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Commodity windfalls, macroeconomic management and welfare∗ Fabrizio Orrego † Germán Vega ‡ March 31, 2014 Abstract We study the implications of the so-called Dutch disease in a small open economy that receives significant inflows of funds due to an extraordinary increase in the international price of copper. We consider three sectors, the tradeable sector, the booming sector and the nontradeable sector in an otherwise standard real-business-cycle model which is consistent with a balanced growth path. We find that the booming sector, that benefits from high international prices, induces the Dutch disease, that is, the tradeable sector declines, the real exchange rate appreciates, wages increase and the non-tradeable sector improves. We then introduce fiscal arrangements that aim to alleviate the consequences of the Dutch disease. We find that a countercyclical rule that boosts the productivity of firms maximizes the welfare of the representative household and seems to offset the effects of the Dutch disease. Keywords: Small open economy, Dutch disease, fiscal policy. JEL classification codes: F31, F41, E62 ∗ We are grateful to Gonzalo Llosa and seminar participants at the Central Bank of Peru and the XXXI BCRP Research Conference for valuable comments and suggestions. This paper has circulated under the title ”Dutch disease and fiscal policy”. The usual disclaimer applies. † Research Department, Central Bank of Peru, Jr. Miro Quesada 441, Lima 1, Peru; and Department of Economics, Universidad de Piura, Calle Mártir José Olaya 162, Lima 18, Peru. Email address: [email protected] ‡ Department of Economics, Universidad de Piura, Calle Mártir José Olaya 162, Lima 18, Peru. Email address: [email protected] 1 1 Introduction In the last decade, several exporters of minerals have benefited from extraordinarily high international prices. Figure 1 shows the case of four countries that belong to the top 10 exporters of copper. We observe that exports of copper significantly increased after 2003-2004 and foreign direct investment in the mining sector picked up shortly after in all countries. Figure 2 shows a close relationship between the share of copper exports and the ratio of non-tradeable GDP to total GDP. Furthermore, Figure 3 shows a clear mapping between the ratio of non-tradeable GDP to total GDP and the real exchange rate. All in all, these figures make us suspect of the existence of the so-called Dutch disease, which may have been induced by high international copper prices. (a) Peru (b) Chile (c) Canada (d) Australia Figure 1: Mining exports and FDI in mining sector. Solid line: Ratio of mining exports to total exports. Dashed line: Ratio of FDI in mining sector to total FDI. Source: Central Banks and World Bank. In this paper, we study how the Dutch disease phenomenon emerges. We use a small open economy model with three sectors, a tradeable sector, a booming sector (that exports copper) and a non-tradeable sector, consistent with a balanced growth path. Firms in the first two sectors produce goods that are traded at world prices. Output in the first two sectors use a factor specific to each sector and labor, but firms in the non-tradeable sector use only labor. Firms in the booming sector produce only for export. Suddenly there is an exogenous rise in the price of its product on the world market. The main effects on the real sector are the following: Labor and total consumption all increase on impact. Wages and prices in the non-tradeable sector also increase. Since the price of tradeables is fixed, the higher price of non-tradeables induces a real appreciation of the exchange rate. This real appreciation deteriorates the competitiveness of the tradeable sector. Hence, output in the tradeable sector decreases on impact and the higher consumption of tradeables leads to a deficit in the balance of trade of tradeable goods. Moreover, there is a reduction of labor demand in the tradeable sector. However, GDP increases, because both the non-tradeable sector and the booming sector (mining sector) increase. These ingredients suggest that an international increase 2 in the price of copper fosters the symptoms of a Dutch disease. Then we introduce an arguably active government that collects taxes from private firms, issues debt, redistributes resources back to households via transfers and invest in public capital. We ask to what extent this government may pursue certain policies that might offset the effects of the Dutch disease and, more importantly, increase the welfare of the representative individual. We find that a countercyclical fiscal rule that boosts the productivity of firms maximizes the welfare of the household and seems to lean against the wind. Our three-sector model follows the spirit of early papers that analyze the Dutch disease, for instance, Bruno and Sachs (1982), Corden and Neary (1982) and Corden (1984). As in Suescun (1997), the source of the disease in our model is the booming sector and the extraordinarily high price