The impact of windfalls: Firm selection, trade and welfare

Transcription

1 The impact of windfalls: Firm selection, trade and welfare Gry Østenstad and Wessel N Vermeulen September 25, 2015 Abstract We ask how a small open economy with heterogeneous firms responds to a resource windfall A resource windfall boosts demand but also affects wages such that production costs increase The result is a higher number of firms and renewed selection among firms: New firms at the lower end of the productivity continuum can produce for the domestic market, while only the most productive firms continue to export While the share of firms that sell traded varieties decreases, the average productivity of exporting firms increases The increase in the number of varieties following the increase in the number of firms and the inflow of additional imports implies that there is an increase in aggregate welfare over and above the direct windfall gain We provide analysis in a model with two types of labor The windfall causes a reallocation of labor types and a change in relative wages, thereby implying different welfare outcomes for each type of labor and the possibility of rising inequality Keywords: Resource windfalls, heterogeneous firms, trade, welfare JEL: F12, Q37 This work is part of a larger research project at ESOP, University of Oslo, funded by the Research Council of Norway through its Centres of Excellence funding scheme, project number This research was also supported by the BP funded Oxford Centre for the Analysis of Resource Rich Economies Drafts of this paper were presented at seminars at OxCARRE, Oxford and Sophia University, Tokyo We thank seminar participants, and in particular Masashige Hamano, Jan Haaland, Halvor Mehlum and Tony Venables for useful comments Buskerud and Vestfold University College and Centre of Equality, Social Organization and Performance (ESOP), Department of Economics, University of Oslo OxCARRE, Department of Economics, University of Oxford 1

2 1 Introduction Economists and policy makers are very interested in understanding whether a resource windfall may have unexpected side effects for the broader economy For instance, countries that develop a natural resource sector following a discovery will quickly find themselves the topic of discussions on the existence of Dutch disease or the resource curse Additional demand due to the resource income will be accompanied by a change in factor prices Such dynamics are bound to affect some firms differently than they do others Therefore, this paper addresses the question of how a small open economy with heterogenous firms responds to a resource windfall on the Dutch disease 1 By pursuing this question, we extend the literature by modeling firm heterogeneity, which allows us to investigate the reallocation following a windfall not only across sectors but also among firms windfall causes an increase in the variety of goods and a new selection of firms, which has implications for average productivity, the share of export sales in industry production, and aggregate welfare Additionally, using multiple factors of production (eg, high- and low-skill labor), we can derive implications for the welfare distribution due to a change in relative factor returns Much of the literature on natural resource exports and the Dutch disease uses the dependent economy framework of Salter (1959), which contains two homogeneous sectors characterized by perfect competition: one producing non-traded goods and the other producing goods that are tradable in the international market The seminal work among these studies is Corden and Neary (1982) However, with the advent of firm level data, interest is growing in how firms within countries are responding to shocks in an economy An example of such a shock is when a country experiences a windfall from a new discovery of natural resource deposit or sudden price shocks that affect existing exports New trade theories offer convenient methods to model monopolistic competition and firm heterogeneity within industries, which in turn offer new insights into the development of sectors and the overall economy Although there is large literature using such methods for international trade, these methods have received very few applications to the issue of natural resources Harding and Venables (2013) and Cherif (2013) are notable exceptions and model forms of Dutch disease in a monopolistic competition framework with homogeneous firms Both present two-sector models with a perfectly competitive non-traded sector and a traded sector characterized by monopolistic competition and homogeneous firms Cherif (2013) investigates the impact of a transfer from a foreign country to the home country He finds that the extent of the crowding-out in the home country s traded sector depends positively on the productivity difference vis-a-vis the foreign country Adding learning- 1 We understand the Dutch disease as the macroeconomic adjustment following natural resource exports or foreign exchange transfer This macroeconomic adjustment has often meant a contraction of a tradable goods sector, which under some conditions could be welfare reducing See further below A 2

3 by-doing in the traded sector, the mechanism is self-reinforcing and leads to productivity divergence Harding and Venables (2013) investigate how exporting firms and import-competing firms may respond to a resource windfall Their model offers the prediction, which is supported by data, that non-resource exports decrease but to a lesser extent than resource exports, the difference being higher imports Moreover, they predict that a resource windfall will decrease the number of varieties and increase the price of each variety This implies an increase in the price index, which has a negative impact on welfare We offer new insights by modeling firm heterogeneity and selection into trade à la Melitz (2003), in combination with two factors of production (Bernard et al, 2007) shared between two sectors This framework allows for an endogenous selection of traded firms, rather than pre-defining the traded goods sector, as is usually done in the Dutch disease literature By modeling firm heterogeneity, we are able to derive new mechanisms and welfare implications associated with Dutch disease Our general aim is to provide new predictions for future empirical studies concerning the development of sectors and firm behaviour in an economy affected by natural resource production Despite abstracting from a pre-defined non-traded goods sector, we obtain predictions that are in line with earlier models of Dutch disease concerning an expanded non-traded part of the economy, albeit through a different mechanism In a recent contribution, Allcott and Keniston (2014) study the impact of natural resource extraction on local economic development in the US, using longitudinal US countyand firm-level data They structure their tests using a theoretical framework based on heterogeneous firms in multiple sectors, where some produce non-traded goods and others produce potentially tradable goods We differ from their approach by using multiple factors of production, which allows us to derive implications for the welfare distribution following a windfall Moreover, we have an entirely endogenous determination of traded and non-traded goods, obtained through the interaction of firm-specific productivity and fixed costs of market entry This highlights the contrasts of our approach with the standard dependent economy framework Additionally, we derive the general equilibrium conditions in a comparative static framework, allowing us to offer greater detail on the mechanisms and provide full welfare implications Our starting point is the two-sector model in Haaland and Venables (2014), where one sector produces a homogeneous good and the other sector consists of heterogeneous firms that produce differentiated goods We depart from their framework by using a straightforward Cobb-Douglas production function in both sectors to have multiple factors of production as in Bernard et al (2007) 2 Our main task is to investigate the impact of a resource windfall We model the 2 See Vannoorenberghe (2011) for an alternative approach to modeling heterogeneous firms and two types of labor 3

