition lim T! T + V t++t 0 we get V t P T i0 i (U t+i ): Using U t ln(c t ) + ln(c 2t+ ) we have (9).

13 An individual of generation t maximizes life time utility given in (9) subject to the two budget constraints (0) and (), and the non-negativity constraint on bequests, by optimally choosing consumption, savings and bequests taking b t ; w t ; r t+ ; e t and e t+ as given. The Lagrangian of period t is equal to life-cycle utility U t with the change, p t+ b t+ p t b t ; in the shadow price p t of b t over a period (Croix and Michel 2002, 244) L t ln(c t ) + ln(c 2t+ ) + p t+ b t+ p t b t : (3) Note that b t+ 0 implies ( + r t+ )(b t + w t + e t ) + ( )e t+ ( + r t+ )c t + c 2t+ : Incorporating this restriction in the maximization problem, the optimality conditions, which are both necessary and su cient, are given by c t ( + r t+) c 2t+ ; (4) and b t+ c t+ 0 ( 0 if b t+ > 0): (5) c 2t+ The transversality condition is lim t! t p t b t 0: (6) Equation (4) describes the trade-o between consumption as young and old. In optimum, the individual is indi erent between consuming as young and saving for old consumption. Equation (5) says that if bequests are positive, marginal utility of own consumption as old has to equal marginal utility of consumption of the o spring as young. If a parent s marginal utility from her o spring s consumption is less than the marginal utility of her own consumption, then bequests are zero and the solution is given by a corner solution. 2

14 3 Competitive Equilibrium For simplicity, we normalize the number of working people L to unity, and we can write E t e t ; Y t y t ; K t k t and G t g t : We obtain the following condition by rewriting (4) using (2): y t Ak t ( )yt k t, y t [A( ) ] kt f(; ; )k t (7) where f(;;) < 0: The larger the share of the natural resource revenues that is spent on direct transfers, the smaller the public service ow. This implies a smaller public service ow capital ratio, gt k t. Due to the AK structure of the model, it also leads to a drop in the output capital ratio. Therefore, all things equal, f(;;) > 0; higher resource in ows increase public services. Using (4), factor market clearing implies and using (7) in (8) and (9), we get r t ( )A( g t k t ) ; (8) w t A( g t k t ) k t : (9) r t ( )f(; ; ) r(; ; ); (20) w t f(; ; )k t w(; ; )k t ; (2) where w(; ; ) denotes the wage capital ratio. Since both the real rate of return and the real wage are positively associated with the public service ow capital ratio g t k t ; more resources allocated to direct transfers decrease both the real rate of return and the real wage; r(;) < 0 and w(;) < 0. The capital market equilibrium requires savings to equal capital installed in the 3

15 productive sector s t k t+ : (22) Finally, the goods market equilibrium is given by the aggregate resource constraint. Using the budget constraints (0), () and the equilibrium conditions (2), (20), (2), and (22) the aggregate resource constraint can be expressed as ( + )y t c t + c 2t + k t+ + g t : (23) The total income period t is the sum of man-made output plus the natural resource revenue given as direct transfers. 3. Dynamics In the following, we distinguish two growth regimes of the economy based on the presence of intergenerational transfers. When parents marginal utility of own consumption is larger than marginal utility of the o spring s consumption, the nonnegativity constraint on bequests is binding and there are no bequests. 3.. Zero Bequests Assume that (5) holds with inequality so that bequests are absent. Letting b t b t+ 0 in (0) and (), we can, by also using (4), derive the an expression for the savings s t : s t + [w(; ; )k t + e t ] ( )e t+ ( + )[ + r(; ; )] : (24) Savings are increasing in wages and resource revenues received as young and decreasing in resource revenues received as old. This is intuitive; the smaller the income as old compared to income as young, consumption smoothing requires higher savings. 4

