Journal of Development Economics

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1 Journal of Develoment Economics 97 (202) Contents lists available at ScienceDirect Journal of Develoment Economics journal homeage Resource abundance, growth and welfare A Schumeterian ersective Pietro F. Peretto Deartment of Economics, Duke University, Durham, NC 27708, United States article info abstract Article history Received 22 February 200 Received in revised form 6 December 200 Acceted 0 December 200 JEL classification E0 L6 O3 O40 Keywords Endogenous growth Endogenous technological change Natural resources This aer takes a new look at the long-run imlications of resource abundance. It develos a Schumeterian model of endogenous growth that incororates an ustream resource-intensive sector and yields an analytical solution for the transition ath. It then derives conditions under which, as the economy's endowment of a natural resource rises, (i) growth accelerates and welfare rises, (ii) growth decelerates but welfare rises nevertheless, and (iii) growth decelerates and welfare falls. Which of these scenarios revails deends on the resonse of the natural resource rice to an increase in the resource endowment. The rice resonse determines the change in income earned by the owners of the resource (the households) and thereby the change in their exenditure on manufacturing goods. Since manufacturing is the economy's innovative sector, this income-to-exenditure effect links resource abundance to the size of the market for manufacturing goods and drives how re-source abundance affects incentives to undertake innovative activity. 200 Elsevier B.V. All rights reserved.. Introduction This aer takes a new look at the long-run effects of resource endowments through the lens of modern Schumeterian growth theory. Using a model of the latest vintage that yields a closed-form solution for the transition ath, it derives conditions under which, as the economy's endowment of a natural resource rises, growth accelerates and welfare rises, conditions under which growth decelerates but welfare rises nevertheless, and conditions under which growth decelerates and welfare falls. Which of these scenarios revails deends on how the attern of factor substitution determines the resonse of the natural resource rice to an increase in the resource endowment. The rice resonse determines the change in income earned by the owners of the resource (the households) and thereby the change in their exenditure on manufacturing goods. Since manufacturing is the economy's innovative sector, this income-to-exenditure effect links resource abundance to the size of the market for manufacturing goods and drives how resource abundance affects incentives to undertake innovative activity. The idea for this aer was conceived during stimulating discussions with several members of the Economics Deartment at the University of Calgary, in articular Sjak Smulders and Francisco Gonzales. Thanks to all for the hositality and the comments. I also thank two anonymous referees and Co-Editor Francesco Caselli for their comments and suggestions. Tel fax address eretto@econ.duke.edu. The model has two factors of roduction in exogenous suly, labor and a natural resource, and two sectors, rimary roduction (or resource rocessing) and manufacturing. I define resource abundance as the endowment of the natural resource relative to labor. The rimary sector uses labor to rocess the raw natural resource the manufacturing sector uses labor and the rocessed natural resource to roduce differentiated consumtion goods. Because both sectors use labor, its reallocation from manufacturing to rimary roduction drives the economy's adjustment to an increase in resource abundance. The manufacturing sector is technologically dynamic firms and entrereneurs undertake R&D to learn how to use factors of roduction more efficiently and to design new roducts. Imortantly, the rocess of roduct roliferation fragments the aggregate market into sub-markets whose size does not increase with the size of the endowments and thereby sterilizes the scale effect. This means that the effect of resource abundance on growth is only temorary. The resulting structure is extremely tractable and yields a closed-form solution for the transition ath. Substitution between labor and resource inuts matters because it determines the rice elasticity of demand for the natural resource. Inelastic demand means that the rice has to fall drastically to induce the market to absorb the additional quantity elastic demand means that the adjustment requires a mild dro in the rice. Imortantly, the two cases are art of a continuum because I use technologies with factor substitution that changes with rices. Now, if the economy exhibits substitution, demand is elastic, the rice effect is mild, the quantity effect dominates, and resource income rises, surring more sending on manufacturing goods and a temorary growth acceleration. If, instead, /$ see front matter 200 Elsevier B.V. All rights reserved. doi0.06/j.jdeveco

2 P.F. Peretto / Journal of Develoment Economics 97 (202) the economy exhibits comlementarity, demand is inelastic, the rice effect is strong, resource income falls, and we have a temorary growth deceleration. Whether the economy exeriences a growth acceleration or deceleration, however, is not sufficient to determine what haens to welfare, since, given technology, the lower resource rice makes consumtion goods cheaer. Assessing the welfare effect of the change in the endowment ratio, therefore, requires resolving the trade-off between short- and long-run effects. y main result is that I identify threshold values of the equilibrium rice of the natural resource and therefore threshold values of the endowment ratio that yield the following sequence of scenarios as we gradually raise the endowment ratio from tiny to very large.. Growth accelerates and welfare rises. This haens when the resource rice is high because the endowment ratio is low. In this situation, demand is elastic, the quantity effect dominates over the rice effect, and, consequently, resource income rises. In other words, starting from a situation of scarcity, the increase in the endowment ratio generates a growth acceleration associated to an initial jum u in consumtion that yields higher welfare. 