of copper. Other papers that blame the massive inflows from abroad are Lartey (2008a), Lartey (2008b) and Acosta, Lartey and Mendelman (2009b). We introduce fiscal policies in the spirit of Kumhof and Laxton (2013) in order to cope with the effects of the so-called Dutch disease. Because our model is of the RBC type, we do not assess the role of monetary policy. However, recent papers by Lama and Medina (2012) or Hevia, Neumeyer and Nicolini (2013) do study the role of monetary and exchange rate policies in economies that suffer from the Dutch disease. (a) Peru (b) Chile (c) Canada (d) Australia Figure 2: Copper exports and non-tradable production. Solid line: Ratio of copper exports to total exports. Dashed line: Ratio of non-tradable production to total production. Source: Central Banks and World Bank. The plan of this paper is as follows. Section 2 introduces the model. Section 3 presents the detrended equations of the model. Section 4 shows the optimality conditions. Section 5 defines the competitive equilibrium. Section 6 presents some results. Section 7 studies welfare. Section 8 concludes. 3 (a) Peru (b) Chile (c) Canada (d) Australia Figure 3: Non-tradable production and real exchange rate. Solid line: Ratio of nontradable production to total production. Dashed line: Effective real exchange rate. Source: Central Banks and World Bank. 2 The model We embed a three-sector model, the booming sector, the tradeable sector and the non-tradeable sector, into a frictionless standard small open economy which is populated by households, firms and government, which is consistent with a balanced growth path. Firms in the first two sectors produce goods that are traded at world prices. Output in the first two sectors use a factor specific to each sector and labor, but firms in the non-tradeable sector use only labor. Since labor is perfectly mobile, the market wage is the same in all sectors. All production functions have a deterministic component that increases at a positive rate. We further assume, in the spirit of Corden (1984), that firms in the booming sector produce only for export and there is an exogenous rise in the price of its product on the world market which induces a Dutch disease. We introduce an arguably active government that collects taxes from private firms, issues debt, redistributes resources back to households via transfers and invest in public capital that boosts the productivity of private firms in the economy. We evaluate different fiscal rules that may maximize the welfare of the household and offset the consequences of the Dutch disease on the economy. 2.1 Households A representative household wants to maximize the discounted value of his lifetime utility from consumption Ct and labor Lt : Et ∞ X U (Cs , Ls ) s=t 4 (1) The instantaneous utility function is: U (Ct , Lt ) = Ct1−σ [1 − κLνt ] 1−σ 1−σ −1 (2) where 1/σ is the intertemporal elasticity of substitution, κ is a constant introduced for analytical convenience and ν is related to the curvature of the labor supply curve. The functional form is consistent with long run growth, that is, is consistent with a balanced growth path in which labor is stationary and consumption increases over time. This particular functional with time separable preferences owes to Uhlig (2009) and Jaimovich and Rebelo (2009). It is straightforward to verify that the utility function in equation (2) is also a special case of King, Plosser and Rebelo (1988). Moreover, as is standard in open economy models, the aggregate consumption good Ct includes both tradeable consumption CT,t and non-tradeable consumption CN T,t in the following fashion: θ h 1 i θ−1 θ−1 θ−1 1 Ct = γ θ (CT,t ) θ + (1 − γ) θ (CN T,t ) θ , (3) where γ is the share of tradeable consumption in the consumption index and θ is the elasticity of intertemporal substitution between tradeables and non-tradeables. For later reference, the consumer price index is: h i 1 1−θ 1−θ , Pt = γ + (1 − γ) (PN T,t ) (4) where PN T,t is the price of non-tradeable goods and the price of tradeable goods serves as a numeraire. In the financial side, the household is allowed to trade a risk-free one-period bond Bt that pays the international interest rate r. In order to close the model, we assume that the representative household must pay some portfolio adjustment costs p(Bt ) whenever Bt deviates from its equilibrium level, in line with Schmitt-Grohe and Uribe (2003). The household may trade as well stocks in the tradeable sector and the booming sector (xT,t and xB,t , respectively). Thus, the budget constraint is: Pt Ct + vT,t xT,t + vB,t xB,t + Bt + p(Bt ) = Wt Lt + (vT,t + dT,t )xT,t−1 + (vB,t + dB,t )xB,t−1 + (1 + r)Bt−1 + T Rt (5) where vT,t and vB,t are the stock prices in the tradeable sector and the booming sector, respectively. On the other hand, dT,t and dB,t represent the dividends paid by firms in the tradeable sector and the booming sector, respectively. Finally, Lt is the household’s labor supply, Wt is the nominal market wage expressed in terms of the domestic tradeable good and T Rt stands for the transfers made by the government. 