16 Using (22), we get k t+ + [w(; ; )k t + e t ] ( )e t+ ( + )[ + r(; ; )] ; which is the law of motion of capital. Dividing both sides by k t ; we get 0 t+ + [w(; ; ) + e t k t ] ( ) et k t ( 0 t+ + ) ( + )[ + r(; ; )] ; where 0 t+ (k t+ k t ) is the growth rate in the economic growth regime without bequests of capital and also capital per worker due to a constant labor force. Rearrange to get 0 t+ et [ + r(; ; )][w(; ; ) + k t ] 0 (; ; ; ; ): (25) ( + )[ + r(; ; )] + ( ) et k t We de ne a balanced growth path as a path along which c t ; c 2t ; k t ; y t ; g t and e t grow at constant relative rates in all periods t > 0. From (7) it follows that capital grows at the same rate as output. Since resource revenues are given as a xed fraction of output (in ()) it follows immediately that also the ow of natural resource revenues grows at the same rate as output. Moreover, as public services are given as a xed fraction of total resource revenues (in (2)), public services grow at the same rate as output. From the goods market equilibrium in (23), it follows that aggregate consumption (c t and c 2t ) grows at the same rate of output. By (4), (20) and r t r(; ; ); it then follows that period one and period two consumption grow at the rate output. Hence, the bequest constrained economy has no transitional economics; c t ; c 2t ; k t ; y t ; g t and e t grow at the same rate along a balanced growth path at all periods t. We denote values taken by the variables on the balanced growth path without bequests with the superscript 0 : Using (20), (2), noting that e t y t f(; ; )k t ; 5

17 and taking k 0 > 0 as given, equilibrium is given by c 0 + ( ) t f(; ; )( + ) ( + )( ) + ( ) k0 t ; (26) c 0 2t f(; ; )[ + ( )]k 0 t ; (27) k 0 t+ ( )f(; ; )( + ) ( + )( ) + ( ) k0 t : (28) On this growth path, parents behave as if they are sel sh as they do not leave intergenerational transfers. Essentially, the economy behaves like a overlapping generations model. Growth is positive when income received in period one is su ciently large to ensure that savings exceeds the capital depreciation. Accordingly, ( )f(; ; )(+ ) > ( + )( ) + ( ) implies that 0 (; ; ; ) > 0: 3..2 Positive Bequests When bequests are positive, (5) holds with equality. The growth rate of period one consumption is found by dividing the rst order solutions given in (4) and (5) I t+ [ + r(; )] I (; ; ; ): (29) Again, we de ne a balanced growth path as a path along which c t ; c 2t ; k t ; y t ; g t ; b t and e t grow at a constant relative rates in all periods t > 0. From (7) it follows that capital grows at the same rate as output. Since resource revenues are given as a xed fraction of output (in ()) it follows immediately that the ow of natural resource revenues grows at the same rate as output. Moreover, as public services are given as a xed fraction of total resource revenues (in (2)), also public services grow at the same rate as output. By the goods market equilibrium in (23) and r t r(; ; ) it must be that if capital and output grow as the same rate, then this rate equals that of consumption. 6

18 From (4) we know that consumption as old and young is a constant ratio, so old consumption grows at the same rate as young consumption. From either of the budget constraints (0) or () it follows that also bequests grow at the same rate as consumption. Thus, the bequest constrained economy has no transitional economics; c t ; c 2t ; k t ; y t ; g t ; b t and e t grow at the same rate along a balanced growth path at all periods t. From the rst order conditions to (3) it can be shown that p t equals c t when bequests are positive 4. Hence, p t decreases at the rate I (; ; ): We can thus conclude that when b t > 0; p t b t is a constant, and the transversality condition in (6) simpli es to <. When (5) holds with equality, parents leave bequests and the economy behaves like a dynasty of in nitely-lived generations. We denote values taken by the variables on the balanced growth path with positive bequests with the superscript I : Equilibrium is given by + [ + ( + )]( ) b I t f(; ; ) + + ( ) c I t f(; ; ) + + ( ) c I 2t f(; ; ) + kt I ; (30) kt I ; (3) kt I ; (32) k I t+ f(; ; )( )k I t ; (33) with k 0 > 0. Along this growth path the growth rate is positive when +r(;;) : This condition says that for a young individual to have positive savings and bequests, the marginal utility of returns to savings discounted at the intergenerational discount factor, the altruism factor, obtained by the o spring must exceed the marginal 4 L By (3), t c t 0 implies that c t p t+ [ + r(; ; )]; and Lt b t 0 implies that p t p t+ [ + r(; ; )], so it follows that c t p t : 7