2. Growth decelerates but welfare rises nevertheless. That is, the rise in the endowment ratio causes a growth deceleration that is offset by an initial jum u in consumtion. This haens when the endowment ratio is between the two thresholds and, corresondingly, the resource rice is in its intermediate range. Relative to the revious case, demand becomes inelastic and the rice effect dominates over the quantity effect, with the result that resource income falls. 3. Growth decelerates and welfare falls. This haens when the resource rice is low because the endowment ratio is high. In this case, demand is inelastic, the rice effect dominates over the quantity effect, and resource income falls. Differently from the revious case, the fall in resource income is now sufficiently large to cause the growth deceleration to dominate over the initial jum u in consumtion or to cause the initial jum in consumtion to be down. There is a large and growing body of literature studying the consequences of natural-resource abundance. Within this literature my aer is most closely related to theoretical models focusing on the reallocation of resources away from the manufacturing sector and towards the resource sector, a reallocation that is sometimes termed Dutch disease in the literature. Dutch-disease models often assume that the manufacturing sector is characterized by learning by doing or other externalities, so these models, like mine, have the otential to induce a fall in the growth rate as well as a fall in welfare. Relative to this literature my model differs in three fundamental dimensions. First, I work with a closed economy rather than an oen economy. Second, I model the roductivity growth rocess in the manufacturing sector through investments in R&D. Third, I introduce vertical integration between the manufacturing sector and the resource sector by making (rocessed) natural resources an inut in the roduction of the manufacturing good. Note that from the closed economy assumtion it follows that there is a distinction between resource endowments (the hysical quantities of natural resources) and resource wealth (its market value, or rice times quantity). In oen-economy models the rice is usually taken as given so a change in the endowment is entirely isomorhic to a change in wealth. From these differences follow major differences in imlications. In my model an increase in resource wealth is never associated with a decline in the growth rate, nor it can reduce welfare. This is because, due to closed economy assumtion, an increase in resource wealth increases demand for domestic manufacturing goods and thus the incentives to engage in R&D. What can reduce growth and welfare is an increase in the resource endowment, if it reciitates a sufficiently large fall in the rice and hence in resource wealth (again, this mechanism is absent in other models the economy takes the rice as given). However, not all declines in resource wealth following increases in endowments are associated with declines in welfare. Even if resource wealth and the subsequent growth rate decline, welfare can increase because of the vertical-integration feature of the model the more abundant endowment reduces roduction costs for manufacturing consumtion goods. The closed economy assumtion also imlies that my model seaks to a different set of facts relative to the Dutch disease literature and most of the emirical literature on the so-called resource curse. Indeed the latter tends to use natural-resource exorts as a share of GDP (or sometimes er caita) as its roxy for resource abundance (clearly my theory has no redictions for the effects of resource exorts) and variation in rices is seen as as imortant and as exogenous a source of variation as variation in hysical endowments. 2 Instead, my theory is alicable to investigating the effects of new resource discoveries in closed economies or, ossibly, of huge new discoveries in the world as a whole. Success stories broadly consistent with my scenario abound. Wright and Czelusta (2007), for examle, argue that the United States overtook the United Kingdom and become the world leader in terms of GDP er worker-hour recisely at the time roughly when it become the world's dominant roducer of virtually every major industrial mineral of the era. They conclude that the condition of abundant resources was a significant factor in shaing, if not roelling, the U.S. ath to world leadershi in manufacturing (. 85). A modernday case that rovides a more secific examle of a growth acceleration is Chile. Wright and Czelusta (. 96) reort that in the 990s it grew at about 8.5% er year and argue that the mining industry was central to this erformance, accounting for about 8.5% of GDP and about half of its total exorts over the eriod. Notably, Chile accounts for 35% of world coer roduction and is a major roducer of several other minerals. It is harder to find examles of failure stories consistent with my scenarios 2 3. The reason is that the literature rarely disentangles rices and quantities to the level of detail needed to isolate the income effect driving my theory. Consequently, it is often imossible to infer from a articular narrative whether the driving factor underlying the growth deceleration is the relative rice effect that my theory emhasizes or the other mechanisms discussed in, e.g., the literature on the natural resource curse. The aer's organization is as follows. Section 2 sets u the model. Section 3 constructs the general equilibrium of the market economy. Section 4 discusses the key roerties of the equilibrium that drive the aer's main results. Section 5 derives the main results. It first studies the conditions under which an increase in the resource endowment results into a growth deceleration or acceleration and then studies the conditions under which it yields lower or higher welfare. It also discusses interesting imlications for our reading of the emirical literature. Section 6 concludes. 2. The model 2.. Overview The basic model that I build on is develoed in Peretto and Connolly (2007). A reresentative household sulies labor services in a cometitive market. It also borrows and lends in a cometitive market for financial assets. The household values variety and buys as many differentiated consumtion goods as ossible. anufacturing firms hire labor to roduce differentiated consumtion goods, undertake R&D, or, See, e.g., Corden and Neary (982), Corden (984), Krugman (987), van Wijnbergen (984), Younger (992), and Torvik (200). 2 See Sachs and Warner (995, 200), Alexeev and Conrad (2009), Brunneschweiler and Bulte (2008), van der Ploeg and Poelhekke (200), van der Ploeg (forthcoming).