4 windfall as an exogenous foreign exchange gift distributed lump-sum to a representative consumer The resource windfall causes an expansion of the differentiated sector and renewed selection among heterogeneous firms Higher demand drives up profits but simultaneously affects wages such that marginal costs increase The mass of entering firms increases, and new firms on the lower end of the productivity continuum can produce for the domestic market Higher marginal costs imply that only the most productive firms continue to export The result is a larger set of non-exporting firms While the share of firms that sell in the export market decreases, the average productivity of exporting firms increases This result is in line with Kuralbayeva and Stefanski (2013) They analyse macro crosscountry data and micro US county data and find that resource-rich regions have small and productive manufacturing sectors and large and unproductive non-manufacturing sectors Interpreting the manufacturing sector as traded and the non-manufacturing sectors as non-traded, they propose a worker-selection mechanism As the non-traded sector expands, the least skilled move from manufacturing to the non-traded sectors, and only those most skilled in the manufacturing sector work will remain in manufacturing Our model can explain the empirical observations in Kuralbayeva and Stefanski (2013) using a different theoretical framework, namely, a selection mechanism for heterogenous firms As in the standard dependent economy framework, the decline in the share of firms that produce traded goods is the appropriate market response to a resource windfall and does not justify government intervention The primary concern in extant Dutch disease literature is that the traded sector benefits the most from learning-by-doing and, as such, drives growth for the economy as a whole (van Wijnbergen, 1984; Krugman, 1987; Matsen and Torvik, 2005) Additionally, fixed costs may prohibit the recovery of a traded sector after resources have been exhausted In contrast, while only the more productive firms continue to export in our model, these firms do not shut down They continue to produce for the domestic market Moreover, the mass of firms increases Hence, in our framework, there is a priori less reason to be concerned about a decrease in learning-by-doing The new allocation of firms following a resource windfall implies that a new selection of goods is available in the market This has implications for consumer welfare that are novel in the Dutch disease literature The differentiated sector expands and additional imports are drawn into the economy as foreign firms identify the increased demand and profitability in the domestic market As consumers have a preference for variety, this implies that there is an increase in aggregate welfare over and above the direct windfall gain Moreover, the use of multiple factors of production allows us to say something about the distribution of gains and losses across different types of workers This relates to Corden and Neary (1982), who analyze the real wage and rental rates on capital, as well 4

5 as sector output, under different labor and capital mobility conditions In our setup, we interpret the two factors of production as types of labor Allowing for different factor intensities in different sectors, we find that the factor that is intensively used in the expanding differentiated sector gains more relative to the other factor Interpreting the differentiated sector as the more advanced sector, it is reasonable to expect that this sector is skill intensive Assuming that high-skill workers have a higher wage than low-skill workers, a windfall of resources may lead to higher inequality, even if the resource rents are distributed equally 2 The model We develop a two-sector model of a small open economy, in which one sector is characterized by perfect competition and produces a homogeneous good, and the other sector consists of heterogeneous firms producing differentiated goods Both sectors use two production inputs, which we interpret as high-skill and low-skill labor, that are sectorally mobile but internationally immobile 3 As a small open economy, the country as a whole takes foreign expenditure, price indices and factor prices as given The homogeneous sector functions as a source of labor to the differentiated sector in which we are specifically interested As Haaland and Venables (2014) argue, such a setup offers a more general representation than do models that either fix the wage rate or the level of employment The homogeneous sector may be interpreted as summarizing the rest of the economy The structure of preferences and the technology in the homogeneous sector combine to determine wage rates and expenditures as a function of labor demand from the differentiated sector, with a resource windfall and total labor force as exogenously given The differentiated sector will define labor demand as a function of the wage rates and expenditures These two parts combine to determine the full equilibrium We begin by outlining the preference structure in the economy We then present the production structure in the homogeneous and differentiated sectors We do not designate a specific non-traded sector and do not require that the heterogenous sector is balanced in trade by itself The overall resource constraint of the economy is governed by the indirect utility function that is outlined below This implies that the homogenous sector will absorb the changes in trade that are necessary to keep trade balanced for the economy as a whole 3 Many results presented in this paper can be replicated using a more simple one-factor model with a specific factor used in the homogeneous sector (see Østenstad, 2015) We believe that, when abstracting from international labor movement, there is a strong empirical interest in understanding the effects of different types of labor in resource-rich economies Additionally, having two types of labor ultimately allows us to derive welfare implications specific to each type of labor 5