19 utility of her own consumption. Clearly, in general the growth rates described by (25) and (29) will di er as will the way they respond to changes in the resource ow and spending policies. 3.2 The Resource Curse We can think of two possibilities of why an economy may wind up being resource cursed, namely when spending policies are such that increased resource ows (i) lead to savings decline, and (ii) lead to a the regime shift to a regime with a lower growth rate. In the following we examine both possibilities Savings Decline Indeed, we nd that savings may be negatively in uenced by increased resource in ows. In particular, Proposition. There exist policies that imply a resource curse only when bequests are absent. Proof. First, when bequests are absent along 0 (; ): 0 (;) n f(;;) ( )( + ) + f(; ; )[( ) ( )(+)( ) (+)( )+( ) ] o R 0: In particular, a policy where 0 and ( 2) > (+)( )+( ) ( ) ( + ) implies 0 (;;;) < 0: Second, in the dynastic growth regime, I (;) ( ) f(;;) > < proves the non-existence of a resource curse when bequests are positive. An operative bequest motive eliminates the resource curse as the growth rate in this regime is increasing in the real rate of return to capital, which, in turn, is increasing in in ows of natural resources, r(;;) > 0. Savings are una ected by the allocation of direct transfers, si t 0; as any change in revenues given to a young 8

20 individual is o set by an identical opposite change in bequests 5. Hence, the rate of growth in this environment I (; ; ) is independent of : When bequests are absent, accumulation of capital responds to the distribution of resource revenues across generations. For example, a policy that distributes all direct transfers solely to the old generation may lead to a resource curse outcome, in which, more generous resource ows result in less savings. The resource curse prevails when the positive e ect that resource ows have on wages is not large enough to increase the marginal utility of young consumption as much as the marginal utility of discounted old consumption. The lower the labor share in production, i.e. the lower ; the worse the curse if present 6. What generates the resource curse is a disproportional large direct transfer to the old generation in the situation where bequests are absent. Therefore, Proposition 2. When direct transfers are absent, or when they, if present, are allocated only to the young generation, the resource curse does not exist. Proof. By proposition we only have to analyze an economy without bequests. h i When 0; 0 (;;;) f(;;) > < and when ; (+) h i 0 (;;;) f(;;) ( )( + ) + f(; ; )( ) > (+)( ) < : A higher in ow of natural resources in the economy allows, ceteris paribus, for more resources to be spent on public service ows. This enhances the public service ow capital ratio and thus the real wage and the real rate of return. When 5 To see this notice that along a balanced growth path (2) can be rewritten as b I t (+r())(w()k I t +ei t c I t )+( )(+I ())e I t w()k I t + e I t ) (+I ())c I t where bi (+ I t ()) (+r()) ei t : Now, write s I t + (bi t + ( )(+ I )e I t (+ I ())b I t (+)(+r()) : Calculating si t (+) (+) +(+)( (+) )+ + 6 It can be shown that if 9 using bi t ei t gives si t 0: then 0 (;;;) 0:

21 direct transfers are positive, also the direct transfers given to the young generation increase, young income goes further up relative to old income, and savings grow. We make an interesting observation about the resource curse: Proposition 3. Higher in ows of natural resource revenues may improve welfare for a young generation, despite causing a resource curse. Proof. See appendix. Next, we turn to examine if the resource curse exist when an economy switch regime as a consequence of higher resource in ows Growth Regime Shifts Though the altruism factor is exogenously given, whether bequests are positive or zero is determined endogenously by the rst order condition given in (5). From (5) we know that when parents marginal utility of own consumption is greater than their marginal utility from the o spring s consumption, the economy is without bequests. A decline in the consumption of the o spring relative to consumption of the parent triggers intergenerational transfers, if the decline is large enough. We de ne the threshold value of the altruism factor such that under a given spending policy (; ) when then 0 (; ; ; ) I (; ; ). In this special case, the non-negativity constraint on bequests is just binding. Inverting (29) and substituting in (25), using (20) and (2) yields ( + ) ( + )( ) + ( ) (; ; ; ; ): (34) Using the de nition of given in (34) we obtain the standard result (Caballe 998; Cardia and Michel 2004; Weil 987) that when the altruism factor is less than the 20