2.2 Production sectors In this section we characterize the behavior of firms in the tradeable sector, the booming sector and the non-tradeable sector. Labor is perfectly mobile across sectors, but capital in the tradeable sector and the mining sector is specific. Non-tradeable firms use only labor. 5 2.2.1 Tradeable sector We assume a Cobb-Douglas technology with constant returns to scale in capital and labor: αG α YT,t = AT,t XT,t KT,t−1 LT,t 1−α ψKG,t−1 (6) where YT,t is the tradeable output, AT,t is the total factor productivity that follows a stationary process and XT,t is a deterministic growth component. As usual, KT,t−1 and LT,t are the capital and labor inputs in the production function and α measures the intensity of capital in the production function. Public capital KG,t−1 may be an additional input in the production function if αG is positive (of course, ψ is a positive constant). In order to verify that the production function in equation (6) is consistent with a balanced growth path, it is enough to have the technical change written in the labor augmenting form: 1−α α YT,t = ÃT,t KT,t−1 X̃T,t LT,t 1 αG 1−α where ÃT,t ≡ ψAT,t KG,t−1 and X̃T,t = XT,t . On the other hand, capital in the tradeable sector follows a standard law of motion: KT,t = IT,t + (1 − δT )KT,t−1 , (7) where δT is the depreciation rate and IT,t stands for investment in the tradeable sector. In this model, firms need to pay capital adjustment costs whenever IT,t 6= KT,t−1 . These costs are summarized by a convex cost function Θ(IT,t , KT,t−1 ). Finally, assume that output in the tradeable sector is taxed at a rate τ and let ΛT,t be the stochastic discount factor. Then the firm’s problem is to maximize the discounted value of dividends ds , that is, revenue minus expenditure: max KT ,s ,IT ,s ,LT ,s Et ∞ X ΛT,s [(1 − τ )YT,s − IT,s − Θ(IT,s , KT,s−1 ) − Ws LT,s ] s=t subject to equations (6) and (7). 2.2.2 Mining sector Firms in the booming sector first use an investment unit to decide upon the optimal composition of local investment and foreign investment. This modeling device is in line with Figure 1, in which we observe that the mining sector receives capital from abroad in the form of foreign direct investment. Investment unit.- The investment unit produces one unit of investment using local investment IH,t and foreign investment IF,t . Firms in the tradeable sector supply local investment and foreign investment comes from abroad. Investment in the booming sector IB,t aggregates the two types of investment via a CES function: ρ i ρ−1 h 1 ρ−1 ρ−1 1 , IB,t = µ ρ (IH,t ) ρ + (1 − µ) ρ (IF,t ) ρ (8) where µ is the share of local investment in the mining sector and ρ is the elasticity of substitution between the two types of investment. If the price of local investment serve as a numeraire and 6 PF I,t stands for the price of foreign investment, the cost minimization problem of the investment unit is the following: min IH,t + PF I,t IF,t IH,t ,IF,t subject to equation (8). In an interior solution, we obtain demands for each type of investment: IH,t = µ(PI,t )ρ IB,t ρ PI,t IB,t IF,t = (1 − µ) PF I,t (9) (10) Production unit.- Firms in the booming sector produce only for export. Because firms want to maximize the discounted value of dividends, they had better establish an optimal demand for capital, given the external demand and export prices. Moreover, firms inelastically demand labor in each period, given the capital stock and factor productivity, regardless of the market wage or the tax system. The production function and the law of motion of capital are: αG α YB,t = AB,t XB,t KB,t−1 L1−α ψK B,t G,t−1 (11) KB,t = IB,t + (1 − δB )KB,t−1 (12) where YB,t is the output in the booming sector, AB,t is the total factor productivity that follows a stationary process and XB,t is a deterministic growth component. Also, KB,t and LB,t are the capital and labor inputs in the production function and α measures the intensity of capital in the production function. Again, ψ is a positive constant. Public capital KG,t−1 may serve as an additional input in the production function whenever αG is positive. On the other hand, IB,t stands for investment in the booming sector. As in the tradeable sector, firms in the booming sector face convex adjustment costs given by Θ(IB,t , KB,t−1 ). If the price of investment in the mining sector PI,t is given by: h i 1 1−ρ 1−ρ PI,t = µ + (1 − µ) (PF I,t ) (13) then the firm’s problem in the booming sector is to maximize the discounted value of dividends dB,s , that is, revenue minus expenditure. Assume that output in the booming sector is taxed at a rate τ and let ΛB,t be the stochastic discount factor: max KB,s ,IB,s ,LB,s Et ∞ X ΛB,s [(1 − τ )PB,s YB,s − PI,s (IB,s + Θ(IB,s , KB,s−1 )) − Ws LB,s ] s=t subject to equations (11) and (12). 