3 44 P.F. Peretto / Journal of Develoment Economics 97 (202) in the case of entrants, set u oerations. Production of consumtion goods also requires a rocessed resource, which is roduced by cometitive suliers using labor and a raw natural resource. The introduction of this ustream rimary sector is the main innovation of this aer. The economy starts out with a given range of goods, each sulied by one firm. Entrereneurs comare the resent value of rofits from introducing a new good to the entry cost. Once in the market, firms establish in-house R&D facilities to roduce cost-reducing innovations. As each firm invests in R&D, it contributes to the ool of ublic knowledge and reduces the cost of future R&D. This allows the economy to grow at a constant rate in steady state Households The reresentative household has a constant mass L of identical members, each one endowed with one unit of labor. It maximizes Ut ðþ= e t ρ ð s t Þ log uðþds s ρ N 0 ðþ subject to the flow budget constraint A = ra + WL + Ω + Π Y ρ is the discount rate, A is assets holding, r is the rate of return on assets, W is the wage rate, L is labor suly since there is no reference for leisure, and Y is consumtion exenditure. In addition to asset and labor income, the household receives rents from ownershi of the endowment, Ω, of a natural resource whose market rice is and dividend income from resource-rocessing firms, Π. 3 The household takes these terms as given. Instantaneous utility in Eq. () is 2 6 log u = log4 N 0 i L ð2þ 3 7 di5 N ð3þ is the elasticity of roduct substitution, i is the household's urchase of each differentiated good, and N is the mass of goods (the mass of firms) existing at time t. The solution for the otimal exenditure lan is well known. The household saves according to r = r A ρ + Y Y and taking as given this time-ath of exenditure maximizes Eq. (3) subject to Y = N 0 P i i di. This yields the demand schedule for roduct i, i = Y N 0 P i P i di ð4þ ð5þ With a continuum of goods, firms are atomistic and take the denominator of Eq. (5) as given therefore, monoolistic cometition revails and firms face isoelastic demand curves anufacturing roduction and innovation The tyical firm roduces with the technology i = Z θ i F L i ϕ i 0 b θ b ϕ N 0 ð6þ i is outut, L i is roduction emloyment, ϕ is a fixed labor cost, i is rocessed resource use (henceforth materials for short), Z i is the firm's stock of firm-secific knowledge, and F ( ) is a standard neoclassical roduction function homogeneous of degree one in its arguments. Technology (Eq. (6)) gives rise to total cost Wϕ + C ðw P ÞZ θ i i ð7þ C ( ) is a standard unit-cost function homogeneous of degree one in the wage W and the rice of materials P. The firm accumulates knowledge according to the R&D technology Z i = αkl Zi α N 0 ð8þ Z i measures the flow of firm-secific knowledge generated by an R&D roject emloying L Zi units of labor for an interval of time dt and αk is the roductivity of labor in R&D as determined by the exogenous arameter α and by the stock of ublic knowledge, K. Public knowledge accumulates as a result of sillovers. When one firm generates a new idea to imrove the roduction rocess, it also generates general-urose knowledge which is not excludable and that other firms can exloit in their own research efforts. Firms aroriate the economic returns from firm-secific knowledge but cannot revent others from using the general-urose knowledge that sills over into the ublic domain. Formally, an R&D roject that roduces Z i units of rorietary knowledge also generates Z i units of ublic knowledge. The roductivity of research is determined by some combination of all the different sources of knowledge. A simle way of caturing this notion is to write K = N 0 N Z idi which says that the technological frontier is determined by the average knowledge of all firms The rimary or resources sector In the rimary sector cometitive firms hire labor, L, to extract and rocess natural resources, R, into materials,, according to the technology = F ðl RÞ ð9þ the function F ( ) is a standard neoclassical roduction function homogeneous of degree one in its arguments. The associated total cost is C ðw Þ ð0þ C ( ) is a standard unit-cost function homogeneous of degree one in the wage W and the rice of resources. This is the simlest way to model the rimary sector for the uroses of this aer. aterials are roduced with labor and a natural resource. The natural resource is in fixed endowment and earns rents. The rimary sector cometes for labor with the manufacturing sector. This catures the fundamental inter-sectoral allocation roblem faced by this economy. 3. Equilibrium of the market economy This section constructs the symmetric equilibrium of the manufacturing sector. It then characterizes the equilibrium of the rimary sector. 3 As is clear from this assumtion, to kee the model as simle as ossible, I osit a non-exhaustible resource like land. For a generalization of the model to the case of a renewable (or exhaustible) resource, see Prasertsom (200). 4 For a detailed discussion of the microfoundations of a sillovers function of this class, see Peretto and Smulders (2002).

4 Finally, it imoses general equilibrium conditions to determine the aggregate dynamics of the economy. The wage rate is the numeraire, i.e., W. P.F. Peretto / Journal of Develoment Economics 97 (202) L = S R P = Y S 45 S R ð6þ 3.. Partial equilibrium of the manufacturing sector The tyical manufacturing firm is subject to a death shock. Accordingly, it maximizes the resent discounted value of net cash flow, V i ðþ= t e s ½rv ð Þ + δšdv t Πi ðþds s δ N 0 t e δt is the instantaneous robability of death. Using the cost function (Eq. (7)), instantaneous rofits are h Π i = P i C ð P ÞZ θ i i i ϕ L Zi L Zi is R&D exenditure. V i is the value of the firm, the rice of the ownershi share of an equity holder. The firm maximizes V i subject to the R&D technology (Eq. (8)), the demand schedule (Eq. (5)), Z i (t)n0 (the initial knowledge stock is given), Z j (t ) for t t and j i (the firm takes as given the rivals' innovation aths), and Z j ðt Þ 0 for t t (innovation is irreversible). The solution of this roblem yields the (maximized) value of the firm given the time ath of the number of firms. To characterize entry, I assume that uon ayment of a sunk cost βp i i, an entrereneur can create a new firm that starts out its activity with roductivity equal to the industry average. 