6 21 Preferences Preferences over the homogeneous good and the differentiated goods take the Cobb- Douglas form Hence, expenditure on the differentiated good E is a fraction µ of income Y : E = µy Preferences over the differentiated good are represented by a sub-utility function that takes Constant Elasticity of Substitution (CES) form: [ σ/(σ 1) u = q(ν) dν] (σ 1)/σ σ > 1, ν Ω where Ω is the set of available varieties, q(ν) is consumption of variety ν, and σ is the elasticity of substitution Maximizing u subject to the budget constraint E = ν Ω p(ν)q(ν)dν, where p(ν) is the price of variety ν, yields the demand for each variety: q(ν) = p(ν) σ G, where G EP σ 1 is the market demand index, which proportionally scales every firm s residual demand It is determined by spending on differentiated goods and the CES price index P [ ν Ω p(ν)1 σ dν ] 1/1 σ) Normalizing the price of the homogeneous good to 1, the overall indirect utility function is given by: U = Y P µ (1) 22 Differentiated sector The differentiated sector consists of heterogeneous firms that produce distinct varieties subject to monopolistic competition The production of each variety incurs fixed and variable costs As in Bernard et al (2007), both fixed and variable costs are in terms of multiple production inputs (high-skill and low-skill labor) While the fixed cost is common to all firms selling in the same market, variable costs vary with firm productivity ψ (1, ) The cost function takes the simple Cobb-Douglas form: c = ( f i + q ) w β H ψ w1 β L, where w L is the low-skill wage, w H is the high-skill wage and f i is the fixed cost to enter market i (X, D) Minimizing costs, first-order conditions require that: 6

7 h l = β w L, (2) 1 β w H where h and l are the employment of high-skill and low-skill labor, respectively Given factor prices, the price index and marginal costs, firms choose how much to sell in the domestic market (D) and the export market (X) Maximizing profits, each firm sets a (consumer) price with a constant markup over the marginal costs of selling in market i: p i (z) = σ σ 1 τ W i ψ, where W w β H w1 β L is a composite factor price and τ i is an iceberg trade cost We have τ D 1 for the domestic market and τ X > 1 for the export market The firms revenue is then given by: ( σ r D (ψ) = pq = p 1 σ P σ 1 E = σ 1 ( r X (ψ) = pq = p 1 σ P σ 1 σ Ē = τ X σ 1 ) 1 σ W EP σ 1, ψ ) 1 σ W Ē P σ 1, ψ where Ē and P are the fixed expenditure level and price index that exporting firms face in the world market A firm s operating profit is a fraction 1/σ of its revenue: π D (ψ) π X (ψ) = ζ = ζ ( W ) 1 σ ψ EP σ 1, ( ) 1 σ W τ X ψ Ē P σ 1, where ζ (σ 1) σ 1 σ σ To enter the industry, firms must pay a sunk entry costs f E W to draw a productivity ψ from a fixed distribution with cumulative distribution G(ψ) Because there are fixed costs of production, only firms that draw a sufficiently high productivity ψ will decide to produce The productivity cut-offs are the lowest levels of productivity at which the firm s profits from an activity are non-negative The productivity cut-off for home firms to produce for the domestic market ψ D is therefore determined by: ( ) 1 σ W EP σ 1 ζ = W f D, Ψ D ψ σ 1 dg, (3) ψ D ψ D where f D is the fixed cost to produce for the domestic market Ψ D is the effective productivity index for home firms selling in the domestic market It aggregates the productivity of active firms according to productivity s impact on sales Similarly, the export cut-off ψ X and the effective productivity index for firms selling in the export market Ψ X are determined by: 7

8 ( ) 1 σ Ē P σ 1 τx W ζ = W f X, Ψ X ψ σ 1 dg, (4) ψ X ψ X where f X is the fixed cost to produce for the export market We assume that only the most productive firms find it profitable to produce for the export market, and hence firms that draw a productivity parameter ψ D < ψ < ψ X only produce non-traded varieties for the domestic market Foreign firms supply imports to the domestic market if profits from such activity are non-negative productivity distribution G The mass of foreign firms is exogenous, and these firms have the same The foreign factor prices are taken as given, and we set w β H w1 β L 1 The import cut-off ψ M and the effective productivity index for foreign firms Ψ M are determined by: EP σ 1 ζ ( τm ψ M ) 1 σ = f M, Ψ M ψ M ψ σ 1 dg, (5) where f M is the fixed cost to produce for the import market and τ M is the variable iceberg trade cost Potential entrants weigh the expected operating profits against the fixed costs Free entry implies that, in equilibrium, expected profits must equal zero: W f E = + ψ D ψ X ( ( ) ) 1 σ W EP σ 1 ζ W f D dg ψ ( ( ) ) 1 σ Ē P σ 1 τx W ζ W f X dg (6) ψ Here, f E is the fixed cost of developing a new variety We can write expressions for the total value of output sold by domestic firms in the domestic market D, in the export market X, and by foreign firms in the domestic market M: D = N r D (ψ)dg = NζσW 1 σ EP σ 1 Ψ D, (7) ψ D X = N r X (ψ)dg = Nζσ (τ X W ) 1 σ Ē P σ 1 Ψ X, (8) ψ X M = N 1 σ r M (ψ)dg = Nζστ M EP σ 1 Ψ M, (9) ψ M where N and N are the number of entrants at home and abroad, respectively It must be the case that expenditure equals domestic sales, E = D + M It follows from (7) and (9) that we can write the price index as follows: 8