22 threshold value, < (; ; ; ); the economy is without bequest and the growth path is described by (25). On the other hand, when the altruism factor is higher than the threshold value, > (; ; ; ), bequests are positive and growth evolves according to (29). We can now compare growth rates in the two regimes: Proposition 4. Under exogenous policies (; ), everything else equal, an economy with an altruism level that ensures positive bequests grows faster than an economy with an altruism level that leads to absence of bequests. Proof. We note that by (34) equation (25) can be rewritten as 0 (; ; ; ) (; ; ; )( a)f(; ; ) : Since the economy follows this growth path as long as < (; ) but changes to I (; ; ) ( a)f(; ; ) with positive bequests when > (; ) it must be that 0 (; ; ; ) < I (; ; ): We observe in particular that (; ; ; ) is a function of the spending policy as well as the size of the natural resource ow. The more direct transfers given to the young ; the more altruistic the parents must be to leave bequests, and the more direct transfers given to the old ( ); less altruistic parents also leave bequests. In general, changes in amplify di erences in direct transfers across generations, and, we give the following direct transfer allocation rules: When [( + )( in ; i.e. (;;;) (;;;) > (<)0: ) + ] is there no e ect on (; ; ; ) from changes 0; and when < (>)[( + )( ) + ] we have that Therefore, changes in may push economies from one growth regime to another. The question, what happens to the growth rate, when increases in cause the regime to shift is answered in the following: 2

23 Proposition 5. For a given spending policy (; ), when the economy moves from one growth regime to another growth regime due to increased in ows of natural resources, the growth rate goes up. Proof. See appendix. Summing up, this section illustrates that spending policies matter and they matter di erently depending on the presence of bequests. The resource curse prevail as a consequence of savings decline, i.e. s t < 0; whereas regime shifts caused by endogenous changes in the threshold altruism factor lead to higher growth rates. Finally, we noted that the resource curse and welfare gains may be opposite sides of the same coin. 4 Political Equilibrium In this section we ask a slightly di erent question, namely if there are economies in which the resource curse exist under endogenous policies. We examine speci c policy objectives with an eye for this. 4. Growth Maximizing Policies Let b 0 and b 0 be the growth maximizing policy when the economy is without bequests, i.e. (b 0 ; b 0 ) arg max ; 0 (; ; ; ): Lemma. Then b 0 and ( 0 if b if 2 > 0 : Proof. See Appendix. The intuition for this result is as follows. When direct transfers are positive 22

24 and given to the young, in uences 0 (; ; ; ) through two channels between which there is a trade-o. The higher the higher direct transfers (to the young generation) which, ceteris paribus, leads to higher savings for retirement. However, the higher ; the less public service input into private production. Lower public service input into production leads to lower marginal factor productivity. Lower wages means less savings for retirement. Moreover, less public service input into production means less man-made output. Since resource revenues are de ned as a xed fraction of total output, this e ect feeds back into lowering the total amount of resource revenues to be distributed in the rst place. When b 0 and b 0 (; ) savings are maximized, and generate the highest feasible growth rate in a no bequest environment. We notice that when the value of b 0 is given by a corner solution, the rate of economic growth would increase further if the government is able to collect lump-sum taxes to expand the public service. In such a situation the size of the public service ow is sub-optimal. Notice also that b 0 (;) > 0 when 2 > 0: This means that the higher the in ow of natural resources, a larger share should be given as direct transfers in order to maximize growth. The reason is that the larger ; the higher the value of one unit of direct transfer. Higher costs, in terms of lower factor payments, can therefore be tolerated. Let b I be the growth maximizing policy when bequests are positive, i.e. b I arg max I (; ; ): Lemma 2. Then b I 0: Proof. Because I (;;) r(;;) < 0 we have that b I 0: 23