5 Once in the market, the new firm imlements rice and R&D strategies that solve a roblem identical to the one outlined above. Hence, a free entry equilibrium requires V i =βp i i. Aendix A shows that the equilibrium thus defined is symmetric and is characterized by the factor demands L = Y S = Y S P S + ϕn ðþ P i C ðw P ÞZi θ = logc ðw P Þ i log P ð2þ Associated to these factor demands are the returns to cost reduction and entry, resectively Yθ r = r Z α ð Þ N L Z N δ ð3þ r = r N β N Y ϕ + L Z + N Ŷ ˆN δ ð4þ Note how both rates of returns deend ositively on firm size Y/N General equilibrium Cometitive resource-rocessing firms roduce u to the oint P =C (,) and demand factors according to R = S R P = Y S S R ð5þ 5 See Etro (2004) and, in articular, Peretto and Connolly (2007) for a more detailed discussion of the microfoundations of this assumtion. S R log C ðw Þ log and I have used Eqs. () and (2) to obtain the exressions after the second equality sign. These factor demands yield that the cometitive resource firms make zero rofits. Equilibrium of the rimary sector requires R=Ω. One can thus think of Eq. (5) as the equation that determines the rice of the natural resource, and therefore resource income for the household, given the level of economic activity, measured by exenditure on consumtion goods Y. The remainder of the model consists of the household's budget constraint (Eq. (2)), the labor demands (Eqs. () and (6)), the returns to saving, cost reduction and entry in Eqs. (4), (3) and (4). The household's budget constraint becomes the labor market clearing condition (see Aendix A for the derivation) L = L N + L + L Z + L L N is aggregate emloyment in entrereneurial activity, L +L Z is aggregate emloyment in roduction and R&D oerations of existing firms and L is aggregate emloyment of resourcesrocessing firms. Assets market equilibrium requires equalization of all rates of return (no-arbitrage), r=r A =r Z =r N, and that the value of the household's ortfolio equals the value of the securities issued by firms, A=NV=βY Dynamics Substituting A=βY into Eq. (2) and using the rate of return to saving Eq. (4), I obtain Y L Ω Y = βρ Then, letting y Y L denote exenditure er caita and ω Ω L denote the endowment ratio, I can use this exression, the demand for the resource (Eq. (5)) and the condition R=Ω to study the instantaneous equilibrium (,y ) as the intersection of the two curves y = +ω βρ ð7þ y = βρ ð8þ S R ðþs ðþ The first describes how resource income determines exenditure on consumtion goods the second how exenditure drives demand for the factors of roduction and thereby determines resource income. The interretation of this solution is that the interaction of the resource and manufacturing goods markets with the exenditure decision of the household determines the endogenous but constant values of all of the relevant nominal variables (given my choice of numeraire W ). As in first-generation endogenous growth models, this roerty yields at any oint in time a constant interest rate and simlifies drastically the overall dynamics, the difference is that here the constant interest rate does not yield a jum to the steady state but a smooth transition. To see this, note that given the air (,y ), Y =Ly is constant and the Euler equation (Eq. (4)) yields r =ρ. Assuming that the economy is always in the region firms invest in vertical R&D (see

5 46 P.F. Peretto / Journal of Develoment Economics 97 (202) Aendix A for details), this result allows me to solve Eqs. (8) and (3) for Ẑ = α L Z N = Y αθð Þ ρ δ N Substituting this result into Eq. (4) then yields ˆN = θð Þ ϕ ρ + δ N ðρ + δþ β α Y ð9þ c C C Consequently, we have log u = log y c Zθ N! The general equilibrium of the model thus reduces to a single differential equation in the mass of firms. The economy converges to θð Þ N = ðρ + δ ϕ ρ + δ α Þβ Y which substituted into Eq. (9) yields ð20þ Ẑ ϕα ðρ + δþ θð Þ = ðρ + δþ ð2þ θð Þ ðρ + δþβ This steady-state growth rate is indeendent of the endowments L and Ω because there is no scale effect. It is insightful to use the value N in Eq. (20) and rewrite the differential equation for N as ˆN = ν N θ ν ð Þ ðρ + δþ ð22þ N β We can reinterret the utility function (Eq. (3)) as a roduction function for a final homogenous good assembled from intermediate goods, so that u is a measure of outut, and define aggregate TFP as T Z θ N ð24þ The key roerty of the model, then, is that the analytical solution for the ath N(t) yields the analytical solution for the ath T(t). To see this, observe first that taking logs and time derivatives Eq. (24) yields ˆT ðþ= t θẑðþ+ t ˆN ðþ t Ẑt ðþis given by Eq. (9) and ˆN ðþby t Eq. (22). In steady state we thus have ˆT = θẑ g which is indeendent of the endowments L and Ω, and thus of ω. oreover, according to Eq. (20) in steady state we have which is a logistic (see, e.g., Banks, 994) with growth coefficient ν and carrying caacity N. It has the solution Y = Y 0 Y N N 0 Y 0 = N N 0 Nt ðþ= N +e νt N N 0 ð23þ N 0 is the initial condition. The interretation of this extremely tractable structure is that at any oint in time the equilibrium of factors market and the consumtion/saving decision of the household determine the size of the market for manufacturing goods Y. This, in turn, determines the carrying caacity coefficient N in the logistic equation characterizing the equilibrium roliferation of roducts in the economy. 4. Proerties of the equilibrium technology, the ath of consumtion and welfare Recall that the variable y studied in the revious section is not consumtion er caita but exenditure er caita. To get consumtion er caita, y needs to be divided by the economy's CPI, h i P Y = N 0 P j dj Accordingly, since manufacturing firms set rices at a marku over marginal cost (see Aendix A), in symmetric equilibrium the flow of consumtion in the utility function (Eq. (3)), is y P Y = y N Z θ c We can thus define Δ N N 0 = Y Y 0 which is the ercentage change in exenditure that the economy exeriences in resonse to changes in fundamentals and/or olicy arameters. In the interretation roosed earlier, it fully summarizes the effects of such changes on the scale of economic activity and, in articular, on the economy's carrying caacity for firms/roducts. The mechanism underlying my results, therefore, is an imulse-resonse dynamics Δ is the (ermanent) imulse and the logistic equation (Eq. (23)) governs the resonse. The following roosition states the result formally. Proosition. Let log u (t) and U be, resectively, the instantaneous consumtion index (3) and the welfare function () evaluated at y. Then, a ath starting at time t=0 with initial condition N 0 and converging to the steady state N is characterized by log T ðþ= t log T 0 + g t + γ ν + αθ γ θ ð Þ ϕ ρ + δ α θð Þ ðρ + δþβ Δ e νt ð25þ