9 P 1 σ = σζ [ NW 1 σ Ψ D + Nτ 1 σ M Ψ M] (10) The wage bill must equal the total value of sales by domestic firms w L l + w H h = D + X Inserting from equation (2), (7) and (8), we obtain: h = βw 1 σ w 1 H Nζσ [ EP σ 1 Ψ D + τ 1 σ X Ē P σ 1 Ψ X ], (11) l = (1 β)w 1 σ w 1 L Nζσ [ EP σ 1 Ψ D + τ 1 σ X Ē P σ 1 Ψ X ] (12) Equations (3)-(12) yield the industry equilibrium values of ψ M, ψ D, ψ X, P, N, l, h, D, X and M, given w H, w L and E, which are determined in general equilibrium 23 Homogeneous sector The homogeneous goods sector is characterized by perfect competition and produces a freely traded good x using the following technology: x = F (H h, L l) = A(H h) α (L l) 1 α Here, H and L are the total number of high-skill and low-skill workers in the economy and A is total factor productivity The wages are given by marginal productivity: 24 General equilibrium ( ) 1 α L l w H = F 1 = αa, (13) H h w L = F 2 = (1 α)a ( ) α H h (14) L l The general equilibrium condition is that total spending equals total income, which is given by the return to production inputs and an exogenous transfer from a resource windfall Z This implies that spending on the differentiated good is a fraction µ of total income: E = µy = µ(w H H + w L L + Z) (15) The system (3)-(15) determines the general equilibrium values of ψ M, ψ D, ψ X, P, N, l, h, D, X, M, w H, w L and E As the system cannot be solved analytically in levels, we use comparative statics techniques The only exogenous variable of interest is the transfer from a resource windfall Z We leave all other exogenous variables unchanged 9

10 3 Comparative statics Equations (3)-(5) define the effective productivity indices Ψ i In the following, we assume that productivity is Pareto distributed, and hence G(ψ) = 1 (ψ min /ψ) k Setting ψ min 1 yields Ψ i = kψ σ k 1 i /(k σ+1) and ˆΨ i = (σ k 1) ˆψ i We make the standard assumption that k > σ 1 Differentiating (3)-(5) we obtain: 1 ˆψ D = σ k 1 ˆΨ D = 1 ] [Ê + (σ 1) ˆP σ Ŵ, (16) σ 1 1 ˆψ M = σ k 1 ˆΨ M = 1 ] [Ê + (σ 1) ˆP, (17) σ 1 1 ˆψ X = σ k 1 ˆΨ X = 1 σŵ, (18) σ 1 where Ĝ = Ê + (σ 1) ˆP is the relative change in the market demand index We see that the productivity cut-off of exporting firms ψ D depends positively on the composite factor price The reason is that exporting firms face fixed world demand An increase in marginal costs implies that only the most productive firms can continue to export The import cut-off ψ M depends negatively on the market demand index The reason is that foreign factor prices are fixed An increase in market demand lowers competition in the import market, and hence new firms on the lower end of the productivity continuum can produce for the import market The domestic survival cut-off ψ D depends negatively on the market demand index, and it depends positively on the composite factor price The two variables are linked by the free entry condition Totally differentiating equation (6) and inserting from equations (16)-(18), we obtain: where s X X D+X ] 0 = (1 s X ) [Ê + (σ 1) ˆP σŵ, (19) is the share of export sales in industry production We see that free entry implies that the market demand index and the composite factor price move in the same direction and, in particular, that Ê +(σ 1) ˆP > σŵ This means that the negative effect of higher market demand on the domestic survival cut-off dominates the positive effect of higher marginal costs Substituting back into equations (16)-(17), we obtain: ˆψ D = ˆψ M = 1 σ k 1 ˆΨ D = σ s X Ŵ, σ 1 1 s X (20) 1 σ k 1 ˆΨ M = σ 1 Ŵ σ 1 1 s X (21) The changes in the value of sales given by equation (7)-(9) satisfy: 10

11 ˆD = ˆN + (1 σ)ŵ + Ê + (σ 1) ˆP + ˆΨ D, ˆX = ˆN + (1 σ)ŵ + ˆΨ X, ˆM = Ê + (σ 1) ˆP + ˆΨ M Inserting from equations (16)-(18), we can decompose the effects at the extensive margin (the mass of active firms) and the intensive margin (average firm sales): ˆD = ˆN k ˆψ D + Ŵ, (22) ˆX = ˆN k ˆψ X + Ŵ, (23) ˆM = k ˆψ M, (24) where ˆN i ˆN k ˆψ i gives the change in the mass of home firms selling in market i, and Ŵ gives the change in the average home firm s sales Foreign firms sales in the domestic market change only at the extensive margin when there is a change in the cutoff Differentiating equation (10), we obtain: (1 σ) ˆP = s D [ ˆN + (1 σ) Ŵ + ˆΨ D ] + (1 s D ) ˆΨ M, where s D D is the share of home firms sales in the domestic market Inserting D+M from equations (19)-(21), we find the change in the mass of entrants given the change in spending and marginal costs: where we define: ˆN = 1 s D Ê (C + 1)Ŵ, (25) C k σ σ 1 1 s D (1 s X ) s D (1 s X ) We see that an increase in spending results in a larger mass of firms entering the sector, while an increase in marginal costs has the opposite effect Differentiating equations (11) and (12), we find that employment of high- and low-skill workers in the industry changes according to: ĥ = (1 σ)ŵ ŵ H + ˆN ] + s X ˆΨX + (1 s X ) [Ê + (σ 1) ˆP + ˆΨD, ˆl = (1 σ) Ŵ ŵ L + ˆN ] + s X ˆΨX + (1 s X ) [Ê + (σ 1) ˆP + ˆΨD 11