25 In the in nitely-lived generations environment, the growth maximizing policy is independent of the magnitude of the in ows of the natural resource revenues: letting resource revenues work as input into production leads to higher growth rates since the real rate of return is maximized when direct transfers are zero. Combining lemma and 2, it can be shown that when 2, the growth max- imizing policy is identical for the two growth regimes, namely zero direct transfers. The lower the value of the resource in ow for given, the lower the value of direct transfers relative to wages, and hence savings are increased when all revenues are used as investment in public services. Proposition 6. A resource curse does not exist under growth maximizing policies; increased in ows of natural resources enhance growth. Proof. See Appendix. The growth maximizing spending policy depends on the strength of altruism in the economy. For high values of the altruism factor, in order to enhance growth, all resource revenues should be invested in public services. However, for low values of the altruism factor, the growth maximizing policy is to allocate a share of the natural resource revenues as direct transfers to the young. Under growth maximizing policies, by proposition, 2, and lemma it follows immediately that when the economy after a change in remains in its initial growth environment, it will not su er from the resource curse in neither growth environment. Yet, by (34) we know that also the threshold altruism factor depends on and in order to completely exclude the resource curse as a possibility under growth maximizing policies, we must also analyze the relationship between the rate of eco- 24

26 nomic growth and when the economy may shifts growth regime in response to changed resource ows. We observe multiplicity of equilibria for a range of resource in ows. However, the government by de nition frame policies as to achieve the highest growth rate. They will therefore not choose policies that send the economy in a regime with a lower growth rate. Yet, growth maximizing policies may su er from another potential problem, namely dynamic ine ciency. When bequests are absent, the only way for the young to provide for themselves when old is to save, which they may do even when the interest is very low. In this case, transferring resources from the young generation to the old generation is Pareto e cient. Dynamic ine ciency in endogenous growth models occurs when the competitive real rate of interest falls short of the growth rate (King and Ferguson 993). This condition corresponds to 0 (; ; ) > r(; ; ), (; )( a)f(; ; ) > ( a)f(; ; ) () (; ) >. Under growth maximizing policies, only the young receives direct transfers if any, i.e. (b 0 ; b 0 ; ; ) (+) ; therefore growth + maximizing policies trigger dynamic ine ciency when > + absent. when bequests are Just like in the exogenous policy case, this section points out a trade-o between growth gains and welfare costs when bequests are absent. We therefore proceed to study the resource impact under welfare maximizing policies. 25

27 4.2 Young and Old Policies In this section, we assume that either the young or the old decide a policy that is implemented by the government. The policy remains unaltered in perpetuity 7. The policy decision is made at the beginning of the period. After determining the policy, the young earn a wage, decide their savings, and possibly receive a direct transfer and/or bequests. The old receive a return on their savings and possibly leave bequests. At time t; the utility of a young person is given as in (9): V Y oung t P i0 i [ln(c t+i ) + ln(c 2t++i )]; (35) + ln(c t ) + ln(c 2t ) + ln[ + (; )] : (36) The young derive utility of own consumption both as young and as old. The old, on the other hand, only derive utility of own consumption as old: V Old t ln(c 2t ) + P i0 ln(c 2t ) + +i [ln(c t+i ) + ln(c 2t++i )]; (37) + ln(c t ) + ln(c 2t ) + ln[ + (; )] : (38) When altruistic, both young and old derive utility of consumption of the o spring. However, Proposition 7. The resource curse exists when spending policies are decided by an old generation with in nitesimal levels of altruism. Proof. See Appendix. When the economy is borderline non-altruistic, a policy decided by the old can trigger a resource curse. This may not be surprising in that the old generation 7 A similar assumption is made in Alesina and Rodrik (994). 26

28 care overridingly about their own consumption. Yet, since the old receive a higher return to savings the higher the real rate of return, the old do not claim all resource revenues. A part, if not all, of the resource ow is still allocated to public services. Therefore, a non altruistic economy ruled by the old is not cursed per de nition. Unfortunately, solving generally the welfare maximizing policy of either generation cannot be done analytically in this model. Yet, by imposing an additional assumption to the problem, we are able to obtain analytical results. Assumption. Only the young receives direct transfers from natural resource revenues. We refer to policies under assumption as semi-endogenous policies, as the assumption exogenously determines the intergenerational allocation of direct transfers. Assumption is not binding when bequests are positive, since any change in the distribution of direct transfers of natural resource revenues across generations is o set by an opposite change in bequests. Assumption does, however, a ect the threshold altruism factor positively, which push economies towards being in the overlapping generations regime. When bequests are absent, by proposition 2, assumption ensures that the resource curse does not prevail due to savings decline. We therefore focus on examining if a resource curse exists due to regime shifts enforced by changed resource ow. Under assumption, let Y oung and Old denote the policy that maximizes V Y oung t and Vt Old. As the public budget is restricted by 0 < ; utility maximizing policies may not be feasible. Therefore, let and denote the spending policy that yields the highest level of utility for the young and the old generation 27