6 P.F. Peretto / Journal of Develoment Economics 97 (202) Therefore, log u ðþ= t log y + c g t + γ ν + Δ e νt ð26þ without loss of generality T 0 =. Uon integration this yields U = ρ log y + g c ρ + μδ ð27þ γ + ν μ ρ + ν Proof. See Aendix A. The way the model's mechanism works, then, is straightforward. First, the lack of scale effects imlies that the endowment shock studied in this aer does not affect steady-state TFP growth g. Second, the endowment shock erturbs the equilibrium of the resource market and causes the resource rice to fall. This in turn has two effects it yields a change in the household resource income Ω, which, through the intertemoral consumtion-saving choice, shows u as an instantaneous change in exenditure er caita y, and a fall in the CPI due to the fall of the cost of roduction of consumtion goods c. The change in exenditure is seen by firms and entrereneurs as a change in market size Y that triggers changes in the level and comosition of R&D activity and thereby a temorary deviation of the economy's growth rate of TFP g(t) from its steady-state value g. The temorary change in the growth rate of TFP drives the temorary deviation of the rate of decay of the economy's CPI from its steady-state value and thereby the temoral evolution of consumtion. Proosition ulls all these effects together as follows the transitional comonent of the TFP oerator in Eq. (25) summarizes the cumulated gain/loss due to above/below steady-state cost reduction and roduct variety exansion the exression for flow utility (Eq. (26)) shows searately the initial jum due to y /c and the smooth evolution due to T the exression for (27) then shows how uon integration the ath of utility collases to a single number whose value changes with Ω through two channels steady-state (real) exenditure calculated holding technology constant, i.e., the initial jum in consumtion, and the transitional acceleration/ deceleration of TFP relative to the steady-state ath. 5. Resource abundance, growth and welfare This section begins with a discussion of the conditions under which a change in the endowment ratio raises or lowers consumtion exenditure so that the market for manufacturing goods exands or contracts. It then shows how the interaction of the initial change in consumtion and the transition dynamics after the shock roduce a change in welfare whose sign can be assessed analytically. 5.. Exenditure and rices The first ste in the assessment of the effects of resource abundance is to use Eqs. (7) and (8) to characterize exenditure and rices. The following roerty of the demand functions (2) and (5) is useful. Lemma 2. Let log = log S = S log P log P P R log R log = log SR log = SR P S S R Then, S R ðþs ðþ = ΓðÞ SR ðþs ðþ ð28þ ΓðÞ ðþ S R ðþ + R ðþ Proof. See Aendix A. Γ() is the elasticity of S R ()S () with resect to. According to Eq. (2), therefore, it is the elasticity of the demand for the resource R with resect to its rice, holding constant exenditure er caita y. It thus catures the artial equilibrium effects of rice changes in the resource and materials markets for given market size and regulates the shae of the income relation. Differentiating Eq. (8), rearranging terms and using Eq. (5) yields d log y ðþ = d ε ε d S R ðþs ðþ d βρ ε ε SR ð ÞS ðþ = ωγðþ which says that the effect of changes in the resource rice on exenditure on manufacturing goods deends on the overall attern of substitution that is reflected in the rice elasticities of materials and resource demand and in the resource share of materials roduction costs. To see the attern most clearly, retend for the time being that Γ() does not change sign with. I comment later on how allowing Γ() to change sign for some makes the model even more interesting. The following roosition states the results formally, Fig. illustrates the mechanism. Proosition 3. Suose that Γ() is ositive, zero or negative for all. Then, there are three cases.. Comlementarity. This occurs when Γ() N0 and the income relation (8) is a monotonically increasing function of with domain [0, ) and codomain y [y (0),y ( )), y ð0þ = βρ S R ð0þs ð0þ y ð Þ = βρ S R ð ÞS ð Þ Then there exists a unique equilibrium ( (ω),y (ω)) with the roerty d ðωþ b 0 ω dy Þ ð0 Þ ½y ð Þ y ð0þþ ðωþ b 0 ω ðωþ ð0 Þ ð 0Þ y ðω 2. Cobb Douglas-like economy. This occurs when S R and S are exogenous constants, Γ()=0 and the income relation (8) is the flat line y = βρ y S R S CD

7 48 P.F. Peretto / Journal of Develoment Economics 97 (202) y y * ( ) y * y * (0) exenditure income changes sign according to the substitution ossibilities between labor and materials in manufacturing and between labor and the natural resource in materials roduction. This brings us to the observation that if Γ() changes sign for some, the model generates endogenously a switch from substitution to comlementarity. Fig. 2, the income relation (Eq. (8)) is a hum-shaed function of, illustrates this case. The attern is best catured by looking at the roerties of the function Γ(). Using the definitions in Lemma 2, y * (0) * exenditure dγðþ d = d ðp dp Þ dp d SR ðþ + ðp Þ ε R ðþ dr ðþ d This derivative is negative if the following two conditions hold y * y * ( ) * income Fig.. General equilibrium monotonic income relation. the elasticities and R are increasing in P and, resectively the terms and R have oosite sign. The hum-shaed income relation in Fig. 2 then obtains if Γ (0)N0 and Γ( )b0. The second condition says that if demand in one sector is elastic, say b, then demand in the other sector is inelastic, N R. Below I rovide an examle of how one can use CES technologies to construct an economy these conditions hold. Here I discuss the general roerty. Proosition 4. Suose that there exists a rice Γ() changes sign, from ositive to negative, so that the income relation (8) is a hum-shaed function of with domain [0, ) and codomain y [y (0),y ( )) or y [y ( ),y (0)), Then there exists a unique equilibrium ( CD CD ðωþ ð 0 Þ ð 0 Þ d ðωþ b 0 ω (ω),y CD ) with the roerty 3. Substitution. This occurs when Γ() b0 and the income relation (8) is a monotonically decreasing function of with domain [0, ) and codomain y (y ( ),y (0)], y ð Þ = y ð0þ = βρ S R ð ÞS ð Þ βρ S R ð0þs ð0þ y ð0þ = y ð Þ = βρ βρ S R S R ð0þs ð0þ ð ÞS ð Þ Then there exists a unique equilibrium ( (ω),y (ω)) with the roerty d ðωþ b 0 ω dy Þ ð0 Þ ½y ð Þ y ð0þþ ðωþn b 0 ω b N ω ðωþ ð0 Þ ð 0Þ y ðω Where ω is the value of ω such that * (ω )=. Then there exists a unique equilibrium ( (ω),y (ω)) with the roerty ðωþ ð0 Þ ð 0Þ d ðωþ b 0 ω y ðωþ ð0 Þ y ð Þ y dy ð0þ ðωþ N 0 ω y y * y * ( ) ω = ω exenditure income Proof. See Aendix A. I refer to the second case as the Cobb Douglas-like economy because this seemingly secial configuration, requiring R =+( )S R,is in fact quite common in the literature as it occurs when both technologies are Cobb Douglas and = R =. Proosition 3 says that the effect of resource abundance on the resource rice is always negative, while the effect on exenditure y * (0) = * ( ω) Fig. 2. General equilibrium hum-shaed income relation. *