12 Inserting from equations (16), (18), (19) and (25), we obtain: ĥ = 1 Ê CŴ s ŵ H, D (26) 1 ˆl = Ê CŴ s ŵ L D (27) We see that an increase in spending or a decrease in marginal costs increases the use of both labor types in the sector In addition, there is a substitution effect An increase in the wage of one worker type lowers the use of this worker type more than the other Turning to the homogeneous sector, we find the change in wages by taking the differentials of equations (13) and (14): where θ L l and θ L l H h H h ( ) ŵ H = (1 α) θ H ĥ θ Lˆl, (28) ( ) ŵ L = α θ H ĥ θ Lˆl, (29) Finally, we find the change in expenditures on differentiated good by taking the differentials of equation (15): Ê = Ŷ = λ Hŵ H + λ L ŵ L + λ Z Ẑ, (30) where λ H w HH, λ Y L w LL and λ Y Z Z Y 4 Note that the parameters are related in the following way: µ = 1 1 s X θ H θ L = s D ( β 1 β λ L θ L ), (31) θ H + λ H 1 + θ L 1 + θ H 1 α α, (32) 1 + θ H 1 + θ L = λ H λ L 1 α α (33) Equations (18)-(30) determine the general equilibrium values of ˆψ D, ˆψ X, ˆψ M, ˆP, Ê, ŵh, ŵ L, ˆN, ˆl, ĥ, ˆD, ˆX and ˆM given Ẑ In the following, we analyze the general equilibrium effects of a resource windfall, represented by Ẑ > 0, on sectoral allocation, firm selection, trade and welfare 4 Note that total income is expressed in rates of change, for which we would need to assume some level of pre-existing resource income Z However the model is more general, λ Z Ẑ = Z dz Y Z = dz Y, which may be interpreted as the flow of resource income over GDP 12

13 4 The impact of a resource windfall A windfall of resources increases total spending This raises expected profits in the differentiated sector, and hence more firms enter the industry, and labor moves from the homogeneous goods sector to the differentiated sector Higher demand for the homogeneous good is satisfied by an increase in net imports If the two sectors differ in skill intensity, wages adjust to accommodate the reallocation of labor between the sectors The change in wages feeds back into the differentiated sector by changing spending and marginal costs 41 Sectoral allocation and the labor market If there is no difference in skill intensity (θ H = θ L ), wages do not respond to a resource windfall: ŵ H = ŵ L = 0 This is because the increase in spending brings about a proportional increase in the employment of high- and low-skill workers: ĥ = ˆl = 1 s D Ê = 1 s D λ Z Ẑ This means that there is no feedback from the homogeneous sector to the differentiated sector As marginal costs are unchanged, the market demand index and the cut-offs are unaffected If there is a difference in skill intensity, the increase in spending following a resource windfall implies a change in the relative wage This feeds back into the differentiated sector, as wages affect spending and marginal costs We determine the general equilibrium effect of a resource windfall on wages by inserting equations (26), (27) and (30) into equations (28) and (29): ŵ H = 1 B (1 α) (θ H θ L ) λ Z Ẑ, (34) ŵ L = 1 B α (θ H θ L ) λ Z Ẑ, (35) where we define: B s D [1 + (1 β)θ H + βθ L + J], [ J (θ H θ L ) (C + 1) (β α) 1 ] [λ H (1 α) λ L α] s D In Appendix A, we show that B > 0 and J 0 Figure 1 illustrates the effect of the windfall on wages, under the assumption that the differentiated sector is skill intensive The two solid factor price curves illustrate all possible combinations of the factor prices in industry equilibrium The steeper curve is derived from equations (13) and (14) and represents the homogeneous sector The flatter 13

14 w H Figure 1: The impact of a windfall on wages Z w 2 H w 1 H w 2 L w 1 L wd H = wd H (w L; Z) wh H = wh H (w L) w L curve is derived from equations (3)-(12) and (15) and depicts all possible combinations of factor prices in the differentiated sector, given the equilibrium wage bill The intersection yields the general equilibrium factor prices wl 1 and w1 H A windfall of resources will shift the differentiated sector s factor price curve up, as the increase in spending drives up expected profits in the differentiated sector The homogeneous sector s factor price curve is unaffected The new intersection gives the new general equilibrium factor prices We observe that the high-skill wage increases and the low-skill wage decreases reason is that expected profits increase in the differentiated sector, which implies that firms bid up the wages to attract labor As labor moves from the homogenous sector to the differentiated sector, the factor used intensively in the differentiated sector becomes relatively scarce It follows, analogously to the Stolper-Samuelson theorem, that the wage of the factor used intensively in the differentiated sector increases, while the other wage decreases, as indicated by equations (34) and (35) The If the differentiated sector is skill intensive, we have that θ H > θ L, which implies that ŵ H > 0 and ŵ L < 0 The composite factor price increases as long as there is a difference in skill intensity (θ H θ L and β α): Ŵ = βŵ H + (1 β)ŵ L = 1 B (β α)(θ H θ L )λ Z Ẑ (36) The change in the wages prompts a further increase in spending The total effect of a 14

15 Figure 2: The impact of a windfall on labor allocation H h 1 h 2 L l 1 l 2 V 0 windfall on spending is given by: Ê =Ŷ = λ zẑ + 1 B (θ H θ L ) [λ H (1 α) λ L α] λ z Ẑ, (37) where the first term represents the increase in spending from the direct increase in income generated by the windfall, while the second term represents the increase in spending following the change in wages Figure 2 illustrates the effect of a resource windfall on the allocation of labor The slope of the solid thin lines depicts the employment of high-skill workers relative to the use of low-skill workers in each sector Assuming that the differentiated sector is skill intensive, the steeper line represents the relative employment of high-skill workers in the differentiated sector, while the flatter line represents the relative employment of high-skill workers in the homogeneous sector The employment of each worker type in each sector must sum to the total endowment of high- and low-skill workers, which is given by the vector V 0 It follows that the employment of high- and low-skill labor in the differentiated sector is given by h 1 and l 1, respectively A windfall of resources implies an expansion of the differentiated sector When the differentiated sector is skill intensive, each sector will employ fewer high-skill workers per 15