29 respectively. Then, 0 if Y oung 0 Y oung if Y oung > 0 and 0 if Old 0 Old if Old > 0 : (39) The utility maximizing resource revenue transfers are negative when a person is willing to make positive lump-sum payments to the government to increase the size of the public service. In this case, expanded public services increase the real wage and the real return to capital leading to an overall increase in utility, thereby making the person better o. We analyze this possibility in the next section, but for now, the size of the public service may be restricted by in ows of natural resource revenues as they were under growth maximizing policies. Let 0 be the spending policy that maximizes young welfare when the economy is without bequests, and let I be the spending policy that maximizes young welfare when bequests are positive. Moreover, de ne 0 ) 0 : Then, under assumption, + and I ( ( )++ Lemma 3. Young policy: ( ( 0 if 0 0 if I 0 0 if (+ 0 ) 0 > and ( ) I I [ ( )] if I > ( ) : (+ I ) Proof. See Appendix. Likewise, let 0 be the spending policy that maximizes welfare of the old generation when bequests are absent, and let I be the spending policy that maximizes old welfare when bequests are present. Moreover, de ne 0 and I ( )( + ) ( ) 2 +( )++ : Then, under assumption, + ( ) 2 +( )++ Lemma 4. Old policy: ( ( 0 if 0 0 if I 0 0 if (+ 0 ) 0 > and ( ) I I [ ( )] if I > ( ) : (+ I ) 28

30 Proof. See Appendix. We notice that the young and old spending policies, and ; are both functions of the intertemporal and intergenerational discount factors as well as the resource in ow; (; ; ; ) and (; ; ; ): For both growth regimes is the marginal loss of increasing direct transfers the decline in public service input into productions and thus factor payments. The marginal bene t stems from increased direct transfers. The trade-o faced by the individual depends on the weights given in her welfare function, which, in turn, depends on whether she is old or young, and the growth dynamics. For example, we notice that when bequests are absent, all things equal, the young are more likely to implement a spending policy that involves direct transfers; 0 > 0 and 0 () 0 > 0 and 0 () 0 > 0: The young generation values the utility of own consumption in their utility function undiscounted, whereas the old discounts the o springs utility of young consumption using the intergenerational discount factor. The marginal utility the young obtain from direct transfers is therefore larger and o sets higher marginal utility costs that the direct transfers impose. It is straightforward to show that under assumption, increased in ow of natural resource revenues increase both growth and welfare of the young and the old under both a young and an old policy when the growth regime remains unaltered. Under both policies, c0 t we have that V Old t > 0; ci t > 0 and V Y oung t > 0; c0 2t > 0; ci 2t > 0; 0 I > 0 and > 0, and > 0 8 and 0 < within regimes. Moreover, lemma 3 and 4 imply that policies, and therefore also growth rates, may vary across generations. However, there is no systematic variation, so either a young economy or an old economy may grow faster in either regime. However, 29

31 when direct transfers are zero, within regimes, no matter if policies are decided by the young or the old the growth rate remains the same Growth Regime Shifts Having laid out the semi-endogenous policies of an economy ruled by the young or the old in lemma 3 and 4, this section focuses on analyzing what happens to the growth rates when increased in ows of natural resources enable growth regime shifts. It su ces to analyze either young or old policy to understand the economics of the regime shifts. We choose an economy ruled by the young and apply a numerical example given by A ; 0:4, 0:4 and 0:8 so that 0 5:4 4:56 and I 3:24 4:56 : Threshold altruism; altruism; growth Xi Figure. Young policy In gure, the thin horizontal line illustrates the altruism factor. The threshold altruism factor is illustrated by the bifurcate line. The horizontal part of the 30