8 P.F. Peretto / Journal of Develoment Economics 97 (202) Proof. See Aendix A. The main message of this analysis is that resource abundance raises exenditure, and thereby results into a larger market for manufacturing goods, when the economy exhibits overall substitution between labor and resources (rocessed and raw) in the manufacturing of consumtion goods and the rocessing of the natural resource into materials. Conversely, when the economy exhibits overall comlementarity resource abundance results into a smaller market for manufacturing goods. ore imortantly, whether the economy exhibits substitution or comlementarity deends on equilibrium rices and thus on the endowment ratio itself. In other words, there are solid reasons to exect that the effect of the endowment ratio on the ath of consumtion is nonmonotonic The ath of consumtion and welfare logu * (t) Case Γ < 0 < Ψ Baseline ath Case 2 0 < Γ < Ψ Case 3 0 < Ψ < Γ For concreteness, consider an economy in steady state (,y ) and imagine an increment in its endowment ratio. Then, by construction we have Δ = y ðωþ + dy ðωþ y ðω Þ = dy ðωþ y ðωþ t = 0 Fig. 3. The ath of consumtion. t and we can use the results of the revious section in a straightforward manner. Let us look first at the initial effect on consumtion. Proosition 5. The imact effect of the change in the endowment ratio is d log y ðω c ðω Þ Þ = Γ d ðωþ Ψ ðωþ ðωþ ω ð29þ Ψð ðωþþ ð Þy ðωþ = κ SR ðωþ S ðωþ κ ð βρþ N Proof. See Aendix A. We can then characterize four scenarios for welfare.. The rise of the endowment ratio generates a growth acceleration associated to an initial jum u in consumtion when ð+μ ÞΓ ðωþ bγ ðωþ 0 b Ψ ðωþ In this case welfare rises unambiguously because the whole ath of utility after the shock lies above the re-shock ath The rise of the endowment ratio causes a growth deceleration, but the deceleration is offset by the fact that resource abundance reduces rices and raises the level of consumtion. This haens when 0 b Γ ðωþ bð+μþγ ðωþ b Ψ ðωþ Proof. See Aendix A. Eq. (26), Proosition 5 and the result in Proosition 3 that d ðωþ b 0 in all cases (comlementarity, Cobb Douglas, substitution) then yield three ossible configurations for the ath of consumtion. Γ( (ω))b0bψ( (ω)). The initial jum is u and then we have a growth acceleration. Welfare rises. 2. 0bΓ( (ω))bψ( (ω)). The initial jum is u and then we have a growth deceleration. The welfare change is ambiguous since we have an intertemoral trade-off. 3. 0bΨ( (ω))bγ( (ω)). The initial jum is down and then we have a growth deceleration. Welfare falls. Fig. 3 illustrates these ossibilities. Case 2 highlights the need to look at welfare directly to resolve the ambiguity. Proosition 6. The welfare effect of a change in the endowment ratio is du ðωþ = ρ λ ð+μþγ d ðωþ Ψ ðωþ ðωþ ω ð30þ In this case as well welfare rises. 3. The rise of the endowment ratio generates a growth deceleration that dominates over the initial jum u in consumtion when 0 b Γ ðωþ b Ψ ðωþ bð+μþγ ðωþ In contrast to the revious case, welfare now falls. 4. The rise of the endowment ratio generates a growth deceleration associated to an initial fall of consumtion when 0 b Ψ ðωþ b Γ ðωþ bð+μþγ ðωþ This is the worst-case scenario in which welfare clearly falls because the whole ath of utility after the shock is below the reshock one. To ma these scenarios into values of the endowment ratio itself it is useful (albeit not necessary) to imose more structure. 6 Notice that this includes the Cobb Douglas economy since in that case = = R and growth does not resond to ω at all while lower rices yield higher utility.

9 50 P.F. Peretto / Journal of Develoment Economics 97 (202) The role of ω a CES economy Consider the following technologies h i = Z θ σ i i ψ L i ϕ + ð ψ Þ σ σ i σ = ψ L σ + ð ψ ÞR σ σ σ From the associated variable unit-cost functions (see Aendix A) one derives (recall that W ) S = + ψ σ σ σ P ψ =+ σ σ S S R R = + ψ =+ σ S R σ σ σ σ ψ As is well known, the CES contains as secial cases the linear roduction function (σ=) in inuts are erfect substitutes, the Cobb Douglas (σ=0) in the elasticity of substitution between inuts is equal to, and the Leontief (σ= ) in inuts are erfect comlements. Let Γω ð Þ Γð ðωþþ = ð ðωþþ S R ð ðωþþ + R ð ðωþþ Ψω ð Þ Ψð ðωþþ = κ S R ð ðωþþs ð ðωþþ Observe that if σ N0 and σ N0, then Γ()b0 for all and growth always accelerates. If σ b0 and σ b0, instead, Γ()N0 for all and growth always slows down. Interestingly, if σ and σ have oosite signs we can cature how the economy moves from one case to the other as the endowment ratio changes. Secifically, let σ N0 and σ b0 so that the manufacturing sector exhibits gross substitution between labor and materials while the resource sector exhibits gross comlementarity between labor and raw resources. Recall that this means that demand for rocessed resources, i.e., materials, in the manufacturing sector is elastic, while demand for raw resources in the rimary sector is inelastic. It is then straightforward to obtain the following three cases.. Welfare rises because growth accelerates and the initial jum in consumtion is u when Γω ð Þ 0 0 b ω b ω First, and most imortant Why does the overall attern of substitution/comlementarity matter so much for growth and welfare? Because it regulates the reduction in the rice required for the economy to absorb the extra endowment of Ω relative to L. oreover, the rimary and manufacturing sectors are vertically related so the adjustment involves the interdeendent resonses of P to the increase in suly of rocessed resources and of to the increase in suly of raw resources. Now, inelastic demand means that the rice has to fall drastically to induce the market to absorb the additional quantity. Hence, if demand is inelastic in both sectors the overall adjustment requires drastic dros in both P and. What matters is that the drastic fall of results in a fall of resources income ω which deresses exenditure y. This is the case ΓN0. In contrast, if demand is elastic