16 low-skill worker following the windfall The bold lines in Figure 2 represent the resulting relative factor use in each sector As a result, we observe that the employment of labor in the differentiated sector increases to h 2 and l 2 Moreover, we note that the employment of low-skill labor increases proportionately more than the use of high-skill labor In general, the differentiated sector s employment of the factor that is intensively used in the homogeneous sector increases proportionately more than the use of the other factor We derive this by substituting from equations (34), (35) and (37) into equations (26) and (27): ĥ = 1 B (1 + θ L)λ Z Ẑ, (38) ˆl = 1 B (1 + θ H)λ Z Ẑ (39) Substituting for the change in spending and the change in the composite factor price in equation (25), we obtain: ˆN = ( 1 J ) λ Z Ẑ (40) s D B We observe that the mass of entrants increases ( ˆN > 0) following the windfall, but it increases less when there is a difference in skill intensity The reason is that while a difference in skill intensity implies a greater increase in spending, the effect of higher spending is dominated by the effect of an increase in marginal costs Note that the mass of firms changes proportionally with effective labor employed: ˆN = β ĥ + (1 β)ˆl When labor is reallocated from the homogeneous sector to the differentiated sector there will be an increase in the effective labor employed in the differentiated sector This increase in effective labor employed is smaller when there is a difference in skill intensity The discussion thus far can be summarized by the following proposition: Proposition 1 A windfall of resources implies: i) an increase in the number of firms, ii) a higher wage of the labor type used intensively in the differentiated sector and a lower wage of the other type of labor, and iii) higher employment of both labor types in the differentiated sector The employment of the factor used intensively in the homogeneous sector increases proportionately more than the employment of the other factor 16

17 42 Firm selection and trade Inserting equation (36) into equation (21), we obtain the general equilibrium effect of a windfall on the productivity cut-off for foreign firms selling in the domestic market: ˆψ M = 1 σ 1 (β α)(θ H θ L )λ Z Ẑ (41) B σ 1 1 s X We observe that the import cut-off decreases, ˆψ M < 0, as long as there is a difference in skill intensity The reason is that foreign firms that produce for the import market face the same marginal costs as before the windfall but higher market demand This implies that firms at the lower end of the productivity continuum can produce for the import market As the mass of entrants in the rest of the world is given, the mass of foreign firms selling in the domestic market must increase Average firm sales in the import market are unchanged because marginal costs are given It follows that foreign firms sales in the domestic market increase ( ˆM > 0), solely due to adjustment at the extensive margin Inserting equation (36) into equation (20), we obtain the general equilibrium effect of a windfall on the domestic survival cut-off: ˆψ D = 1 σ s X (β α)(θ H θ L )λ Z Ẑ (42) B σ 1 1 s X We observe that the domestic survival cut-off decreases ( ˆψ D < 0) as long as there is a difference in skill intensity The reason is that while firms face higher marginal costs, the increase in the market demand index outweighs the effect of marginal costs, and hence even less productive firms can survive in the domestic market The decline in the domestic survival cut-off implies that new firms at the lower end of the productivity continuum enter the industry As a consequence, the average active firm has lower productivity than before the windfall Firms that produce for the export market face the same demand as before but higher marginal costs Inserting equation (36) into (18), we obtain the change in the export cut-off: ˆψ X = 1 B σ σ 1 (β α)(θ H θ L )λ Z Ẑ (43) We observe that an increase in resource rents increases the export cut-off ( ˆψ X > 0) as long as there is a difference in skill intensity, which implies that only the most productive firms can continue to export It follows that the average exporting firm has higher productivity than before the windfall As the export cut-off increases, the domestic survival cut-off decreases and the mass of entrants increases, there will be a larger set of non-exporting firms, ie, an expanded nontraded goods sector This result is consistent with the standard Dutch disease predictions However, the mechanism at play here is somewhat different from that in the standard 17

18 dependent economy framework In the standard framework, for instance as considered in Corden and Neary (1982), traded and non-traded goods are distinct goods that are complementary Higher spending implies that the consumption of both goods increases As the non-traded good cannot be imported, domestic production of this good must increase In our framework, the distinction between traded and non-traded goods is that non-traded goods are produced by firms that are not sufficiently productive to profitably export their product The increase in spending following a windfall of resources implies that more firms, even those that are less productive, can enter the market However, only the most productive firms can continue to export This implies that there will be a larger set of firms producing non-traded goods than before the windfall The average non-exporting firm after the windfall will have lower productivity, as the number of firms entering from the lower end of the productivity continuum is higher than the number of high-productivity firms that cease to export The total mass of active firms unambiguously increases ( ˆN D > 0), as there is a higher mass of entrants ( ˆN > 0) and the survival cut-off decreases ( ˆψ D < 0): ˆN D = ˆN k ˆψ D = 1 B [ 1 + (1 β)θ H + βθ L + (θ H θ L )(β α) kσ σ 1 s X 1 s X The change in the mass of firms that produce traded varieties is given by: ] λ Z Ẑ (44) ˆN X = ˆN k ˆψ X = 1 B [ 1 + (1 β)θ H + βθ L (θ H θ L )(β α) kσ ] λ Z Ẑ (45) σ 1 While the mass of firms that produce traded varieties unambiguously increases when there is no difference in skill intensity, the effect is ambiguous otherwise On the one hand, there is a larger mass of entrants ( ˆN > 0) On the other hand, the export cutoff increases ( ˆψ X > 0) when there is a difference in skill intensity If the second effect dominates, a lower number of firms will produce traded varieties We find the relative change in the share of firms that produce traded varieties by subtracting (45) from (44): ˆN X ˆN ( D = k ˆψX ˆψ ) D = 1 B (β α)(θ H θ L )k σ σ 1 1 λ Z Ẑ 1 s X We find that an increase in resource rents implies a decline in the share of firms that produce traded goods as long as there is a difference in skill intensity Substituting for the change in the mass of active firms from (44) and the change in the composite factor price from (36) into equation (22), we obtain the general equilibrium effect of a windfall on home firms domestic sales: 18