2.2.3 Non-tradeable sector The production function in the non-tradeable sector is linear in labor: 7 αG YN T,t = Zt XN T,t LN T,t ψKG,t−1 (14) where Zt is the labor productivity, XN T,t is a deterministic component in the non-tradeable sector and LN T,t is the demand of labor in the non-tradeable sector. As in the other sectors, assume that output in the non-tradeable sector is taxed at a rate τ . Hence the problem of the firm is: max (1 − τ )PN T,t YN T,t − Wt LN T,t LN T ,t subject to equation (14). 2.3 Government In this section we basically borrow from Kumhof and Laxton (2013). We study the effects of several fiscal rules on consumption, capital accumulation, labor, wages and the like in the presence of the commodity windfall. These rules are supposed to help households cope with the transitory increase in commodity prices. In principle, if there were complete markets, these rules would not make much sense since households would be able to insure themselves against all possible states of nature. Nevertheless, in this model households are not allowed to trade a complete set of contingent claims and therefore cannot deal with all possible shocks (AT,t , AB,t , Zt ) in the Cartesian product ∆T × ∆B × ∆, not to mention the impact of copper prices and foreign investment PB,t and PF I,t , respectively. Of course, these fiscal rules are not optimal in the sense of the new dynamic public finance (recent papers by Lama and Medina (2012) and Hevia et al. (2013) do include exercises on Ramsey taxation). Basically, the rules are either procyclical or countercyclical. First we will explain the main ingredients of the government budget constraint and then we will disclose the main features of the fiscal rules. 2.3.1 Government budget constraint The government budget constraint in this economy is: τ Yt + Dt = Gt + (1 + r)Dt−1 + T Rt where τ Yt is the government revenue, Dt is the public debt issued abroad, Gt is the total government expenditure (includes both investment and consumption), r is the international interest rate and T Rt are the gross transfers made to households. Since Gt includes two types of expenditures, it will be useful to explain the nature of each component: Investment.- Investment expenditures help build the stock of public capital KG that depreciates itself at a rate δG . These expenditures mainly take the form of infrastructure projects such as railroads, bridges and homeland security. The corresponding law of capital accumulation is: KG,t = IG,t + (1 − δG )KG,t−1 Public investment KG behaves like a positive externality since it raises the total factor productivity of all sectors in the economy. 8 Consumption.- For the case of consumption expenditures, the government may buy goods from either the tradeable sector or the non-tradeable sector. We assume that the share of expenditures in each sector mimics that of the consumption basket of the households: CGT,t = γCG,t CGN T,t = (1 − γ) CG,t PN T Hence public purchases may be written as: CG,t = CGT,t + PN T,t CGN T,t Transfers.- For the case of public transfers to households, we assume for simplicity that T Rt = τT R Yt , that is, transfers are highly procyclical. 2.3.2 Fiscal rules Now we study some alternative rules that stem from the following equation: sYt = τ Yt Yt Ȳ ς − Gt − rDt−1 where s is a constant that stands for the economic deficit (if negative) or superavit (if positive) of the public sector, Ȳ is the stationary level of GDP and, more importantly, ς is the elasticity of fiscal expenditures to fiscal revenues. We evaluate three different scenarios, each associated to a particular value of ς: 1. Rule I: Procyclical behavior when ς = 0.5. 2. Rule II: Neutral behavior when ς = 0. 3. Rule III: Countercyclical behavior when ς = −0.5. In each scenario, we also assess the impact of public capital on the productivity of private firms, that is, we consider two possibilities: 1. Rule A: Public capital is neutral when αG = 0. 2. Rule B: Public capital is a positive externality when αG = 0.2. All in all, we present six cases, the combinations of rules I, II and III, with rules A and B. 3 Detrending For analytical convenience, we will assume that XT,t = XB,t = Xt , that is, both the tradeable sector and the mining sector share the same growth trend. However, since the non-tradeable sector 9 1−αG 1−α−αG only uses labor, we further assume that XN T,t = Xt is X 1 1−α−αG . In this model, the detrending factor and detrended variables are written as: Mt M̂t = X 1 1−α−αG As is standard in this class of models, we assume that the growth rate is equal to gX as follows: 1 1−α−αG Xt 1 1−α−αG 1 = (1 + gX ) 1−α−αG Xt−1 1 For later use, we let (1 + g) = (1 + gX ) 1−α−αG . As in King et al. (1988), we work with the transformed economy with detrended variables. Households.- In the case of households, we need to detrend the objective function and the budget constraint: Ĉt1−σ [1 − κLνt ] 1−σ 1−σ −1 1−σ and the new discount factor is β̂ = β(1 + g) 1−α−αG . Furthermore the detrended budget constraint is: ι Pt Ĉt + v̂T,t xT,t + v̂B,t xB,t + B̂t + (B̂t − B̄)2 = Ŵt Lt + (v̂T,t + dˆT,t )xT,t−1 2 + (v̂B,t + dˆB,t )xB,t−1 + (1 + r)B̂t−1 + TˆRt (15) where ι is a positive constant. Production sectors.