in both sectors the overall adjustment requires mild dros in rices. The crucial difference is that in this case Γb0 so that resources income ω rises because the quantity effect dominates the rice effect. With this intuition in hand, we can now interret the analytical results of the model. The function Γ(ω) starts out negative and increases monotonically, changing sign at ω and converging to its ositive uer bound as ω. To see this, write Γ ðωþ = dγð Þd d N 0 ω and observe that this economy satisfies the conditions for dγ()/ db0,namely N and increasing in P R b and increasing in. The function Ψ(ω) is hum-shaed with a eak exactly at ω, Γ(ω) changes sign. The reason is that this is the value the derivative of S R ()S () with resect to equals zero. Notice also that Γ(ω)bΨ(ω) for all ω (see Aendix A for the roof) so that Case 3 from Fig. 3 and Scenario 4 from the analysis of welfare no longer aly because initial consumtion cannot fall. The resulting attern is the following The endowment ratio is initially very low and rices are very high, that is, ω 0 P =C (,). Under these conditions, Γ(0)b0bΨ(0) so that an increase in ω roduces a growth acceleration associated to a jum u in initial consumtion. Intuitively, this says that in a situation of extreme scarcity and extremely high rice a helicoter dro of natural resource is good. As the relative endowment grows, the overall attern of substitution changes. In articular, Γ(ω) changessignatω = ω and we enter the region we get a curse of natural resources becauseanincreasein resource abundance yields a decrease in exenditure on manufacturing goods that triggers a slowdown of TFP growth. This, curse, however, is not really a curse since we are to the left of ω and the slowdown is Ψ( ω) (+ μ) Γ( ω) 2. Welfare rises because the initial jum u in consumtion dominates the growth deceleration when 0bð+μ ÞΓω ð Þb Ψω ð Þ ω b ω b ω 3. Welfare falls because the initial jum u in consumtion is dominated by the growth deceleration when κ σ σ ω ω ~ Γ( ω) ω 0bΨðωÞbð+μÞΓω ð Þ ω b ω b Fig. 4 illustrates this analysis. Aendix A establishes formally the roerties of the curves Γ(ω) and Ψ(ω) used in the figure to find the threshold values of the endowment ratio. Here I focus on the economics. σ σ Fig. 4. The endowment ratio and equilibrium outcomes.

10 P.F. Peretto / Journal of Develoment Economics 97 (202) associated to an initial jum u in consumtion that dominates in the intertemoral trade-off. As we kee moving to the right and enter the next region, ω b ω b, the growth deceleration is again associated to an initial jum u in consumtion but now the deceleration dominates in the intertemoral trade-off and welfare falls. It is here that we have a curse. In the analysis above I set σ b0 and σ N0 because resource economists see oor substitution in the resource-intensive sector and good substitution in manufacturing as the emirically lausible configuration. The model, however, rovides a comlete characterization for any configuration of substitution/comlementarity across the two sectors. It is useful to look at one that generates the initial fall in consumtion ruled out under σ b0 and σ N0. Recall that if σ b0 and σ b0 we have Γ()N0 for all and the curse always occurs because dy /b0 for all ω. Interestingly, in this case the Γ(ω) and Ψ(ω) curves are both monotonically increasing in ω with Γ(0) =0, Ψ(0)=κ, Γ( )= σ /( σ ), and Ψ( )=κ. Consequently, if we assume κb σ /( σ ) the curves intersect and there exists a threshold value of ω such that for ω larger than that value Ψ(ω)bΓ(ω). This is the condition for Case 3 from Fig. 3 and Scenario 4 from the analysis of welfare initial consumtion falls. The intuition for this roerty is that by setting σ b0 we imose comlementarity in manufacturing as well and we exacerbate its adverse effects throughout the economy's vertical roduction structure. When σ N0, in contrast, substitution in manufacturing softens the adverse effect exerienced by the resource rocessing sector and recludes the initial fall of consumtion. It is useful to close this section with some remarks on the generality of the analysis. CES technologies yield a highly tractable structure. However, they are restrictive in that they yield that within each sector demand is either always inelastic or always elastic. To obtain the economy-wide cross over from comlementarity to substitution one then needs to exloit the sectoral comosition effect and osit that σ and σ have oosite sign. Nevertheless, the results of Section 5.2 do not require this assumtion. Insection of the function Γ(ω) suggests that to obtain Γ(0) b0 and Γ( ) N0, and therefore the threshold ω, all that are needed are technologies that deliver rice elasticities of demand that start out below one and turn larger than one as the rice of the good rises The labor reallocation It is insightful to characterize the economy's reallocation of labor across sectors in detail. Using Eq. (6) we have L L = y S S R It is then easy to show that (see Aendix A) d L L N 0 ω so that, intuitively, resource abundance yields a reallocation of labor from manufacturing to rimary roduction. This result imlies that L L + L Z + L N L = L L falls to its new steady state value when ω increases. This is an interesting roerty as it says that there is a reallocation of labor from roduction of manufacturing goods to roduction of materials, but that this reallocation is not necessarily associated to a TFP slowdown. This is a fundamental difference between this model and models that generate the curse of natural resources by tying roductivity growth to manufacturing emloyment through learning by doing mechanisms. Since the inter-sectoral reallocation is instantaneous, the dynamics that drive the time ath of TFP take lace within manufacturing. Eqs. (4), (4) and the formulation of the entry cost yield L Z + L N L = L Z L + N L β Y N Recall that Y jums on imact to its steady-state value Y =Ly while N is redetermined and does not jum. Then, using Eq. (23) at any time t we have L Z + L N L = y βρ+ ð δþ ϕ N +e νt Δ Y we know from the analysis of Section 3 that N is indeendent Y of ω. Thus, when the economy exeriences a growth acceleration because y rises, the R&D share of emloyment jums u and converges from above to a ermanently higher value, while the ratio L jums down and converges from below to a ermanently lower L value. The reverse haens when y falls and the economy exeriences a growth deceleration. 