19 ˆD = 1 [ ( 1 + (1 β)θ H + βθ L + (θ H θ L )(β α) k σ )] s X + 1 λ Z Ẑ (46) B σ 1 1 s X At the intensive margin, the the average firm s sales increase (Ŵ > 0) At the extensive margin, the mass of active firms increases ( ˆN D > 0), implying an unambiguous increase in home firms sales in the domestic market ( ˆD > 0) We derive the relative change in export sales by substituting for the change in the mass of firms that produce traded goods from equation (45) and the composite factor price from (36) into equation (23): ˆX = 1 [ ( 1 + (1 β)θ H + βθ L (θ H θ L )(β α) k σ )] B σ 1 1 λ Z Ẑ (47) There is an ambiguous effect on export sales Based on the above, we can state the following proposition: Proposition 2 A windfall of resources implies: i) that only the most productive firms continue to export, ii) higher productivity of the average exporting firm and lower productivity of the average non-exporting firm, and iii) a decline in the share of firms that produce traded varieties The decline in the share of firms that produce traded goods is in line with the standard Dutch disease predictions However, referring to this as a disease is rather misleading for two main reasons First, the mass of firms that continue to export will be composed of more productive firms than before the windfall This observation is in line with Kuralbayeva and Stefanski (2013), who find that countries with natural resources have smaller but more productive traded sectors In their model, this is a result of worker selection In our model, the average productivity difference between traded and non-traded goods is a result of firm selection that makes the least productive firms lose foreign sales Second, even when the mass of exporting firms decreases, export sales may nevertheless increase The reason for this is that firms sales increases at the intensive margin 43 Welfare We determine the change in overall welfare by differentiating equation (21): Û = Ŷ µ ˆP (48) While a windfall of resources increases income, there is an ambiguous effect on the price index The relative change in income is equal to the relative change in spending given 19

20 by equation (37) We determine the relative change in the price index by inserting the change in spending and the change in the composite factor price from equation (36) into (19): ˆP = 1 [ 1 1 ( )] σ σ 1 B (θ H θ L ) (β α) (λ H (1 α) λ L α) λ Z Ẑ (49) 1 s X On the one hand, the number of varieties increases On the other hand, the price of each variety increases as marginal costs increase What is the net effect? Exploiting that Ŷ = Ê, substituting for the change in spending from (37) and the change in the price index from (49), and using the relationship between the parameters (equations 31-33), we obtain: Û = λ Z Ẑ + 1 µ B σ 1 s D [1 + (1 β)θ H + βθ L ] λ Z Ẑ + 1 B (θ µ 1 H θ L )(β α) [s D (1 s X )(C + 1) σ + s D (σ 1)] λ Z Ẑ σ 1 1 s X All terms in this expression are positive when there is spending on heterogeneous goods (µ > 0) and people value variety (σ > 1), and the first term provides the direct gain in income from the windfall Hence, there is an increase in welfare that is more than proportional to the direct windfall gain in income (Û > λ ZẐ > 0) The reason that we observe an increase in welfare that is more than proportional to the direct windfall gain in income is that there is further increase in income due to the change in factor prices and that there is an increase in the number of varieties available for consumption These effects dominate the upward pull on the price index due to higher marginal costs The windfall has different effect on the welfare of the two worker types While both are equally affected by the change in the price index, the effects on their income differ Assuming that the oil rents are distributed equally among people, the income of each worker type can be expressed as: y H = z + w H, (50) y L = z + w L, (51) where z Z/(H + L) Taking the differentials of (50) and (51) and inserting from (34) and (35), we find the relative change in the income of each worker type: ŷ H = ŷ L = w H z w H + z Ẑ + 1 B w H + z (1 α) (θ H θ L ) λ Z, (52) z w L + z Ẑ 1 w L B w L + z α (θ H θ L ) λ Z Ẑ (53) 20