- In the case of productive firms, we need to detrend the production functions: αG α ŶT,t = AT,t K̂T,t−1 L1−α ψ K̂ T,t G,t−1 αG 1−α α ŶB,t = AB,t K̂B,t−1 LB,t ψ K̂G,t−1 b αG ŶN T,t = Zt LB,t ψ K G,t−1 (16) (17) (18) And we also need to care of the laws of capital accumulation: (1 + g)K̂T,t = IˆT,t + (1 − δT )K̂T,t−1 (19) = IˆB,t + (1 − δB )K̂B,t−1 (20) (1 + g)K̂B,t (21) b M,t , KM,t−1 ) = Furthermore, the detrended convex cost function is Θ(I for M that belongs to {T, B}. φ 2 IˆM,t K̂M,t−1 − g − δM 2 Government.- In the case of the public sector, we need to detrend the budget constraint, the 10 fiscal rule and the law of capital accumulation: τ Ŷt = Ĝt + (1 + r)D̂t−1 − D̂t + TˆRt !ς ˆ YT,t − Ĝt − rD̂t−1 sŶt = τ Ŷt Yˆ (1 + g)K̂G,t = IˆG,t + (1 − δG )K̂G,t−1 (22) (23) (24) We also detrend the other relationships: Ĝt = ĈG,t + IˆG,t 4 (25) ĈG,t = τC Ĝt (26) ĈG,t = ĈGT,t + PN T,t ĈGN T,t (27) ĈGT,t = γ ĈG,t (28) TˆRt = τT R Ŷt (29) Optimality conditions In the transformed model, the optimality conditions for an interior solution are characterized by the following first order conditions: Households.- The necessary conditions for an optimum are: λĈ,t [1 + g + ι(B̂t − B̄)] = β̂Et λĈ,t+1 (1 + r)Pt /Pt+1 (30) (1 + g)v̂T,t λĈ,t = β̂Et λĈ,t+1 (v̂T,t+1 + dˆT,t+1 )Pt /Pt+1 (31) (1 + g)v̂B,t λĈ,t = β̂Et λĈ,t+1 (v̂B,t+1 + ρdˆB,t+1 )Pt /Pt+1 (32) − λL,t Ŵt = λĈ,t Pt (33) θ ĈT,t = γ (Pt ) Ĉt θ Pt Ĉt ĈN T,t = (1 − γ) PN T,t (34) (35) where λĈ,t = Ĉt−σ [1 − κLνt ]1−σ is the marginal utility of consumption and λL,t = −κν Ĉt1−σ [1 − κLνt ]−σ Lν−1 is the disutility of labor. Notice that equation (30) is a standard Euler equation. t Equations (31) and (32) reflect optimality conditions related to financial purchases. In these cases, the marginal utility of forgoing one unit of stock must be equal to the (discounted) expected utility of the real return of the stock. Equation (33) determines labor supply. On the other hand, consumption in the tradeable sector and non-tradeable sector are given by (34) and (35), respectively. Production sectors.- In an interior solution, the optimal decisions of the firm in the tradeable sector give rise to the following conditions: 11 ( α(1 − τ ) (1 + g)QT,t = Et ΛT,t+1 + IˆT,t+1 φ 2 K̂T,t ŶT,t+1 K̂T,t !2 − δT − g −φ IˆT,t+1 K̂T,t ! − δT − g ˆ It+1 K̂t + Qt+1 (1 − δT ) (36) QT,t = 1 + φ ! IˆT,t K̂T,t−1 Ŵt = (1 − α)(1 − τ ) − δT − g (37) ŶT,t LT,t (38) where QT,t is the shadow price of capital in the tradeable sector and equation (36) is a standard investment Euler equation. Moreover, equation (37) determines the current value of QT,t and equation (38) shows the labor demand in the tradeable sector. In the booming sector, the optimality conditions give rise to the following equations: ( (1 + g)QB,t = Et ΛB,t+1 α(1 − τ )PB,t+1 φ + PI,t+1 2 IˆB,t+1 K̂B,t ŶB,t+1 K̂B,t !2 − δB − g −φ IˆB,t+1 K̂B,t ! − δB − g IˆB,t+1 K̂B,t + QB,t+1 (1 − δB ) (39) " QB,t = PI,t 1 + φ IˆB,t K̂B,t−1 !# − δB − g (40) where QB,t is the shadow price of capital in the booming sector. Notice that there are three differences with the problem of the firm in the tradeable sector, namely the price of copper PB,t and the price of investment, PI,t . Furthermore, the demand for labor is completely inelastic. Finally, the static optimization problem of the firm yields the following equilibrium condition: (1 − τ ) ŶN T,t Ŵt = , LN T,t PN T,t (41) Government.- The detrended equations of the government were already included in the previous section. 5 Market clearing conditions, competitive equilibrium and calibration 5.1 Market clearing conditions In this section, we state the market-clearing conditions of the model. For simplicity, we assume that adjustment costs in the tradeable and booming sectors are expressed in terms of tradeable goods. The market clearing conditions in the goods market and the labor market are: 12 Ybt = YbT,t + PN T,t YbN T,t + PB,t YbB,t (42) bT,t + C bGT,t + IbT,t + IbG,t + IbH,t + BC d T,t YbT,t = C !2 φ IbB,t b B,t−1 + φ + PI,t − δ − gy K b B,t−1 2 K 2 IbT,t − δ − gy b T,t−1 K !2 b T,t−1 K bN T,t + C bGN T,t YbN T,t = C (43) (44) Lt = LT,t + LB,t + LN T,t (45) The demand for local tradeable goods does not necessarily match the local supply and the difference is captured in the balance of trade without minerals or BoTT,t . We also need to define some variables such as exports of minerals (XB,t ), external demand for exports (YRoW,t ), real exchange rate (RERt ), balance of trade (BoTt ) and current account (CAt ). Since firms in the booming sector produce only for export, it must be the case that XB,t = YB,t in equilibrium. $ X̂B,t = γB PB,t ŶRoW,t 1 RERt = Pt [ t = BoT [ T,t + PB,t X̂B,t BoT d t = rB̂t−1 − ι (B̂t − B̄)2 + BoT [ t − PF I,t IˆF,t − rD̂t−1 CA 2 (46) (47) (48) (49) Equation (46) shows that nominal exports of minerals depend on both the international price and the demand of the rest of world. Moreover, equation (47) suggests that an increase of RERt implies a real depreciation. On the other hand, equation (48) shows all transactions with international partners. Finally, equation (49) shows the current account of the small open economy. 