6. Conclusion The debate on whether natural resource abundance is good or bad for the long-run fortunes of the economy is almost as old as economics itself. To contribute to this debate and exand its scoe in this aer I develoed a closed economy Schumeterian model of R&D-driven endogenous growth that incororates an ustream resource-intensive sector. The model yields the analytical solution for the transition ath and thus allows one to resolve the intertemoral trade-off and determine whether the effects of natural resource abundance on initial income and growth yield an increase or a decrease in welfare. I found that resource abundance has non-monotonic effects on growth and welfare. ore recisely, following the classic rocedure for the construction of growth regressions (Barro and Sala-i-artin, 2004), I showed that average growth over a time interval and the associated welfare level can be reresented as hum-shaed functions of resource abundance. The non-monotonic effect of resource abundance on welfare suggests that there is an otimal value of the endowment ratio. Since for simlicity the model considers a non-exhaustible resource that rovides a constant flow of roductive services land, for examle and assigns diffuse ownershi of it to atomistic households, it is not immediate to extract olicy imlications from this otimality result. It is lausible to envision institutional arrangements that regulate the suly of the resource services in order to revent the economy from moving into the downward sloing art of the welfare curve. But this would require changing drastically the model's assumtions about ownershi and owners' freedom of use of the resource, something surely interesting but beyond the scoe of this aer. Extending the model to the case of exhaustible or renewable resources it is more natural to think of suly decisions that regulate the ratio of resource services to labor services available to roducers is another romising and intuitive way to ursue further this insight (for an examle, see Prasertsom, 200). Aendix A A.. The decisions of firms and entrereneurs Consider the Current Value Hamiltonian h CVH i = P i C ð P ÞZ θ i i i ϕ L Zi + z i αkl Zi

11 52 P.F. Peretto / Journal of Develoment Economics 97 (202) the firm's knowledge, Z i, is the state variable, R&D investment, L Zi, and the roduct's rice, P i, are the control variables, z i is the shadow value of Z i and the firm takes ublic knowledge, K, as given. Since the Hamiltonian is linear, one has three cases. The case Nz i αk imlies that the value of the marginal unit of knowledge is lower than its cost. The firm, then, does not invest. The case bz i αk imlies that the value of the marginal unit of knowledge is higher than its cost. Since the firm demands an infinite amount of labor to emloy in R&D, this case violates the general equilibrium conditions and is ruled out. The first order conditions for the interior solution are given by equality between marginal revenue and marginal cost of knowledge, =z i αk, the constraint on the state variable, Eq. (8), the terminal condition, s lim s e t ½rv ð Þ + δ Šdv z i ðþz s i ðþ=0 s and a differential equation in the costate variable, r + δ = z i z i + θc ð P ÞZ θ i i z i that defines the rate of return to R&D as the ratio between revenues from the knowledge stock and its shadow rice lus (minus) the areciation (dereciation) in the value of knowledge. The revenue from the marginal unit of knowledge is given by the cost reduction it yields times the scale of roduction to which it alies. The rice strategy is P i = C ð P ÞZ θ i ð3þ Peretto (998, Proosition ) shows that under the restriction Nθ( ) the firm is always at the interior solution, =z i αk holds, and equilibrium is symmetric. The cost function (7) gives rise to the conditional factor demands L i = C ð W P W i = C ð W P P Þ Þ Z θ i i + ϕ Z θ i i Then, Eq. (3), symmetry and aggregation across firms yield Eqs. () and (2). Also, in symmetric equilibrium K=Z=Z i yields K = K = αl Z = N, L Z is aggregate R&D. Taking logs and time derivatives of =z i αk and using the demand curve (Eq. (5)), the R&D technology (Eq. (8)) and the rice strategy (Eq. (32)), one reduces the first-order conditions to Eq. (3). Taking logs and time-derivatives of V i yields r + δ = Π i V + i V i V i which is a erfect-foresight, no-arbitrage condition for the equilibrium of the caital market. It requires that the rate of return to firm ownershi equal the rate of return to a loan of size V i. The rate of return to firm ownershi is the ratio between rofits and the firm's stock market value lus the caital gain (loss) from the stock areciation (dereciation). In symmetric equilibrium the demand curve (Eq. (5)) yields that the cost of entry is β Y. The corresonding demand for labor in entry is N L N = N + δn β Y N The case V N β Y yields an unbounded demand for labor in entry, N L N =+, and is ruled out since it violates the general equilibrium conditions. The case Vb β Y N yields L N =, whichmeansthatthe non-negativity constraint on L N binds and N = δn, which imlies negative net entry due to the death shock. Free-entry requires V = β Y. Using the rice strategy (Eq. (3)),therateofreturnto N entry becomes Eq. (4). A.2. The economy's resources constraint I now show that the household's budget constraint reduces to the economy's labor market clearing condition. Starting from Eq. (2), recall that A=NV and ðr + δþv = Π + V. Substituting into Eq. (2) yields ṄV = NΠ + L + Ω + Π Y Observing that NΠ =NP L L Z P, NP=Y, Π =P L R, R=Ω, and that the free entry condition yields that total emloyment in entrereneurial activity is L N = NV, this becomes L = L N + L + L Z + L A.3. Detailed derivation of the logistic equation for N(t) For simlicity, in the text I focussed on the case in which firms always invest in vertical R&D. ore generally, taking into account the non-negativity constraint on L Zi, the equation getting the rate of vertical innovation in symmetric equilibrium is 8 Ẑ = α L >< Y αθð Þ Z N = ρ δ Nb N N 0 N N > αθ N Y ð Þ ðρ + δþ Substituting this result into Eq. (4) yields 8 θð Þ ϕ ρ + δ N >< β α Y ˆN = β ϕ N > Y which converges to 8 θð Þ ðρ + δþβ >< ϕ ρ + δ N = α > ðρ + δþβ Y ϕ Y ðρ + δþ Nb N ðρ + δþ N N θð Þ ðρ + δþβ b θð Þ ϕα ðρ + δþ ðρ + δþ θð Þ ðρ + δþβ θð Þ ϕα ðρ + δþ ðρ + δþ These solutions exist only if the feasibility condition N ðρ + δþβ holds. The interior steady state with both vertical and horizontal R&D requires the additional conditions αϕnρ+δ and ðρ + δ Þβ + θð Þ b b ð ρ + δ αϕ θð Þ Þβ + ρ + δ As discussed in detail in Peretto (998) and Peretto and Connolly (2007), models of this class have well-defined dynamics also when one