21 If there is no difference in skill intensity between the sectors, wages are unaffected, and the change in each worker type s income is given by the first term in equation (52) and (53) In this case, the income of the worker type that initially had the lowest wage increases relative to the welfare of the other worker type This implies that initial inequalities are dampened as long as the resource rents are equally distributed among people If there is a difference in skill intensity, there is an increase in the wage of the worker type that is used intensively in the differentiated sector and a decrease in the other wage The effect of the change in wages on each worker type s income is given by the second term in equation (52) and (53) This means that if the differentiated sector, which we regard as the modern sector, is skill intensive and high-skill workers initially have the highest wage, the change in wages will tend to amplify initial inequalities If the relative increase in the high-skill wage is sufficiently large, a windfall of resources will magnify the relative position of high-skill workers and increase inequality The main points of this discussion can be summarized by the following proposition: Proposition 3 A windfall of resources: i) implies an increase in overall welfare over and above the direct gain from an increase in income and ii) affects the different worker types differently and may lead to higher inequality even if the resource rents are distributed equally among people 5 Numerical example Although the theory gives clear direction on the effect of most variables, in order to obtain an indication to the size of the effects, we present a numerical example of a stylized economy We use the following calibration We set the fraction of income spent on the differentiated goods µ to 06, while the elasticity of substitution over the varieties σ is 38 following the literature (Bernard et al, 2007) We set the sector factor intensities such that the differentiated sector is skill intensive In particular, α is set to 02, while β is set to 04 For the Pareto distribution we use the standard shape parameter value of k = 34 Fixed and variable trade cost are set at f E = 05, f D = 05, f X = 05, f M = 1, and τ = 15 The size of the economy is normalized by setting total low skilled labor to 2, and high skilled labor to 1 Foreign expenditure, firm mass and price index are also set to 1 The model is calibrated by setting total factor productivity in the homogenous sector A to 05, so that initially, w H > w L, and the labor allocation, the cut-off levels, and shares of productions are at reasonable levels 21

22 Figure 3: Simulations of an economy with resource windfall % w H /w L 5 % h/l % E -5 5 % ψ D % ψ X /ψ D -5 % ψ X % P 0 5 % ψ M % N 0 5 % X Z/Y initial % s X Z/Y initial % s D Z/Y initial Note: y-axes indicate deviations from baseline in percentages Parameters, Domestic: µ=06, σ=38, L=20, H=10, α=02, A=05, β=04, k=34, fd =05, f X =05, f M =05, f E =10, τ=15; Foreign: expenditures, firm mass = 1 The initial values of the variables are w H /w L =101, h/l=066, E=18, ψ D =132, ψ X =255, ψ M =199, ψ X /ψ D =193, P =105, N=018, X=008, s X =01, s D =042 22

23 Figure 3, presents plots of some relevant variables The lines present the change in percentage as resource wealth over (initial) GDP increases from 0 to 25% We find that most variables respond in the order of 5 to 10% from their original level to change in resources Some variables respond to a lesser extent, such as the price index, which remains practically flat In contrast, the share of exports in total domestic production, s X decreases by more than 10% from its original value The domestic production cut-off decreases only slightly, while the export cut-off increases substantially In the model we found that effect on export sales was ambiguous In these specific simulations we find that exports sales decreases substantially 6 Conclusion We presented a model of heterogeneous firms with two factors of production and focused on how the economy responds to a resource windfall This framework allowed us to derive new insights previously undocumented in the large literature on the Dutch disease The framework of our model differs from the approach used in most of the literature, as we consider an endogenously defined non-traded sector and endogenously implied average productivity differences between trading and non-trading firms We define two main cases, one in which skill intensity in the heterogenous sector is the same as in the rest of the economy and a second case in which it differs When the skill intensity in the two sectors is equal, the heterogenous sector will expand relative to the rest of the economy because the additional demand will increase the number of firms, thereby lowering the price index and increasing welfare Wages remain unchanged, and thus, firm selection remains constant When skill intensity differs, labor demand in the heterogenous sector will differ between high- and low-skilled workers, wages will be affected similarly, and consequentially, so will the equilibrium cut-off points at which firms decide to enter or remain in the domestic or export market The difference in skill intensity therefore allows for a firm selection effect following a resource windfall Specifically, new firms at the lower end of the productivity continuum can produce for the domestic market, while only the most productive firms can continue to export This implies that there will be a decrease in the share of firms that export Moreover, the wage differences imply that high- and low-skilled workers are affected differently The type of labor that is used intensively in the differentiated sector will experience larger increases in income than the other factor will If the type of labor that is used intensively in the differentiated sector has a relatively higher wage, then a windfall of resources may lead to higher inequality, even if the resource rents are distributed equally among people 23

24 References Allcott, H and Keniston, D (2014) Dutch disease or agglomeration? The local economic effects of natural resource booms in modern America NBER Working Paper No Bernard, A B, Redding, S J, and Schott, P K (2007) Comparative advantage and heterogeneous firms Review of Economic Studies, 74:31 66 Cherif, R (2013) The Dutch disease and the technological gap Journal of Development Economics, 101: Corden, W M and Neary, J P (1982) Booming sector and de-industrialisation in a small open economy Economic Journal, 92: Haaland, J I and Venables, A J (2014) Optimal trade policy with monopolistic competition and heterogeneous firms Discussion Paper No Centre for Economic Policy Research Harding, T and Venables, A J (2013) The implications of natural resource exports for non-resource trade OxCARRE Research Paper 103 Oxford Centre for the Analysis of Resource Rich Economies Krugman, P (1987) The narrow moving band, the Dutch disease, and the competitive consequences of mrs thatcher: notes on trade in the presence of dynamic scale economies Journal of Development Economics, 27(1-2):41 55 Kuralbayeva, K and Stefanski, R (2013) Windfalls, structural transformation and specialization Journal of International Economics, 90: Matsen, E and Torvik, R (2005) Optimal Dutch disease Journal of Development Economics, 78: Melitz, M J (2003) The impact of trade on intra-industry reallocations and aggregate industry productivity Econometrica, 71(6): Østenstad, G (2015) Windfall gains and migration Unpublished working paper University of Oslo Salter, W E G (1959) Internal and external balance: the role op price and expenditure effects Economic Record, 35(71): van Wijnbergen, S (1984) Dutch disease : A disease after all? Economic Journal, 94(373):41 55 Vannoorenberghe, G (2011) Trade between symmetric countries, heterogeneous firms, and the skill premium Canadian Journal of Economics, 44(1):