5.2 Equilibrium We solve the model up to a first-order approximation around the non-stochastic steady state. We use the Dynare toolbox in Matlab. The equations we need are: • Given prices, wages, tranfers, interest rates and dividends, households choose consumption, labor supply and bond holdings according to equations (15), (30), (33), (34) and (35). • Given wages, the total factor productivity and the stochastic discount factor, firms in the tradeable sector chooses labor, capital, the shadow price of capital and determines the level of output according to equations (16), (19), (36), (37) and (38). • Given the foreign demand for copper, the foreign price of investment, the stochastic discount factor and the total factor productivity, firms in the booming sector chooses investment, capital, the shadow price of capital and labor according to equations (9), (10), (46), (20), (39) and (40). • Given prices, total factor productivity and stochastic discount factor, firms in the nontradeable sector chooses labor and determines the level of output according to equations (14) and (41). 13 • Total output in the economy is determined according to equation (42). • Fiscal revenue and fiscal rules obey equations (22), (24), (23), (25), (26), (27), (28) and (29). • Relative prices and wages obey equations (4), (13),(44) and (45). • The gap between domestic demand and supply of tradeable goods determine the balance of trade according to equation (43). • Foreign demand for copper, real exchange rate, total balance of trade and current account obey equations (46), (47),(48) and (49). • All six exogenous variables follow stationary processes that are mutually uncorrelated. There are two types of exogenous variables in this model. On the one hand, there are internal exogenous variables such as total factor productivity of the tradeable sector (AT,t ), the booming sector (AB,t ) and the non-tradeable sector (Zt ). On the other hand, we have exogenous variables that are determined in international markets such as the price of the booming sector (PB,t ), the price of international investment (PF I,t ) and the stance of the world economy (YRoW,t ). In particular, PB,t follows a stationary AR(2) process. 5.3 Calibration Table 1 depicts the baseline calibration in this paper. Few parameters are fairly standard in the literature, such as α, ν and δ. We also assume that σ =2 to ensure certain curvature of the utility function. The international interest rate is 0.028, which means that the discount factor is 0.99 in any stationary equilibrium. We follow Devereux, Lane and Xu (2006) and set the share of tradeable consumption equal to 0.45. As in Acosta et al. (2009b), the elasticity of substitution θ between tradeables and non-tradeables is 0.4. Since it turns out that this parameter is important, we perform robustness checks with alternative values of 0.2 and 0.8 (available upon request). Furthermore, the elasticity of substitution between domestic investment and foreign investment, ρ, is equal to 1.5. We calibrate κ and γB so as to match the ratios of balance of trade to GDP and exports of copper to GDP. Finally, we assume that capital adjustment costs are equal to 3. In the presence of fiscal rules, we set the tax rate in order to match the ratio of public expenditures to GDP of Peru in the period 1994-2012, that is, 0.14. The ratio of government expenditures to GDP is 0.12, consistent with Peruvian data. We further assume that ψ is equal to 1.0169 in order not to overestimate the effects of the positive externality of public capital. Because we want to compare among the different fiscal rules, we calibrate κ and γB to ensure that the ratios of balance of trade to GDP and exports of minerals to GDP are equal to -0.02 and 0.09, respectively, as in the data. In order to evaluate the calibration, we plug the parameters in the equations that characterize the non-stochastic steady state without fiscal expenditures and calculate several ratios with respect to GDP. Table 2 shows the comparison between the ratios obtained from the model and the real ratios calculated with Peruvian data from 1994 to 2012 (we use quarterly data that have been previously seasonally adjusted and detrended). The main differences that arise are the low ratio of investment and the high ratio of consumption, because the model, by construction, does not have capital in the non-tradeable sector, which reduces the aggregate amount of investment. The ratio of non-tradable consumption to total consumption is close to the real ratio and the share of non-tradable labor is 0.6, which is a stylized fact in small open economies. In any stationary 14 Parameter σ β ν κ α ι γ θ δT δB δG φ µ ρ g r ω γB τ τC αG ς ψ s Value 2 0.99 1.455 0.465 0.33 0.074x10−2 0.45 0.4 0.05 0.05 0.05 3 0.8 1.5 0.005 0.028 1 0.112 0.14 0.68 0 0 1.0169 -0.004 Parameters of standard model Description Source Elasticity of intertemporal substitution Lartey (2008a) Discount factor Standard in SoE Inverse of elasticity of labor supply Mendoza (1991) Adjusts labor supply Match BoT of −0.02% in SS Share of capital in production Standard in SoE Portfolio adjustment cost Schmitt-Grohe and Uribe (2003) Share of tradeable goods in consumption Devereux et al. (2006) Elasticity of substitution Acosta, Lartey and Mandelman (2009a) Depreciation rate Standard in SoE Depreciation rate Standard in SoE Depreciation rate Standard in SoE Capital adjustment cost Acosta et al. (2009a) Share of domestic inv. in booming sector Lartey (2008a) Elasticity of substitution in investment Lartey (2008a) Technology growth Trend growth of 0.9% quarterly. Foreign interest rate Determined by g and β Elasticity of exports Acosta et al. (2009a) Adjustment in foreign demand Match Exports/GDP Tax rate Match G/GDP Share of government purchases Match Peruvian data Intensity of public capital Baseline scenario Fiscal rule Baseline scenario Intensity of public externality Imply no productivity gain Government deficit Match debt to GDP of 40% in SS Table 1: Baseline parameterization Comparison of model with public expenditures and Peruvian data Variable Model Data Consumption 0.8 0.70 Investment 0.1 0.19 Balance of trade -0.02 -0.02 Exports of copper 0.09 0.09 Government expenditures 0.12 0.13 Ratio non-tradable labor 0.6 0.6 Table 2: We compare the ratios from the model with the real ratios obtained with Peruvian data between 1994 and 2012. Here we consider the baseline model. equilibrium, the current account is zero, and the balance of trade and exports of copper roughly match the data. 6 Results Baseline model.- We perturb the model with a 10% (transitory) increase in PB,t . Figure 4 depicts the responses of the relevant endogenous variables in the economy when government is absent (that is, when αG = ς = 0). Labor and total consumption all increase on impact. Wages and prices in the non-tradeable sector also increase. Since the price of tradeables is fixed, the higher price of non-tradeables induces a real appreciation of the exchange rate. This real appreciation deteriorates the competitiveness of the tradeable sector. Hence, output in the tradeable sector decreases on impact and the higher consumption of tradeables leads to a deficit in the balance of trade of tradeable goods. Moreover, we observe a reduction of labor demand in the tradeable sector. However, GDP increases, because both the non-tradeable sector and the booming sector (mining sector) increase. These ingredients suggest that an inter- 15 national increase in the price of copper fosters the symptoms of a Dutch disease. Fiscal rules.- Figure 5 depicts the IRFs associated with the case in which public capital does not foster the productivity of private firms (that is, Rule A when αG = 0). We observe Rules I, II and III in action though. The IRFs suggest that in the countercyclical case, the government accumulates foreign assets and output and employment in the non-tradeable sector do not increase vigorously on impact. On the contrary, in the procyclical case, the government spends more, accumulates more debt and fosters employment and production in the non-tradeable sector. In this case, the government worsens the balance of trade, since the tradeable sector deteriorates on impact. Figure 6 depicts the IRFs associated with the case in which public capital acts as a positive externality in the production functions of private firms (that is, Rule A when αG = 0.2). Again we observe Rules I, II and III. Now we see more action coming from the IRFs. When public investment generates a positive externality in all sectors, the impact of higher commodity prices on output is highly persistent. When the fiscal rule is countercyclical, households do not receive higher wages, consumption is more stable and the real exchange rate suffers less on impact. On the other hand, when the fiscal rule is procyclical, the productivity of firms increases in the tradeable sector, consumption increases and the balance of trade heavily deteriorates on impact. 7 Welfare Unfortunately, we do not know from the previous section what the best rule is. Some rules perform really well in some aspects, but not that well in others. Hence, in this section we want to rank the different rules in terms of the welfare of the representative household. That is, we look for the rule that minimizes the variance of consumption. We closely follow Woodford (2002) and Elekdag and Tchakarov (2007) to accomplish this task. We work with detrended variables (even though we do not write the hats over the variables) and apply a second order Taylor expansion of the utility function around the non-stochastic steady state: E(Ut ) = U + C −σ Υ1−σ E(Ct − C) − κνC 1−σ Υ−σ Lv−1 E(Lt − L) σ κν 1−σ v−2 −σ − C −σ−1 Υ1−σ Var(Ct ) − C L Υ (v − 1) + σκνLν Υ−1 Var(Lt ) 2 2 (50) where Υ = [1 − κLνt ]. Then we ask how much the household is willing to pay to smooth consumption, that is, we want to find ξ in the following equation: U ((1 + ξ)C, 1 − L) = (C(1 + ξ))1−σ Υ − 1 = E(Ut ) 1−σ 16 (51) In order to pin down ξ we manipulate equation (51) as follows: (1 − σ) (1 − σ)κνLν−1 σ ξ = 1+ E(Ct − C) − E(Lt − L) − (1 − σ)C −2 Var(Ct ) C Υ 2 1 1−σ v−2 ν κν (1 − σ)L σκνL (ν − 1) + Var(Lt ) −1 − 2 Υ Υ (52) Finally, Table 3 says unambiguously that households would prefer a countercyclical fiscal rule with productive capital, because it minimizes the variance in consumption. 8 Final remarks We study a small open economy with three sectors, the tradeable sector, the booming sector and the non-tradeable sector. We show that after an unanticipated increase in the price of copper, there is a real appreciation of the exchange rate, a deterioration of the tradeable sector and more favorable conditions for the non-tradeable sector and the booming sector. Then we evaluate the usefulness of alternative fiscal rules that aim to minimize the variance of consumption of the representative household. We find that a countercyclical fiscal rule that boosts the productivity of firms maximizes the welfare of the household and seems to lean against the wind. In this fashion, fiscal rules counteract the Dutch disease, as originally suggested in Corden (1984). However, we are left to pursue several avenues. First, we may want to contrast the effects of the Dutch disease with other sources of real exchange appreciations, such as the typical BalassaSamuelson effect, and rank the associated welfare gains or losses. We are currently undertaking all these issues. References Acosta, P., E. Lartey, and F. Mandelman, “Remittances and Dutch disease,” Journal of Internacional Economics, 2009, 79 (1), 102–116. , , and F. Mendelman, “Remittances and the Dutch disease,” Journal of International Economics, 2009, 79, 102–116. Bruno, M. and J. Sachs, “Energy and resource allocation: A dynamic model of the Dutch disease,” The Review of Economic Studies, 1982, 49 (5), 845–859. Corden, M., “Booming sector and Dutch disease economics: Survey and consolidation,” Oxford Economic Papers, November 1984, 36 (3), 359–380. Corden, W. and J. Neary, “Booming sector and de-industrialisation in a small open economy,” Economic Journal, 1982, 92 (368), 825–848. Devereux, M., P. Lane, and J. Xu, “Exchange rates and monetary policy in emerging market economies,” Economic Journal, September 2006, 116 (511), 478–506. Elekdag, S. and I. Tchakarov, “Balance sheets, exchange rate policy and welfare,” Journal of Economic Dynamics and Control, December 2007, 31 (12), 3986–4015. 17 Hevia, C., A. Neumeyer, and J. Nicolini, “Optimal monetary and fiscal policy in a New Keynesian model with a Dutch disease: The case of complete markets,” Working Paper, Universidad Torcuato Di Tella 2013. Jaimovich, N. and S. Rebelo, “Can news about the future drive the business cycle,” American Economic Review, September 2009, 99 (4), 1097–1118. King, R., C. Plosser, and S. Rebelo, “Production, growth and business cycles: I. The basic neoclassical model,” Journal of Monetary Economics, March-May 1988, 21 (2-3), 195–232. Kumhof, M. and D. Laxton, “Simple fiscal policy rules for small open economies,” Journal of International Economics, September 2013, 91 (1), 113–127. Lama, R. and J. Medina, “Is exchange rate stabilization an appropriate cure of the Dutch disease?,” International Journal of Central Banking, March 2012, 8 (1), 5–46. Lartey, E., “Capital inflows, Dutch disease effects, and monetary policy in a open small economy,” Review of International Economics, 2008, 16 (5), 971–989. , “Capital inflows, resource reallocation and the real exchange rate,” International Finance, 2008, 11 (2), 131–152. Mendoza, E., “Real business cycles in a small open economy,” American Economic Review, 1991, 81 (4), 797–818. Schmitt-Grohe, S. and M. Uribe, “Closing small open economy models,” Journal of International Economics, 2003, 61 (1), 163–185. Suescun, R., “Commodity booms, Dutch disease and real business cycles in a small open economy: The case of coffee in Colombia,” Borradores de Economia 73, Banco de la Republica 1997. Uhlig, H., “Some fiscal calculus,” American Economic Review, May 2009, 100 (2), 30–34. Woodford, M., “Inflation stabilization and welfare,” Contributions to macroeconomics, 2002, 2 (1). 18 Fiscal rules Countercyclical rule with ς = −0.5 Neutral rule with ς = 0 Procyclical rule with ς = 0.5 Welfare gains Neutral KG with αG = 0 0.0353% 0.0352% 0.0399% Productive KG with αG = 0.2 0.0512% 0.0425% 0.0345% Table 3: We compute welfare gains from eliminating consumption fluctuations. 19 Figure 4: Impulse response functions (in %) after a 10% increase in copper prices in the baseline scenario with αG = 0 and no government at all. The IRFs are the natural responses of the economy to the foreign shock. 20 Figure 5: Impulse response functions (in %) after a 10% increase in copper prices with αG = 0. Solid line is the neutral case (with ς = 0). Dotted line is the countercyclical case ((with ς < 0). Dashed line is the procyclical case (with ς > 0). 21 Figure 6: Impulse response functions (in %) after a 10% increase in copper prices with αG > 0. Solid line is the neutral case (with ς = 0). Dotted line is the countercyclical case ((with ς < 0). Dashed line is the procyclical case (with ς > 0). 22